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Math Curriculum Grade Level Expectations by Strand compiled

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					Deerfield Community School



Mathematics Curriculum




           August 2005




              1 of 11
                                 Deerfield Community School
                                         Mathematics Curriculum

                                           Table of Contents

Contents                                        Pages

Philosophy and Essentials                       1 through 11

Grade Level Curriculum
                  Kindergarten                  K-1 through K-7
                  1st Grade                     1-1 through 1-11
                  2nd Grade                     2-1 through 2-13
                  3rd Grade                     3-1 through 3-8
                  4th Grade                     4-1 through 4-10
                  5th Grade                     5-1 through 5-11
                  6th Grade                     6-1 through 6-13
                  7th Grade                     7-1 through 7-12
                  8th Grade                     8-1 through 8-11

Resources
                  Number and Operations         NO-1 through NO-33
                  Geometry                      G-1 through G-58
                  Functions and Algebra         FA-1 through FA-52
                  Data, Statistics, and         DS-1 through DS-50
                  Probability

Appendix A M(N&O)- 2-3                          A1
Appendix B Measurement Benchmarks               B1 through B2




                                                 2 of 11
                                            THE EDUCATION OF DEERFIELD’S CHILDREN
                                                    A SCHOOL PHILOSOPHY



       The purpose of the Deerfield Community School is to educate the young people of Deerfield by supporting goals which encourage
growth in their personal lives, their homes, and community. Members of the staff are partners with parents and the larger community in
supporting these goals. As partners we will meet, listen, and share knowledge. In this way we, as a community, share the commitment and the
responsibility to provide for the growth of each child.

        We will offer each child the tools with which to live a healthy life, encouraging health as a value in itself and as an important element
for social and intellectual functioning.

        We will foster the social development of each child, encouraging attention to others’ thoughts and a willingness to express one’s own as
essential elements of learning.

       We will encourage the intellectual growth of each child. Each child is a ready learner. Teachers must provide children with
developmentally appropriate learning opportunities which challenge and inspire.

        As adults, we are committed to preparing children for life as they become responsible and competent participants in the community.
Children seek us as models and will listen to us. As we learn together, we will: read and write, work with concepts of number and shape,
practice thinking scientifically, take an interest in the social goals of humanity, develop an involvement in the arts, and seek to live healthy
lives. To do these things is basic to education.

      If we are successful, young people of Deerfield will grow up valuing themselves and others, and will contribute harmoniously in their
own communities.




                                                                       1 of 11
                                                        Mathematics Curriculum
In developing the mathematics curriculum, we recognize that the Deerfield Community School is committed to five primary goals:

•      students will develop a firm grounding in essential computational skills;
•      students will develop strong mathematical problem solving and reasoning abilities;
•      students will develop positive attitudes about mathematics;
•      students will develop the ability to use appropriate technology to solve mathematical problems; and
•      students will develop the ability to effectively communicate their understanding of mathematics.


Problem solving, while not a direct strand, should serve as the organizing feature of the mathematics curriculum as well as other areas of study
and be applied to everyday activities. Problem solving must not be seen as a separate topic, but rather the centerpiece of the mathematics
curriculum. Students should have many experiences in posing and solving problems from their world, from data that are meaningful to them,
and from mathematical investigations. Students will use problem solving strategies to investigate and understand increasingly complex
mathematical content.

Students will communicate their understanding of mathematics. Reading, writing, talking, listening, and modeling provide students with the
opportunity to integrate the language of mathematics into their world and help them to develop understanding. Actively exploring,
investigating, describing, and explaining mathematical ideas promote communication which leads to a greater comprehension of mathematical
concepts.




                                                                      2 of 11
ESSENTIAL ENVIRONMENT

       The Essential Environment for the student working with mathematics is a setting which recognizes each person's abilities and looks
forward to each person's contributions to the classroom community. The community supports individuals and sets standards which define what
is expected of contributing members. As learning takes place, members of the learning community communicate their questions and
understandings, reason their ways to solutions, connect what they have learned within mathematics and to other areas of learning, and undergo
a process of problem solving in which mathematics is applied to everyday life.


This Essential Environment includes these elements:

Validation: The student is viewed directly and responded to directly by the teacher. The teacher does not label the student, but instead values
   his mathematical work and his actions in order to better understand his perspective. In this way appropriate work plans are determined in
   consultation with the student. The teacher's behavior in this regard becomes a model for students as they generate work plans in
   consultation with one another. There is an atmosphere of respect for the genuine efforts of each person. Evidence of this atmosphere
   appears in the actions of adults and students as they listen carefully and respond honestly to one another through constructive criticism and
   praise and help one another to revisit, extend, or deepen work.

Involvement: Each student is encouraged to share particular mathematical interests and to develop expertise based upon these interests.
   Students realize that mathematics touches many places in people's lives and provides many points through which to develop interests and
   expertise. Students value one another's involvement in the various strands and seek each other out in order to share knowledge,
   understanding, and their excitement about learning.

Expectation: The teacher expects the student to follow through on planned work. The student expects to be able to use the teacher and other
   students as resources to be called upon at appropriate times to help in the work. The teacher is open to consulting on expectations about
   student work, showing flexibility when this is important for student learning. Each student expects to refine some of his mathematical
   work for public use or display.



Immersion: Mathematics is given real purpose. Students use calendars, clocks, tallies of lunch counts, order forms, and more as they go about
  the business of daily life in the classroom. Further, mathematics is linked with and used for other areas of study. Students gather data as
  they study the lives of others and as they investigate the natural world. Students create patterns as they undertake an art project. Students
  measure out quantities for a cooking project or a science experiment. Along with many other experiences, these uses of mathematics make
  it an essential part of everyday learning.

                                                                      3 of 11
Wondering: A spirit of inquiry is encouraged. The teacher models this by openly acknowledging his own questions and his own mistakes.
  Students are given plenty of opportunity to share their own wonderings and to learn from their mistakes. Approximation is viewed as a
  valid tool of thinking in some situations. Problem solving, based on wonderings and careful thinking, becomes a part of life in the
  classroom.




                                                                   4 of 11
ILLUSTRATING ESSENTIAL ENVIRONMENT
       We are a part of our environment, and the environment is a part of us. Illustrations of how the different elements of the Essential
Environment work will show them working together, as in the following anecdotal record:

        When I arrived, the class was having a group meeting. The children had paired up and were conducting surveys among class members.
Conversations I had had with the teacher prior to the visit established that the idea of surveys and data collection, along with representation of
data through graphing, were understandings and actions which the teacher wanted the students to develop over a period of time. She does not
want the students to merely learn how to read a graph. She wants them to develop reasoning skills related to data collection and
interpretation.

        Today's steps in this ongoing process include communication. The intent of the meeting includes reviewing purpose and checking
details: "Nicholas, who's your partner and what's your survey question?" Issues are fleshed out as a part of problem solving: "So how will
someone answer your survey question?" Connections are made: "It'll be interesting to compare your data with the data we collected the other
day."

        The teacher ends the group meeting by setting out the agenda for what will come next. Students who had finished compiling data based
on their surveys would meet with her. Others would continue with their surveys, asking classmates the questions they had formulated.

        In this brief snapshot of a class meeting we see several elements described as essential to the classroom environment. The teacher is
setting out the expectation, making certain that students understand their plans and have thought about how their plans will work. There is an
element of wondering here. A question is asked which might prompt the student to put himself in the place of the person answering his
question. A question is implied which refers back to previous work, to the immersion which has been established around this mathematical
topic. There is validation. Students are addressed directly. The teacher has knowledge of the students' work. She also knows her purposes
for the students. She has expertise in the area of mathematics and is directing students as they develop their plans and their own expertise.
There is involvement. While the overall mathematical understandings and actions of the data collection project fits with the teacher's
knowledge of what students need to learn, the content of the project is largely student determined. The teacher has modeled the process prior to
this class meeting. All of the students have witnessed the development of a class graph based on a survey they participated in together. Now,
they are off on their own, working with their own survey questions, developing their own graph models - pursuing their own interests and
questions, following through on expectations, and growing in expertise.




                                                                      5 of 11
ESSENTIAL ACTIONS

       The Essential Actions of mathematics form a web of strategies which give the person power to use mathematics for his own problem
solving purposes. The Actions discussed below are common to most mathematical situations and many other learning situations, as a person
organizes for problem solving.


Recognizing: First, there must be recognition of a problem situation. Problem here is not meant in the negative sense. The problem to be
   solved may be a practical one, something in need of a solution before moving on; or it may be a source of wondering. As an example, we'll
   take a practical situation.

   It is a dry fall. Your dug well has been known to run out of water at this time of year. This is a problem. You need to have some idea of
   how much water you have available so that you can plan. The mathematical recognition of the problem situation spots the application of
   mathematics as a help toward planning for the lack of water. You figure that you will have to call upon your understanding of how to
   measure volume. This is also another aspect of recognition - a kind of classification - knowing what the situation entails and the
   understandings upon which you will have to call as you work toward a solution.

Planning: After recognizing a problem situation and how math would apply to that situation, it becomes essential to develop a plan for
   working toward a solution. Planning involves mapping out the possibilities, then choosing from among them to develop a route which
   makes sense, given a person's mathematical understandings.

   Based upon your recognition of the problem situation and your mathematical understanding, you think that you need to find the volume of
   water and that volume can be measured by multiplying length times width times height. Finding volume will be step one.
   Next, you realize that you will have to find out your rate of use of the water in your well. In order to determine this you will have to
   compare the water levels at different times.
   Finally, you will need to use this comparison to figure out when you could expect to run out of water at your current rate of use. This will
   help you to know how much you will need to conserve water.




                                                                     6 of 11
Researching: After recognizing a problem situation and developing a plan for coming to a solution there may be a need to gather more
   information. The initial need for research should become apparent as the problem situation is defined, but may come into play at any time
   during the problem solving process. To return to our example:

   You aren't sure just how much water you have now. Research here takes the form of the physical act of lifting the well cover and using
   some kind of measuring device to determine the depth of the water. Perhaps you have an idea of your own, but this may be a time to use
   another of the Essential Actions which may come into play at any time during the problem solving process - consulting. Your neighbor
   has an idea. Use a piece of rope which is weighted on the drop end, put it into the well and see how far up the wetness comes by measuring
   with a tape measure after bringing the rope up out of the well. Now that you have the height, you think that you need to find length and
   width. Suddenly, you are hit with a new problem. Your well is roughly circular. You will need to call upon another Essential Action. You
   will need to rethink your strategy.


Rethinking: The need to think back upon a plan comes up frequently, the more frequently the more complicated the problem. Taking action,
   really working on something, may reveal gaps in planning which the initial thinking through did not reveal. Futhermore, assumptions may
   have been made which do not fit with the problem situation. The case of the dug well involves the latter.

   You suddenly realize that there is no way to measure width and length since the structure that you are measuring is not rectangular in shape.
   You are tempted to bring in another Essential Action, approximation, by inscribing a square on the top of your well (using fastened down
   string), allowing for a measurement of width and length which will help determine a large portion of the volume of the water. [You are
   already approximating (estimating) somewhat since you are unsure of how high the intake pipe is from the bottom of the well.] Or you
   could go back to researching, checking reference books for a formula which will help you determine volume for a cylindrical object. The
   wondering part of you wants to do this, but the physical act of measuring with the rope over a couple of days has brought you to a new
   realization. All you really need to know is how much the water goes down over a period of time. Length is the crucial factor, since
   distance across will remain the same over time (no matter how low the water gets - until it runs out!). You return to planning, having
   chosen a new strategy for problem solving, and in this case, having simplified the problem greatly.


Solving: When the plan has been established, the research undertaken, and the rethinking accomplished, the problem may be solved. In the
   example of the dug well:

   You measured the length of wetness on the rope on Monday and find you have 8 feet. On Wednesday you have 7 feet six inches. On
   Friday you have 7 feet two inches. On Sunday you have 6 feet 7 inches. You convert to inches: Monday=96" Wednesday=90"
   Friday=86" Sunday=79", a loss of 6 inches, then 4 inches, then 7 inches. Your rate of loss is uneven, probably due to wash days being on
   some days and not on others. You rethink, realizing that the variables of the situation, including uneven use of water and the (much hoped
   for!) possibility of rain, make an exact calculation of the date of no water fairly useless. You could keep measuring and averaging loss per
   day to calculate this, but you realize that something else may be more useful. You go public with your information.
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Communicating: When we communicate what we have discovered, we share our information and understandings. The form of expression
  becomes important. What is the best way to get my message across? Also important is the attention to appearance. What will someone
  else want to see and find easy to use? Mathematical expression may come out of the excitement of discovery and the desire to let the other
  person in on what has been found, seen, or understood. It may also serve a practical purpose, as in the case of the well.

   You call your family together around the dining room table. You have begun a graph entitled The Height of the Water in Our Well. You
   invite the family to help you color in the bars which show heights for the days you've tabulated so far. There is space left for information
   from future days to be entered. You also have a chart to take outside for recording height. Though the children are not to measure the
   length of wetness of the rope on their own (fortunately, the well cover is very heavy), you invite them to accompany you as you work on
   this project together. The chart will go on the kitchen wall, a reminder to conserve water, but also a possible reassurance that things aren't
   as bad as they seem. Then your daughter makes a suggestion.


Extending: Communicating a mathematical discovery or mathematical information does bring a point of closure, but in many cases it may
   only be a pause along the way towards more work. Perhaps that piece of work will spark a new idea and be useful as a part of future work.
   Such was the case with the family facing drought.

   Recently, your daughter's class had set out a rain gauge at school to measure any rain that did fall during that dry season. She knows how
   to make a gauge and says she'd like to keep track of how much it rains at home. "Wouldn't it be interesting to see how much our well water
   changes after it rains?"
   Everyone agrees to help make and fill in a graph which will measure rainfall.


Deepening: Deepening comes through reflection. After working through problems, a person may take stock of new understandings and new
   strategies. The person engages in self-assessment, considering what he knows and understands, and how to use what he has gained. The
   new learning will become a part of what the person brings to problem solving situations in the future. In the case of the well:

   You really knew it all along, but you didn't know that you knew it. Realizing that you just needed to measure the change in water height,
   you saw more clearly the logic of a situation involving a constant factor and a variable. You know that what really matters is how much
   water there is in the well, and that that has to do with a change in volume. But volume is a little harder to measure. Since length will
   change with volume and width will not, measuring length will be sufficient to indicate changes in the amount of water available. Hence,
   your new strategy has been to measure length only.



                                                                      8 of 11
Additional Essential Actions embedded in the problem solving process:

Consulting: Consulting may happen informally, or it may be a part of a strategy for problem solving. In some situations a person may consult
   the expertise of another person. Consulting is like researching, except that it implies working with another person to seek out information
   or ideas. It is natural to enter into consultations with others frequently during the problem solving process.


Approximating: Approximating or estimating is useful for several purposes. First, estimation will give a good idea of the reasonableness of
  an answer. Thus, after a formal calculation or measurement takes place, comparing that answer with an estimate will be a good check.
  Second, some situations really require only an approximate answer. Since approximations can be done more easily in the head, they make
  sense when they are all that is required to fit a situation. Third, the world is rough. Building a house will require some close to exact
  measurements if the house is to stand right. This is true for many human made things. But if we are measuring some phenomenon, such as
  the depth of a dug well, an approximation will have to do.




                                                                     9 of 11
ILLUSTRATING ESSENTIAL ACTIONS

        The Essential Actions of mathematics form the solid bed of purpose upon which mathematical knowledge and understandings can be
built. In the home, in the work place, and in the school, problem solving becomes meaningful within the context of real action. In the example
of the well, the setting for problem solving was the home, though there was a home/school connection when the rain gauge built in school was
brought in to solve a problem at home. Home/school connections involving real action purposes for mathematics can work the other way as
well. At the Deerfield Community School, one example of this is a project in which a grade level takes the perceived need for useful and
informative calendars and meets this need through creating, designing, producing, and marketing calendars. Connections here exist not only
between home and school, but also through the areas of learning and within mathematics. Students employ decision making, informational
research skills, artistic skills, writing, measurement, patterning, data collection, graphing, data analysis, and more.

        During the fall of the year, students produce these calendars which will be sold to the general public in December. Students determine a
theme for the calendar, develop a design both for the month grid and for facing pages, work through the specifics of layout, write and draw to
provide content relative to the theme, then market the calendar, account for sales, and analyze sales data. All of these steps require problem
solving strategies common to all learning, as well as problem solving strategies specific to mathematics. Students recognize problems, develop
plans for solutions, consult with one another, research as needed, approximate on initial drafts, rethink plans, solve, then communicate
solutions. Through this learning process, they extend and deepen their learning. The calendar project is an example of integrated learning in
which mathematics plays a pivotal role.




                                                                     10 of 11
ESSENTIAL UNDERSTANDINGS
The section of the guide which follows is organized according to the state Grade Level Expectations (GLEs) which are broken down into the
following four strands: Number and Operations; Geometry and Measurement; Functions and Algebra; Data, Statistics and Probability.

Number and Operations: Students will develop number sense and an understanding of our numeration system. Students must
understand numbers if they are to make sense of the ways numbers are used in their everyday world. Numbers are used to describe and
interpret real-world phenomenon. Students need to use numbers to quantify, to identify location, to identify a specific object in a collection, to
name, to measure, and to model real-world situations. They need to understand relative magnitude in order to make sense of everyday
situations.


Geometry and Measurement: Students will name, describe, model, classify, and compare geometric shapes and their properties with
an emphasis on their wide applicability in human activity. Geometry helps students represent and describe the world in which they live.
Students need to investigate, experiment, and explore geometric properties using both technology and hands on materials.



Functions and Algebra: Students will recognize patterns and describe and represent relations and functions with tables, graphs, equations
and rules, and analyze how a change in one element results in a change in another. One of the central themes of mathematics is the study of
patterns, relations, and functions. This study requires students to recognize, describe, and generalize patterns and build mathematical models to
predict the behavior of real-world phenomenon that exhibit the observed pattern. This study of patterns leads to an exploration of functions, a
concept which is an important unifying idea in all aspects of mathematics.



Data, Statistics, and Probability: Students will use data analysis, statistics and probability to analyze given situations and the outcomes
of experiments. Collecting, organizing, displaying, and interpreting data, as well as using the information to make decisions and predictions,
have become very important in our society. Statistical instruction should be carried out in a spirit of investigation and exploration so students
can answer questions about data. Probability must be studied in familiar contexts encouraging students to model situations. Students need to
investigate fairness, chances of winning, and uncertainty. Technology should be used as a tool throughout the investigation process.




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                                                Grade Level K Expectations by Strand

                                                        Number and Operations
GLE
          Grade Level Expectations                                   Terms Defined (Definition Number)           Notes and Resources
Number

M(N&O)-   Demonstrates conceptual understanding of rational          o   Rational number (N&O-1)           Developing Number Concepts
K-1       numbers with respect to:                                   o   Whole number (N&O-2)              Book 1 – chapter 1
          whole numbers from 0 to 12 through investigations          o   Fraction (N&O-3)
          that apply the concepts of equivalency in composing or     o   Equivalent numbers (N&O-14)       Investigations in Number, Data
          decomposing numbers using models, explanations,            o   Composition of numbers            and Space Series
          or other representations.                                      (N&O-15)
                                                                     o   Decomposition of numbers
          Demonstrates conceptual understanding of rational
                                                                         (N&O-16)                          Materials – unifix cubes, color
          numbers with respect to:
          positive fractional numbers (1/2) as “fair share” (i.e.,   o   Area model to represent part to   tiles, teddy bear counters etc.
          equal sized parts or sets) using models, explanations,         whole relationship (N&O-17)
          or other representations.                                  o   Set model (N&O-18)                These resources apply to all
                                                                                                           GLE’s in this section

M(N&O)-   Demonstrates understanding of the relative                 o   Whole number (N&O-2)              Developing Number Concepts
K-2       magnitude of numbers from 0 to 20 through                  o   Area model to represent part to   Book 1 – chapters 1 & 3
          investigations that demonstrate one-to-one                     whole relationship (N&O-17)
          correspondence.                                            o   Set model (N&O-18)                Investigations in Number Data
                                                                     o   Linear model (N&O-19)             and Space Series
          Demonstrates understanding of the relative                 o   Relative magnitude (N&O-20)
          magnitude of numbers from 0 to 20 through
                                                                     o   Within number formats
          investigations that compare whole numbers to each
                                                                         (N&O-21)                          Materials – beans, unifix cubes,
          other or to benchmark whole numbers (5, 10).
                                                                     o   Ordering (N&O-26)                 etc.
          Demonstrates understanding of the relative                 o   Comparing (N&O-27)
          magnitude of numbers from 0 to 20 through                  o   Number line (N&O-28)
          investigations that demonstrate an understanding of
          the relation of inequality when comparing whole
          numbers by using “1 more” or “1 less”.

          Demonstrates understanding of the relative
          magnitude of numbers from 0 to 20 through
          investigations that connect numbers orally and written
          as numerals to the quantities that they represent using
          models, representations, or number lines.                                                        These resources apply to all
                                                                                                           GLE’s in this section

                                                                         K-1
                                                        Number and Operations
GLE
          Grade Level Expectations                                  Terms Defined (Definition Number)           Notes and Resources
Number

M(N&O)-   Demonstrates conceptual understanding of                  o   Whole number (N&O-2)            Developing Number Concepts –
K-3       mathematical operations through investigations            o   Composition of numbers          Book 2
          involving addition and subtraction of whole numbers           (N&O-15)
          (from 0 to 10) by solving problems involving joining      o   Decomposition of numbers
          actions, separating actions, part-part whole                  (N&O-16)                        Investigations in Number, Data
          relationships, and comparison situations.                                                     and Space Series
          Demonstrates conceptual understanding of
          mathematical operations through investigations
          involving addition of multiple one-digit whole numbers.                                       Materials – teddy bear counters,
          (See Appendix A.)                                                                             color tiles etc.


                                                                                                        These resources apply to all
                                                                                                        GLE’s in this section

M(N&O)-   None
K-4

          Demonstrates understanding of monetary value              o   Decimal (N&O-7)                 None
          through investigations involving knowing the names        o   Equivalent numbers (N&O-14)
M(N&O)-   and values for coins (penny, nickel and dime).            o   Composition of numbers
K-5                                                                     (N&O-15)
                                                                    o   Decomposition of numbers
                                                                        (N&O-16)


M(N&O)-   Mentally adds and subtracts whole numbers by                                                  All of this is referred to mentally!
K-6       naming the number that is one more or one less than
          the original number.
                                                                                                        Developing Number Concepts – Book
          (IMPORTANT: The intent of this GLE is to embed                                                1 Chapter 3 and Book 2 Chapter 2
          mental arithmetic throughout the instructional program,
          not to teach it as a separate unit.)




                                                                        K-2
                                                         Number and Operations
GLE
          Grade Level Expectations                                    Terms Defined (Definition Number)         Notes and Resources
Number

M(N&O)-   Makes estimates of the number of objects in a set (up                                           Developing Number Concepts –
K-7       to 20) by making and revising estimates as objects are                                          Book 1 Chapters 1 & 3
          counted (e.g., A student estimates the number of
          pennies in a jar as 20. Then the student counts the first                                       Investigations in Number Data
          10 and makes another estimate based on those that                                               and Space Series
          have been counted and those that remain in the jar.).

          (IMPORTANT: Estimation should be imbedded
                                                                                                          Materials – Pennies, beans,
          instructionally throughout all strands.)
                                                                                                          blocks etc.




M(N&O)-   None
K-8



                                                                         K-3
                                                   Geometry and Measurement
GLE
          Grade Level Expectations                                 Terms Defined (Definition Number)         Notes and Resources
Number

M(G&M)-   Uses properties, attributes, composition, or             o   Attributes and properties
K-1       decomposition to sort or classify polygons (triangles,       (G&M-1)
          squares, rectangles, rhombi, trapezoids, and hexagons)   o   Uses composition and            Investigations in Number Data
          or objects by using one non-measurable or measurable         decomposition (G&M-5)           and Space –“Making Shapes and
          attribute.                                               o   Polygons (G&M-2)                Building Blocks” & “Collecting,
                                                                   o   Non-measurable attribute        Counting and Measuring”
          Uses properties, attributes, composition, or
                                                                       (G&M-8)
          decomposition to recognize, name, and build polygons
                                                                   o   Measurable attribute (G&M-9)    Also found in software form
          and circles in the environment.
                                                                                                       under school wide applications




                                                                                                       Materials – Pattern blocks, craft
                                                                                                       sticks, geoblocks etc.

M(G&M)-   None
K-2

M(G&M)-   None
K-3

M(G&M)-   None
K-4

M(G&M)-
          None
K-5


M(G&M)-   None
K-6
                                                                       K-4
                                                         Geometry and Measurement
GLE
          Grade Level Expectations                                         Terms Defined (Definition Number)         Notes and Resources
Number

M(G&M)-   Demonstrates conceptual understanding of                         o   Measures and uses units of      Developing Number Concepts –
K-7       measurable attributes using comparative language to                  measure appropriately and       Book 1 Chapters 1 & 3
          describe and compare attributes of objects (length                   consistently (G&M-31)
          [longer, shorter], height [taller, shorter], weight [heavier ,   o   Makes conversions within and
          lighter], temperature [warmer, cooler], and capacity                 across systems (G&M-32)
          [more, less]).                                                                                       Investigations in Number, Data
                                                                                                               and Space: “Collecting, Counting
          Demonstrates conceptual understanding of                                                             and Measuring”
          measurable attributes and compares objects visually
          and with direct comparison.                                                                          Materials – ribbons, unifix cubes,
                                                                                                               blocks etc.


M(G&M)-   Determines elapsed and accrued time as it relates to                                                 Investigations in Number, Data
K-8       calendar patterns (days of the week, yesterday, today,                                               and Space: “Mathematical
          and tomorrow), the sequence of events in a day.                                                      Thinking in Kindergarten”

          Identifies a clock and calendar as measurement tools                                                 Developing Number Concepts –
          (days of week, months of the year).                                                                  Book 1 Chapter 2




M(G&M)-   Demonstrates understanding of spatial                                                                Investigation in Number, Data
K-9       relationships by location and position using                                                         and Space – Series
          positional words to locate and describe where an object
          is found in the environment.
                                                                                                               Developing Number Concepts –
                                                                                                               Books 1 & 2




M(G&M)-   None
K-10


                                                                               K-5
                                                          Functions and Algebra
GLE
          Grade Level Expectations                                     Terms Defined (Definition Number)          Notes and Resources
Number

M(F&A)–   Identifies and extends to specific cases a variety of        o   Patterns (F&A-1)                 Investigations in Number, Data
K–1       patterns (sequences of shapes, sounds, movement,             o   Extend a pattern (F&A-5)         and Space: “Pattern Trains and
          colors, and letters) by extending the pattern to the next    o   Numeric patterns (F&A-3)         Hopscotch Paths
          one, two or three elements, or by translating AB             o   Non-numeric patterns (F&A-4)
          patterns across formats (e.g., an abb pattern can be         o   Sequence (F&A-6)
          represented as snap, clap, clap or red, yellow, yellow) or   o   Pattern Summary Table by grade   Developing Number Concepts –
          by identifying number patterns in the environment.
                                                                           level (F&A-9)                    Book 1 Chapter 2



                                                                                                            Materials – pattern blocks, unifix
                                                                                                            cubes, teddy bear counters etc.




M(F&A)–   None
K–2


M(F&A)–   None
K–3


M(F&A)–   None                                                         o   Equality (F&A-30)
K–4                                                                    o   Demonstrates conceptual
                                                                           understanding of equality by
                                                                           solving equivalence (F&A-31)
                                                                       o   Number sentences (F&A-33)
                                                                       o   Equation (F&A-32)
                                                                       o   Algebraic equation notation
                                                                           (F&A-34)
                                                                       o   Examples of forms of equations
                                                                           (F&A-35)




                                                                           K-6
                                                     Data, Statistics, and Probability
GLE
           Grade Level Expectations                                   Terms Defined (Definition Number)             Notes and Resources
Number

M(DSP) –   Interprets a given representation created by the           o   Interprets a given representation   Investigations in Number, Data
K-1        class (models and tally charts) to answer questions            (DSP-21)                            and Space: “Counting Ourselves
           related to the data, or to analyze the data to formulate   o   Representation (DSP-1)              and Others”
           conclusions using words, diagrams, or verbal/scribed       o   Pictograph (DSP-2)
           responses to express answers.                              o   Line plot (DSP-5)
                                                                      o   Tally chart (DSP-3)
           (IMPORTANT: Analyzes data consistent with concepts
                                                                      o   Frequency table (DSP-4)
           and skills in M(DSP)–K–2.)




M(DSP) –   Analyzes patterns, trends, or distributions in data in     o   Pattern (F&A-1)                     Investigations in Number, Data
K-2        a variety of contexts by determining or using more,                                                and Space: “Counting Ourselves
           less, or equal (e.g., Have there been more, less, or the                                           and Others”
           same number of cloudy days compared to sunny days
           this week?).                                                                                       Developing Number Concepts
                                                                                                              Book 1 Chapter 2

M(DSP) –   None
K-3


M(DSP) –   None
K-4


M(DSP) –   None                                                       o   Combination (DSP-41)
K-5                                                                   o   Frequency table (DSP-4)
                                                                      o   Tree diagram (DSP-28)
                                                                      o   Solves problems using a variety
                                                                          of counting strategies (DSP-39)


M(DSP) –   None
K-6


                                                                          K-7
                                                Grade Level 1 Expectations by Strand

                                                       Number and Operations
GLE
          Grade Level Expectations                                   Terms Defined (Definition Number)           Notes and Resources
Number

M(N&O)-   Demonstrates conceptual understanding of rational          o   Rational number (N&O-1)
1-1       numbers with respect to:                                   o   Whole number (N&O-2)              Developing Number Concepts,
          whole numbers from 0 to 100 using place value, by          o   Fraction (N&O-3)                  Book 1:Counting, Comparing, &
          applying the concepts of equivalency in composing or       o   Proper fraction (N&O-4)           Pattern
          decomposing numbers; and in expanded notation using        o   Improper fraction (N&O-5)
          models, explanations, or other representations.            o   Ratio (N&O-12)                    Developing Number Concepts,
                                                                     o   Expanded Notation (N&O-13)        Book :Addition & Subtraction
          Demonstrates conceptual understanding of rational
                                                                     o   Equivalent numbers (N&O-14)
          numbers with respect to:
          positive fractional numbers (benchmark fractions: a/2,     o   Composition of numbers            Developing Number Concepts,
          a/3, or a/4, where a is a whole number greater than 0          (N&O-15)                          Book 3: Place Value,
          and less than or equal to the denominator) as a part to    o   Decomposition of numbers          Multiplication & Division
          whole relationship in area models where the                    (N&O-16)
          denominator is equal to the number of parts in the whole   o   Area model to represent part to   Investigations In Number, Data,
          using models, explanations, or other                           whole relationship (N&O-17)       Space: Mathematical Thinking At
          representations.                                           o   Set model (N&O-18)                Grade 1

                                                                                                           Investigations In Number, Data,
                                                                                                           Space: Building Number Sense

                                                                                                           Investigations: Quilt Squares &
                                                                                                           Block Towns

                                                                                                           Understanding Geometry (K.
                                                                                                           Richardson)




                                                                         1-1
                                                        Number and Operations
GLE
          Grade Level Expectations                                   Terms Defined (Definition Number)           Notes and Resources
Number

M(N&O)-   Demonstrates understanding of the relative                 o   Whole number (N&O-2)
1-2       magnitude of numbers from 0 to 100 by ordering             o   Area model to represent part to   Developing Number Concepts,
          whole numbers.                                                 whole relationship (N&O-17)       Book 1:Counting, Comparing, &
                                                                     o   Set model (N&O-18)                Pattern
          Demonstrates understanding of the relative                 o   Linear model (N&O-19)
          magnitude of numbers from 0 to 100 by comparing            o   Relative magnitude (N&O-20)       Developing Number Concepts,
          whole numbers to each other or to benchmark whole
                                                                     o   Within number formats             Book 2: Addition & Subtraction
          numbers (5, 10, 25, 50, 75, 100).
                                                                         (N&O-21)
          Demonstrates understanding of the relative                 o   Ordering (N&O-26)
          magnitude of numbers from 0 to 100 by demonstrating        o   Comparing (N&O-27)                Investigations In Number, Data,
          an understanding of the relation of inequality when        o   Number line (N&O-28)              Space: Mathematical Thinking At
          comparing whole numbers by using “1 more”, “1 less”,                                             Grade 1
          “5 more”, “5 less”, “10 more”, “10 less”.
                                                                                                           Investigations In Number, Data,
          Demonstrates understanding of the relative                                                       Space: Building Number Sense
          magnitude of numbers and by connecting number
          words (from 0 to 20) and numerals (from 0 to 100) to the                                         Investigations In Number, Data,
          quantities and positions that they represent using                                               Space: Number Games & Story
          investigations, models, representations, or number                                               Problems
          lines.

                                                                                                           Developing Number Concepts,
M(N&O)-   Demonstrates conceptual understanding of                   o   Whole number (N&O-2)              Book 2: Addition & SuUbtraction
1-3       mathematical operations involving addition and             o   Composition of numbers
          subtraction of whole numbers (from 0 to 30) by solving         (N&O-15)                          Investigations In Number, Data,
          problems involving joining actions, separating actions,    o   Decomposition of numbers          Space: Mathematical Thinking At
          part-part whole relationships, and comparison                  (N&O-16)                          Grade 1
          situations.
                                                                                                           Investigations In Number, Data,
          Demonstrates conceptual understanding of
                                                                                                           Space: Building Number Sense
          mathematical operations involving addition of
          multiple one-digit whole numbers.
          (See Appendix A.)                                                                                Investigations In Number, Data,
                                                                                                           Space: Number Games & Story
                                                                                                           Problems

M(N&O)-   None
1-4

                                                                         1-2
                                                         Number and Operations
GLE
          Grade Level Expectations                                    Terms Defined (Definition Number)           Notes and Resources
Number

          Demonstrates understanding of monetary value by             o   Decimal (N&O-7)                 Investigations In Number, Data,
          knowing the names and values for coins (penny, nickel,      o   Expanded Notation (N&O-13)      Space: Number Games & Story
M(N&O)-
          dime, and quarter).                                         o   Equivalent numbers (N&O-14)     Problems
1-5                                                                   o   Composition of numbers
          Demonstrates understanding of monetary value by                 (N&O-15)
          adding collections of like coins together to a sum no       o   Decomposition of numbers
          greater than $1.00.
                                                                          (N&O-16)

M(N&O)-   Mentally adds and subtracts whole numbers by                                                    All of this is referred to mentally!
1-6       naming the number that is one or two more or less than
          the original number.

          Mentally adds and subtracts whole number facts to
          ten (e.g., 5 + 3 = 8; 8 – 5 = 3).

          (IMPORTANT: The intent of this GLE is to embed
          mental arithmetic throughout the instructional program,
          not to teach it as a separate unit.)

                                                                                                          Developing Number Concepts,
M(N&O)-   Makes estimates of the number of objects in a set (up                                           Book 1:Counting, Comparing, &
1-7       to 30) and revises estimates as objects are counted                                             Pattern
          (e.g., A student estimates the number of pennies in a jar
          as 28. Then the student counts the first 10 and makes                                           Developing Number Concepts,
          another estimate based on those that have been                                                  Book :Addition & Subtraction
          counted and those that remain in the jar.).

          (IMPORTANT: Estimation should be embedded
          instructionally throughout all strands.)



                                                                                                          Investigations In Number, Data,
                                                                                                          Space: Mathematical Thinking At
                                                                                                          Grade 1

                                                                                                          Investigations In Number, Data,
                                                                                                          Space: Building Number Sense

                                                                          1-3
                                                       Number and Operations
GLE
          Grade Level Expectations                                 Terms Defined (Definition Number)         Notes and Resources
Number
                                                                                                       Developing Number Concepts,
M(N&O)-   Applies properties of numbers (odd, even,                                                    Book 1:Counting, Comparing, &
1-8       composition, and decomposition [e.g., 5 is the same as                                       Pattern
          2 + 3]) and field properties (commutative and identity
          for addition) to solve problems and to simplify                                              Developing Number Concepts,
          computations involving whole numbers.                                                        Book :Addition & Subtraction

                                                                                                       Investigations In Number, Data,
                                                                                                       Space: Mathematical Thinking At
                                                                                                       Grade 1

                                                                                                       Investigations In Number, Data,
                                                                                                       Space: Building Number Sense




                                                                      1-4
                                                     Geometry and Measurement
GLE
          Grade Level Expectations                                    Terms Defined (Definition Number)         Notes and Resources
Number
                                                                                                          Understanding Geometry
M(G&M)-   Uses properties, attributes, composition, or                o   Attributes and properties       (K.Richardson)
1-1       decomposition to sort or classify polygons                      (G&M-1)
          (triangles, squares, rectangles, rhombi, trapezoids, and    o   Uses composition and            Investigations In Number, Data,
          hexagons) or objects by a combination of two                    decomposition (G&M-5)           Space: Mathematical Thinking At
          nonmeasurable or measurable attributes.                     o   Polygons (G&M-2)                Grade 1
                                                                      o   Non-measurable attribute
          Uses properties, attributes, composition, or
                                                                          (G&M-8)                         Investigations In Number, Data,
          decomposition to recognize, name, build, and draw
                                                                      o   Measurable attribute (G&M-9)    Space: Quilt Squares & Block
          polygons and circles in the environment.
                                                                                                          Towns

M(G&M)-   None
1-2

M(G&M)-   Given an example of a three-dimensional geometric                                               Understanding Geometry
1-3       shape (rectangular prisms, cylinders, or spheres) finds                                         (K.Richardson)
          examples of objects in the environment that are of the
          same geometric shape (e.g., show a wooden cylinder                                              Investigations In Number, Data,
          and students identify common objects of the same                                                Space: Quilt Squares & Block
          shape).                                                                                         Towns

                                                                                                          Understanding Geometry
M(G&M)-   Demonstrates conceptual understanding of                                                        (K.Richardson)
1-4       congruency by making mirror images and creating
          shapes that have line symmetry.                                                                 Investigations In Number, Data,
                                                                                                          Space: Quilt Squares & Block
                                                                                                          Towns

M(G&M)-
          None
1-5

                                                                                                          Investigations In Number, Data,
M(G&M)-   Demonstrates conceptual understanding of the
                                                                                                          Space: Quilt Squares & Block
1-6       length/height of a two-dimensional object using non-
                                                                                                          Towns
          standard units (e.g. comparing objects to trains of small
          cubes, using iterations of a small unit to measure an                                           Investigations In Number, Data,
          object).                                                                                        Space: Bigger, Taller, Heavier,
                                                                                                          Smaller

                                                                          1-5
                                                         Geometry and Measurement
GLE
          Grade Level Expectations                                        Terms Defined (Definition Number)         Notes and Resources
Number

M(G&M)-   Demonstrates conceptual understanding of                        o   Measures and uses units of
1-7       measurable attributes using comparative language to                 measure appropriately and
          describe and compare attributes of objects (length                  consistently (G&M-31)
          [longer, shorter], height [taller, shorter], weight [heavier,   o   Makes conversions within and
          lighter], temperature [warmer, cooler], and capacity                across systems (G&M-32)
          [more, less]).                                                                                      Investigations In Number, Data,
                                                                                                              Space: Bigger, Taller, Heavier,
          Demonstrates conceptual understanding of                                                            Smaller
          measurable attributes and compares objects visually,
          with direct comparison, and using non-standard units.




M(G&M)-   Determines elapsed and accrued time as it relates to                                                Investigations In Number, Data,
1-8       calendar patterns (days of the week, months of the                                                  Space: Mathematical Thinking At
          year), the sequence of events in a day
                                                                                                              Grade 1
          Recognizes an hour and “on the ½ hour”.
                                                                                                              Investigations In Number, Data,
                                                                                                              Space: Bigger, Taller, Heavier,
                                                                                                              Smaller

                                                                                                              Investigations In Number, Data,
M(G&M)-   Demonstrates understanding of spatial                                                               Space: Mathematical Thinking At
1-9       relationships using location and position by using                                                  Grade 1
          positional words (e.g., close by, on the right,
          underneath, above, beyond) to describe one location in
          reference to another on a map, in a diagram, and in the                                             Investigations In Number, Data,
          environment.                                                                                        Space: Quilt Squares & Block
                                                                                                              Towns
                                                                                                              Investigations In Number, Data,
                                                                                                              Space: Bigger, Taller, Heavier,
                                                                                                              Smaller




                                                                              1-6
                                     Geometry and Measurement
GLE
          Grade Level Expectations           Terms Defined (Definition Number)   Notes and Resources
Number

M(G&M)-   None
1-10




                                                1-7
                                                         Functions and Algebra
GLE
          Grade Level Expectations                                  Terms Defined (Definition Number)          Notes and Resources
Number
                                                                                                         Developing Number Concepts,
M(F&A)–   Identifies and extends to specific cases a variety of     o   Patterns (F&A-1)                 Book 1:Counting, Comparing, &
1–1       patterns (repeating and growing [numeric and non-         o   Extend a pattern (F&A-5)         Pattern
          numeric]) represented in models, tables, or sequences     o   Numeric patterns (F&A-3)
          by extending the pattern to the next one, two, or three   o   Non-numeric patterns (F&A-4)     Developing Number Concepts,
          elements, by finding a missing element (e.g., 2, 4, 6,    o   Sequence (F&A-6)                 Book :Addition & Subtraction
          ___, 10), or by translating repeating patterns across     o   Pattern Summary Table by grade
          formats (e.g., an abb pattern can be represented as
                                                                        level (F&A-9)                    Investigations In Number, Data,
          snap, clap, clap; or red, yellow, yellow; or 1,2,2).
                                                                                                         Space: Mathematical Thinking At
                                                                                                         Grade 1

                                                                                                         Investigations In Number, Data,
                                                                                                         Space: Building Number Sense

                                                                                                         Investigations In Number, Data,
                                                                                                         Space: Number Games & Story
                                                                                                         Problems




M(F&A)–   None
1–2



M(F&A)–   None
1–3




                                                                        1-8
                                                         Functions and Algebra
GLE
          Grade Level Expectations                                   Terms Defined (Definition Number)          Notes and Resources
Number

M(F&A)–   Demonstrates conceptual understanding of equality          o   Equality (F&A-30)                Developing Number Concepts,
1–4       by finding the value that will make an open sentence       o   Demonstrates conceptual          Book 1:Counting, Comparing, &
          true (e.g., 2 + ��= 7) (limited to one operation and            understanding of equality by     Pattern
          limited to use of addition or subtraction) using models,       solving equivalence (F&A-31)
          verbal explanations, or written equations.                 o   Number sentences (F&A-33)        Developing Number Concepts,
                                                                     o   Equation (F&A-32)                Book :Addition & Subtraction
                                                                     o   Algebraic equation notation
                                                                         (F&A-34)                         Investigations In Number, Data,
                                                                     o   Examples of forms of equations   Space: Mathematical Thinking At
                                                                         (F&A-35)                         Grade 1

                                                                                                          Investigations In Number, Data,
                                                                                                          Space: Building Number Sense

                                                                                                          Investigations In Number, Data,
                                                                                                          Space: Number Games & Story
                                                                                                          Problems




                                                                         1-9
                                                   Data, Statistics, and Probability
GLE
           Grade Level Expectations                                   Terms Defined (Definition Number)             Notes and Resources
Number
                                                                                                              Investigations In Number, Data,
M(DSP) –   Interprets a given representation created by the           o   Interprets a given representation   Space: Mathematical Thinking At
1-1        class (models, tally charts, pictographs with one-to-one       (DSP-21)                            Grade 1
           correspondence, and tables) to answer questions            o   Representation (DSP-1)
           related to the data, or to analyze the data to formulate   o   Pictograph (DSP-2)                  Investigations In Number, Data,
           conclusions using words, diagrams, or verbal/scribed       o   Line plot (DSP-5)                   Space: Survey Questions &
           responses to express answers.                              o   Tally chart (DSP-3)                 Secret Rules
                                                                      o   Frequency table (DSP-4)
           (IMPORTANT: Analyzes data consistent with concepts
                                                                                                              Investigations In Number, Data,
           and skills in M( DSP)– 1– 2. )
                                                                                                              Space: Number Games & Story
                                                                                                              Problems
                                                                                                              Developing Number Concepts,
M(DSP) –   Analyzes patterns, trends, or distributions in data in     o   Pattern (F&A-1)                     Book 1:Counting, Comparing, &
1-2        a variety of contexts by determining or using more,                                                Pattern
           less, or equal.
                                                                                                              Developing Number Concepts,
                                                                                                              Book :Addition & Subtraction

                                                                                                              Investigations In Number, Data,
                                                                                                              Space: Mathematical Thinking At
                                                                                                              Grade 1

                                                                                                              Investigations In Number, Data,
                                                                                                              Space: Building Number Sense

                                                                                                              Investigations In Number, Data,
                                                                                                              Space: Number Games & Story
                                                                                                              Problems

                                                                                                              Investigations In Number, Data,
                                                                                                              Space: Survey Questions & Secret
                                                                                                              Rules

M(DSP) –   None
1-3

M(DSP) –   None
1-4

                                                                          1 - 10
                                                     Data, Statistics, and Probability
GLE
           Grade Level Expectations                                     Terms Defined (Definition Number)     Notes and Resources
Number

M(DSP) –   For a probability event in which the sample space            o   Combination (DSP-41)
1-5        may or may not contain equally likely outcomes,              o   Frequency table (DSP-4)
           groups use experiments to describes the likelihood or        o   Tree diagram (DSP-28)
           chance of an event (using “more likely,” “less likely”, or   o   Solves problems using a variety
           “equally likely”).                                               of counting strategies (DSP-39)




M(DSP) –   None
1-6




                                                                            1 - 11
                                                Grade Level 2 Expectations by Strand

                                                       Number and Operations
GLE
          Grade Level Expectations                                   Terms Defined (Definition Number)           Notes and Resources
Number
                                                                                                           Developing Number Concepts,
M(N&O)-   Demonstrates conceptual understanding of rational          o   Rational number (N&O-1)           Book 2: Addition & Subtraction
2-1       numbers with respect to:                                   o   Whole number (N&O-2)
          whole numbers from 0 to 199 using place value, by          o   Fraction (N&O-3)                  Developing Number Concepts,
          applying the concepts of equivalency in composing or       o   Proper fraction (N&O-4)           Book 3: Place Value,
          decomposing numbers (e.g., 34 = 17 + 17; 34 = 29 + 5);     o   Improper fraction (N&O-5)         Multiplication & Division
          and in expanded notation (e.g., 141 = 1 hundred + 4        o   Ratio (N&O-12)
          tens + 1 one or 141 = 100 + 40 + 1) using models,
                                                                     o   Expanded Notation (N&O-13)
          explanations, or other representations.
                                                                     o   Equivalent numbers (N&O-14)       Developing Number Concepts
          Demonstrates conceptual understanding of rational          o   Composition of numbers            Using Unifix Cubes
          numbers with respect to:                                       (N&O-15)
          positive fractional numbers (benchmark fractions: a/2,     o   Decomposition of numbers
          a/3, or a/4, where a is a whole number greater than 0          (N&O-16)                          Math Their Way
          and less than or equal to the denominator) as a part to    o   Area model to represent part to
          whole relationship in area and set models where the            whole relationship (N&O-17)
          denominator is equal to the number of parts in the whole   o   Set model (N&O-18)                Investigations: Mathematical
          using models, explanations, or other                                                             Thinking At Grade 2
          representations.
                                                                                                           Investigations: Coins, Coupons &
                                                                                                           Combinations

                                                                                                           Investigations: Shapes, Halves &
                                                                                                           Symmetry

                                                                                                           Investigations: Putting Together
                                                                                                           & Taking Apart




                                                                         2-1
                                                       Number and Operations
GLE
          Grade Level Expectations                               Terms Defined (Definition Number)           Notes and Resources
Number
                                                                                                       Developing Number Concepts,
M(N&O)-   Demonstrates understanding of the relative             o   Whole number (N&O-2)              Book 2: Addition & Subtraction
2-2       magnitude of numbers from 0 to 199 by ordering         o   Area model to represent part to
          whole numbers.                                             whole relationship (N&O-17)       Developing Number Concepts,
                                                                 o   Set model (N&O-18)                Book 3: Place Value,
          Demonstrates understanding of the relative             o   Linear model (N&O-19)             Multiplication & Division
          magnitude of numbers by comparing whole numbers        o   Relative magnitude (N&O-20)
          to each other or to benchmark whole numbers (10, 25,
                                                                 o   Within number formats             Math Their Way
          50, 75, 100, 125, 150, or 175).
                                                                     (N&O-21)
          Demonstrates understanding of the relative             o   Ordering (N&O-26)                 Investigations: Mathematical
          magnitude of numbers by demonstrating an               o   Comparing (N&O-27)                Thinking At Grade 2
          understanding of the relation of inequality when       o   Number line (N&O-28)
          comparing whole numbers by using "1 more", "1 less",                                         Investigations: Coins, Coupons &
          "10 more", "10 less", "100 more", or "100 less".                                             Combinations

          Demonstrates understanding of the relative                                                   Investigations: Putting Together
          magnitude of numbers or by connecting number                                                 & Taking Apart
          words and numerals to the quantities they represent
          using models, number lines, or explanations.                                                 Developing Number Concepts
                                                                                                       Using Unifix Cubes




                                                                     2-2
                                                          Number and Operations
GLE
          Grade Level Expectations                                   Terms Defined (Definition Number)         Notes and Resources
Number
                                                                                                         Developing Number Concepts,
M(N&O)-   Demonstrates conceptual understanding of                   o   Whole number (N&O-2)            Book 2: Addition & Subtraction
2-3       mathematical operations involving addition and             o   Composition of numbers
          subtraction of whole numbers by solving problems               (N&O-15)                        Developing Number Concepts,
          involving joining actions, separating actions, part-part   o   Decomposition of numbers        Book 3: Place Value,
          whole relationships, and comparison situations.                (N&O-16)                        Multiplication & Division
          Demonstrates conceptual understanding of
                                                                                                         Math Their Way
          mathematical operations involving addition of
          multiple one-digit whole numbers.
          (See Appendix A.)                                                                              Investigations: Mathematical
                                                                                                         Thinking At Grade 2

                                                                                                         Investigations: Coins, Coupons &
                                                                                                         Combinations

                                                                                                         Investigations: Putting Together
                                                                                                         & Taking Apart

                                                                                                         Developing Number Concepts
                                                                                                         Using Unifix Cubes

M(N&O)-   None
2-4


M(N&O)-   Demonstrates understanding of monetary value by            o   Decimal (N&O-7)                 Math Their Way
2-5       adding coins together to a value no greater than $1.99     o   Expanded Notation (N&O-13)
          and representing the result in dollar notation;            o   Equivalent numbers (N&O-14)     Investigations: Coins, Coupons &
                                                                     o   Composition of numbers          Combinations
          Demonstrates understanding of monetary value                   (N&O-15)
          making change from $1.00 or less.                          o   Decomposition of numbers        Investigations: Putting Together
                                                                         (N&O-16)                        & Taking Apart
          Demonstrates understanding of monetary value by
          recognizing equivalent coin representations of the same
          value (values up to $1.99).




                                                                         2-3
                                                        Number and Operations
GLE
          Grade Level Expectations                                  Terms Defined (Definition Number)         Notes and Resources
Number

M(N&O)-   Mentally adds and subtracts whole number facts to                                             Developing Number Concepts,
2-6       a sum of 20.                                                                                  Book 1:Counting, Comparing &
                                                                                                        Pattern
          Names the number that is 10 more or less than the
          original number, and mentally adds and subtracts two-                                         Developing Number Concepts,
          digit multiplies of ten (e.g., 60 + 80, 90 – 30).                                             Book 2: Addition & Subtraction
          (IMPORTANT: The intent of this GLE is to embed                                                Developing Number Concepts,
          mental arithmetic throughout the instructional program,
                                                                                                        Book 3: Place Value,
          not to teach it as a separate unit.)
                                                                                                        Multiplication & Division

                                                                                                        Math Their Way

                                                                                                        Investigations: Mathematical
                                                                                                        Thinking At Grade 2

                                                                                                        Investigations: Coins, Coupons &
                                                                                                        Combinations

                                                                                                        Investigations: Putting Together
                                                                                                        & Taking Apart

                                                                                                        Developing Number Concepts
                                                                                                        Using Unifix Cubes




                                                                       2-4
                                                          Number and Operations
GLE
          Grade Level Expectations                                   Terms Defined (Definition Number)         Notes and Resources
Number
                                                                                                         Developing Number Concepts,
M(N&O)-   Makes estimates of the number of objects in a set (up                                          Book 2: Addition & Subtraction
2-7       to 50) by selecting an appropriate method of estimation.
                                                                                                         Developing Number Concepts,
          (IMPORTANT: The intent of this GLE is to embed                                                 Book 3: Place Value,
          estimation throughout the instructional program, not to                                        Multiplication & Division
          teach it as a separate unit.)
                                                                                                         Math Their Way

                                                                                                         Investigations: Mathematical
                                                                                                         Thinking At Grade 2

                                                                                                         Investigations: Putting Together
                                                                                                         & Taking Apart

                                                                                                         Developing Number Concepts
                                                                                                         Using Unifix Cubes


                                                                                                         Developing Number Concepts,
M(N&O)-   Applies properties of numbers (odd and even) and                                               Book 2: Addition & Subtraction
2-8       field properties (commutative for addition, identity for
          addition, and associative for addition) to solve                                               Developing Number Concepts,
          problems and to simplify computations involving                                                Book 3: Place Value,
          whole numbers.                                                                                 Multiplication & Division

                                                                                                         Math Their Way

                                                                                                         Investigations: Mathematical
                                                                                                         Thinking At Grade 2

                                                                                                         Investigations: Coins, Coupons &
                                                                                                         Combinations

                                                                                                         Investigations: Putting Together
                                                                                                         & Taking Apart



                                                                        2-5
                                    Number and Operations
GLE
         Grade Level Expectations          Terms Defined (Definition Number)   Notes and Resources
Number




                                              2-6
                                                    Geometry and Measurement
GLE
          Grade Level Expectations                                  Terms Defined (Definition Number)         Notes and Resources
Number
                                                                                                        Understanding Geometry (K.
M(G&M)-   Uses properties, attributes, composition, or              o   Attributes and properties       Richardson)
2-1       decomposition to sort or classify polygons or objects         (G&M-1)
          by a combination of two or more non-measurable or         o   Uses composition and            Investigations: Does It Walk,
          measurable attributes.                                        decomposition (G&M-5)           Crawl, or Swim?
                                                                    o   Polygons (G&M-2)
                                                                    o   Non-measurable attribute        Investigations: How Long? How
                                                                        (G&M-8)                         Far?
                                                                    o   Measurable attribute (G&M-9)
                                                                                                        Investigations: Shapes, Halves &
                                                                                                        Symmetry

M(G&M)-   None
2-2


M(G&M)-   None
2-3


M(G&M)-   Demonstrates conceptual understanding of
2-4       congruency by composing and decomposing two-
          dimensional objects using models or explanations (e.g.,
          using triangular pattern blocks to construct a figure
          congruent to the hexagonal pattern block).                                                    Understanding Geometry (K.
                                                                                                        Richardson)
          Demonstrates conceptual understanding of
          congruency and uses line symmetry to demonstrate                                              Investigations: How Long? How
          congruent parts within a shape.                                                               Far?

                                                                                                        Investigations: Shapes, Halves &
                                                                                                        Symmetry




M(G&M)-
2-5       None

                                                                        2-7
                                                      Geometry and Measurement
GLE
          Grade Level Expectations                                   Terms Defined (Definition Number)          Notes and Resources
Number

M(G&M)-   Demonstrates conceptual understanding of                   o   Polygons (G&M-9)                 Understanding Geometry (K.
2-6       perimeter and area by using models or manipulatives        o   Demonstrates conceptual          Richardson)
          to surround and cover polygons.                                understanding of perimeter and
                                                                         area using models and            Investigations: How Long? How
                                                                         manipulatives to surround and    Far?
                                                                         cover polygons (G&M-26)
                                                                                                          Investigations: Shapes, Halves &
                                                                                                          Symmetry


M(G&M)-   Measures and uses units of measures appropriately          o   Measures and uses units of
                                                                                                          Investigations: How Long? How
2-7       and consistently, and makes conversions within                 measure appropriately and
          systems when solving problems across the content                                                Far?
                                                                         consistently (G&M-31)
          strands.                                                   o   Makes conversions within and
                                                                                                          Investigations: Does It Walk,
                                                                         across systems (G&M-32)
          Benchmarks in Appendix B.                                                                       Crawl, or Swim?


M(G&M)-
2-8       None


M(G&M)-   Demonstrates understanding of spatial
2-9       relationships using location and position by using
          positional language in two- and three-dimensional                                               Understanding Geometry (K.
          situations to describe and interpret relative positions                                         Richardson)
          (e.g., above the surface of the desk, below the triangle
          on the paper).                                                                                  Investigations: How Long? How
                                                                                                          Far?
          Demonstrates understanding of spatial
          relationships using location and position by creating                                           Investigations: Shapes, Halves &
          and interpreting simple maps and naming locations on                                            Symmetry
          simple coordinate grids.



M(G&M)-   None
2-10

                                                                         2-8
                                                          Functions and Algebra
GLE
          Grade Level Expectations                                   Terms Defined (Definition Number)          Notes and Resources
Number
                                                                                                          Developing Number Concepts,
M(F&A)–   Identifies and extends to specific cases a variety of      o   Patterns (F&A-1)                 Book 2: Addition & Subtraction
2–1       patterns (linear and non-numeric) represented in           o   Extend a pattern (F&A-5)
          models, tables, or sequences by extending the pattern      o   Numeric patterns (F&A-3)         Developing Number Concepts,
          to the next element, or finding a missing element (e.g.,   o   Non-numeric patterns (F&A-4)     Book 3: Place Value,
          2, 4, 6, ___, 10).                                         o   Sequence (F&A-6)                 Multiplication & Division
                                                                     o   Pattern Summary Table by grade
                                                                         level (F&A-9)                    Math Their Way

                                                                                                          Investigations: Mathematical
                                                                                                          Thinking At Grade 2

                                                                                                          Developing Number Concepts
                                                                                                          Using Unifix Cubes




M(F&A)–   None
2–2




M(F&A)–   None
2–3



                                                                         2-9
                                                            Functions and Algebra
GLE
          Grade Level Expectations                                      Terms Defined (Definition Number)          Notes and Resources
Number
                                                                                                             Developing Number Concepts,
M(F&A)–   Demonstrates conceptual understanding of equality             o   Equality (F&A-30)                Book 2: Addition & Subtraction
2–4       by finding the value that will make an open sentence          o   Demonstrates conceptual
          true (e.g. 2 + □ = 7) (limited to one operation and limited       understanding of equality by     Developing Number Concepts,
          to use of addition or subtraction).                               solving equivalence (F&A-31)     Book 3: Place Value,
                                                                        o   Number sentences (F&A-33)        Multiplication & Division
                                                                        o   Equation (F&A-32)
                                                                        o   Algebraic equation notation      Math Their Way
                                                                            (F&A-34)
                                                                        o   Examples of forms of equations   Investigations: Mathematical
                                                                            (F&A-35)                         Thinking At Grade 2

                                                                                                             Investigations: Coins, Coupons &
                                                                                                             Combinations

                                                                                                             Investigations: Putting Together
                                                                                                             & Taking Apart




                                                                            2 - 10
                                                    Data, Statistics, and Probability
GLE
           Grade Level Expectations                                  Terms Defined (Definition Number)             Notes and Resources
Number
                                                                                                             Investigations: Does It Walk,
M(DSP) –   Interprets a given representation (pictographs with       o   Interprets a given representation   Crawl, or Swim?
2-1        one-to-one correspondence, line plots, tally charts, or       (DSP-21)
           tables) to answer questions related to the data, or to    o   Representation (DSP-1)              Developing Number Concepts,
           analyze the data to formulate conclusions.                o   Pictograph (DSP-2)                  Book 2: Addition & Subtraction
                                                                     o   Line plot (DSP-5)
           (IMPORTANT: Analyzes data consistent with concepts        o   Tally chart (DSP-3)                 Developing Number Concepts,
           and skills in M(DSP)-2-2.)
                                                                     o   Frequency table (DSP-4)             Book 3: Place Value,
                                                                                                             Multiplication & Division

                                                                                                             Math Their Way


                                                                                                             Investigations: Mathematical
                                                                                                             Thinking At Grade 2

                                                                                                             Investigations: Coins, Coupons &
                                                                                                             Combinations

                                                                                                             Investigations: Shapes, Halves &
                                                                                                             Symmetry

                                                                                                             Investigations: Putting Together
                                                                                                             & Taking Apart

                                                                                                             Developing Number Concepts
                                                                                                             Using Unifix Cubes




                                                                         2 - 11
                                                    Data, Statistics, and Probability
GLE
           Grade Level Expectations                                 Terms Defined (Definition Number)           Notes and Resources
Number
                                                                                                          Developing Number Concepts,
M(DSP) –   Analyzes patterns, trends, or distributions in data in   o   Pattern (F&A-1)                   Book 2: Addition & Subtraction
2-2        a variety of contexts by determining or using more,
           less, or equal.                                                                                Developing Number Concepts,
                                                                                                          Book 3: Place Value,
                                                                                                          Multiplication & Division

                                                                                                          Math Their Way

                                                                                                          Investigations: Mathematical
                                                                                                          Thinking At Grade 2

                                                                                                          Investigations: Coins, Coupons &
                                                                                                          Combinations

                                                                                                          Developing Number Concepts
                                                                                                          Using Unifix Cubes

M(DSP) –
           None
2-3
                                                                                                          Developing Number Concepts,
M(DSP) –   Uses counting techniques to solve problems               o   Combination (DSP-41)              Book 2: Addition & Subtraction
2-4        involving combinations using a variety of strategies     o   Frequency table (DSP-4)
           (e.g., student diagrams, organized lists, tables, tree   o   Tree diagram (DSP-28)             Developing Number Concepts,
           diagrams, or others)                                     o   Solves problems using a variety   Book 3: Place Value,
           (e.g., How many ways can you make 50 cents using             of counting strategies (DSP-39)   Multiplication & Division
           nickels, dimes, and quarters?).

                                                                                                          Math Their Way

                                                                                                          Investigations: Mathematical
                                                                                                          Thinking At Grade 2




                                                                        2 - 12
                                                    Data, Statistics, and Probability
GLE
           Grade Level Expectations                                   Terms Defined (Definition Number)         Notes and Resources
Number
                                                                                                          Investigations: Does It Walk,
M(DSP) –   For a probability event in which the sample space                                              Crawl, or Swim?
2-5        may or may not contain equally likely outcomes,
           uses experiments to describe the likelihood or chance                                          Math Their Way
           of an event using “more likely,” “less likely,” “equally
           likely,” certain or impossible.                                                                Investigations: How Many
                                                                                                          Pockets? How Many Teeth?




M(DSP) –   In response to a teacher or student generated                                                  Math Their Way
2-6        question or hypothesis, groups decide the most
           effective method (e.g., survey, observation,                                                   Investigations: Does It Walk,
           experimentation) to collect the data (numerical or                                             Crawl, or Swim?
           categorical) necessary to answer the question.
                                                                                                          Investigations: Mathematical
           In response to a teacher or student generated
                                                                                                          Thinking At Grade 2
           question or hypothesis, groups collect, organize, and
           appropriately display the data.

           In response to a teacher or student generated
           question or hypothesis, groups analyze the data to
           draw conclusions about the question or hypothesis
           being tested, and when appropriate make predictions.

           (IMPORTANT: Analyzes data consistent with concepts
           and skills in M(DSP)–2–2.)




                                                                        2 - 13
                                                Grade Level 3 Expectations by Strand

                                                        Number and Operations
GLE
          Grade Level Expectations                                   Terms Defined (Definition Number)     Notes and Resources
Number

M(N&O)-   Demonstrates conceptual understanding of rational          o   Rational number (N&O-1)
3-1       numbers with respect to:                                   o   Whole number (N&O-2)
          whole numbers from 0 to 999 through equivalency,           o   Fraction (N&O-3)
          composition, decomposition, or place value using           o   Proper fraction (N&O-4)
          models, explanations, or other representations.            o   Improper fraction (N&O-5)
                                                                     o   Decimal (N&O-7)
          Demonstrates conceptual understanding of rational
                                                                     o   Ratio (N&O-12)
          numbers with respect to:
                                                                     o   Equivalent numbers (N&O-14)
          positive fractional numbers (benchmark fractions: a/2,
          a/3, a/4, a/6, or a/8, where a is a whole number greater   o   Composition of numbers
          than 0 and less than or equal to the denominator) as a         (N&O-15)
          part to whole relationship in area and set models where    o   Decomposition of numbers
          the number of parts in the whole is equal to the               (N&O-16)
          denominator using models, explanations, or other           o   Area model to represent part to
          representations.                                               whole relationship (N&O-17)
                                                                     o   Set model (N&O-18)
          Demonstrates conceptual understanding of rational
          numbers with respect to:
          decimals (within a context of money) as a part of 100
          using models, explanations, or other representations.
                                                                     o   Whole number (N&O-2)
M(N&O)-   Demonstrates understanding of the relative                 o   Fraction (N&O-3)
3-2       magnitude of numbers from 0 to 999 by ordering             o   Proper fraction (N&O-4)
          whole numbers or by comparing whole numbers to             o   Improper fraction (N&O-5)
          benchmark whole numbers (100, 250, 500, or 750).           o   Equivalent numbers (N&O-14)
                                                                     o   Area model to represent part to
          Demonstrates understanding of the relative                     whole relationship (N&O-17)
          magnitude of numbers from 0-999 by comparing
                                                                     o   Set model (N&O-18)
          whole numbers to each other.
                                                                     o   Linear model (N&O-19)
          Demonstrates understanding of the relative                 o   Relative magnitude (N&O-20)
          magnitude of numbers by comparing or identifying           o   Within number formats
          equivalent positive fractional numbers (a/2, a/3, a/4          (N&O-21)
          where a is a whole number greater than 0 and less than     o   Ordering (N&O-26)
          or equal to the denominator) using models, number          o   Comparing (N&O-27)
          lines, or explanations.                                    o   Number line (N&O-28)


                                                                         3-1
                                                         Number and Operations
GLE
          Grade Level Expectations                                    Terms Defined (Definition Number)       Notes and Resources
Number

M(N&O)-   Demonstrates conceptual understanding of                    o   Whole number (N&O-2)
3-3       mathematical operations by describing or illustrating       o   Area model to represent part to
          the inverse relationship between addition and                   whole relationship (N&O-17)
          subtraction of whole numbers.                               o   Set model (N&O-18)
                                                                      o   Number line (N&O-28)
          Demonstrates conceptual understanding of                    o   Linear model (N&O-19)
          mathematical operations by describing or illustrating
                                                                      o   Inverse relationships in
          the relationship between repeated addition and
                                                                          operations (N&O-29)
          multiplication using models, number lines, or
          explanations.                                               o   Relationship between repeated
                                                                          addition and multiplication of
                                                                          whole numbers (N&O-30)
                                                                      o   Concept of multiplication
                                                                          (N&O-37)




M(N&O)-   Accurately solves problems involving addition and           o   Decimal (N&O-7)
3-4       subtraction with regrouping to 999.                         o   Relationship between repeated
                                                                          addition and multiplication of
          Accurately solves problems involving the concept of             whole numbers (N&O-30)
          multiplication.                                             o   Relationship between repeated
                                                                          subtraction and division of whole
          Accurately solves problems involving addition or
                                                                          numbers (N&O-31)
          subtraction of decimals with regrouping in the context of
                                                                      o   Accurately solves problems
          money.
                                                                          (N&O-35)
                                                                      o   In and out of context (N&O-36)
                                                                      o   Concept of multiplication
                                                                          (N&O-37)




M(N&O)-
          None
3-5


                                                                          3-2
                                                         Number and Operations
GLE
          Grade Level Expectations                                     Terms Defined (Definition Number)           Notes and Resources
Number

M(N&O)-   Mentally adds whole number facts through 20; adds                                                All of this is referred to mentally!
3-6       two-digit and one-digit whole numbers; adds
          combinations of two-digit and three-digit whole numbers
          that are multiples of ten (e.g., 60 +50, 300 + 400, 320 +
          90).
          Mentally subtracts whole number facts through 20; a
          one-digit whole number from a two-digit whole number
          (e.g., 37 – 5); and subtracts two-digit whole numbers
          that are multiples of ten and three-digit whole numbers
          that are multiples one hundred (e.g., 50 – 20, 500 –
          200).

          (IMPORTANT: The intent of this GLE is to embed
          mental arithmetic throughout the instructional program,
          not to teach it as a separate unit.)


M(N&O)-   Makes estimates in a given situation by identifying
3-7       when estimation is appropriate, selecting the
          appropriate method of estimation, and evaluating the
          reasonableness of solutions appropriate to grade level
          GLEs across content strands.

          (IMPORTANT: The intent of this GLE is to embed
          estimation throughout the instructional program, not to
          teach it as a separate unit.)


M(N&O)-   Applies properties of numbers (odd, even, and
3-8       multiplicative property of zero for single-digit whole
          numbers [6 x 0 = 0]) to solve problems and to
          simplify computations involving whole numbers.

          Applies field properties (commutative for addition,
          associative for addition, identity for multiplication, and
          commutative for multiplication for single digit whole
          numbers [e.g., 3 x 4 = 4 x 3]) to solve problems and to
          simplify computations involving whole numbers.


                                                                          3-3
                                                        Geometry and Measurement
GLE
          Grade Level Expectations                                       Terms Defined (Definition Number)   Notes and Resources
Number

M(G&M)-   Uses properties or attributes of angles (number of             o   Attributes and properties
3-1       angles) or sides (number of sides or length of sides) or           (G&M-1)
          composition or decomposition of shapes to identify,            o   Non-measurable attribute
          describe, or distinguish among triangles, squares,                 (G&M-8)
          rectangles, rhombi, trapezoids, hexagons, or circles.          o   Measurable attribute (G&M-9)
                                                                         o   Angles (G&M-10)
                                                                         o   Triangle (G&M-3)
                                                                         o   Quadrilaterals (G&M-4)
                                                                         o   Polygons (G&M-2)
                                                                         o   Uses composition and
                                                                             decomposition (G&M-5)

M(G&M)-   None
3-2
M(G&M)-   None
3-3

M(G&M)-   Demonstrates conceptual understanding of
3-4       congruency by matching congruent figures using
          reflections, translations, and rotations (flips, slides, and
          turns) (e.g., recognizing when pentominoes are
          reflections, translations and rotations of each other).

          Demonstrates conceptual understanding of
          congruency by composing and decomposing two and
          three-dimensional objects using models or explanations
          (e.g., Given a cube, students use blocks to construct a
          congruent cube.).

          Demonstrates conceptual understanding of
          congruency by using line symmetry to demonstrate
          congruent parts within a shape.


M(G&M)-   Demonstrates conceptual understanding of
3-5       similarity by identifying similar shapes.

                                                                             3-4
                                                      Geometry and Measurement
GLE
          Grade Level Expectations                                  Terms Defined (Definition Number)    Notes and Resources
Number

M(G&M)-   Demonstrates conceptual understanding of                  o   Polygons (G&M-2)
3-6       perimeter of polygons on grids using a variety of         o   Demonstrates conceptual
          models or manipulatives. Expresses all measures using         understanding of perimeter and
          appropriate units.                                            area using models and
                                                                        manipulatives to surround and
          Demonstrates conceptual understanding of area of              cover polygons (G&M-26)
          rectangles on grids using a variety of models or          o   Measures and uses units of
          manipulatives. Expresses all measures using
                                                                        measure appropriately and
          appropriate units.
                                                                        consistently (G&M-31)

M(G&M)-   Measures and uses units of measures appropriately         o   Measures and uses units of
3-7       and consistently, and makes conversions within                measure appropriately and
          systems when solving problems across the content              consistently (G&M-31)
          strands.                                                  o   Makes conversions within and
                                                                        across systems (G&M-32)
          Benchmarks in Appendix B.
M(G&M)-
          None
3-8
M(G&M)-   Demonstrates understanding of spatial
3-9       relationships using location and position by
          interpreting and giving directions from one location to
          another (e.g., classroom to the gym, from school to
          home) using positional words.

          Demonstrates understanding of spatial
          relationships using location and position between
          locations on a map or coordinate grid (first quadrant)
          using positional words or compass directions.

M(G&M)-   Demonstrates conceptual understanding of spatial
3-10      reasoning and visualization by copying, comparing,
          and drawing models of triangles, squares, rectangles,
          rhombi, trapezoids, hexagons, and circles.

          Demonstrates conceptual understanding of spatial
          reasoning and visualization by building models of
          rectangular prisms from three-dimensional
          representations.

                                                                        3-5
                                                         Functions and Algebra
GLE
          Grade Level Expectations                                 Terms Defined (Definition Number)    Notes and Resources
Number

M(F&A)–   Identifies and extends to specific cases a variety of    o   Patterns (F&A-1)
3–1       patterns (linear and non-numeric) represented in         o   Extend a pattern (F&A-5)
          models, tables, or sequences by extending the pattern    o   Numeric patterns (F&A-3)
          to the next one, two, or three elements, or finding      o   Non-numeric patterns (F&A-4)
          missing elements.                                        o   Sequence (F&A-6)
                                                                   o   Pattern Summary Table by grade
                                                                       level (F&A-9)




M(F&A)–   None
3–2


M(F&A)–   None
3–3


M(F&A)–   Demonstrates conceptual understanding showing            o   Equality (F&A-30)
3–4       equivalence between two expressions using                o   Demonstrates equality (F&A-31)
          representations of the expressions; or by finding open   o   Number sentences (F&A-33)
          sentence true (e.g., 2 + �� = 7). (Limited to one         o   Equation (F&A-32)
          operation and limited to use addition, subtraction, or   o   Algebraic equation notation
          multiplication.)                                             (F&A-34)
                                                                   o   Examples of forms of equations
                                                                       (F&A-35)




                                                                       3-6
                                                    Data, Statistics, and Probability
GLE
           Grade Level Expectations                                   Terms Defined (Definition Number)       Notes and Resources
Number

M(DSP) -   Interprets a given representation (line plots, tally       o   Interprets a given representation
3-1        charts, tables, or bar graphs) to answer questions             (DSP-21)
           related to the data, to analyze the data to formulate      o   Representation (DSP-1)
           conclusions, or to make predictions.                       o   Line plot (DSP-5)
                                                                      o   Tally chart (DSP-3)
           (IMPORTANT: Analyzes data consistent with concepts         o   Frequency table (DSP-4)
           and skills in M(DSP)-3-2.)                                 o   Bar graph (DSP-6)



M(DSP) -   Analyzes patterns, trends, or distributions in data in     o   Pattern (F&A-1)
3-2        a variety of contexts by determining or using most         o   Mode (DSP-17)
           frequent (mode), least frequent, largest, or smallest.




M(DSP) -   Identifies or describes representations or elements        o   Representation (DSP-1)
3-3        of representations that best display a given set of        o   Identifies or describes
           data or situation, consistent with the representations         representations or elements of
           required in M(DSP)–3–1.                                        representations that best display
                                                                          a given set of data or situation
           Organizes and displays data using tables, tally                (DSP-23)
           charts, and bar graphs, to answer questions related to
           the data, to analyze the data to formulate conclusions,
           to make predictions, or to solve problems.

           (IMPORTANT: Analyzes data consistent with concepts
           and skills in M(DSP)–3–2.)



M(DSP) -   Uses counting techniques to solve problems                 o   Combinations (DSP-41)
3-4        involving combinations and simple permutations using a     o   Simple Permutations (DSP-42)
           variety of strategies (e.g., student diagrams, organized
           lists, tables, tree diagrams, or others).


                                                                          3-7
                                                       Data, Statistics, and Probability
GLE
           Grade Level Expectations                                      Terms Defined (Definition Number)   Notes and Resources
Number

M(DSP) -   For a probability event in which the sample space             o   Sample space (DSP-30)
3-5        may or may not contain equally likely outcomes,               o   Event (DSP-31)
           determines the likelihood of the occurrence of an event
           (using “more likely”, “less likely”, or “equally likely”).

           For a probability event in which the sample space
           may or may not contain equally likely outcomes,
           predicts the likelihood of an event using “more likely,”
           “less likely,” “equally likely,” certain, or impossible and
           tests the prediction through experiments; and
           determines if a game is fair.



M(DSP) -   In response to a teacher or student generated
3-6        question or hypothesis, groups decide the most
           effective method (e.g., survey, observation,
           experimentation) to collect the data (numerical or
           categorical) necessary to answer the question;

           In response to a teacher or student generated
           question or hypothesis, groups collect, organize, and
           appropriately display the data.

           In response to a teacher or student generated
           question or hypothesis, groups analyze the data to
           draw conclusions about the question or hypothesis
           being tested, and when appropriate make predictions.
           (IMPORTANT: Analyzes data consistent with concepts
           and skills in M(DSP)–3–2.)




                                                                             3-8
                                                 Grade Level 4 Expectations by Strand

                                                         Number and Operations
GLE
          Grade Level Expectations                                     Terms Defined (Definition Number)           Notes and Resources
Number
          Demonstrates conceptual understanding of rational            o   Rational number (N&O-1)           Fraction Hamburger: puzzle
M(N&O)-   numbers with respect to:                                     o   Whole number (N&O-2)              Investigations
4-1       whole numbers from 0 to 999,999 through equivalency,         o   Fraction (N&O-3)                  Fraction Bars
          composition, decomposition, or place value using             o   Proper fraction (N&O-4)           Graph Paper
          models, explanations, or other representations.              o   Improper fraction (N&O-5)         Geoboards
                                                                       o   Decimal (N&O-7)
          Demonstrates conceptual understanding of rational            o   Ratio (N&O-12)
          numbers with respect to:
                                                                       o   Equivalent numbers (N&O-14)
          positive fractional numbers (benchmark fractions: a/2,
                                                                       o   Composition of numbers
          a/3, a/4, a/5, a/6, a/8, or a/10, where a is a whole
          number greater than 0 and less than or equal to the              (N&O-15)
          denominator) as a part to whole relationship in area, set,   o   Decomposition of numbers
          or linear models where the number of parts in the whole          (N&O-16)
          are equal to, and a multiple or factor of the denominator    o   Area model to represent part to
          using models, explanations, or other                             whole relationship (N&O-17)
          representations.                                             o   Set model (N&O-18)
                                                                       o   Linear model (N&O-19)
          Demonstrates conceptual understanding of rational            o   In and out of context (N&O-36)
          numbers with respect to:                                     o   Factor (N&O-38)
          decimals as hundredths within the context of money, or       o   Multiples (N&O-39)
          tenths within the context of metric measurements (e.g.,
          2.3 cm) using models, explanations, or other
          representations.
                                                                       o   Fraction (N&O-3)
M(N&O)-   Demonstrates understanding of the relative                   o   Proper fraction (N&O-4)
4-2       magnitude of numbers from 0 to 999,999 by ordering           o   Decimal (N&O-7)
          or comparing whole numbers using models, number              o   Equivalent numbers (N&O-14)
          lines, or explanations.                                      o   Area model to represent part to
                                                                           whole relationship (N&O-17)
          Demonstrates understanding of the relative                   o   Set model (N&O-18)
          magnitude of numbers from 0 to 999,999 by ordering,
                                                                       o   Linear model (N&O-19)
          comparing, or identifying equivalent proper positive
                                                                       o   Relative magnitude (N&O-20)
          fractional numbers; or decimals using models, number
          lines, or explanations.                                      o   Within number formats
                                                                           (N&O-21)
                                                                       o   Ordering (N&O-26)
                                                                       o   Comparing (N&O-27)
                                                                       o   Number line (N&O-28)

                                                                           4-1
                                                           Number and Operations
GLE
          Grade Level Expectations                                      Terms Defined (Definition Number)          Notes and Resources
Number
                                                                                                              Math Their Way: Beans and
M(N&O)-   Demonstrates conceptual understanding of                      o   Fraction (N&O-3)                  Cups
4-3       mathematical operations by describing or illustrating         o   Proper fraction (N&O-4)           Family Math
          the relationship between repeated subtraction and             o   Improper fraction (N&O-5)         Unifix Cubes
          division (no remainders).                                     o   Area model to represent part to   Math Bingo (all concepts)
                                                                            whole relationship (N&O-17)       Power Blocks
          Demonstrates conceptual understanding of                      o   Set model (N&O-18)
          mathematical operations the inverse relationship
                                                                        o   Linear model (N&O-19)
          between multiplication and division of whole numbers;
                                                                        o   Number line (N&O-28)
          or the addition or subtraction of positive fractional
          numbers with like denominators using models, number           o   Inverse relationships in
          lines, or explanations.                                           operations (N&O-29)
                                                                        o   Relationship between repeated
                                                                            addition and multiplication of
                                                                            whole numbers (N&O-30)
                                                                        o   Concept of multiplication
                                                                            (N&O-37)


M(N&O)-   Accurately solves problems involving multiple                 o   Whole number (N&O-2)
4-4       operations on whole numbers or the use of the                 o   Fraction (N&O-3)
          properties of factors and multiples.                          o   Proper fraction (N&O-4)
                                                                        o   Decimal (N&O-7)
          Accurately solves problems involving addition or              o   Accurately solves problems
          subtraction of decimals and positive proper fractions             (N&O-35)
          with like denominators. (Multiplication limited to 2 digits
                                                                        o   Concept of multiplication
          by 2 digits, and division limited to 1 digit divisors.)
                                                                            (N&O-37)
          (IMPORTANT: Applies the conventions of order of               o   Factor (N&O-38)
          operations where the left to right computations are           o   Multiples (N&O-39)
          modified only by the use of parentheses.)




M(N&O)-
          None
4-5


                                                                            4-2
                                                         Number and Operations
GLE
          Grade Level Expectations                                    Terms Defined (Definition Number)           Notes and Resources
Number

M(N&O)-   Mentally adds whole number facts through 20; adds                                               All of this is referred to mentally!
4-6       two-digit whole numbers, combinations of two-digit and
          3-digit whole numbers that are multiples of ten, and 4-
          digit whole numbers that are multiples of 100 (limited to
          two addends) (e.g., 67 + 24; 320 + 430; 320 + 90;
          1,300 + 1,400)

          Mentally subtracts a one-digit whole number from a
          two-digit whole number (e.g., 67 – 9); and subtracts
          combinations of two digit and three-digit whole numbers
          that are multiples of ten (e.g., 50 – 20, 230 – 80, 520 –
          200).

          Mentally multiplies whole number facts to a product
          of 100 and calculates related division facts.

          (IMPORTANT: The intent of this GLE is to embed
          mental arithmetic throughout the instructional program,
          not to teach it as a separate unit.)
                                                                                                          Unifix Cubes
M(N&O)-   Makes estimates in a given situation by identifying
4-7       when estimation is appropriate, selecting the
          appropriate method of estimation, and evaluating the
          reasonableness of solutions appropriate to grade level
          GLEs across content strands.

          (IMPORTANT: The intent of this GLE is to embed
          estimation throughout the instructional program, not to
          teach it as a separate unit.)


M(N&O)-   Applies properties of numbers (odd, even,
4-8       multiplicative property of zero, and remainders) to solve
          problems and to simplify computations.

          Applies field properties (commutative, associative,
          and identity) to solve problems and to simplify
          computations.


                                                                         4-3
                                                         Geometry and Measurement
GLE
          Grade Level Expectations                                     Terms Defined (Definition Number)             Notes and Resources
Number

M(G&M)-   Uses properties or attributes of angles (number of           o   Attributes and properties
4-1       angles) or sides (number of sides, length of sides,              (G&M-1)                             Geoboards
          parallelism, or perpendicularity) to identify, describe,     o   Angles (G&M-10)                     Tangrams
          or distinguish among triangles, squares, rectangles,         o   Parallel lines (G&M-7)              Human Bodies
          rhombi, trapezoids, hexagons, or octagons; or classify       o   Perpendicular (G&M-6)               3-D space figures
                               o
          angles relative to 90 as more than, less than, or equal      o   Triangle (G&M-3)                    Power Blocks
          to.
                                                                       o   Quadrilaterals (G&M-4)
                                                                       o   Polygons (G&M-2)
M(G&M)-   None
4-2

M(G&M)-   Uses properties or attributes (shape of bases or             o   Attributes and properties(G&M-3)
4-3       number of lateral faces) to identify, compare, or            o   Three-dimensional shapes
          describe three-dimensional shapes (rectangular                   (G&M-15)
          prisms, triangular prisms, cylinders, or spheres).


M(G&M)-   Demonstrates conceptual understanding of                     o   Congruent (G&M-16)
4-4       congruency by matching congruent figures using               o   Reflection (G&M-17)
          reflections, translations, or rotations (flips, slides, or   o   Translation (G&M-18)
          turns), or as the result of composing or decomposing         o   Rotation (G&M-19)
          shapes using models or explanations.                         o   Composing and decomposing
                                                                           shapes (G&M-21)
                                                                       o   Matching congruent figures using
                                                                           reflections, translations, and
                                                                           rotations (G&M-20)
                                                                                                               Mirrors
                                                                       o   Similar figures (G&M-23)
                                                                       o   Describes the proportional effect
                                                                           on linear dimensions of polygons
                                                                           or circles when scaling up or
                                                                           down while preserving the angles
                                                                           of polygons (G&M-24)




                                                                           4-4
                                                       Geometry and Measurement
GLE
          Grade Level Expectations                                     Terms Defined (Definition Number)               Notes and Resources
Number

M(G&M)-   Demonstrates conceptual understanding of                     o   Similar figures (G&M-23)
4-5       similarity by applying scales on maps, or applying           o   Describes the proportional effect
          characteristics of similar figures (same shape but not           on linear dimensions of polygons
                                                                                                               Maps
          necessarily the same size) to identify similar figures, or       or circles when scaling up or
          to solve problems involving similar figures. Describes           down while preserving the angles
          relationships using models or explanations.                      of polygons (G&M-24)
                                                                       o   Proportional reasoning (N&O-44)

M(G&M)-   Demonstrates conceptual understanding of                     o   Polygons (G&M-2)
4-6       perimeter of polygons, on grids using a variety of           o   Demonstrates conceptual
          models, manipulatives, or formulas.                              understanding of perimeter and
                                                                           area of polygons and irregular
          Demonstrates conceptual understanding of area of                 figures on grids (G&M-26)
          rectangles, polygons or irregular shapes on grids using      o   Measures and uses units of
          a variety of models, manipulatives, or formulas.
                                                                           measure appropriately and
                                                                                                               Tiles
                                                                           consistently (G&M-31)
          Expresses all measures using appropriate units.
                                                                       o   Whole number bases and whole
                                                                           number exponents, and
                                                                           fractional bases with whole
                                                                           number exponents (N&O-24)
                                                                       o   Concept of multiplication
                                                                           (N&O-7)


M(G&M)-   Measures and uses units of measures appropriately            o   Measures and uses units of
4-7       and consistently, and makes conversions within                   measure appropriately and
          systems when solving problems across the content                 consistently (G&M-31)               Tpe measure
          strands.                                                     o   Makes conversions within and        Scale
                                                                           across systems (G&M-32)             rulers
          Benchmarks in Appendix B.
                                                                                                               yard sticks
                                                                                                               meter sticks




M(G&M)-
          None
4-8

                                                                           4-5
                                                     Geometry and Measurement
GLE
          Grade Level Expectations                                    Terms Defined (Definition Number)        Notes and Resources
Number

M(G&M)-   Demonstrates understanding of spatial
4-9       relationships using location and position by
          interpreting and giving directions between locations on a
          map or coordinate grid (first quadrant).

          Demonstrates understanding of spatial
          relationships using location and position by plotting
                                                                                                          Computer CD
          points in the first quadrant in context (e.g., games,
                                                                                                          Maps
          mapping);

          Demonstrates understanding of spatial
          relationships using location and position by finding
          the horizontal and vertical distances between points on
          a coordinate grid in the first quadrant.



M(G&M)-   Demonstrates conceptual understanding of spatial
4-10      reasoning and visualization by copying, comparing,
          and drawing models of triangles, squares, rectangles,
          rhombi, trapezoids, hexagons, octagons, and circles.


          Demonstrates conceptual understanding of spatial
          reasoning and visualization by building models of
          rectangular prisms from two- or three dimensional
          representations.                                                                                Geoboards
                                                                                                          Blocks




                                                                         4-6
                                                        Functions and Algebra
GLE
          Grade Level Expectations                                 Terms Defined (Definition Number)             Notes and Resources
Number

M(F&A)–   Identifies and extends to specific cases a variety of    o   Patterns (F&A-1)                    Unifix Cubes
4–1       patterns (linear and nonlinear) represented in models,   o   Extend a pattern (F&A-5)
          tables or sequences; and writes a rule in words or       o   Numeric patterns (F&A-3)
          symbols to find the next case.                           o   Sequence (F&A-6)
                                                                   o   Expresses generalization or rule
                                                                       using words or symbols (F&A-7)
                                                                   o   Pattern Summary Table by grade
                                                                       level (F&A-9)


M(F&A)–   Demonstrates conceptual understanding of linear
4–2       relationships (y = kx) as a constant rate of change by
          identifying, describing, or comparing situations that
          represent constant rates of change.


M(F&A)–   Demonstrates conceptual understanding of                 o   Whole number (N&O-2)
4–3       algebraic expressions by using letters or symbols to     o   Algebraic expressions (F&A-25)
          represent unknown quantities to write simple linear      o   Evaluating algebraic expressions
          algebraic expressions involving any one of the four          (F&A-26)
          operations; or by evaluating simple linear algebraic     o   Linear relationships (F&A-10)
          expressions using whole numbers.                         o   Proportional linear relationships
                                                                       (y = kx)     (F&A-11)
                                                                   o   Non-proportional linear
                                                                       relationships (y = mx + b)
                                                                       (F&A-12)
                                                                   o   Number sentences (F&A-33)
                                                                   o   Equation (F&A-32)
                                                                   o   Algebraic equation notation
                                                                       (F&A-34)
                                                                   o   Examples of forms of equations
                                                                       (F&A-35)




                                                                       4-7
                                                         Functions and Algebra
GLE
          Grade Level Expectations                                   Terms Defined (Definition Number)    Notes and Resources
Number

M(F&A)–   Demonstrates conceptual understanding of equality          o   Equality (F&A-30)
4–4       by showing equivalence between two expressions using       o   Demonstrates equality (F&A-31)
          models or different representations of the expressions,    o   Number sentences (F&A-33)
          by simplifying numerical expressions where left to right   o   Equation (F&A-32)
          computations may be modified only by the use of            o   Algebraic equation notation
          parentheses [e.g., 14 - (2 × 5)]                               (F&A-34)
                                                                     o   Examples of forms of equations
          and by solving one-step linear equations of the form
                                                                         (F&A-35)
          ax = c and/or
          x±b=c
          where a, b, and c are whole numbers with a≠ 0.




                                                                         4-8
                                                      Data, Statistics, and Probability
GLE
           Grade Level Expectations                                     Terms Defined (Definition Number)             Notes and Resources
Number

M(DSP) -   Interprets a given representation (line plots, tables,       o   Interprets a given representation   Graphing
4-1        bar graphs, pictographs, or circle graphs) to answer             (DSP-21)                            Time Liner
           questions related to the data, to analyze the data to        o   Representation (DSP-1)
           formulate or justify conclusions, to make predictions, or    o   Line plot (DSP-5)
           to solve problems.                                           o   Frequency table (DSP-4)
                                                                        o   Bar graph (DSP-6)
           (IMPORTANT: Analyzes data consistent with concepts
                                                                        o   Pictograph (DSP-2)
           and skills in M(DSP)-4-2.)
                                                                        o   Circle graph (DSP-8)


M(DSP) -   Analyzes patterns, trends, or distributions in data in       o   Pattern (F&A-1)
4-2        a variety of contexts by determining or using                o   Median (DSP-16)
           measures of central tendency (median or mode), or            o   Mode (DSP-17)
           range.                                                       o   Range (DSP-18)



M(DSP) -   Organizes and displays data using tables, line plots,
4-3        bar graphs, and pictographs to answer questions related
           to the data, to analyze the data to formulate or justify
           conclusions, to make predictions, or to solve problems.

           (IMPORTANT: Analyzes data consistent with concepts
           and skills in M(DSP)–4–2.)



M(DSP) -   Uses counting techniques to solve problems in                o   Solves problems using a variety
4-4        context involving combinations or simple permutations            of counting strategies (DSP-25)
           (e.g., Given a map - Determine the number of paths           o   Combination (DSP-41)
           from point A to point B.) using a variety of strategies      o   Permutation (DSP-42)
           (e.g., organized lists, tables, tree diagrams, or others).   o   Frequency table (DSP-4)
                                                                        o   Tree diagram (DSP-28)




                                                                            4-9
                                                     Data, Statistics, and Probability
GLE
           Grade Level Expectations                                      Terms Defined (Definition Number)            Notes and Resources
Number

M(DSP) -   For a probability event in which the sample space             o   Sample space (DSP-30)              Tiles – different colored
4-5        may or may not contain equally likely outcomes,               o   Event (DSP-31)                     Dice
           determines the theoretical probability of an event and        o   Theoretical probability (DSP-32)   Red beans
           expresses the result as part to whole (e.g., two out of       o   Ratio (N&O-12)                     Playing cards
           five).

           For a probability event in which the sample space
           may or may not contain equally likely outcomes
           predicts the likelihood of an event as a part to whole
           relationship (e.g., two out of five, zero out of five, five
           out of five) and tests the prediction through experiments;
           and determines if a game is fair.


M(DSP) -   In response to a teacher or student generated
4-6        question or hypothesis, groups decide the most
           effective method (e.g., survey, observation,
           experimentation) to collect the data (numerical or
           categorical) necessary to answer the question.

           In response to a teacher or student generated
           question or hypothesis, groups collect, organize, and
           appropriately display the data.

           In response to a teacher or student generated
           question or hypothesis, groups analyze the data to
           draw conclusions about the question or hypothesis
           being tested, and when appropriate make predictions.

           In response to a teacher or student generated
           question or hypothesis, groups ask new questions
           and make connections to real world situations.

           (IMPORTANT: Analyzes data consistent with concepts
           and skills in M(DSP)–4–2.)




                                                                             4 - 10
                                                 Grade Level 5 Expectations by Strand

                                                         Number and Operations
GLE
          Grade Level Expectations                                    Terms Defined (Definition Number)           Notes and Resources
Number

M(N&O)-   Demonstrates conceptual understanding of rational           o   Rational number (N&O-1)           From the series Investigations
5-1       numbers with respect to:                                    o   Whole number (N&O-2)              of Number, Data and Space
          whole numbers from 0 to 9,999,999 through                   o   Fraction (N&O-3)
          equivalency, composition, decomposition, or place value         Proper fraction (N&O-4)
                                                                      o                                     Mathematical Thinking at Grade 5
          using models, explanations, or other representations.       o   Improper fraction (N&O-5)
                                                                      o   Mixed number (N&O-6)              Factors, multiples, square
          Demonstrates conceptual understanding of rational
                                                                      o   Decimal (N&O-7)                   number, prime number, addition
          numbers with respect to:
                                                                      o   Percent (N&O-8)                   and subtraction games, landmark
          positive fractional numbers (proper, mixed number,
          and improper) (halves, fourths, eighths, thirds, sixths,    o   Ratio (N&O-12)                    numbers –100, 1000, 10,000,
          twelfths, fifths, or powers of ten (10, 100, 1000)),        o   Equivalent numbers (N&O-14)       solving larger number operations
          decimals (to thousandths), or benchmark percents            o   Composition of numbers            using cluster patterns includes
          (10%, 25%, 50%, 75% or 100%) as a part to whole                 (N&O-15)                          games, mental math, worksheets
          relationship in area, set, or linear models using models,   o   Decomposition of numbers          (tiles and graph paper)
          explanations, or other representations*.                        (N&O-16)
                                                                      o   Area model to represent part to   Building on Numbers You Know
                                                                          whole relationship (N&O-17)
                                                                      o   Set model (N&O-18)                Strategies for estimation and
                                                                      o   Linear model (N&O-19)             computation, algebraic patterns
                                                                      o   * Specifications for Area, Set,   includes games and worksheets
                                                                          and Linear Models (Pg. NO-12)

                                                                                                            Name That Portion

                                                                                                            Fractions, decimals and percents
                                                                                                            includes several games and
                                                                                                            worksheets




                                                                          5-1
                                                         Number and Operations
GLE
          Grade Level Expectations                                     Terms Defined (Definition Number)           Notes and Resources
Number

M(N&O)-   Demonstrates understanding of the relative                   o   Rational number (N&O-1)           From the series Investigations
5-2       magnitude of numbers by ordering, comparing, or              o   Whole number (N&O-2)              of Number, Data and Space
          identifying equivalent positive fractional numbers,          o   Fraction (N&O-3)
          decimals, or benchmark percents within number formats        o   Proper fraction (N&O-4)           Name That Portion
          (fractions to fractions, decimals to decimals, or percents   o   Improper fraction (N&O-5)
          to percents); or integers in context using models or         o   Mixed number (N&O-6)              Fractions, decimals and percents
          number lines.
                                                                       o   Decimal (N&O-7)                   includes several games and
                                                                       o   Percent (N&O-8)                   worksheets
                                                                       o   Ratio (N&O-12)
                                                                       o   Equivalent numbers (N&O-14)       Patterns of Change
                                                                       o   Composition of numbers
                                                                           (N&O-15)                          Tables and graphs includes
                                                                       o   Decomposition of numbers          software
                                                                           (N&O-16)
                                                                       o   Area model to represent part to
                                                                           whole relationship (N&O-17)
                                                                       o   Set model (N&O-18)
                                                                       o   Linear model (N&O-19)


M(N&O)-   Demonstrates conceptual understanding of                     o   Whole number (N&O-2)              Building on Numbers You Know
5-3       mathematical operations by describing or illustrating        o   Meaning of remainders with
          the meaning of a remainder with respect to division of           respect to division of whole      Strategies for estimation and
          whole numbers using models, explanations, or solving             numbers (N&O-32)                  computation, algebraic patterns
          problems.                                                    o   Accurately solves problems        includes games and worksheets
                                                                           (N&O-35)
          Demonstrates conceptual understanding of
          mathematical operations with respect to addition and
          subtraction of decimals and positive proper fractions
          with unlike denominators.




                                                                           5-2
                                                         Number and Operations
GLE
          Grade Level Expectations                                    Terms Defined (Definition Number)           Notes and Resources
Number
                                                                                                          From the series Investigations
M(N&O)-   Accurately solves problems involving multiple               o   Whole number (N&O-2)            of Number, Data and Space
5-4       operations on whole numbers or the use of the               o   Fraction (N&O-3)
          properties of factors, multiples, prime, or composite       o   Proper fraction (N&O-4)         Building on Numbers You Know
          numbers.                                                    o   Decimal (N&O-7)
                                                                      o   Accurately solves problems      Strategies for estimation and
          Accurately solves problems involving addition or                (N&O-35)                        computation, algebraic patterns
          subtraction of fractions (proper) and decimals to the
                                                                      o   Factor (N&O-38)                 includes games and worksheets
          hundredths place. (Division of whole numbers by a one-
                                                                      o   Multiples (N&O-39)
          or two-digit divisor.)
                                                                      o   Prime numbers (N&O-40)          Name That Portion
          (IMPORTANT: Applies the conventions of order of             o   Composite numbers (N&O-41)
          operations with and without parentheses.)                                                       Fractions, decimals and percents
                                                                                                          includes several games and
                                                                                                          worksheets


M(N&O)-
          None
5-5


M(N&O)-   Mentally calculates change back from $1.00, $5.00,                                              All of this is referred to mentally!
5-6       and $10.00;
          Mentally calculates multiplication and related division                                         Mathematical Thinking at Grade 5
          facts to a product of 144; multiplies a two-digit whole
          number by a one-digit whole number (e.g., 45 x 5), two-                                         Factors, multiples, square
          digit whole numbers that are multiples of ten (e.g., 50 x                                       number, prime number, addition
          60), a three-digit whole number that is a multiple of 100                                       and subtraction games, landmark
          by a two- or three-digit number which is a multiple of 10                                       numbers –100, 1000, 10,000,
          or 100, respectively (e.g., 400 x 50, 400 x 600).                                               solving larger number operations
                                                                                                          using cluster patterns includes
          Mentally calculates division of 3- and 4-digit multiples
          of powers of ten by their compatible factors (e.g.,                                             games, mental math, worksheets
          360 ÷ 6;    360 ÷ 60;      3600 ÷ 6;    3600 ÷ 60;                                              (tiles and graph paper)
          3600 ÷ 600;    360 ÷ 12;     360 ÷ 120;     3600 ÷ 12;
          3600 ÷ 120;     3600 ÷ 1200).
          (IMPORTANT: The intent of this GLE is to embed
          mental arithmetic throughout the instructional program,
          not to teach it as a separate unit.)

                                                                          5-3
                                                         Number and Operations
GLE
          Grade Level Expectations                                  Terms Defined (Definition Number)         Notes and Resources
Number
                                                                                                        From the series Investigations
M(N&O)-   Makes estimates in a given situation by identifying                                           of Number, Data and Space
5-7       when estimation is appropriate, selecting the
          appropriate method of estimation, determining the level                                       Mathematical Thinking at Grade 5
          of accuracy needed given the situation, analyzing the
          effect of the estimation method on the accuracy of                                            Factors, multiples, square
          results, and evaluating the reasonableness of solutions                                       number, prime number, addition
          appropriate to grade level GLEs across content strands.
                                                                                                        and subtraction games, landmark
                                                                                                        numbers –100, 1000, 10,000,
          (IMPORTANT: The intent of this GLE is to embed
          estimation throughout the instructional program, not to                                       solving larger number operations
          teach it as a separate unit.)                                                                 using cluster patterns includes
                                                                                                        games, mental math, worksheets
                                                                                                        (tiles and graph paper)


                                                                                                        Mathematical Thinking at Grade 5
M(N&O)-   Applies properties of numbers (odd, even, and
5-8       divisibility) to solve problems and to simplify                                               Factors, multiples, square
          computations.                                                                                 number, prime number, addition
                                                                                                        and subtraction games, landmark
          Applies field properties (commutative, associative,                                           numbers –100, 1000, 10,000,
          identity, and distributive) to solve problems and to                                          solving larger number operations
          simplify computations.
                                                                                                        using cluster patterns includes
                                                                                                        games, mental math, worksheets
                                                                                                        (tiles and graph paper)

                                                                                                        Building on Numbers You Know

                                                                                                        Strategies for estimation and
                                                                                                        computation, algebraic patterns
                                                                                                        includes games and worksheets




                                                                       5-4
                                                     Geometry and Measurement
GLE
          Grade Level Expectations                                   Terms Defined (Definition Number)         Notes and Resources
Number

M(G&M)-   Uses properties or attributes of angles (right, acute,     o   Attributes and properties       From the series Investigations
5-1       or obtuse) or sides (number of congruent sides,                (G&M-1)                         of Number, Data and Space
          parallelism, or perpendicularity) to identify, describe,   o   Angles (G&M-10)
          classify, or distinguish among different types of          o   Parallel lines (G&M-7)          Picturing Polygons
          triangles (right, acute, obtuse, equiangular, or           o   Perpendicular (G&M-6)
          equilateral) or quadrilaterals (rectangles, squares,       o   Triangle (G&M-3)                2-D geometry includes software
          rhombi, trapezoids, or parallelograms).                    o   Quadrilaterals (G&M-4)          and manipulatives (Power
                                                                                                         Polygons)

M(G&M)-   None
5-2

M(G&M)-   Uses properties or attributes (shape of bases,             o   Attributes and properties
5-3       number of lateral faces, or number of bases) to                (G&M-1)
          identify, compare, or describe three-dimensional           o   Three-dimensional shapes        Containers and Cubes
          shapes (rectangular prisms, triangular prisms,                 (G&M-15)
          cylinders, spheres, pyramids, or cones).                                                       3-D geometry and volume
                                                                                                         includes manipulatives for
                                                                                                         volume




M(G&M)-   None
5-4

M(G&M)-   Demonstrates conceptual understanding of
5-5       similarity by describing the proportional effect on the
          linear dimensions of triangles and rectangles when
          scaling up or down while preserving angle measures, or                                         Picturing Polygons
          by solving related problems (including applying scales
          on maps). Describes effects using models or
                                                                                                         2-D geometry includes software
          explanations.
                                                                                                         and manipulatives (Power
                                                                                                         Polygons)




                                                                         5-5
                                                    Geometry and Measurement
GLE
          Grade Level Expectations                                Terms Defined (Definition Number)          Notes and Resources
Number

M(G&M)-   Demonstrates conceptual understanding of                o   Triangle (G&M-3)
5-6       perimeter of polygons, and the area of rectangles or    o   Polygons (G&M-2)
          right triangles through models, manipulatives, or       o   Three-dimensional shapes
          formulas.                                                   (G&M-15)
                                                                                                       From the series Investigations
                                                                  o   Demonstrates conceptual
          Demonstrates conceptual understanding of area of                                             of Number, Data and Space
                                                                      understanding of perimeter and
          polygons or irregular figures on grids, and volume of
                                                                      area of polygons and irregular
          rectangular prisms (cubes) using a variety of models,                                        Picturing Polygons
                                                                      figures on grids (G&M-26)
          manipulatives, or formulas.
                                                                  o   Demonstrates conceptual
                                                                                                       2-D geometry includes software
                                                                      understanding of perimeter,
          Expresses all measures using appropriate units.                                              and manipulatives (Power
                                                                      area, volume, or surface area
                                                                                                       Polygons)
                                                                      using models and manipulatives
                                                                      (G&M-28)
                                                                                                       Containers and Cubes
                                                                  o   Measures and uses units of
                                                                                                       3-D geometry and volume
                                                                      measure appropriately and
                                                                                                       includes manipulatives for
                                                                      consistently (G&M-31)
                                                                                                       volume
                                                                  o   Whole number bases and whole
                                                                      number exponents, and
                                                                      fractional bases with whole
                                                                      number exponents (N&O-24)


M(G&M)-   Measures and uses units of measures appropriately       o   Measures and uses units of
5-7       and consistently, and makes conversions within              measure appropriately and
          systems when solving problems across the content            consistently (G&M-31)            Measurement Benchmarks
          strands.                                                o   Makes conversions within and
                                                                      across systems (G&M-32)          Estimating and measuring
          Benchmarks in Appendix B.
                                                                                                       standard and metric linear,
                                                                                                       weight, capacity and time
                                                                                                       (scales, metric and standard
                                                                                                       weights, metric and standard
                                                                                                       measuring tapes, metric and
                                                                                                       standard rulers, stop watches)




                                                                      5-6
                                                 Geometry and Measurement
GLE
          Grade Level Expectations                              Terms Defined (Definition Number)         Notes and Resources
Number
M(G&M)-
          None
5-8

M(G&M)-   Demonstrates understanding of spatial
5-9       relationships using location and position by
          interpreting and giving directions between
          locations on a map or coordinate grid (all four                                           From the series Investigations
          quadrants).                                                                               of Number, Data and Space

          Demonstrates understanding of spatial                                                     Picturing Polygons
          relationships using location and position by
          plotting points in four quadrants in context (e.g.,                                       2-D geometry includes software
          games, mapping, identifying the vertices of                                               and manipulatives (Power
          polygons as they are reflected, rotated, and                                              Polygons)
          translated).
                                                                                                    Patterns of Change
          Demonstrates understanding of spatial
          relationships using location and position by                                              Tables and graphs includes
          determining horizontal and vertical distances                                             software
          between points on a coordinate grid in the first
          quadrant.                                                                                 Math A Way of Thinking

                                                                                                    Coordinate graphing section




M(G&M)-   Demonstrates conceptual understanding of
5-10      spatial reasoning and visualization by
          building models of rectangular and triangular                                             Containers and Cubes
          prisms, cones, cylinders, and pyramids from
          two- or three dimensional representations.                                                3-D geometry and volume
                                                                                                    includes manipulatives for
                                                                                                    volume




                                                                   5-7
                                                          Functions and Algebra
GLE
          Grade Level Expectations                                    Terms Defined (Definition Number)             Notes and Resources
Number
                                                                                                              From the series Investigations
M(F&A)–   Identifies and extends to specific cases a variety of       o   Numeric patterns (F&A-3)            of Number, Data and Space
5–1       patterns (linear and nonlinear) represented in models,      o   Extend a pattern (F&A-5)
          tables, sequences, or in problem situations; and writes a   o   Sequence (F&A-6)                    Patterns of Change
          rule in words or symbols for finding specific cases of a    o   Linear relationships (F&A-10)
          linear relationship.                                        o   Proportional linear relationships   Tables and graphs includes
                                                                          (y = kx)     (F&A-11)               software
                                                                      o   Non-proportional linear
                                                                          relationships (y = mx + b)          Building Blocks for Algebra K-
                                                                          (F&A-12)                            8
                                                                      o   Expresses generalization or rule
                                                                          using words or symbols (F&A-7)      patterns and functions includes
                                                                      o   Concrete situations (F&A-20)        games
                                                                      o   Pattern Summary Table by grade
                                                                          level (F&A-9)



                                                                                                              Patterns of Change
M(F&A)–   Demonstrates conceptual understanding of linear
5–2       relationships (y = kx) as a constant rate of change by                                              Tables and graphs includes
          identifying, describing, or comparing situations that                                               software
          represent constant rates of change (e.g., tell a story
          given a line graph about a trip).




                                                                          5-8
                                                          Functions and Algebra
GLE
          Grade Level Expectations                                     Terms Defined (Definition Number)             Notes and Resources
Number
                                                                                                               Patterns of Change
M(F&A)–   Demonstrates conceptual understanding of                     o   Whole number (N&O-2)
5–3       algebraic expressions by using letters to represent          o   Algebraic expression (F&A-25)       Tables and graphs includes
          unknown quantities to write linear algebraic expressions     o   Evaluating algebraic expressions    software
          involving any two of the four operations; or by evaluating       (F&A-26)
          linear algebraic expressions using whole numbers.            o   Linear relationships (F&A-10)
                                                                       o   Proportional linear relationships   Building Blocks for Algebra K-
                                                                           (y = kx) (F&A-11)                   8
                                                                       o   Non-proportional linear
                                                                           relationships (y = mx =b)           patterns and functions includes
                                                                           (F&A-12)                            games
                                                                       o   Number sentences (F&A-33)
                                                                       o   Equation (F&A-32)
                                                                       o   Examples of forms of equations
                                                                           (F&A-35)
                                                                       o   Algebraic equation notation
                                                                           (F&A-34)


                                                                                                               Patterns of Change
M(F&A)–   Demonstrates conceptual understanding of equality            o   Whole number (N&O-2)
5–4       by showing equivalence between two expressions               o   Equality (F&A-30)                   Tables and graphs includes
          using models or different representations of the             o   Demonstrates equality (F&A-31)      software
          expressions,                                                 o   Number sentences (F&A-33)
          by solving one-step linear equations of the form             o   Equation (F&A-32)                   Building Blocks for Algebra K-
          ax = c     and/or                                            o   Algebraic equation notation         8
          x ± b = c and/or
                                                                           (F&A-34)
          x/a = c,
                                                                       o   Examples of forms of equations      patterns and functions includes
          where a, b, and c are whole numbers with a≠ 0;
          or by determining which values of a replacement set              (F&A-35)                            games
          make the equation (multi-step of the form ax ± b = c         o   Linear relationships (F&A-10)
          where a, b, and c are whole numbers with a≠ 0) a true        o   Proportional linear relationships
          statement (e.g., 2x + 3 = 11, {x: x = 2, 3, 4, 5}).              (y = kx)      (F&A-11)
                                                                       o   Non-proportional linear
                                                                           relationships (y = mx+b)
                                                                           (F&A-12)




                                                                           5-9
                                                   Data, Statistics, and Probability
GLE
           Grade Level Expectations                                    Terms Defined (Definition Number)             Notes and Resources
Number
                                                                                                               From the series Investigations
M(DSP) –   Interprets a given representation (tables, bar graphs,      o   Interprets a given representation   of Number, Data and Space
5-1        circle graphs, or line graphs) to answer questions              (DSP-21)
           related to the data, to analyze the data to formulate or    o   Representation (DSP-1)              Data: Kids, Cats and Ads
           justify conclusions, to make predictions, or to solve       o   Frequency table (DSP-4)
           problems.                                                   o   Bar graph (DSP-6)                   Statistics (stop watches)
                                                                       o   Circle graph (DSP-8)
           (IMPORTANT: Analyzes data consistent with concepts
                                                                       o   Line graph (DSP-12)
           and skills in M(DSP)-5-2.)



                                                                                                               Data: Kids, Cats and Ads
M(DSP) –   Analyzes patterns, trends, or distributions in data in      o   Pattern (F&A-1)
5-2        a variety of contexts by determining or using               o   Mean (DSP-15)                       Statistics (stop watches)
           measures of central tendency (mean, median, or mode)        o   Median (DSP-16)
           or range to analyze situations, or to solve problems.       o   Mode (DSP-17)
                                                                       o   Range (DSP-18)


                                                                                                               Data: Kids, Cats and Ads
M(DSP) –   Identifies or describes representations or elements         o   Representation (DSP-1)
5-3        of representations that best display a given set of         o   Identifies or describes             Statistics (stop watches)
           data or situation, consistent with the representations          representations or elements of
           required in M(DSP)-5-1.                                         representations that best display
                                                                           a given set of data or situation
           Organizes and displays data using tables, bar                   (DSP-23)
           graphs, or line graphs to answer questions related to the
           data, to analyze the data to formulate or justify
           conclusions, to make predictions, or to solve problems.

           (IMPORTANT: Analyzes data consistent with concepts
           and skills in M(DSP)-5-2.)




M(DSP) –   None
5-4
                                                                           5 - 10
                                                    Data, Statistics, and Probability
GLE
           Grade Level Expectations                                   Terms Defined (Definition Number)            Notes and Resources
Number
                                                                                                             Between Never and Always
M(DSP) –   For a probability event in which the sample space          o   Sample space (DSP-30)
5-5        may or may not contain equally likely outcomes,            o   Experimental probability           Probability includes games
           determines the experimental or theoretical probability         (DSP-33)                           (spinners, colored cubes)
           of an event and expresses the result as a fraction.        o   Theoretical probability (DSP-32)
                                                                      o   Event (DSP-31)
           For a probability event in which the sample space          o   Fraction (N&O-3)
           may or may not contain equally likely outcomes,
                                                                      o   Ratio (N&O-12)
           predicts the likelihood of an event as a fraction and
           tests the prediction through experiments; and
           determines if a game is fair.

                                                                                                             Between Never and Always
M(DSP) –   In response to a teacher or student generated
5-6        question or hypothesis decides the most effective                                                 Probability includes games
           method (e.g., survey, observation, experimentation) to                                            (spinners, colored cubes)
           collect the data (numerical or categorical) necessary to
           answer the question.

           In response to a teacher or student generated
           question or hypothesis collects, organizes, and
           appropriately displays the data.

           In response to a teacher or student generated
           question or hypothesis analyzes the data to draw
           conclusions about the question or hypothesis being
           tested, and when appropriate makes predictions.

           In response to a teacher or student generated
           question or hypothesis asks new questions and
           makes connections to real world situations.

           (IMPORTANT: Analyzes data consistent with concepts
           and skills in M(DSP)–5–2.)




                                                                          5 - 11
                                                Grade Level 6 Expectations by Strand

                                                       Number and Operations
GLE
          Grade Level Expectations                                  Terms Defined (Definition Number)              Notes and Resources
Number

M(N&O)-   Demonstrates conceptual understanding of rational         o   Rational number (N&O-1)              Glencoe Mathematics Application
6-1       numbers with respect to ratios (comparison of two         o   Whole number (N&O-2)                 and Concepts course 1 2004
          whole numbers by division a/b, a : b, and a ÷ b , where   o   Proper fraction (N&O-4)              edition plus corresponding
          b ≠ 0); and rates (e.g., a out of b, 25%) using models,   o   Improper fraction (N&O-5)            Resource Masters
          explanations, or other representations*.                  o   Mixed number (N&O-6)
                                                                    o   Percent (N&O-8)                      Calculators (classroom set)
                                                                    o   Ratio (N&O-12)
                                                                    o   Equivalent numbers (N&O-14)
                                                                    o   Area model to represent part to
                                                                        whole relationship (N&O-17)
                                                                    o   Set model     (N&O-18)
                                                                    o   Linear model (N&O-19)
                                                                    o   Proportional reasoning
                                                                        (N&O-44)
                                                                    o   *Specifications for Area, Set, and
                                                                        Linear Models (Pg. NO-12)




                                                                        6-1
                                                       Number and Operations
GLE
          Grade Level Expectations                                 Terms Defined (Definition Number)          Notes and Resources
Number

M(N&O)-   Demonstrates understanding of the relative               o   Rational number (N&O-1)          Glencoe Mathematics Application
6-2       magnitude of numbers by ordering or comparing            o   Fraction (N&O-3)                 and Concepts course 1 2004
          numbers with whole number bases and whole number
                             3  3
                                                                   o   Proper fraction (N&O-4)          edition plus corresponding
          exponents (e.g.,3 , 4 ), integers, or rational numbers   o   Improper fraction (N&O-5)        Resource Masters
          within and across number formats (fractions, decimals,   o   Mixed number (N&O-6)
          or whole number percents from 1- 100) using number       o   Decimal (N&O-7)                  Calculators (classroom set)
          lines or equality and inequality symbols.
                                                                   o   Percent (N&O-8)
                                                                   o   Integer (N&O-9)
                                                                   o   Equivalent numbers (N&O-14)
                                                                   o   Relative magnitude (N&O-20)
                                                                   o   Within number formats
                                                                       (N&O-21)
                                                                   o   Across number formats
                                                                       (N&O-22)
                                                                   o   Whole number bases and whole
                                                                       number exponents, and
                                                                       fractional bases with whole
                                                                       number exponents (N&O-24)
                                                                   o   Ordering (N&O-26)
                                                                   o   Comparing (N&O-27)
                                                                   o   Number line (N&O-28)
                                                                   o   Describing or illustrating the
                                                                       meaning of a power (N&O-33)




                                                                       6-2
                                                          Number and Operations
GLE
          Grade Level Expectations                                   Terms Defined (Definition Number)             Notes and Resources
Number

M(N&O)-   Demonstrates conceptual understanding of                   o   Proper fraction (N&O-4)             Glencoe Mathematics Application
6-3       mathematical operations by describing or illustrating      o   Improper fraction (N&O-5)           and Concepts course 1 2004
          the meaning of a power by representing the relationship    o   Decimal (N&O-7)                     edition plus corresponding
          between the base (whole number) and the exponent           o   Whole number bases and whole        Resource Masters
                                3   3
          (whole number) (e.g.,3 , 4 ).                                  number exponents, and
                                                                         fractional bases with whole         Calculators (classroom set)
          Demonstrates conceptual understanding of
                                                                         number exponents (N&O-24)
          mathematical operations and the effect on the
                                                                     o   Relationship between repeated       Fraction Bars
          magnitude of a whole number when multiplying or
          dividing it by a whole number, decimal, or fraction.           addition and multiplication of
                                                                         whole numbers (N&O-30)
                                                                     o   Relationship between repeated
          Demonstrates conceptual understanding of                       subtraction and division of whole
          mathematical operations of addition and subtraction of         numbers (N&O-31)
          positive fractions and integers; and multiplication and    o   Effect on magnitude of a whole
          division of fractions and decimals.                            number when multiplying or
                                                                         dividing by a whole number,
                                                                         fraction, or decimal (N&O-34)
                                                                     o   Describing or illustrating the
                                                                         meaning of a power (N&O-33)



M(N&O)-   Accurately solves problems involving single or             o   Fraction (N&O-3)                    Glencoe Mathematics Application
6-4       multiple operations on fractions (proper, improper, and    o   Proper fraction (N&O-4)             and Concepts course 1 2004
          mixed), or decimals;                                       o   Improper fraction (N&O-5)           edition plus corresponding
                                                                     o   Mixed number (N&O-6)                Resource Masters
          Accurately solves problems involving addition or           o   Decimal (N&O-7)
          subtraction of integers; percent of a whole; or problems   o   Percent (N&O-8)                     Calculators (classroom set)
          involving greatest common factor or least common
                                                                     o   Accurately solves problems
          multiple.
                                                                         (N&O-35)                            Fraction Bars
          (IMPORTANT: Applies the conventions of order of            o   GCF (N&O-42)
          operations with and without parentheses.)                  o   LCM (N&O-43)                        Inter Chips

                                                                                                             Connected Mathematics Series

M(N&O)-   None
6-5

                                                                         6-3
                                                        Number and Operations
GLE
          Grade Level Expectations                                  Terms Defined (Definition Number)           Notes and Resources
Number

M(N&O)-   Mentally calculates change back from $5.00, $10.00,
6-6       $20.00, $50.00, and $100.00.                                                                  All of this is referred to mentally!

          Mentally multiplies a two-digit whole number by a one-                                        Glencoe Mathematics Application
          digit whole number (e.g., 45 x 5), two-digit whole                                            and Concepts course 1 2004
          numbers that are multiples of ten (e.g., 50 x 60), a                                          edition plus corresponding
          three-digit whole number that is a multiple of 100 by a                                       Resource Masters
          two- or three-digit number which is a multiple of 10 or
          100, respectively (e.g., 400 x 50, 400 x 600).                                                Calculators (classroom set)
          Mentally divides 3- and 4-digit multiples of powers of
          ten by their compatible factors
          (e.g., 360 ÷ 6;    360 ÷ 60;     3600 ÷ 6;
          3600 ÷ 60;      3600 ÷ 600;     360 ÷ 12;
          360 ÷ 120;      3600 ÷ 12;      3600 ÷ 120;
          3600 ÷ 1200).

          Mentally determines the part of a whole number using
          benchmark percents (1%, 10%, 25%, 50%, and 75%).

          (IMPORTANT: The intent of this GLE is to embed
          mental arithmetic throughout the instructional program,
          not to teach it as a separate unit.)




                                                                       6-4
                                                           Number and Operations
GLE
          Grade Level Expectations                                       Terms Defined (Definition Number)         Notes and Resources
Number

M(N&O)-   Makes estimates in a given situation by identifying                                                Glencoe Mathematics Application
6-7       when estimation is appropriate, selecting the                                                      and Concepts course 1 2004
          appropriate method of estimation, determining the level                                            edition plus corresponding
          of accuracy needed given the situation, analyzing the                                              Resource Masters
          effect of the estimation method on the accuracy of
          results, and evaluating the reasonableness of solutions                                            Calculators (classroom set)
          appropriate to grade level GLEs across content strands.

          (IMPORTANT: The intent of this GLE is to embed
          estimation throughout the instructional program, not to
          teach it as a separate unit.)




M(N&O)-   Applies properties of numbers (odd, even,                                                          Glencoe Mathematics Application
6-8       remainders, divisibility, and prime factorization) to                                              and Concepts course 1 2004
          solve problems and to simplify computations.                                                       edition plus corresponding
                                                                                                             Resource Masters
          Applies field properties (commutative,
          associative, identity [including the multiplicative property                                       Calculators (classroom set)
          of one, e.g., 1 = 2/2 and 2/2 x ¾ = 6/8, so ¾ = 6/8],
          distributive, and additive inverses) to solve problems
          and to simplify computations.




                                                                            6-5
                                                      Geometry and Measurement
GLE
          Grade Level Expectations                                    Terms Defined (Definition Number)         Notes and Resources
Number

M(G&M)-   Uses properties or attributes of angles (right, acute,      o   Attributes and properties       Glencoe Mathematics Application
6-1       or obtuse) or sides (number of congruent sides,                 (G&M-1)                         and Concepts course 1 2004
          parallelism, or perpendicularity) to identify, describe,    o   Angles (G&M-10)                 edition plus corresponding
          classify, or distinguish among different types of           o   Parallel lines (G&M-7)          Resource Masters
          triangles (right, acute, obtuse, equiangular, scalene,      o   Perpendicular (G&M-6)
          isosceles, or equilateral) or quadrilaterals (rectangles,   o   Triangle (G&M-3)
          squares, rhombi, trapezoids, or parallelograms).                                                Calculators (classroom set)
                                                                      o   Quadrilaterals (G&M-4)
                                                                                                          Connected Mathematics Series

                                                                                                          Geo Boards


M(G&M)-   None
6-2
                                                                                                          Glencoe Mathematics Application
M(G&M)-   Uses properties or attributes (shape of bases,              o   Attributes and properties       and Concepts course 1 2004
6-3       number of lateral faces, number of bases, number of             (G&M-1)                         edition plus corresponding
          edges, or number of vertices) to identify, compare, or      o   Three-dimensional shapes        Resource Masters
          describe three-dimensional shapes (rectangular                  (G&M-15)
          prisms, triangular prisms, cylinders, spheres, pyramids,                                        Calculators (classroom set)
          or cones).
                                                                                                          Connected Mathematics Series

                                                                                                          Geo Boards

M(G&M)-   Demonstrates conceptual understanding of                                                        Glencoe Mathematics Application
6-4       congruency by predicting and describing the                                                     and Concepts course 1 2004
          transformational steps (reflections, translations, and                                          edition plus corresponding
          rotations) needed to show congruence (including the                                             Resource Masters
          degree of rotation) and as the result of composing and
          decomposing two- and three-dimensional objects using                                            Calculators (classroom set)
          models or explanations.
                                                                                                          Connected Mathematics Series
          Demonstrates conceptual understanding of
          congruency by using line and rotational symmetry to                                             Geo Boards
          demonstrate congruent parts within a shape.

                                                                          6-6
                                                    Geometry and Measurement
GLE
          Grade Level Expectations                                   Terms Defined (Definition Number)             Notes and Resources
Number

M(G&M)-   Demonstrates conceptual understanding of                   o   Similar figures (G&M-23)            Glencoe Mathematics Application
6-5       similarity by describing the proportional effect on the    o   Polygons (G&M-2)                    and Concepts course 1 2004
          linear dimensions of polygons or circles when scaling up   o   Sum of the measures of interior     edition plus corresponding
          or down while preserving the angles of polygons, or by         angles of polygons (G&M-13)         Resource Masters
          solving related problems (including applying scales on     o   Describes the proportional effect
          maps). Describes effects using models or explanations.         on linear dimensions of polygons    Calculators (classroom set)
                                                                         or circles when scaling up or
                                                                         down while preserving the angles    Connected Mathematics Series
                                                                         of polygons (G&M-24)
                                                                     o   Solves problems involving scaling   Geo Boards
                                                                         up or down and their impact on
                                                                         angle measure, linear
                                                                         dimensions, and areas of
                                                                         polygons and circles when the
                                                                         linear dimensions are multiplied
                                                                         by a constant factor (G&M-25)
                                                                     o   Proportional reasoning
                                                                         (N&O-44)




                                                                         6-7
                                                     Geometry and Measurement
GLE
          Grade Level Expectations                               Terms Defined (Definition Number)            Notes and Resources
Number
                                                                 o   Polygons (G&M-2)
M(G&M)-   Demonstrates conceptual understanding of               o   Triangle (G&M-3)                   Glencoe Mathematics Application
6-6       perimeter of polygons, the area of quadrilaterals or   o   Three-dimensional shapes           and Concepts course 1 2004
          triangles, and the volume of rectangular prisms by         (G&M-15)                           edition plus corresponding
          using models, formulas, or by solving problems.        o   Demonstrates conceptual            Resource Masters
                                                                     understanding of perimeter,
          Demonstrates conceptual understanding of the               area, volume, or surface area      Calculators (classroom set)
          relationships of circle measures (radius to diameter
                                                                     using models and manipulatives
          and diameter to circumference) by solving related
                                                                     (G&M-28)                           Connected Mathematics Series
          problems. Expresses all measures using appropriate
          units.                                                 o   Demonstrates conceptual
                                                                     understanding of perimeter,        Geo Boards
                                                                     area, volume, or surface area by
                                                                     solving problems (G&M-29)
                                                                 o   Demonstrates conceptual
                                                                     understanding of the
                                                                     relationships of circle measures
                                                                     by solving related problems
                                                                     (G&M-30)
                                                                 o   Measures and uses units of
                                                                     measure appropriately and
                                                                     consistently (G&M-31)
                                                                 o   Irrational number (N&O-10)
                                                                 o   Whole number bases and whole
                                                                     number exponents, and
                                                                     fractional bases with whole
                                                                     number exponents (N&O-24)
                                                                 o   Measures and uses units of
M(G&M)-   Measures and uses units of measures appropriately          measure appropriately and          Glencoe Mathematics Application
6-7       and consistently, and makes conversions within             consistently                       and Concepts course 1 2004
          systems when solving problems across the content       o   Makes conversions within and       edition plus corresponding
          strands.                                                   across systems                     Resource Masters
                                                                 o   Irrational number                  Calculators (classroom set)
          Benchmarks in Appendix B.                                                                     Connected Mathematics Series
                                                                                                        Geo Boards

M(G&M)-
6-8       None


                                                                     6-8
                                     Geometry and Measurement
GLE
          Grade Level Expectations           Terms Defined (Definition Number)   Notes and Resources
Number

M(G&M)-   None
6-9

M(G&M)-   None
6-10




                                                6-9
                                                            Functions and Algebra
GLE
          Grade Level Expectations                                       Terms Defined (Definition Number)             Notes and Resources
Number

M(F&A)–   Identifies and extends to specific cases a variety of          o   Patterns (F&A-1)                    Glencoe Mathematics Application
6–1       patterns (linear and nonlinear) represented in models,         o   Numeric patterns (F&A-3)            and Concepts course 1 2004
          tables, sequences, graphs, or in problem situations; or        o   Non-numeric patterns (F&A-4)        edition plus corresponding
          writes a rule in words or symbols for finding specific         o   Extend a pattern (F&A-5)            Resource Masters
          cases of a linear relationship; or writes a rule in words or   o   Sequence (F&A-6)
          symbols for finding specific cases of a nonlinear              o   Linear relationships (F&A-10)       Calculators (classroom set)
          relationship.
                                                                         o   Proportional linear relationships
                                                                             (y = kx)     (F&A-11)
          Identifies and extends to specific cases a variety of
          patterns and writes an expression or equation using            o   Non-proportional linear
          words or symbols to express the generalization of a                relationships (y = mx + b)
          linear relationship (e.g., twice the term number plus 1 or         (F&A-12)
          2n + 1).                                                       o   Non-linear relationships
                                                                             (F&A-18)
                                                                         o   Expresses generalization or rule
                                                                             using words or symbols (F&A-7)
                                                                         o   Concrete situations (F&A-20)
                                                                         o   Pattern Summary Table by grade
                                                                             level (F&A-9)

M(F&A)–   Demonstrates conceptual understanding of linear                o   Ratio (N&O-12)                      Glencoe Mathematics Application
6–2       relationships (y = kx; y = mx + b) as a constant rate          o   Proportional reasoning (N&O-44)     and Concepts course 1 2004
          of change by constructing or interpreting graphs of real       o   Linear relationships (F&A-10)       edition plus corresponding
          occurrences and describing the slope of linear                 o   Proportional linear relationships   Resource Masters
          relationships (faster, slower, greater, or smaller) in a           (y = kx) (F&A-11)
          variety of problem situations.                                 o   Non-proportional linear             Calculators (classroom set)
                                                                             relationships (y = mx + b)
          Demonstrates conceptual understanding of linear
                                                                             (F&A-12)
          relationships (y = kx; y = mx + b) as a constant rate
          of change and describes how change in the value of             o   Distinguishes between constant
          one variable relates to change in the value of a                   and varying rates (F&A-19)
          second variable in problem situations with constant            o   Slope (F&A-14)
          rates of change.                                               o   Describes the meaning of slope
                                                                             and intercept in concrete
                                                                             situations (F&A-15)
                                                                         o   Concrete situations (F&A-20)



                                                                             6 - 10
                                                         Functions and Algebra
GLE
          Grade Level Expectations                                   Terms Defined (Definition Number)             Notes and Resources
Number

M(F&A)–   Demonstrates conceptual understanding of                   o   Algebraic expression (F&A-25)       Glencoe Mathematics Application
6–3       algebraic expressions by using letters to represent        o   Evaluating algebraic expressions    and Concepts course 1 2004
          unknown quantities to write linear algebraic expressions       (F&A-26)                            edition plus corresponding
          involving two or more of the four operations; or by        o   Number sentences (F&A-33)           Resource Masters
          evaluating linear algebraic expressions (including those   o   Equation (F&A-32)
          with more than one variable); or by evaluating an          o   Algebraic equation notation         Calculators (classroom set)
          expression within an equation (e.g., determine the value
                                                                         (F&A-34)
          of y when x = 4 given y = 3x - 2).
                                                                     o   Examples of forms of equations
                                                                         (F&A-35)
                                                                     o   Linear relationships (F&A-10)
                                                                     o   Proportional linear relationships
                                                                         (y = kx) (F&A-11)
                                                                     o   Non-proportional linear
                                                                         relationships (y = mx + b)
                                                                         (F&A-12)


M(F&A)–   Demonstrates conceptual understanding of equality          o   Whole number (N&O-2)                Glencoe Mathematics Application
6–4       by showing equivalence between two expressions using       o   Equality (F&A-30)                   and Concepts course 1 2004
          models or different representations of the expressions,    o   Demonstrates equality               edition plus corresponding
          solving multi-step linear equations of the form                (F&A-31)                            Resource Masters
          ax ± b = c, where a, b, and c are whole numbers with       o   Linear relationships (F&A-10)
          a≠ 0.                                                      o   Proportional linear relationships   Calculators (classroom set)
                                                                         (y = kx) (F&A-11)
                                                                     o   Non-proportional linear
                                                                         relationships (y = mx =b)
                                                                         (F&A-12)
                                                                     o   Number sentences (F&A-33)
                                                                     o   Equation (F&A-32)
                                                                     o   Algebraic equation notation
                                                                         (F&A-34)
                                                                     o   Examples of forms of equations
                                                                         (F&A-35)




                                                                         6 - 11
                                                      Data, Statistics, and Probability
GLE
           Grade Level Expectations                                        Terms Defined (Definition Number)             Notes and Resources
Number

M(DSP) –   Interprets a given representation (circle graphs, line          o   Interprets a given representation   Glencoe Mathematics Application
6-1        graphs, or stem-and-leaf plots) to answer questions                 (DSP-21)                            and Concepts course 1 2004
           related to the data, to analyze the data to formulate or        o   Representation (DSP-1)              edition plus corresponding
           justify conclusions, to make predictions, or to solve           o   Circle graph (DSP-8)                Resource Masters
           problems.                                                       o   Line graph (DSP-12)
                                                                           o   Stem-and-leaf plot (DSP-9)          Calculators (classroom set)
           (IMPORTANT: Analyzes data consistent with concepts
           and skills in M(DSP)-6-2).
                                                                                                                   Connected Mathematics Series


M(DSP) –   Analyzes patterns, trends or distributions in data in           o   Pattern (F&A-1)                     Glencoe Mathematics Application
6-2        a variety of contexts by determining or using                   o   Mean (DSP-15)                       and Concepts course 1 2004
           measures of central tendency (mean, median, or mode)            o   Median (DSP-16)                     edition plus corresponding
           or dispersion (range) to analyze situations, or to solve        o   Mode (DSP-17)                       Resource Masters
           problems.                                                       o   Dispersion (DSP-19)
                                                                           o   Range (DSP-18)                      Calculators (classroom set)

                                                                                                                   Connected Mathematics Series

M(DSP) –   Organizes and displays data using tables, line                                                          Glencoe Mathematics Application
6-3        graphs, or stem-and-leaf plots to answer questions                                                      and Concepts course 1 2004
           related to the data, to analyze the data to formulate or                                                edition plus corresponding
           justify conclusions, to make predictions, or to solve                                                   Resource Masters
           problems.
                                                                                                                   Calculators (classroom set)
           (IMPORTANT: Analyzes data consistent with concepts
           and skills in M(DSP)–6–2).
                                                                                                                   Connected Mathematics Series


M(DSP) –   Uses counting techniques to solve problems in                   o   Solves problems using a variety     Glencoe Mathematics Application
6-4        context involving combinations or simple permutations               of counting strategies (DSP-25)     and Concepts course 1 2004
           using a variety of strategies (e.g., organized lists, tables,   o   Combination (DSP-26)                edition plus corresponding
           tree diagrams, models, Fundamental Counting Principle,          o   Permutation (DSP-27)                Resource Masters
           or others).                                                     o   Frequency table (DSP-4)
                                                                           o   Tree diagram (DSP-28)               Calculators (classroom set)
                                                                           o   Fundamental Counting Principle
                                                                               (DSP-29)                            Connected Mathematics Series
                                                                               6 - 12
                                                    Data, Statistics, and Probability
GLE
           Grade Level Expectations                                     Terms Defined (Definition Number)            Notes and Resources
Number

M(DSP) –   For a probability event in which the sample space            o   Sample space (DSP-30)              Glencoe Mathematics Application
6-5        may or may not contain equally likely outcomes,              o   Experimental probability           and Concepts course 1 2004
           determines the experimental or theoretical probability           (DSP-33)                           edition plus corresponding
           of an event in a problem-solving situation.                  o   Theoretical probability (DSP-32)   Resource Masters
                                                                        o   Event (DSP-31)
           For a probability event in which the sample space                                                   Calculators (classroom set)
           may or may not contain equally likely outcomes,
           predicts the theoretical probability of an event and tests
                                                                                                               Connected Mathematics Series
           the prediction through experiments and simulations; and
           designs fair games.



M(DSP) –   In response to a teacher or student generated                                                       Glencoe Mathematics Application
6-6        question or hypothesis decides the most effective                                                   and Concepts course 1 2004
           method (e.g., survey, observation, experimentation) to                                              edition plus corresponding
           collect the data (numerical or categorical) necessary to                                            Resource Masters
           answer the question.
                                                                                                               Calculators (classroom set)
           In response to a teacher or student generated
           question or hypothesis collects, organizes, and
                                                                                                               Connected Mathematics Series
           appropriately displays the data.

           In response to a teacher or student generated
           question or hypothesis analyzes the data to draw
           conclusions about the question or hypothesis being
           tested, and when appropriate makes predictions.

           In response to a teacher or student generated
           question or hypothesis asks new questions and
           makes connections to real world situations.

           (IMPORTANT: Analyzes data consistent with concepts
           and skills in M(DSP)–6–2.)




                                                                            6 - 13
                                                Grade Level 7 Expectations by Strand

                                                       Number and Operations
GLE
          Grade Level Expectations                                  Terms Defined (Definition Number)           Notes and Resources
Number

M(N&O)-   Demonstrates conceptual understanding of rational         o   Rational number (N&O-1)           Glencoe Applications and
7-1       numbers with respect to percents as a means of            o   Percent (N&O-8)                   Concepts Course 2 (2004)
          comparing the same or different parts of the whole when   o   Ratio (N&O-12)
          the wholes vary in magnitude (e. g., 8 girls in a         o   Equivalent numbers (N&O-14)       Glencoe Applications and
          classroom of 16 students compared to 8 girls in a         o   Area model to represent part to   Concepts Course 2 (2004)
          classroom of 20 students, or 20% of 400 compared to           whole relationship (N&O-17)       Resource Kit
          50% of 100) using models, explanations, or other
                                                                    o   Set model (N&O-18)
          representations*.
                                                                    o   Linear model (N&O-19)             Mathimagination Series
          Demonstrates conceptual understanding of rational         o   Whole number bases and whole      (Steve and Janis Marcy)
          numbers with respect to percents as a way of                  number exponents, and
          expressing multiples of a number (e. g., 200% of 50)          fractional bases with whole       Mathematics – A Way of Thinking
          using models, explanations, or other                          number exponents (N&O-24)         (Robert Baratta-Lorton)
          representations*.                                         o   Comparing (N&O-27)
                                                                    o   Number line (N&O-28)              Guiding Children’s Learning of
          Demonstrates conceptual understanding of square roots     o   Multiples (N&O-39)                Mathematics
          of perfect squares, rates, and proportional reasoning.    o   Proportional reasoning            (Kennedy and Tipps)
                                                                        (N&O-44)
                                                                    o   * Specifications for Area, Set,
                                                                        and Linear Models (Pg. NO-12)


M(N&O)-   Demonstrates understanding of the relative                o   Rational number (N&O-1)           Pre-Algebra with Pizzazz Series
7-2       magnitude of numbers by ordering, comparing, or           o   Integer (N&O-9)                   (Steve and Janis Marcy)
          identifying equivalent rational numbers across number     o   Equivalent numbers (N&O-14)
          formats, numbers with whole number bases and whole        o   Relative magnitude (N&O-20)       Glencoe Applications and
                                      3   3
          number exponents (e.g., 3 , 4 ), integers, absolute       o   Across number formats             Concepts Course 2 (2004)
          values, or numbers represented in scientific notation         (N&O-21)
          using number lines or equality and inequality symbols.
                                                                    o   Absolute value (N&O-23)           Glencoe Applications and
                                                                    o   Scientific notation (N&O-25)      Concepts Course 2 (2004)
                                                                    o   Ordering (N&O-26)                 Resource Kit
                                                                    o   Comparing (N&O-27)
                                                                    o   Describing or illustrating the
                                                                        meaning of a power (N&O-33)



                                                                        7-1
                                                          Number and Operations
GLE
          Grade Level Expectations                                    Terms Defined (Definition Number)           Notes and Resources
Number

M(N&O)-   Demonstrates conceptual understanding of
7-3       operations with integers and whole number exponents
          (where the base is a whole number) using models,
          diagrams, or explanations.


M(N&O)-   Accurately solves problems involving proportional           o   Percent (N&O-8)                 Glencoe Applications and
7-4       reasoning, percents involving discounts, tax or tips, and   o   Ratio (N&O-12)                  Concepts Course 2
          rates.                                                      o   Accurately solves problems
                                                                          (N&O-35)                        Glencoe Applications and
          Accurately solves problems involving addition or            o   Proportional reasoning          Concepts Course 2 (2004)
          subtraction of integers, raising numbers to whole               (N&O-44)                        Resource Kit
          number powers, and determining square roots of perfect
          square numbers and non- perfect square numbers.
                                                                                                          Pre-Algebra with Pizzazz Series
          (IMPORTANT: Applies the conventions of order of                                                 (Steve and Janis Marcy)
          operations, including parentheses, brackets, or
          exponents).




M(N&O)-
          None
7-5


M(N&O)-   Mentally calculates benchmark perfect squares and                                               All of this is referred to mentally!
                                        2   2    2    2    2    2
7-6       related square roots (e. g., 1 , 2 … 12 , 15 , 20 , 25 ,
              2      2
          100 , 1000 ).

          Mentally determines the part of a number using
          benchmark percents and related fractions (1%, 10%,
          25%, 33⅓ %, 50%, 66⅔%, 75%, and 100%) (e. g., 25%
          of 16; 33⅓% of 330).

          (IMPORTANT: Mental arithmetic should be imbedded
          instructionally throughout all strands .)


                                                                          7-2
                                                          Number and Operations
GLE
          Grade Level Expectations                                      Terms Defined (Definition Number)         Notes and Resources
Number

M(N&O)-   Makes estimates in a given situation (including tips,
7-7       discounts, and tax) by identifying when estimation is
          appropriate, selecting the appropriate method of
          estimation, determining the level of accuracy needed
          given the situation, analyzing the effect of the estimation
          method on the accuracy of results, and evaluating the
          reasonableness of solutions appropriate to grade level
          GLEs across content strands.

          (IMPORTANT: The intent of this GLE is to embed
          estimation throughout the instructional program, not to
          teach it as a separate unit.)


M(N&O)-   Applies properties of numbers (odd, even,                                                         Glencoe Applications and
7-8       remainders, divisibility, and prime factorization) to solve                                       Concepts Course 2 (2004)
          problems and to simplify computations.
                                                                                                            Glencoe Applications and
          Applies field properties (commutative, associative,                                               Concepts Course 2 (2004)
          identity, distributive, inverses) to solve problems and                                           Resource Kit
          to simplify computations.
                                                                                                            Pre-Algebra with Pizzazz
          Demonstrates conceptual understanding of field
          properties as they apply to subsets of the real numbers
          (e. g., the set of whole numbers does not have additive
          inverses, the set of integers does not have multiplicative
          inverses).




                                                                           7-3
                                                      Geometry and Measurement
GLE
          Grade Level Expectations                                     Terms Defined (Definition Number)            Notes and Resources
Number
                                                                                                              Glencoe Applications and
M(G&M)-   Uses properties of angle relationships resulting from        o   Attributes and properties          Concepts Course 2
7-1       two or three intersecting lines (adjacent angles, vertical       (G&M-1)
          angles, straight angles, or angle relationships formed by    o   Angle (G&M-10)                     Glencoe Applications and
          two non-parallel lines cut by a transversal), or two         o   Angle relationships formed by      Concepts Course 2 (2004)
          parallel lines cut by a transversal to solve problems.           two or more lines cut by a         Resource Kit
                                                                           transversal (G&M-11)
                                                                       o   Parallel lines (G&M-7)             Mathimagination Series

                                                                                                              Math – A Way of Thinking

                                                                                                              Moving On with Geoboards
                                                                                                              (Creative Publications)

M(G&M)-
7-2       Applies theorems or relationships (triangle inequality       o   Triangle (G&M-3)                   Glencoe Applications and
          or sum of the measures of interior angles of polygons)       o   Triangle inequality (G&M-12)       Concepts Course 2
          to solve problems.                                           o   Sum of the measures of interior
                                                                           angles of polygons (G&M-13)        Glencoe Applications and
                                                                       o   Angles (G&M-10)                    Concepts Course 2 (2004)
                                                                       o   Polygons (G&M-2)                   Resource Kit




M(G&M)-   None
7-3

M(G&M)-   Applies the concepts of congruency by solving                o   Congruent (G&M-16)                 Glencoe Applications and
7-4       problems on a coordinate plane involving reflections,        o   Reflection (G&M-17)                Concepts Course 2
          translations, or rotations.                                  o   Translation (G&M-18)
                                                                       o   Rotation (G&M-19)                  Glencoe Applications and
                                                                       o   Solving problems on a coordinate   Concepts Course 2 (2004)
                                                                           plane using reflections,           Resource Kit
                                                                           translations, or rotations
                                                                           (G&M-22)



                                                                           7-4
                                                     Geometry and Measurement
GLE
          Grade Level Expectations                                   Terms Defined (Definition Number)             Notes and Resources
Number

M(G&M)-   Applies concepts of similarity by solving problems         o   Similar figures (G&M-23)            Glencoe Applications and
7-5       involving scaling up or down and their impact on angle     o   Angles (G&M-10)                     Concepts Course 2 (2004)
          measures, linear dimensions and areas of polygons,         o   Polygons (G&M-2)
          and circles when the linear dimensions are multiplied by   o   Sum of the measures of interior     Mathimagination Series
          a constant factor. Describes effects using models or           angles of polygons (G&M-13)
          explanations.                                              o   Describes the proportional effect   Math – A Way of Thinking
                                                                         on linear dimensions of polygons
                                                                         or circles when scaling up or       Moving On with Geoboards
                                                                         down while preserving the angles    (Creative Publications)
                                                                         of polygons (G&M-24)
                                                                     o   Solves problems involving scaling   Geoboards
                                                                         up or down and their impact on
                                                                         angle measure, linear
                                                                         dimensions, and areas of
                                                                         polygons and circles when the
                                                                         linear dimensions are multiplied
                                                                         by a constant factor (G&M-25)
                                                                     o   Factor (N&O-38)
                                                                     o   Proportional reasoning
                                                                         (G&M-44)




                                                                         7-5
                                                     Geometry and Measurement
GLE
          Grade Level Expectations                                    Terms Defined (Definition Number)            Notes and Resources
Number

M(G&M)-   Demonstrates conceptual understanding of the area           o   Quadrilaterals (G&M-4)             Glencoe Applications and
7-6       of circles or the area or perimeter of composite figures    o   Triangle (G&M-3)                   Concepts Course 2 (2004)
          (quadrilaterals, triangles, or parts of circles), and the   o   Three-dimensional shapes
          surface area of rectangular prisms, or volume of                (G&M-15)                           Mathimagination Series
          rectangular prisms, triangular prisms, or cylinders using   o   Demonstrates conceptual
          models, formulas, or by solving related problems.               understanding of perimeter,        Math – A Way of Thinking
          Expresses all measures using appropriate units.
                                                                          area, volume, or surface area
                                                                          using models and manipulatives     Moving On with Geoboards
                                                                          (G&M-28)                           (Creative Publications)
                                                                      o   Demonstrates conceptual
                                                                          understanding of perimeter,        Geoboards
                                                                          area, volume, or surface area by
                                                                          solving problems (G&M-29)          Tessellations – The Geometry of
                                                                      o   Demonstrates conceptual            Patterns
                                                                          understanding of the                (Creative Publications)
                                                                          relationships of circle measures
                                                                          by solving related problems
                                                                          (G&M-30)
                                                                      o   Measures and uses units of
                                                                          measure appropriately and
                                                                          consistently (G&M-31)
                                                                      o   Irrational number (N&O-10)
                                                                      o   Whole number bases and whole
                                                                          number exponents, and
                                                                          fractional bases with whole
                                                                          number exponents (N&O-24)
M(G&M)-
7-7       None
M(G&M)-
          None
7-8
M(G&M)-
7-9       None
          Demonstrates conceptual understanding of spatial
M(G&M)-   reasoning and visualization by sketching three-
7-10      dimensional solids; and draws nets of rectangular and
          triangular prisms, cylinders, and pyramids and uses the
          nets as a technique for finding surface area.

                                                                          7-6
                                                          Functions and Algebra
GLE
          Grade Level Expectations                                   Terms Defined (Definition Number)             Notes and Resources
Number

M(F&A)–   Identifies and extends to specific cases a variety of      o   Patterns (F&A-1)                    Glencoe Applications and
7–1       patterns (linear and nonlinear) represented in models,     o   Numeric patterns (F&A-3)            Concepts Course 2
          tables, sequences, graphs, or in problem situations.       o   Non-numeric patterns (F&A-4)
                                                                     o   Extend a pattern (F&A-5)            Glencoe Applications and
          Identifies and extends to specific cases a variety of      o   Sequence (F&A-6)                    Concepts Course 2 (2004)
          patterns and generalizes a linear relationship using       o   Linear relationships (F&A-10)       Resource Kit
          words and symbols.
                                                                     o   Proportional linear relationships
                                                                         (y = kx) (F&A-11)
          Identifies and extends to specific cases a variety of
          patterns and generalizes a linear relationship to find a   o   Non-proportional linear             Pre-Algebra with Pizzazz
          specific case; or writes an expression or equation using       relationships (y = mx + b)
          words or symbols to express the generalization of a            (F&A-12)
          nonlinear relationship.                                    o   Non-linear relationships
                                                                         (F&A-18)
                                                                     o   Equation (F&A-32)
                                                                     o   Expresses generalization or rule
                                                                         using words or symbols
                                                                         (F&A-7)
                                                                     o   Generalizes a pattern to find a
                                                                         specific case (F&A-8)
                                                                     o   Concrete situations (F&A-20)
                                                                     o   Pattern Summary Table by grade
                                                                         level (F&A-9)




                                                                         7-7
                                                           Functions and Algebra
GLE
          Grade Level Expectations                                     Terms Defined (Definition Number)             Notes and Resources
Number

M(F&A)–   Demonstrates conceptual understanding of linear              o   Ratio (F&A-12)                      Glencoe Applications and
7–2       relationships (y = kx; y = mx + b) as a constant rate        o   Proportional reasoning (N&O-44)     Concepts Course 2
          of change by solving problems involving the                  o   Linear relationships (F&A-10)
          relationship between slope and rate of change, by            o   Proportional linear relationships   Glencoe Applications and
          describing the meaning of slope in concrete situations,          (y = kx)     (F&A-11)               Concepts Course 2 (2004)
          or informally determining the slope of a line from a table   o   Non-proportional linear             Resource Kit
          or graph.
                                                                           relationships (y = mx + b)
                                                                           (F&A-12)                            Pre-Algebra with Pizzazz
          Demonstrates conceptual understanding of linear
          relationships and distinguishes between constant             o   Slope (F&A-14)
          and varying rates of change in concrete situations           o   Intercept (F&A-17)
          represented in tables or graphs; or describes how            o   Non-linear relationships
          change in the value of one variable relates to                   (F&A-18)
          change in the value of a second variable in problem          o   Informally determines slope
          situations with constant rates of change.                        (F&A-16)
                                                                       o   Distinguishes between constant
                                                                           and varying rates     (F&A-19)
                                                                       o   Solves problems involving linear
                                                                           relationships (F&A-13)
                                                                       o   Concrete situations (F&A-20)


M(F&A)–   Demonstrates conceptual understanding of                     o   Whole number bases and whole        Glencoe Applications and
7–3       algebraic expressions by using letters to represent              number exponents, and               Concepts Course 2
          unknown quantities to write algebraic expressions                fractional bases with whole
          (including those with whole number exponents or more             number exponents (N&O-24)           Glencoe Applications and
          than one variable); or by evaluating algebraic               o   Algebraic expression (F&A-25)       Concepts Course 2 (2004)
          expressions (including those with whole number               o   Evaluating algebraic expressions    Resource Kit
          exponents or more than one variable); or by evaluating
                                                                           (F&A-26)
          an expression within an equation (e.g., determine the
                                             3                         o   Number sentences (F&A-33)           Pre-Algebra with Pizzazz
          value of y when x = 4 given y = 5x - 2).
                                                                       o   Equation (F&A-32)
                                                                       o   Examples of forms of equations
                                                                           (F&A-35)
                                                                       o   Algebraic equation notation
                                                                           (F&A-34)




                                                                           7-8
                                                           Functions and Algebra
GLE
          Grade Level Expectations                                      Terms Defined (Definition Number)             Notes and Resources
Number

M(F&A)–   Demonstrates conceptual understanding of equality             o   Equality (F&A-30)                   Glencoe Applications and
7–4       by showing equivalence between two expressions                o   Demonstrates equality               Concepts Course 2
          (expressions consistent with the parameters of the left-          (F&A-31)
          and right-hand sides of the equations being solved at         o   Linear relationships (F&A-10)       Glencoe Applications and
          this grade level) using models or different                   o   Proportional linear relationships   Concepts Course 2 (2004)
          representations of the expressions, solving multi-step            (y = kx) (F&A-11)                   Resource Kit
          linear equations of the form ax ± b = c with a ≠ 0,
                                                                        o   Non-proportional linear
          ax ± b = cx ± d with a, c≠ 0, and (x/a) ± b = c with a ≠ 0,
                                                                            relationships (y = mx + b)          Pre-Algebra with Pizzazz
          where a, b, c and d are whole numbers; or by translating
          a problem-solving situation into an equation consistent           (F&A-12)
          with the parameters of the type of equations being            o   Number sentences (F&A-33)
          solved for this grade level.                                  o   Equation (F&A-32)
                                                                        o   Examples of forms of equations
                                                                            (F&A-35)
                                                                        o   Algebraic equation notation
                                                                            (F&A-34)




                                                                            7-9
                                                    Data, Statistics, and Probability
GLE
           Grade Level Expectations                                   Terms Defined (Definition Number)             Notes and Resources
Number

M(DSP) –   Interprets a given representation (circle graphs,          o   Interprets a given representation   Glencoe Applications and
7-1        scatter plots that represent discrete linear                   (DSP-21)                            Concepts Course 2
           relationships, or histograms) to analyze the data to       o   Representation (DSP-1)
           formulate or justify conclusions, to make                  o   Circle graph (DSP-8)                Glencoe Applications and
           predictions, or to solve problems.                         o   Scatter plot (DSP-13)               Concepts Course 2 (2004)
                                                                      o   Histogram (DSP-7)                   Resource Kit
           (IMPORTANT: Analyzes data consistent with concepts
                                                                      o   Linear relationships (F&A-10)
           and skills in M(DSP)-7-2.)
                                                                      o   Proportional linear relationship
                                                                          (F&A-11)
                                                                      o   Non-proportional linear
                                                                          relationship (F&A-12)

M(DSP) –   Analyzes patterns, trends, or distributions in data in     o   Pattern (DSP-1)                     Glencoe Applications and
7-2        a variety of contexts by solving problems using            o   Mean (DSP-15)                       Concepts Course 2
           measures of central tendency (mean, median, or mode),      o   Median (DSP-16)
           dispersion (range or variation), or outliers to analyze    o   Mode (DSP-17)                       Glencoe Applications and
           situations to determine their effect on mean, median, or   o   Dispersion (DSP-19)                 Concepts Course 2 (2004)
           mode;                                                      o   Range (DSP-18)                      Resource Kit
                                                                      o   Outlier (DSP-20)
           Analyzes patterns, trends, or distributions in data in
                                                                      o   Analyzes the impact of outliers
           a variety of contexts by evaluating the sample from
           which the statistics were developed (bias).                    on the mean, median and mode
                                                                          (DSP-22)
                                                                      o   Evaluates samples from which
                                                                          the statistics were developed
                                                                          (bias) (DSP-24)


M(DSP) –   Identifies or describes representations or elements        o   Representation (DSP-1)              Glencoe Applications and
7-3        of representations that best display a given set of        o   Identifies or describes             Concepts Course 2
           data or situation, and organizes and displays data             representations or elements of
           using tables, line graphs, scatter plots, and circle           representations that best display   Glencoe Applications and
           graphs to answer questions related to the data, to             a given set of data or situation    Concepts Course 2 (2004)
           analyze the data to formulate or justify conclusions, to       (DSP-23)                            Resource Kit
           make predictions, or to solve problems.

           (IMPORTANT: Analyzes data consistent with concepts
           and skills in M( DSP)– 7– 2 .)

                                                                          7 - 10
                                                    Data, Statistics, and Probability
GLE
           Grade Level Expectations                                     Terms Defined (Definition Number)            Notes and Resources
Number

M(DSP) –   Uses counting techniques to solve problems in                                                       Glencoe Applications and
7-4        context involving combinations or permutations (e.g.,                                               Concepts Course 2
           How many different ways can eight students place first,
           second, and third in a race?) using a variety of                                                    Glencoe Applications and
           strategies (e.g., organized lists, tables, tree diagrams,                                           Concepts Course 2 (2004)
           models, Fundamental Counting Principle, or others).                                                 Resource Kit

                                                                                                               What Are My Chances
                                                                                                                Book A, Book B
                                                                                                               (Creative Publications)



M(DSP) –   For a probability event in which the sample space            o   Sample space (DSP-30)              Glencoe Applications and
7-5        may or may not contain equally likely outcomes,              o   Experimental probability           Concepts Course 2
           determines the experimental or theoretical probability           (DSP-33)
           of an event in a problem- solving situation.                 o   Theoretical probability (DSP-32)   Glencoe Applications and
                                                                        o   Event (DSP-31)                     Concepts Course 2 (2004)
           For a probability event in which the sample space                                                   Resource Kit
           may or may not contain equally likely outcomes,
           predicts the theoretical probability of an event and tests
           the prediction through experiments and simulations

           For a probability event in which the sample space
           may or may not contain equally likely outcomes
           compares and contrasts theoretical and experimental
           probabilities.




                                                                            7 - 11
                                                     Data, Statistics, and Probability
GLE
           Grade Level Expectations                                     Terms Defined (Definition Number)         Notes and Resources
Number

M(DSP) –   In response to a teacher or student generated                                                    Glencoe Applications and
7-6        question or hypothesis decides the most effective                                                Concepts Course 2
           method (e. g., survey, observation, experimentation) to
           collect the data (numerical or categorical) necessary to                                         Glencoe Applications and
           answer the question.                                                                             Concepts Course 2 (2004)
                                                                                                            Resource Kit
           In response to a teacher or student generated
           question or hypothesis collects, organizes, and
           appropriately displays the data.

           In response to a teacher or student generated
           question or hypothesis analyzes the data to draw
           conclusions about the question or hypothesis being
           tested while considering the limitations that could affect
           interpretations.

           In response to a teacher or student generated
           question or hypothesis, makes predictions when
           appropriate.

           In response to a teacher or student generated
           question or hypothesis asks new questions and
           makes connections to real world situations.

           (IMPORTANT: Analyzes data consistent with concepts
           and skills in M( DSP)– 7– 2. )




                                                                          7 - 12
                                                Grade Level 8 Expectations by Strand

                                                        Number and Operations
GLE
          Grade Level Expectations                                 Terms Defined (Definition Number)           Notes and Resources
Number

M(N&O)-   Demonstrates conceptual understanding of rational        o   Rational number (N&O-1)           Glencoe, Pre-Algebra (2003)
8-1       numbers with respect to percents as a way of             o   Percent (N&O-8)                   Textbook
          describing change (percent increase and decrease)        o   Ratio (N&O-12)
          using explanations, models, or other                     o   Area model to represent part to   Glencoe, Pre-Algebra (2003)
          representations*.                                            whole relationship (N&O-17)       Resource Kit
                                                                   o   Set model (N&O-18)
                                                                   o   Linear model (N&O-19)             Glencoe, Applications and
                                                                   o   Proportional reasoning            Connections (1995)
                                                                       (N&O-44)                          Resource Kit
                                                                   o   * Specifications for Area, Set,
                                                                       and Linear Models (Pg. NO-12)     Algebra In the Real World –
                                                                                                         Futures Channel

M(N&O)-   Demonstrates understanding of the relative               o   Rational number (N&O-1)           Glencoe, Algebra I (2003)
8-2       magnitude of numbers by ordering or comparing            o   Integer (N&O-9)
          rational numbers, common irrational numbers (e.g.        o   Irrational number (N&O-10)        Creative Publications, Middle
          , , ), numbers with whole number or fractional bases     o   Real numbers (N&O-11)             School Math with Pizzazz (1989)
          and whole number exponents, square roots, absolute       o   Equivalent numbers (N&O-14)
          values, integers, or numbers represented in scientific   o   Relative magnitude (N&O-20)
          notation using number lines or equality and inequality   o   Across number formats
          symbols.                                                     (N&O-21)
                                                                   o   Absolute value (N&O-23)
                                                                   o   Whole number bases and whole
                                                                       number exponents, and
                                                                       fractional bases with whole
                                                                       number exponents (N&O-24)
                                                                   o   Scientific notation (N&O-25)
                                                                   o   Ordering (N&O-26)
                                                                   o   Comparing (N&O-27)
                                                                   o   Number line (N&O-28)
                                                                   o   Describing or illustrating the
                                                                       meaning of a power (N&O-33)
M(N&O)-
8-3       None

                                                                       8-1
                                                        Number and Operations
GLE
          Grade Level Expectations                                   Terms Defined (Definition Number)           Notes and Resources
Number

M(N&O)-   Accurately solves problems involving proportional          o   Percent (N&O-8)                 Glencoe, Pre-Algebra (2003)
8-4       reasoning (percent increase or decrease, interest rates,   o   Integer (N&O-9)                 Textbook
          markups, or rates).                                        o   Ratio (N&O-12)
                                                                     o   Whole number bases and whole    Glencoe, Pre-Algebra (2003)
          Accurately solves problems involving                           number exponents, and           Resource Kit
          multiplication or division of integers.                        fractional bases with whole
                                                                         number exponents (N&O-24)       Glencoe, Applications and
          Accurately solves problems involving squares,
                                                                     o   Accurately solves problems      Connections (1995)
          cubes, and taking square or cube roots.
                                                                         (N&O-35)                        Resource Kit
          (IMPORTANT: Applies the conventions of order of            o   Proportional reasoning
          operations.)                                                   (N&O-44)                        Algebra In the Real World –
                                                                                                         Futures Channel

                                                                                                         Glencoe, Algebra I (2003)


                                                                                                         Creative Publications, Middle
M(N&O)-
          None                                                                                           School Math with Pizzazz (1989)
8-5



M(N&O)-   Mentally calculates benchmark perfect squares and                                              All of this is referred to mentally!
                               2   2    2    2    2    2     2
8-6       square roots (e.g., 1 , 2 … 12 , 15 , 20 , 25 , 100 ,
              2
          1000 ).

          Mentally determines the part of a number using
          benchmark percents and related fractions (1%, 10%,
          25%,33⅓ %, 50%,66 ⅔%, 75%, and 100%) (e.g., 25%
          of 16; 33⅓ % of 330).

          (IMPORTANT: Mental arithmetic should be imbedded
          instructionally throughout all strands.)




                                                                         8-2
                                                            Number and Operations
GLE
          Grade Level Expectations                                       Terms Defined (Definition Number)         Notes and Resources
Number

M(N&O)-   Makes estimates in a given situation (including tips,                                              Glencoe, Pre-Algebra (2003)
8-7       discounts, tax, and the value of a non-perfect square                                              Textbook
          root as between two whole numbers) by identifying
          when estimation is appropriate, selecting the                                                      Glencoe, Pre-Algebra (2003)
          appropriate method of estimation; determining the level                                            Resource Kit
          of accuracy needed given the situation; analyzing the
          effect of the estimation method on the accuracy of
                                                                                                             Glencoe, Applications and
          results; and evaluating the reasonableness of solutions
                                                                                                             Connections (1995)
          appropriate to grade level GLEs across content strands.
                                                                                                             Resource Kit
          (IMPORTANT: The intent of this GLE is to embed
          estimation throughout the instructional program, not to                                            Algebra In the Real World –
          teach it as a separate unit.)                                                                      Futures Channel

                                                                                                             Glencoe, Algebra I (2003)

                                                                                                             Creative Publications, Middle
                                                                                                             School Math with Pizzazz (1989)


M(N&O)-   Applies properties of numbers (odd, even,
8-8       remainders, divisibility, and prime factorization) to solve                                        Glencoe, Pre-Algebra (2003)
          problems and to simplify computations.                                                             Textbook
          .
          Applies field properties (commutative, associative,                                                Glencoe, Pre-Algebra (2003)
          identity [including the multiplicative property of one, e.g.                                       Resource Kit
            0   3     0+3   3      0
          2 x 2 = 2 = 2 , so 2 = 1], distributive, inverses) to
          solve problems and to simplify computations.
                                                                                                             Glencoe, Applications and
          Demonstrates conceptual understanding of                                                           Connections (1995)
          field properties as they apply to subsets of real                                                  Resource Kit
          numbers when addition and multiplication are not
          defined in the traditional ways (e.g., If a ∆ b = a + b - 1,                                       Glencoe, Algebra I (2003)
          is ∆ a commutative operation?).




                                                                            8-3
                                                        Geometry and Measurement
GLE
          Grade Level Expectations                                      Terms Defined (Definition Number)             Notes and Resources
Number

M(G&M)-   None
8-1
                                                                                                                Glencoe, Applications and
M(G&M)-   Applies the Pythagorean Theorem to find a missing             o   Pythagorean Theorem
                                                                                                                Connections (1995)
8-2       side of a right triangle, or in problem solving situations.       (G&M-14)
                                                                                                                Resource Kit
                                                                        o   Triangle (G&M-3)

M(G&M)-   None
8-3

M(G&M)-   None
8-4

M(G&M)-   Applies concepts of similarity to determine the impact        o   Three-dimensional shapes            Glencoe, Applications and
8-5       of scaling on the volume or surface area of three-                (G&M-15)                            Connections (1995)
          dimensional figures when linear dimensions are                o   Similar figures (G&M-23)            Resource Kit
          multiplied by a constant factor;                              o   Triangle (G&M-3)
                                                                        o   Describes the proportional effect   Native American Geometry
          Applies concepts of similarity to determine the length            on linear dimensions of polygons    Replacement Unit -
          of sides of similar triangles
                                                                            or circles when scaling up or       http://www.earthmeasure.com
                                                                            down while preserving the angles
          Applies concepts of similarity to solve problems
          involving growth and rate.                                        of polygons    (G&M-24)             Compasses, Protractors,
                                                                        o   Solves problems involving scaling   Straightedges
                                                                            up or down and their impact on
                                                                            angle measure, linear
                                                                            dimensions, and areas of            Glencoe, Algebra I (2003)
                                                                            polygons and circles when the
                                                                            linear dimensions are multiplied
                                                                            by a constant factor (G&M-25)
                                                                        o   Ratio (N&O-12)
                                                                        o   Proportional reasoning (N&O-44)




                                                                            8-4
                                                     Geometry and Measurement
GLE
          Grade Level Expectations                                   Terms Defined (Definition Number)            Notes and Resources
Number

M(G&M)-   Demonstrates conceptual understanding of surface           o   Demonstrates conceptual            Glencoe, Applications and
8-6       area or volume by solving problems involving                   understanding of perimeter,        Connections (1995)
          surface area and volume of rectangular prisms,                 area, volume, or surface area      Resource Kit
          triangular prisms, cylinders, or pyramids. Expresses all       using models and manipulatives
          measures using appropriate units.                              (G&M-28)                           Centimeter Cubes
                                                                     o   Demonstrates conceptual
                                                                         understanding of perimeter,
                                                                         area, volume, or surface area by
                                                                         solving problems (G&M-29)          Glencoe, Algebra I (2003)
                                                                     o   Three-dimensional shapes
                                                                         (G&M-15)
                                                                     o   Measures and uses units of
                                                                         measure appropriately and
                                                                         consistently    (G&M-31)
                                                                     o   Irrational number     (N&O-10)
                                                                     o   Whole number bases and whole
                                                                         number exponents, and
                                                                         fractional bases with whole
                                                                         number exponents       (N&O-24)



M(G&M)-   None
8-7


M(G&M)-
          None
8-8


M(G&M)-   None
8-9


M(G&M)-   None
8-10


                                                                         8-5
                                                         Functions and Algebra
GLE
          Grade Level Expectations                                   Terms Defined (Definition Number)             Notes and Resources
Number
                                                                     o   Patterns (F&A-1)
M(F&A)–   Identifies and extends to specific cases a variety of      o   Numeric patterns (F&A-3)            Glencoe, Pre-Algebra (2003)
8–1       patterns (linear and nonlinear) represented in models,     o   Non-numeric patterns (F&A-4)        Textbook
          tables, sequences, graphs, or in problem situations.       o   Extend a pattern (F&A-5)
                                                                     o   Sequence (F&A-6)                    Glencoe, Pre-Algebra (2003)
          Identifies and extends to specific cases a variety of      o   Expresses generalization or rule    Resource Kit
          patterns and generalizes a linear relationship (non-           using words or symbols (F&A-7)
          recursive explicit equation)
                                                                     o   Pattern Summary Table by grade      Glencoe, Applications and
                                                                         level (F&A-9)                       Connections (1995)
          Identifies and extends to specific cases a variety of
          patterns and generalizes a linear relationship to find a   o   Linear relationships (F&A-10)       Resource Kit
          specific case.                                             o   Proportional linear relationships
                                                                         (y = kx)     (F&A-11)               Algebra In the Real World –
          Identifies and extends to specific cases a variety of      o   Non-proportional linear             Futures Channel
          patterns and generalizes a nonlinear relationship              relationships (y = mx + b)
          using words or symbols, or generalizes a common                (F&A-12)
          nonlinear relationship to find a specific case.            o   Non-linear relationships (F&A-18)   Glencoe, Algebra I (2003)
                                                                     o   Concrete situations (F&A-20)
                                                                     o   Generalizes a pattern to find a
                                                                         specific case (F&A-8)




                                                                         8-6
                                                         Functions and Algebra
GLE
          Grade Level Expectations                                  Terms Defined (Definition Number)             Notes and Resources
Number

M(F&A)–   Demonstrates conceptual understanding of linear           o   Ratio (N&O-12)                      Glencoe, Pre-Algebra (2003)
8–2       relationships (y = kx; y = mx + b) as a constant rate     o   Proportional reasoning (N&O-44)     Textbook
          of change by solving problems involving the               o   Linear relationships (F&A-10)
          relationship between slope and rate of change.            o   Proportional linear relationships   Glencoe, Pre-Algebra (2003)
          Demonstrates conceptual understanding of linear               (y = kx) (F&A-11)                   Resource Kit
          relationships (y = kx; y = mx + b) as a constant rate     o   Non-proportional linear
          of change by informally and formally determining              relationships (y = mx + b)          Glencoe, Applications and
          slopes and intercepts represented in graphs, tables, or       (F&A-12)                            Connections (1995)
          problem situations.                                       o   Non-linear relationships (F&A-18)   Resource Kit
          Demonstrates conceptual understanding of linear           o   Intercept (F&A-17)
          relationships (y = kx; y = mx + b) as a constant rate     o   Slope (F&A-14)                      Algebra In the Real World –
          of change by describing the meaning of slope and          o   Informally determines slope         Futures Channel
          intercept in context                                          (F&A-16)
                                                                    o   Solves problems involving linear    Glencoe, Algebra I (2003)
          Distinguishes between linear relationships
                                                                        relationships (F&A-13)
          (constant rates of change) and nonlinear
                                                                    o   Describes the meaning of slope
          relationships (varying rates of change) represented
                                                                        and intercept in concrete
          in tables, graphs, equations, or problem situations.
                                                                        situations (F&A-15)
          Describes how change in the value of one variable         o   Distinguishes between constant
          relates to change in the value of a second variable in        and varying rates (F&A-19)
          problem situations with constant and varying rates of
          change.




                                                                        8-7
                                                         Functions and Algebra
GLE
          Grade Level Expectations                                   Terms Defined (Definition Number)             Notes and Resources
Number
                                                                     o   Rational number (N&0-1)
M(F&A)–   Demonstrates conceptual understanding of                   o   Whole number bases and whole        Glencoe, Pre-Algebra (2003)
8–3       algebraic expressions by evaluating and simplifying            number exponents, and               Textbook
          algebraic expressions (including those with square             fractional bases with whole
          roots, whole number exponents, or rational numbers); or        number exponents (N&O-24)           Glencoe, Pre-Algebra (2003)
          demonstrates conceptual understanding of algebraic         o   Algebraic expression (F&A-25)       Resource Kit
          expressions by evaluating an expression within an          o   Evaluating algebraic expressions
          equation (e.g., determine the value of y when x = 4            (F&A-26)                            Glencoe, Applications and
          given y  7 x  2 x ).                                     o   Simplifying algebraic equations     Connections (1995)
                                                                         (F&A-27)                            Resource Kit
                                                                     o   Number sentences (F&A-33)
                                                                     o   Equation (F&A-32)                   Algebra In the Real World –
                                                                     o   Examples of forms of equations      Futures Channel
                                                                         (F&A-35)
                                                                     o   Algebraic equation notation
                                                                         (F&A-34)

M(F&A)–   Demonstrates conceptual understanding of equality          o   Equality (F&A-30)                   Glencoe, Pre-Algebra (2003)
8–4       by showing equivalence between two expressions             o   Demonstrates equality (F&A-31)      Textbook
          (expressions consistent with the parameters of the left-   o   Linear relationships (F&A-10)
          and right-hand sides of the equations being solved at      o   Proportional linear relationships   Glencoe, Pre-Algebra (2003)
          this grade level) using models or different                    (y = kx)     (F&A-11)               Resource Kit
          representations of the expressions, solving formulas for   o   Non-proportional linear
          a variable requiring one transformation (e.g., d = rt;
                                                                         relationships (y = mx =b)           Glencoe, Applications and
          d/r = t).
                                                                         (F&A-12)                            Connections (1995)
          Demonstrates conceptual understanding of equality          o   Number sentences (F&A-33)           Resource Kit
          by solving multi-step linear equations with integer        o   Formula (F&A-28)
          coefficients.                                              o   Write equivalent forms of           Algebra In the Real World –
                                                                         formulas (F&A-29)                   Futures Channel
          Demonstrates conceptual understanding of equality          o   Equation (F&A-32)
          by showing that two expressions are or are not             o   Examples of forms of equations      Glencoe, Algebra I (2003)
          equivalent by applying commutative, associative, or            (F&A-35)
          distributive properties, order of operations, or           o   Simplifying algebraic equations
          substitution.                                                  (F&A-27)
                                                                     o   Algebraic equation notation
          Demonstrates conceptual understanding of equality              (F&A-34)
          by informally solving problems involving systems of
          linear equations in a context.

                                                                         8-8
                                                     Data, Statistics, and Probability
GLE
           Grade Level Expectations                                      Terms Defined (Definition Number)             Notes and Resources
Number

M(DSP) –   Interprets a given representation (line graphs, scatter       o   Interprets a given representation   Glencoe, Pre-Algebra (2003)
8-1        plots, histograms, or box-and-whisker plots) to analyze           (DSP-21)                            Textbook
           the data to formulate or justify conclusions, to make         o   Representation (DSP-1)
           predictions, or to solve problems.                            o   Histogram (DSP-7)                   Glencoe, Pre-Algebra (2003)
                                                                         o   Scatter plot (DSP-13)               Resource Kit
           (IMPORTANT: Analyzes data consistent with concepts            o   Box-and-whisker plot (DSP-21)
           and skills in M(DSP)-8-2.)
                                                                                                                 Glencoe, Applications and
                                                                                                                 Connections (1995)
                                                                                                                 Resource Kit

M(DSP) –   Analyzes patterns, trends, or distributions in data in        o   Pattern (DSP-1)                     Glencoe, Pre-Algebra (2003)
8-2        a variety of contexts by determining or using                 o   Mean     (DSP-15)                   Textbook
           measures of central tendency (mean, median, or mode),         o   Median (DSP-16)
           dispersion (range or variation), outliers, quartile values,   o   Mode     (DSP-17)                   Glencoe, Pre-Algebra (2003)
           or estimated line of best fit to analyze situations, or to    o   Dispersion (DSP-19)                 Resource Kit
           solve problems.                                               o   Range (DSP-19)
                                                                         o   Outlier (DSP-20)                    Glencoe, Applications and
           Analyzes patterns, trends, or distributions in data in
                                                                         o   Quartiles (DSP-11)                  Connections (1995)
           a variety of contexts by evaluating the sample from
           which the statistics were developed (bias, random, or         o   Estimated line of best fit          Resource Kit
           non-random).                                                      (DSP-14)
                                                                         o   Evaluates samples from which        Glencoe, Algebra I (2003)
                                                                             the statistics were developed
                                                                             (bias) (DSP-24)
                                                                         o   Analyzes the impact of outliers
                                                                             on the mean, median and mode
                                                                             (DSP-22)
                                                                                                                 Glencoe, Pre-Algebra (2003)
M(DSP) –   Organizes and displays data using scatter plots to            o   Scatter plot    (DSP-13)            Textbook
8-3        answer questions related to the data, to analyze the          o   Representation (DSP-1)
           data to formulate or justify conclusions, to make             o   Identifies or describes             Glencoe, Pre-Algebra (2003)
           predictions, or to solve problems; or identifies                  representations or elements of      Resource Kit
           representations or elements of representations that best          representations that best display
           display a given set of data or situation, consistent with         a given set of data or situation    Glencoe, Applications and
           the representations required in M(DSP)-8-1.
                                                                             (DSP-23)                            Connections (1995)
                                                                                                                 Resource Kit
           (IMPORTANT: Analyzes data consistent with concepts
           and skills in M(DSP)-8-2.)                                                                            Glencoe, Algebra I (2003)
                                                                             8-9
                                                     Data, Statistics, and Probability
GLE
           Grade Level Expectations                                     Terms Defined (Definition Number)           Notes and Resources
Number

M(DSP) –   Uses counting techniques to solve problems in                o   Solves problems using a variety   Glencoe, Pre-Algebra (2003)
8-4        context involving combinations or permutations using a           of counting strategies (DSP-25)   Textbook
           variety of strategies (e.g., organized lists, tables, tree   o   Permutation (DSP-27)
           diagrams, models, Fundamental Counting Principle, or         o   Frequency table (DSP-4)           Glencoe, Pre-Algebra (2003)
           others).                                                     o   Tree diagram (DSP-28)             Resource Kit
                                                                        o   Fundamental Counting Principle
                                                                            (DSP-29)                          Glencoe, Applications and
                                                                                                              Connections (1995)
                                                                                                              Resource Kit

                                                                                                              Glencoe, Algebra I (2003)




M(DSP) –   For a probability event in which the sample space                                                  Glencoe, Pre-Algebra (2003)
8-5        may or may not contain equally likely outcomes,                                                    Textbook
           determines the experimental or theoretical probability
           of an event in a problem-solving situation.                                                        Glencoe, Pre-Algebra (2003)
                                                                                                              Resource Kit
           For a probability event in which the sample space
           may or may not contain equally likely outcomes,
                                                                                                              Glencoe, Applications and
           predicts the theoretical probability of an event and tests
                                                                                                              Connections (1995)
           the prediction through experiments and simulations.
                                                                                                              Resource Kit
           For a probability event in which the sample space
           may or may not contain equally likely outcomes,                                                    Glencoe, Algebra I (2003)
           compares and contrasts theoretical and experimental
           probabilities.




                                                                            8 - 10
                                                     Data, Statistics, and Probability
GLE
           Grade Level Expectations                                     Terms Defined (Definition Number)         Notes and Resources
Number

M(DSP) –   In response to a teacher or student generated                                                    Glencoe, Pre-Algebra (2003)
8-6        question or hypothesis decides the most effective                                                Textbook
           method (e. g., survey, observation, experimentation) to
           collect the data (numerical or categorical) necessary to                                         Glencoe, Pre-Algebra (2003)
           answer the question.                                                                             Resource Kit
           In response to a teacher or student generated
                                                                                                            Glencoe, Applications and
           question or hypothesis collects, organizes, and
                                                                                                            Connections (1995)
           appropriately displays the data.
                                                                                                            Resource Kit
           In response to a teacher or student generated
           question or hypothesis analyzes the data to draw                                                 Glencoe, Algebra I (2003)
           conclusions about the question or hypothesis being
           tested while considering the limitations that could affect
           interpretations.

           In response to a teacher or student generated
           question or hypothesis makes predictions when
           appropriate.

           In response to a teacher or student generated
           question or hypothesis asks new questions and
           makes connections to real world situations.

           (IMPORTANT: Analyzes data consistent with concepts
           and skills in M(DSP)–8–2.)




                                                                          8 - 11

				
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