# Math Computation Skills Strategies Level 8

Document Sample

```					                                                                                                        BY TEACHERS FOR TEACHERS                                                                                                      1st Quarter
MATH CURRICULUM GUIDE

Standard 1: Students utilize language, symbolism, and technology to develop number sense and to communicate those mathematical ideas.

BENCHMARK 1.1: Demonstrate meanings for whole numbers and commonly-used fractions and decimals (for example, 1/3, 3/4, 0.5, 0.75), and represent equivalent forms of the same number through the same number through the use of physical models,
drawings, calculators, and computers.

Enduring Understanding                                                                         Assessment            Key        Suggested Instructional                             Differentiation-             Quarter
State Frameworks                                                 Essential Questions             Essential Skills                                                                               Resources
Conceptual Vocabulary                                                                           Methods            Strategy            Practice                                  Adaptations/Extensions          Taught

1.1a Identify whether a                                                                          NUMBER AND                  "Euler's Dilemma"      McREL      McREL Nonlinguistic            Math Text         Visual demonstrations                 1
What is number sense, and how
given number is odd or                                                                           NUMBER                      Exemplar                SIOP      representations                Math Exemplars    Utilization of visual or multi-
is it used in problem solving?
even.                                                                                            RELATIONSHIPS               Classroom                         * patterning                   Mountain Math     sensory materials
How many different ways can
Mathematics is dependent on                                        Recognize odd/even          evidence                          Identifying similarities and   Success Maker     Small group
you write this number ____?
place value.                                                       numbers                                                       differences                                      Time for repeated review/drill
Why do numbers have
A sense of number is necessary                                                                 Terra Nova                        *compare/contrast
designated places?
to communicate the reasoning                                                                   Quarterly                         SIOP
What mathematics vocabulary do
used in problem solving.                                                                       Assessment                        Mnemonics
you need to communicate
mathematical ideas?

1.1c Using concrete                                                                              NUMBER AND                  "Getting Ready"        McREL      McREL Nonlinguistic            Math Text         Visual demonstrations                 1
materials or pictures identify                                  What is number sense, and how    NUMBER                      (Vol II) Exemplar       SIOP      representations                Math Exemplars    Utilization of visual or multi-
different combinations of                                       is it used in problem solving?                               Quarterly                         SIOP                           Mountain Math     sensory materials
RELATIONSHIPS
coins up to \$0.99                                               How many different ways can      Money-combinations of       Assessment                        * concrete models              Success Maker     Small group
Mathematics is dependent on
you write this number ____?      coins up to \$1.00           Terra Nova                        *personal connections-                           Time for repeated review/drill
place value.
Why do numbers have
A sense of number is necessary
designated places?
to communicate the reasoning
What mathematics vocabulary do
used in problem solving.
you need to communicate
mathematical ideas?

BENCHMARK 1.2: Read and write whole numbers and know place-value concepts and numeration through their relationships to counting, ordering, and grouping.

1.2a Read, write and order                                   What is number sense, and how       NUMBER AND                  "Book Club" (Vol II)   McREL      McREL Nonlinguistic            Math Text         Visual demonstrations                 1
numerals from zero to 9,999                                                                      NUMBER                      Exemplar                SIOP      representations                Math Exemplars    Utilization of visual or multi-
is it used in problem solving?
RELATIONSHIPS               Classroom                         * patterning                   Mountain Math     sensory materials
How many different ways can
Mathematics is dependent on                                        Reads, writes, and orders   evidence                          *ordering                      Success Maker     Small group
you write this number ____?
place value.                                                       numbers to 10,000           Quarterly                                                                          Time for repeated review/drill
Why do numbers have
A sense of number is necessary                                                                 Assessment
designated places?
to communicate the reasoning                                                                   Terra Nova
What mathematics vocabulary do
used in problem solving.
you need to communicate
mathematical ideas?

1.2c Identify place value                                    What is number sense, and how       NUMBER AND                  "Planely a Problem"    McREL      McREL Nonlinguistic            Math Text         Visual demonstrations                 1
through ten-thousands (i.e.                                  is it used in problem solving?      NUMBER                      (Vol II) Exemplar       SIOP      representations                Math Exemplars    Utilization of visual or multi-
86,243, "6" is in the                                        How many different ways can         RELATIONSHIPS               Quarterly                         * patterning                   Mountain Math     sensory materials
thousands place).             Mathematics is dependent on                                        Place value- identify to    Assessment                        *ordering                      Success Maker     Small group
you write this number ____?
place value.                                                       10,000                                                                                                         Time for repeated review/drill
Why do numbers have
A sense of number is necessary                                                                 Terra Nova
designated places?
to communicate the reasoning
What mathematics vocabulary do
used in problem solving.
you need to communicate
mathematical ideas?

Revised 04-26-2006/jkw                                                                                                                                                                                                                    1
BY TEACHERS FOR TEACHERS                                                                                                       1st Quarter
MATH CURRICULUM GUIDE

Standard 1: Students utilize language, symbolism, and technology to develop number sense and to communicate those mathematical ideas.

BENCHMARK 1.1: Demonstrate meanings for whole numbers and commonly-used fractions and decimals (for example, 1/3, 3/4, 0.5, 0.75), and represent equivalent forms of the same number through the same number through the use of physical models,
drawings, calculators, and computers.

Enduring Understanding                                                                     Assessment            Key        Suggested Instructional                               Differentiation-             Quarter
State Frameworks                                                Essential Questions             Essential Skills                                                                               Resources
Conceptual Vocabulary                                                                       Methods            Strategy            Practice                                    Adaptations/Extensions          Taught

1.2e Compare whole                                                                           NUMBER AND                   "Book Club" (Vol II)   McREL      McREL Identifying similarities   Math Text         Visual demonstrations                 1
numbers as greater than,                                      What is number sense, and how                               Exemplar                                                           Math Exemplars    Utilization of visual or multi-
NUMBER                                               SIOP      and differences
less than, or equal to one                                    is it used in problem solving?                              Quarterly                                                          Mountain Math     sensory materials
RELATIONSHIPS                                                  *compare/contrast
another using words or                                        How many different ways can                                 Assessment                        Nonlinguistic representations    Success Maker     Small group
Mathematics is dependent on                                   Compare 0 - 10,000
symbols (>, <, =).                                            you write this number ____?                                                                   *charts and tables                                 Time for repeated review/drill
place value.
Why do numbers have                                         Terra Nova
A sense of number is necessary
designated places?
to communicate the reasoning
What mathematics vocabulary do
used in problem solving.
you need to communicate
mathematical ideas?

BENCHMARK 1.3: Use numbers to count, to measure, to label, and to indicate location.
1.3a Locate, label, or count                                                                   NUMBER AND                 "Meddling with         McREL      McREL Nonlinguistic              Math Text         Visual demonstrations                 1
forward from any even                                         What is number sense, and how    NUMBER                     Medals" (Vol II)        SIOP      representations                  Math Exemplars    Utilization of visual or multi-
number by 2's and from any                                    is it used in problem solving?   RELATIONSHIPS              Exemplar                          *patterning                      Mountain Math     sensory materials
number by 10's and 100's up Mathematics is dependent on       How many different ways can      Locate, label, or count    Classroom                         *ordering                        Success Maker     Small group
to 999.                                                       you write this number ____?      forward and backward by    evidence                          Homework and practice                              Time for repeated review/drill
place value.
Why do numbers have              twos, tens, and hundreds                                     *practicing skills
A sense of number is necessary
designated places?               from any number up to      Terra Nova
to communicate the reasoning
What mathematics vocabulary do   1,000                      Quarterly
used in problem solving.
you need to communicate                                     Assessment
mathematical ideas?

BENCHMARK 1.4: Develop, test, and explain conjectures about properties of whole numbers, and commonly-used fractions and decimals (for example, 1/3, 3/4, 0.5, 0.75)

1.4b Solve addition and                                                                        NUMBER AND                 "Ant in the Well"      McREL      McREL Nonlinguistic              Math Text         Time for repeated review/drill        1
subtraction problems using                                    What is number sense, and how    NUMBER                     Exemplar                SIOP      representations                  Math Exemplars    Small group
commutative and                                               is it used in problem solving?   RELATIONSHIPS              "Equations Galore"                * patterning                     Mountain Math     Functional level materials
associative properties ( for                                  How many different ways can      Solve addition and         Puddles                           *multiple representations        Success Maker
Mathematics is dependent on
example, 2+3+6=6+3+2;the                                      you write this number ____?      subtraction problems       Quarterly                         Identifying similarities and
place value.
words commutative and                                         Why do numbers have              using commutative and      Assessment                        differences
A sense of number is necessary
associative will not be used                                  designated places?               associative properties     Classroom                         *compare/contrast
to communicate the reasoning
in test items).                                               What mathematics vocabulary do   (for example,              evidence
used in problem solving.
you need to communicate          2+3+6=6+3+2)
mathematical ideas?                                         Terra Nova

Revised 04-26-2006/jkw                                                                                                                                                                                                                   2
BY TEACHERS FOR TEACHERS                                                                                                     1st Quarter
MATH CURRICULUM GUIDE

Standard 1: Students utilize language, symbolism, and technology to develop number sense and to communicate those mathematical ideas.

BENCHMARK 1.5: Use number sense to estimate and justify the reasonableness of solutions to problems involving whole numbers and commonly-used fractions and decimals (for example, 1/3, 3/4, 0.5, 0.75)

Enduring Understanding                                                                        Assessment        Key        Suggested Instructional                                Differentiation-            Quarter
State Frameworks                                               Essential Questions              Essential Skills                                                                              Resources
Conceptual Vocabulary                                                                          Methods        Strategy            Practice                                     Adaptations/Extensions         Taught

1.5a Use estimation                                                                            NUMBER AND                   "Raccoons"         McREL      McREL Generating and              Math Text         Time for repeated review/drill       1
strategies to determine the                                  What is number sense, and how     NUMBER                       Exemplar            SIOP      testing hypotheses                Math Exemplars    Small group
reasonableness of solutions                                  is it used in problem solving?    RELATIONSHIPS                Classroom                     *guess and check                  Mountain Math     Functional level materials
to problems                                                  How many different ways can       Use estimation skills to     evidence                      SIOP                              Success Maker
Mathematics is dependent on
you write this number ____?       find a reasonable solution                                 Teacher uses a variety of
place value.
Why do numbers have                                            Terra Nova                    question types, including those
A sense of number is necessary
designated places?                                             Quarterly                     that promote higher-order
to communicate the reasoning
What mathematics vocabulary do                                 Assessment                    thinking skills.
used in problem solving.
you need to communicate
mathematical ideas?

Standard 7: Students communicate the reasoning used in problem-solving situations.

BENCHMARK A: Communicate the use of NUMBER SENSE, INCLUDING ESTIMATIONS AND MENTAL MATH , needed to solve problems, and determine the reasonableness of the solution.

Enduring Understanding                                                                        Assessment        Key        Suggested Instructional                                Differentiation-            Quarter
State Frameworks                                               Essential Questions              Essential Skills                                                                              Resources
Conceptual Vocabulary                                                                          Methods        Strategy            Practice                                     Adaptations/Extensions         Taught

District Indicator: 7a4-                                                                     PROBLEM SOLVING                "Winning Ticket"   McREL      McREL Nonlinguistic               Math Text          Functional level materials          1
Evaluate the                                                                                 Understand and solve           Exemplar            SIOP      representation                    Math Exemplars    Highlighted texts (clue words
solutions/arguments of                                        In what ways can I communicate problems using mental          "Work Schedule"               *act it out; draw a picture;      Mountain Math     and/or phrases)
mathematical and real-world                                                                  math and estimation.           Puddles                       guess and check; find a           Success Maker     Small group
A sense of number is necessary   the reasoning used in problem
problems for                                                                                                                                              pattern; partners; charts and
to solve problems and            solving situations?
reasonableness.                                                                                                             Quarterly                     tables; build a model; choose
communicate the reasoning        What makes a quality solution?
Assessments                   an operation
used in problem solving.         What essential components are
*Choose an appropriate
needed to solve problems?
strategy

Revised 04-26-2006/jkw                                                                                                                                                                                                                 3
BY TEACHERS FOR TEACHERS                                                                                                 1st Quarter
MATH CURRICULUM GUIDE

Standard 2: Students apply algebraic and/or other mathematical methods to understand and explore models, data, graphs, patterns, functions, and spatial relationships.

BENCHMARK 2.3: Recognize when a pattern exists and use that information to solve a problem.

Enduring Understanding                                                                      Assessment         Key        Suggested Instructional                           Differentiation-             Quarter
State Frameworks                                               Essential Questions             Essential Skills                                                                          Resources
Conceptual Vocabulary                                                                        Methods         Strategy            Practice                                Adaptations/Extensions          Taught

2.3a Identify a rule using                                                                     PATTERNS                    "Another Domino     McREL      McREL Nonlinguistic          Math Text         Visual demonstrations                 1
addition or subtraction                                                                        Identify, describe, and     Dilemma" Exemplar    SIOP      representations              Math Exemplars    Utilization of visual or multi-
patterns and solve a new                                                                       extend increasing and       Quarterly                      * patterning                 Mountain Math     sensory materials
problem using the rule.                                                                        decreasing patterns         Assessment                     *draw a picture              Success Maker     Small group
What is a pattern?               (what's my rule (+, -)?)    Classroom                      *charts and tables                             Time for repeated review/drill
Recognizing patterns helps us                                                                 evidence
How do we find patterns?
make sense of our world.
What can patterns reveal?
Terra Nova
Quarterly
Assessment

District Indicator: 2A-1                                                                       PATTERNS                    "Bulletin Board     McREL      McREL Nonlinguistic          Math Text         Visual demonstrations                 1
Identify describe, and extend                                                                  Identify, describe, and     Border" Exemplar     SIOP      representations              Math Exemplars    Utilization of visual or multi-
geometric and numeric                                         What is a pattern?               extend geometric and        Quarterly                      *patterning                  Mountain Math     sensory materials
Recognizing patterns helps us                                                                Assessment                                                  Success Maker     Small group
patterns including growing                                    How do we find patterns?         numeric patterns                                           *draw a picture
make sense of our world.                                                                                                                                                   Time for repeated review/drill
and shrinking patterns.                                       What can patterns reveal?                                                                   *charts and tables
Terra Nova                     *concrete models

BENCHMARK 2.4: Observe and explain how a change in one quantity can produce a change in another (for example, the relationship between the number of bicycles and the number of wheels).

2.4a Using whole numbers,                                                                      PATTERNS                    "Party Seating"     McREL      McREL Nonlinguistic          Math Text         Visual demonstrations                 1
determine how the change in                                                                    Identify, describe, and     Exemplar             SIOP      representations              Math Exemplars    Utilization of visual or multi-
one quantity affects the                                                                       extend increasing and       Classroom                      *draw a picture              Mountain Math     sensory materials
change in the other by                                                                         decreasing patterns using   evidence                       *graphs and tables           Success Maker     Small group
addition or subtraction (for                                                                   pictures and charts                                                                                       Time for repeated review/drill
example, one bicycle has 2                                    What is a pattern?                                           Terra Nova
wheels, 2 bicycles have 4    Recognizing patterns helps us                                                                 Quarterly
How do we find patterns?
wheels, and 3 bicycles have make sense of our world.          What can patterns reveal?                                    Assessment
6 wheels. How many wheels
do 4 bicycles have? The
solution could be presented
in chart or picture form).

Revised 04-26-2006/jkw                                                                                                                                                                                                            4
BY TEACHERS FOR TEACHERS                                                                                                 1st Quarter
MATH CURRICULUM GUIDE

Standard 7: Students communicate the reasoning used in problem-solving situations.

BENCHMARK B: Communicate the use of PATTERNS AND FUNCTIONS needed to model real-world situations and solve appropriate problems.

Enduring Understanding                                                                           Assessment          Key        Suggested Instructional                               Differentiation-           Quarter
State Frameworks                                                     Essential Questions                Essential Skills                                                                          Resources
Conceptual Vocabulary                                                                             Methods          Strategy            Practice                                    Adaptations/Extensions        Taught

District Indicator: 7b1-                                                                           PROBLEM SOLVING             "A New Necklace"     McREL      McREL Nonlinguistic              Math Text          Functional level materials         1
Generate a hypothesis or                                                                           Understand and solve        Exemplar              SIOP      representation                   Math Exemplars    Highlighted texts (clue words
conjecture and solve                                                In what ways can I communicate problems using              "Work Schedule"                 *act it out; draw a picture;     Mountain Math     and/or phrases)
problems of appropriate       A sense of number is necessary       the reasoning used in problem   patterning                  Puddles                         guess and check; find a          Success Maker     Small group
complexity created from real- to solve problems and                solving situations?                                                                         pattern; partners; charts and
world problems.               communicate the reasoning            What makes a quality solution?                              Quarterly                       tables; build a model; choose
used in problem solving.             What essential components are                               Assessments                     an operation
needed to solve problems?                                   Terra Nova                      *Choose an appropriate
strategy

Standard 3: Students use mathematical strategies, data collection and analysis, statistics, and probability in everyday situations.

BENCHMARK 3.1: Construct, read, and interpret displays of data including table, charts, pictographs, and bar graphs.

Enduring Understanding                                                                           Assessment          Key        Suggested Instructional                               Differentiation-           Quarter
State Frameworks                                                     Essential Questions                Essential Skills                                                                          Resources
Conceptual Vocabulary                                                                             Methods          Strategy            Practice                                    Adaptations/Extensions        Taught

3.1a Organize and display                                                                           DATA AND GRAPHS            "Making a Fair       McREL      McREL Identifying similarities   Math Text         Utilization of supplemental         1
data using tallies, bar                                                                             Organize and display       Decision" Exemplar    SIOP      and differences                  Math Exemplars    aids: vocabulary,
graphs, pictographs, and                                                                            data using tally charts;   "Pet Survey"                    *compare/contrast                Mountain Math     multiplication cards, example
tables using a given set of   Graphics are tools used to clarify                                                               Puddles                                                          Success Maker     of graphs, etc.
What are the tools used to clarify bar, line, and picto-                                      Nonlinguistic representations
data                          data.                                                                                            Classroom                                                                          Functional level materials
data, and when do we use them? graphs; and tables                                             *concrete models
Analyzing data displays allows                                                                   evidence                                                                           Small groups
How do we analyze data?
us to interpret and explain data
How do probability and statistics
and make predictions based on                                                                    Terra Nova
help us to make predictions?
probability and statistics..                                                                     Quarterly
Assessment

BENCHMARK 3.2: Interpret data using the concepts of largest, smallest, most often, and middle.

3.2b Using various displays                                                                             DATA AND GRAPHS        "Building Block      McREL      McREL Cooperative learning       Math Text         Utilization of supplemental         1
of data, interpret and draw                                                                             Analyze data to make   Dilemma" Exemplar     SIOP      SIOP                             Math Exemplars    aids: vocabulary,
conclusions.                                                                                            predictions            "Pet Survey"                    Personal connections             Mountain Math     multiplication cards, example
Graphics are tools used to clarify                                                               Puddles                                                          Success Maker     of graphs, etc.
What are the tools used to clarify
data.                                                                                            Classroom                                                                          Functional level materials
data, and when do we use them?
Analyzing data displays allows                                                                   evidence                                                                           Small groups
How do we analyze data?
us to interpret and explain data
How do probability and statistics
and make predictions based on                                                                    Terra Nova
help us to make predictions?
probability and statistics..                                                                     Quarterly
Assessment

Revised 04-26-2006/jkw                                                                                                                                                                                                                    5
BY TEACHERS FOR TEACHERS                                                                                                          1st Quarter
MATH CURRICULUM GUIDE

Standard 7: Students communicate the reasoning used in problem-solving situations.

BENCHMARK C: Communicate the use of PROBABILITY AND STATISTICS needed to represent and solve problems involving uncertainty.

Quarter
Enduring Understanding                                                                         Assessment             Key        Suggested Instructional                              Differentiation-             Taught
State Frameworks                                                 Essential Questions             Essential Skills                                                                                 Resources
Conceptual Vocabulary                                                                           Methods             Strategy            Practice                                   Adaptations/Extensions

District Indicator: 7c1-                                                                       PROBLEM SOLVING               "Fair Snack" (Vol II)   McREL      McREL Nonlinguistic             Math Text          Functional level materials           1
Generate a hypothesis or                                                                       Understand and solve          Exemplar                 SIOP      representation                  Math Exemplars    Highlighted texts (clue words
conjecture and solve                                            In what ways can I communicate problems related to           Classroom                          *act it out; draw a picture;    Mountain Math     and/or phrases)
problems of appropriate                                                                        probability, data, graphs,    evidence                           guess and check; find a         Success Maker     Small group
A sense of number is necessary   the reasoning used in problem
complexity created from real-                                                                  and tables                                                       pattern; partners; charts and
to solve problems and            solving situations?
world problems.                                                                                                              Terra Nova                         tables; build a model; choose
communicate the reasoning        What makes a quality solution?
Quarterly                          an operation
used in problem solving.         What essential components are
Assessment                         *Choose an appropriate
needed to solve problems?
strategy

Standard 4: Students use geometric reasoning to gather evidence, build an argument, and make conjectures in one-, two-, and three-dimensional problem solving situations.

BENCHMARK 4.1: Recognize shapes and their relationships (for example, symmetry, congruence) using a variety of materials (for example, pasta, boxes, pattern blocks).

Enduring Understanding                                                                         Assessment             Key        Suggested Instructional                              Differentiation-             Quarter
State Frameworks                                                 Essential Questions             Essential Skills                                                                                 Resources
Conceptual Vocabulary                                                                           Methods             Strategy            Practice                                   Adaptations/Extensions          Taught

4.1b Identify a line of                                                                          GEOMETRY                    "Telephone Talk"        McREL      McREL Nonlinguistic             Math Text         Visual demonstrations                 1
symmetry of regular                                                                              Identify line of symmetry   Puddles                  SIOP      representations                 Math Exemplars    Utilization of visual or multi-
polygons and other familiar                                    What is geometry?                 in regular polygons and     Quarterly                          *draw a picture                 Mountain Math     sensory materials
objects                       Geometry builds our world.       How do we use geometry in         other familiar objects      Assessment                         *concrete models                Success Maker     Small group
every day life?
Terra Nova

BENCHMARK 4.2: Identify, describe, draw, compare, classify, and build physical models geometric figures.
4.2a Identify characteristics                                                                    GEOMETRY                    "Telephone Talk"        McREL      McREL Nonlinguistic             Math Text         Visual demonstrations                 1
of two-dimensional figures                                                                       Recognize & identify        Puddles                  SIOP      representations                 Math Exemplars    Utilization of visual or multi-
(for example, number of                                                                          geometric shapes            Classroom                          *concrete models                Mountain Math     sensory materials
sides or vertices, contains a                                  What is geometry?                                             evidence                           *vocabulary-graphic             Success Maker     Small group
right angle, contains parallel Geometry builds our world.      How do we use geometry in                                     Quarterly                          organizers-SIOP
sides).                                                        every day life?                                               Assessment

Terra Nova

BENCHMARK 4.4 Solve problems using geometric relationships and spatial reasoning (for example, using rectangular coordinates to locate objects, constructing models of three-dimensional objects).
4.4 Solving problems using                                                                       GEOMETRY                 "Paleontologist"           McREL      McREL Nonlinguistic             Math Text         Visual demonstrations                 1
geometric relationships and                                                                      Sort shapes & objects by Exemplar                    SIOP      representations                 Math Exemplars    Utilization of visual or multi-
spatial reasoning (for                                                                           attributes               Classroom                             *attribute blocks               Mountain Math     sensory materials
example, using rectangular                                                                                                evidence                              Identifying similarities and    Success Maker     Small group
coordinates to locate                                          What is geometry?                                                                                differences
objects, constructing models Geometry builds our world.        How do we use geometry in                                     Terra Nova                         *classifying
or three-dimensional                                           every day life?                                                                                  *compare/contrast
objects).

Revised 04-26-2006/jkw                                                                                                                                                                                                                      6
BY TEACHERS FOR TEACHERS                                                                                                   1st Quarter
MATH CURRICULUM GUIDE

Standard 4: Students use geometric reasoning to gather evidence, build an argument, and make conjectures in one-, two-, and three-dimensional problem solving situations.

BENCHMARK 4.5: Recognize geometry in their world (for example in art and in nature).

Enduring Understanding                                                                     Assessment         Key        Suggested Instructional                              Differentiation-             Quarter
State Frameworks                                                    Essential Questions            Essential Skills                                                                          Resources
Conceptual Vocabulary                                                                       Methods         Strategy            Practice                                   Adaptations/Extensions          Taught

Recognizing geometry in                                                                            GEOMETRY                   Classroom          McREL      McREL Nonlinguistic             Math Text         Utilization of visual or multi-       1
their world (for example in                                                                        Identify geometric figures Evidence            SIOP      representation                  Math Exemplars    sensory materials
What is geometry?
art and in nature).                                                                                in art and nature                                        *concrete models                Success Maker     Visual demonstrations
Geometry builds our world.        How do we use geometry in
every day life?

Standard 7: Students communicate the reasoning used in problem-solving situations.

BENCHMARK D: Communicate the use of GEOMETRIC CONCEPTS needed to model real-world situations and solve appropriate problems.

Enduring Understanding                                                                     Assessment         Key        Suggested Instructional                              Differentiation-             Quarter
State Frameworks                                                    Essential Questions            Essential Skills                                                                          Resources
Conceptual Vocabulary                                                                       Methods         Strategy            Practice                                   Adaptations/Extensions          Taught

District Indicator: 7d1-                                                                            PROBLEM SOLVING          "Telephone Talk"-   McREL      McREL Nonlinguistic             Math Text          Functional level materials           1
Generate a hypothesis or                                                                            Understand and solve     Puddles              SIOP      representation                  Math Exemplars    Highlighted texts (clue words
conjecture and solve                                                 In what ways can I communicate problems related to      Classroom                      *act it out; draw a picture;    Mountain Math     and/or phrases)
problems of appropriate       A sense of number is necessary        the reasoning used in problem   geometric concepts       evidence                       guess and check; find a         Success Maker     Small group
complexity created from real- to solve problems and                 solving situations?                                                                     pattern; partners; charts and
world problems.               communicate the reasoning             What makes a quality solution?                           Terra Nova                     tables; build a model; choose
used in problem solving.              What essential components are                            Quarterly                      an operation
Assessment                     *Choose an appropriate
needed to solve problems?
strategy

Standard 5: Students use a variety of tools and techniques to measure and use measurement in problems and in everyday situations.

BENCHMARK 5.1: Know, use, describe, and estimate measures of length, perimeter, capacity, weight, time, and temperature.

Enduring Understanding                                                                     Assessment         Key        Suggested Instructional                              Differentiation-             Quarter
State Frameworks                                                    Essential Questions            Essential Skills                                                                          Resources
Conceptual Vocabulary                                                                       Methods         Strategy            Practice                                   Adaptations/Extensions          Taught

5.1a Using an analog and                                                                           MEASUREMENT               Classroom           McREL      McREL Nonlinguistic             Math Text         Small group                           1
digital clock, tell time to the                                                                    Tell time to nearest 5    evidence             SIOP      representations                 Math Exemplars    Visual demonstrations
nearest five minutes                                                Why measure?                   minute (digital and                                      *concrete models                Mountain Math     Functional level materials
Appropriate tools and units are
In measuring situations what   analog)                   Terra Nova                     Homework and practice           Success Maker
needed to measure.
tool(s) would you use?                                   Quarterly
Recognize and communicate
What are the units used to                               Assessment
measurement relationships.
communicate a measurement?

5.1c Choose the                                                                                    MEASUREMENT                                   McREL      McREL Cooperative learning;     Math Text         Small group                           1
appropriate tool to measure                                                                        Select correct tools to   Terra Nova           SIOP      Generating and testing          Math Exemplars    Visual demonstrations
Why measure?
familiar objects in situations    Appropriate tools and units are                                  measure length, weight,   Quarterly                      hypotheses;                     Mountain Math     Functional level materials
In measuring situations what
that contain length, weight,      needed to measure.                                               temp., time               Assessment                     *Vocabulary-graphic             Success Maker
tool(s) would you use?
temperature, or time.             Recognize and communicate                                                                  "The Puddle                    organizers-SIOP
What are the units used to                               Problem" Puddles
measurement relationships.
communicate a measurement?

Revised 04-26-2006/jkw                                                                                                                                                                                                                7
BY TEACHERS FOR TEACHERS                                                                                                   1st Quarter
MATH CURRICULUM GUIDE

Standard 5: Students use a variety of tools and techniques to measure and use measurement in problems and in everyday situations.

BENCHMARK 5.2: Compare and order objects according to measurable attributes (for example, longest to shortest, lightest to heaviest)

Enduring Understanding                                                                     Assessment          Key         Suggested Instructional                              Differentiation-           Quarter
State Frameworks                                                   Essential Questions            Essential Skills                                                                            Resources
Conceptual Vocabulary                                                                       Methods          Strategy             Practice                                   Adaptations/Extensions        Taught

5.2a Compare objects                                                                             MEASUREMENT                                     McREL     McREL Nonlinguistic             Math Text          Small group                         1
according to the measurable                                                                      Select correct tools to                          SIOP     representations                 Math Exemplars     Visual demonstrations
Why measure?
attributes of length, capacity, Appropriate tools and units are                                  measure length, weight,                                   *concrete models                Mountain Math      Functional level materials
In measuring situations what
weight, or temperature          needed to measure.                                               temp., time                                               Homework and practice           Success Maker
tool(s) would you use?
Recognize and communicate                                                                                                  Supplementary materials
What are the units used to
measurement relationships.                                                                                                 (graphs, models, visuals)
communicate a measurement?

BENCHMARK 5.4: Use the approximate measures of familiar objects (for example, the width of your finger, the temperature of a room, the weight of a gallon of milk) to develop a sense of measurement.

5.4a Approximate the            Appropriate tools and units are   Why measure?                   MEASUREMENT               "The Puddle           McREL     McREL Cooperative learning; Math Text              Small group                         1
measurement of familiar         needed to measure.                In measuring situations what   Approximate the           Problem" Puddles       SIOP     Generating and testing      Math Exemplars         Visual demonstrations
objects using standard units    Recognize and communicate         tool(s) would you use?         measurement of objects    Classroom                       hypotheses                  Mountain Math          Functional level materials
(for example, a paper clip is   measurement relationships.        What are the units used to     using standard and non-   Evidence                                                    Success Maker
about one inch)                                                   communicate a measurement?     standard units

Standard 7: Students communicate the reasoning used in problem-solving situations.
BENCHMARK E: Communicate the use of APPROPRIATE MEASUREMENT TECHNIQUES needed to solve problems, and determine whether the report the degree of accuracy required.

Enduring Understanding                                                                     Assessment          Key         Suggested Instructional                              Differentiation-           Quarter
State Frameworks                                                   Essential Questions            Essential Skills                                                                            Resources
Conceptual Vocabulary                                                                       Methods          Strategy             Practice                                   Adaptations/Extensions        Taught

District Indicator: 7e3-                                                                          PROBLEM SOLVING          "Wrapping a Lamp"     McREL     McREL Nonlinguistic             Math Text           Functional level materials         1
Choose and apply a strategy                                                                       Understand and solve     Exemplar               SIOP     representation                  Math Exemplars     Highlighted texts (clue words
to solve mathematical and                                          In what ways can I communicate problems using           Classroom                       *act it out; draw a picture;    Mountain Math      and/or phrases)
real-world problems.        A sense of number is necessary        the reasoning used in problem   appropriate              evidence                        guess and check; find a         Success Maker      Small group
to solve problems and                 solving situations?             measurement tools                                        pattern; partners; charts and
communicate the reasoning             What makes a quality solution?                           Terra Nova                      tables; build a model; choose
used in problem solving.              What essential components are                            Quarterly                       an operation
needed to solve problems?                                Assessment                      *Choose an appropriate
strategy

Revised 04-26-2006/jkw                                                                                                                                                                                                               8
BY TEACHERS FOR TEACHERS                                                                                                      1st Quarter
MATH CURRICULUM GUIDE

Standard 6: Students understand, develop, and use computational skills and techniques, including estimation, mental math, paper and pencil, calculators, and computers in problem-solving situations.

BENCHMARK 6.1: Demonstrate conceptual meanings for the four basic arithmetic operations of addition, subtraction, multiplication, and division.

Enduring Understanding                                                                         Assessment           Key         Suggested Instructional                              Differentiation-            Quarter
State Frameworks                                                   Essential Questions               Essential Skills                                                                               Resources
Conceptual Vocabulary                                                                           Methods           Strategy             Practice                                   Adaptations/Extensions         Taught

6.1a Using pictures,                                                                                COMPUTATION                  Quarterly             McREL       McREL Nonlinguistic             Math Text         Small group                          1
diagrams, numbers or                                              What strategies are used to solve Solve 2-digit addition and   Assessments                       representations                 Math Exemplars    Visual demonstrations
SIOP
words, demonstrate addition                                       problems?                         subtraction problems         "Raccoons"                        *modeling                       Mountain Math     Functional level materials
and subtraction of whole     A sense of number is necessary       How are computation skills and    without regrouping           Exemplar                          *base ten blocks                Success Maker     Time for repeated review/drill
numbers with 2-digit        to communicate the reasoning          strategies used daily?                                         "Equations Galore!"               Homework and practice
numbers.                    used in problem solving.              Why be fluent at computation?                                  Puddles
Estimation and computation are        How do you use estimation to
vital tools.                          determine whether your solution                                Terra Nova
is reasonable?

BENCHMARK 6.3 Demonstrate understanding of and proficiency with basic addition, subtraction, multiplication, and division facts without the use of a calculator.

6.3 b Demonstrate                                                                                   COMPUTATION                                        McREL       McREL Homework and              Math Text         Small group                          1
proficiency with basic                                            What strategies are used to solve Add 3 digit numbers with Terra Nova                 SIOP       practice                        Math Exemplars    Visual demonstrations
addition and subtraction                                          problems?                         regrouping               Quarterly                             *Demonstration (modeling)-      Mountain Math     Functional level materials
facts                              A sense of number is necessary How are computation skills and                             Assessment                            SOP                             Success Maker     Time for repeated review/drill
to communicate the reasoning    strategies used daily?
used in problem solving.        Why be fluent at computation?
Estimation and computation are How do you use estimation to
vital tools.                    determine whether your solution
is reasonable?

BENCHMARK 6.4: Construct, use, and explain procedures to compute and estimate with whole numbers.

6.4a Use estimation                                                                                   COMPUTATION                "The Tower            McREL       McREL Generating and            Math Text         Small group                          1
strategies with whole                                             What strategies are used to solve   Use rounding and           Problem" Exemplar      SIOP       testing hypotheses              Math Exemplars    Visual demonstrations
numbers prior to performing                                       problems?                           estimation of whole                                          *guess and check                Mountain Math     Functional level materials
on operation (+,-); (for           A sense of number is necessary How are computation skills and      numbers to make            Terra Nova                        Nonlinguistic representations   Success Maker     Time for repeated review/drill
example, front-end                to communicate the reasoning    strategies used daily?              predictions before         Quarterly                         *concrete models
estimation, estimation by         used in problem solving.        Why be fluent at computation?       computation                Assessment
rounding, friendly numbers,       Estimation and computation are How do you use estimation to
flexible rounding, clustering).   vital tools.                    determine whether your solution
is reasonable?

Revised 04-26-2006/jkw                                                                                                                                                                                                                       9
BY TEACHERS FOR TEACHERS                                                                                                   1st Quarter
MATH CURRICULUM GUIDE

Standard 6: Students understand, develop, and use computational skills and techniques, including estimation, mental math, paper and pencil, calculators, and computers in problem-solving situations.

BENCHMARK 6.5: Select and use appropriate methods for computing with whole numbers in problem-solving situations from among mental arithmetic, estimation, paper-and-pencil, calculator and computer methods.

Enduring Understanding                                                                       Assessment        Key        Suggested Instructional                                 Differentiation-             Quarter
State Frameworks                                                   Essential Questions              Essential Skills                                                                      Resources
Conceptual Vocabulary                                                                         Methods        Strategy            Practice                                      Adaptations/Extensions          Taught

6.5a Given a real world                                                                           COMPUTATION                "What's the        McREL      McREL Cooperative learning   Math Text               Small group                           1
problem-solving situation,                                      What strategies are used to solve Select and use             Problem?"           SIOP      *Choose an operation         Math Exemplars          Visual demonstrations
use addition, subtraction, or                                   problems?                         appropriate operation      Exemplar                                                   Mountain Math           Functional level materials
multiplication to solve the      A sense of number is necessary How are computation skills and    solve problems (+, -)      "Catalog                                                   Success Maker           Time for repeated review/drill
problem.                        to communicate the reasoning    strategies used daily?                                       Calculations"
used in problem solving.        Why be fluent at computation?                                Puddles
Estimation and computation are How do you use estimation to
vital tools.                    determine whether your solution                              Terra Nova
is reasonable?                                               Quarterly
Assessment

6.5b Determine from real-                                                                           COMPUTATION              "The Winning       McREL      McREL Cooperative learning; Math Text                Small group                           1
What strategies are used to solve
world problems, whether an                                                                          Determine from real-     Ticket" Exemplar    SIOP      Generating and testing      Math Exemplars           Visual demonstrations
problems?
estimated or exact sum,                                                                             world problems whether                                 hypotheses;                 Mountain Math            Functional level materials
A sense of number is necessary How are computation skills and
difference, or product is                                                                           an estimated or exact    Terra Nova                                                Success Maker            Time for repeated review/drill
to communicate the reasoning    strategies used daily?
acceptable.                                                                                         sum/difference is        Quarterly                     *Vocabulary-graphic
used in problem solving.        Why be fluent at computation?
acceptable.              Assessment                    organizers-SIOP
Estimation and computation are How do you use estimation to
vital tools.                    determine whether your solution
is reasonable?

District Indicator: 1C1 Show                                                                      COMPUTATION                Quarterly          McREL      McREL Homework and           Math Text               Small group                           1
relationship between inverse                                    What strategies are used to solve Math fact fluency in       Assessment                    practice                     Math Exemplars          Visual demonstrations
SIOP
operations.                                                     problems?                         addition and subtraction                                                              Mountain Math           Functional level materials
A sense of number is necessary How are computation skills and    to 24                      Terra Nova                                                 Success Maker           Time for repeated review/drill
to communicate the reasoning    strategies used daily?
used in problem solving.        Why be fluent at computation?
Estimation and computation are How do you use estimation to
vital tools.                    determine whether your solution
is reasonable?

Revised 04-26-2006/jkw                                                                                                                                                                                                                  10
BY TEACHERS FOR TEACHERS                                                                                                1st Quarter
MATH CURRICULUM GUIDE

Standard 7: Students communicate the reasoning used in problem-solving situations.

BENCHMARK F: Communicate the use of APPROPRIATE COMPUTATIONAL TECHNIQUES needed to solve problems, and determine whether the results are reasonable.

Enduring Understanding                                                                   Assessment        Key        Suggested Instructional                              Differentiation-            Quarter
State Frameworks                                               Essential Questions            Essential Skills                                                                         Resources
Conceptual Vocabulary                                                                     Methods        Strategy            Practice                                   Adaptations/Extensions         Taught

District Indicator: 7 f.3-                                                                   PROBLEM SOLVING            "More for the     McREL      McREL Nonlinguistic             Math Text          Functional level materials          1
Choose and apply a strategy                                                                  Understand and solve       Money" Exemplar    SIOP      representation                  Math Exemplars    Highlighted texts (clue words
to solve mathematical and                                                                    problems using                                          *act it out; draw a picture;    Mountain Math     and/or phrases)
real-world problems.                                                                         appropriate                Terra Nova                   guess and check; find a         Success Maker     Small group
In what ways can I communicate computational techniques   Quarterly                    pattern; partners; charts and
A sense of number is necessary the reasoning used in problem                              Assessment                   tables; build a model; choose
to solve problems and          solving situations?                                                                     an operation
communicate the reasoning      What makes a quality solution?                                                          *Choose an appropriate
used in problem solving.       What essential components are                                                           strategy
needed to solve problems?

Revised 04-26-2006/jkw                                                                                                                                                                                                         11
BY TEACHERS FOR TEACHERS                                                                                                   2nd Quarter
MATH CURRICULUM GUIDE

Standard 1: Students utilize language, symbolism, and technology to develop number sense and to communicate those mathematical ideas.

BENCHMARK 1.1: Demonstrate meanings for whole numbers and commonly-used fractions and decimals (for example, 1/3, 3/4, 0.5, 0.75), and represent equivalent forms of the same number through the use of physical models, drawings, calculators, and
computers.

Enduring Understanding                                                                      Assessment       Key        Suggested Instructional                                Differentiation-             Quarter
State Frameworks                                                 Essential Questions              Essential Skills                                                                       Resources
Conceptual Vocabulary                                                                        Methods       Strategy           Practice                                      Adaptations/Extensions          Taught

1.1b Identify the fractional                                   What is number sense, and how     NUMBER AND                   Quarterly     McREL      McRel Nonlinguistic            Math Text            Use visual aids and media              2
part of a drawing or a set                                     is it used in problem solving?    NUMBER                       Assessment     SIOP      representations                Success Maker        Utilization of visual or multi-
(restricted to halves,                                         How many different ways can you   RELATIONSHIPS                                         *multiple representations      Mountain Math        sensory materials
thirds, fourths)             Mathematics is dependent on
write this number ____?           Identify fractional parts of Terra Nova               Identifying similarities and                        Emphasis on success
place value.                                                        a drawing (1/2, 1/3, 1/4)                             differences                                         experiences
Why do numbers have
A sense of number is necessary                                                                                            *compare/contrast
designated places?
to communicate the reasoning                                                                                              *SIOP-personal connections
What mathematics vocabulary do
used in problem solving.
you need to communicate
mathematical ideas?

1.1c Using concrete                                                                              NUMBER AND                 Quarterly       McREL      McREL Nonlinguistic            Math Text            Visual demonstrations                  2
materials or pictures                                          What is number sense, and how     NUMBER                     Assessment       SIOP      representations                Success Maker        Utilization of visual or multi-
identify different                                             is it used in problem solving?    RELATIONSHIPS              "Holiday Fair              * multiple representations     Mountain Math        sensory materials
combinations of coins up                                       How many different ways can you   Money combinations to      Shopping                   *SIOP-personal connections                          Emphasis on success
Mathematics is dependent on
to \$0.99                                                       write this number ____?           \$5.00                      Spree"                                                                         experiences
place value.
Why do numbers have                                          Exemplar
A sense of number is necessary
designated places?
to communicate the reasoning
What mathematics vocabulary do                               Terra Nova
used in problem solving.
you need to communicate
mathematical ideas?

BENCHMARK 1.2: Read and write whole numbers and know place-value concepts and numeration through their relationships to counting, ordering, and grouping.
1.2c Identify place value                                                                        NUMBER AND                 Quarterly       McREL      McREL Nonlinguistic            Math Text            Visual demonstrations                  2
through ten-thousands (i.e.                                    What is number sense, and how     NUMBER                     Assessment       SIOP      representations                Success Maker        Utilization of visual or multi-
86,243, "6" is in the                                          is it used in problem solving?    RELATIONSHIPS                                         * multiple representations     Mountain Math        sensory materials
thousands place)                                               How many different ways can you   Place value-identify to    Terra Nova                 *ordering                                           Emphasis on success
Mathematics is dependent on                                                                                                                                                  experiences
write this number ____?           hundred-thousands
place value.
Why do numbers have
A sense of number is necessary
designated places?
to communicate the reasoning
What mathematics vocabulary do
used in problem solving.
you need to communicate
mathematical ideas?

1.2d Generate equivalent                                                                         NUMBER AND                 Quarterly       McREL      McREL Nonlinguistic            Math Text            Visual demonstrations                  2
representations for the                                        What is number sense, and how     NUMBER                     Assessment       SIOP      representations                Success Maker        Utilization of visual or multi-
same number up to 4 digit                                      is it used in problem solving?    RELATIONSHIPS                                         *multiple representations      Mountain Math        sensory materials
number (for example,                                           How many different ways can you   Equivalent                 Terra Nova                 Cooperative learning                                Emphasis on success
Mathematics is dependent on
25=20+5 or 10+15 or                                            write this number ____?           representations up to 4-                              Generating and testing                              experiences
place value.
2tens and 5 ones).                                             Why do numbers have               digit numbers (25=20+5                                hypotheses
A sense of number is necessary
designated places?                or 10+15 or 2 tens 5                                  *more than one solution
to communicate the reasoning
What mathematics vocabulary do    ones)
used in problem solving.
you need to communicate
mathematical ideas?

Revised 4-26-2006/jkw                                                                                                                                                                                                               12
BY TEACHERS FOR TEACHERS                                                                                                  2nd Quarter
MATH CURRICULUM GUIDE

Standard 1: Students utilize language, symbolism, and technology to develop number sense and to communicate those mathematical ideas. Number sense is necessary to solve problems and communicate reasoning.

BENCHMARK 1.2: Read and write whole numbers and know place-value concepts and numeration through their relationships to counting, ordering, and grouping.

Enduring Understanding                                                                        Assessment     Key        Suggested Instructional                               Differentiation-             Quarter
State Frameworks                                                 Essential Questions              Essential Skills                                                                         Resources
Conceptual Vocabulary                                                                          Methods     Strategy           Practice                                     Adaptations/Extensions          Taught

1.2e Compare whole                                                                               NUMBER AND                   Quarterly     McREL      McREL                         Math Text            Visual demonstrations                  2
numbers as greater than,                                       What is number sense, and how     NUMBER                       Assessment     SIOP      Identifying similarities and  Success Maker        Utilization of visual or multi-
less than, or equal to one                                     is it used in problem solving?    RELATIONSHIPS                Classroom                differences *compare/contrast Mountain Math        sensory materials
another using words or                                         How many different ways can you   Reads, writes, orders        Evidence                                                                    Emphasis on success
Mathematics is dependent on
symbols (>, <, =).                                             write this number ____?           and compares numbers                                                                                     experiences
place value.
Why do numbers have               to 100,000                   Terra Nova
A sense of number is necessary
designated places?
to communicate the reasoning
What mathematics vocabulary do
used in problem solving.
you need to communicate
mathematical ideas?

BENCHMARK 1.3: Use numbers to count, to measure, to label and to indicate location.

1.3a Locate, label, or                                                                           NUMBER AND                                 McREL      McREL Nonlinguistic              Math Text         Visual demonstrations                  2
What is number sense, and how
count forward from any                                                                           NUMBER                       Terra Nova     SIOP      representations                  Success Maker     Utilization of visual or multi-
is it used in problem solving?
even number by 2,s and                                                                           RELATIONSHIPS                Quarterly                *ordering                        Mountain Math     sensory materials
How many different ways can you
from any number by 10's       Mathematics is dependent on                                        Writes and orders            Assessment               *patterns                                          Emphasis on success
write this number ____?
and 100's up to 999           place value.                                                       numbers to 100,000           Classroom                                                                   experiences
Why do numbers have
A sense of number is necessary                                     counting by 2's, 10's, and   Evidence
designated places?
to communicate the reasoning                                       100's forward and
What mathematics vocabulary do
used in problem solving.                                           backward
you need to communicate
mathematical ideas?

1.3b Locate and label                                          What is number sense, and how     NUMBER AND                                 McREL      McREL Homework and               Math Text         Visual demonstrations                  2
1/2's between whole                                            is it used in problem solving?    NUMBER                       Terra Nova     SIOP      practice;                        Success Maker     Utilization of visual or multi-
numbers on the number                                          How many different ways can you   RELATIONSHIPS                Quarterly                Nonlinguistic representations;   Mountain Math     sensory materials
Mathematics is dependent on
line                                                           write this number ____?           Locate and label             Assessment               *multiple representations                          Emphasis on success
place value.
Why do numbers have               common fractions (1/2's                               Identifying similarities and                       experiences
A sense of number is necessary
designated places?                between wholes I.e. 1/2,                              differences
to communicate the reasoning
What mathematics vocabulary do    1 1/2, 2 1/2)                                         *classifying
used in problem solving.
you need to communicate
mathematical ideas?

BENCHMARK 1.5: Use number sense to estimate and justify the reasonableness of solutions to problems involving whole numbers and commonly-used fractions and decimals (for example, 1/3, 3/4, 0.5, 0.75)

1.5a Use estimation                                                                              NUMBER AND                                 McREL      McREL Generating and testing Math Text             Visual demonstrations                  2
strategies to determine the                                    What is number sense, and how     NUMBER                       Terra Nova     SIOP      hypotheses                   Success Maker         Utilization of visual or multi-
reasonableness of                                              is it used in problem solving?    RELATIONSHIPS                Classroom                *estimating                  Mountain Math         sensory materials
solutions to problems                                          How many different ways can you   Use reasonable               Evidence                 *guess and check                                   Emphasis on success
Mathematics is dependent on                                                                                                                                                 experiences
write this number ____?           estimation to solve
place value.
Why do numbers have               problems
A sense of number is necessary
designated places?
to communicate the reasoning
What mathematics vocabulary do
used in problem solving.
you need to communicate
mathematical ideas?

Revised 4-26-2006/jkw                                                                                                                                                                                                              13
BY TEACHERS FOR TEACHERS                                                                                                    2nd Quarter
MATH CURRICULUM GUIDE

Standard 7: Students communicate the reasoning used in problem-solving situations.

BENCHMARK A: Communicate the use of NUMBER SENSE, INCLUDING ESTIMATIONS AND MENTAL MATH , needed to solve problems, and determine the reasonableness of the solution.

Enduring Understanding                                                                         Assessment        Key        Suggested Instructional                               Differentiation-             Quarter
District Indicators                                             Essential Questions              Essential Skills                                                                           Resources
Conceptual Vocabulary                                                                           Methods        Strategy           Practice                                     Adaptations/Extensions          Taught

District Indicator: 7A2-                                                                        PROBLEM SOLVING                              McREL      McREL Nonlinguistic             Math Text          Small group                            2
Choose and apply a                                                                              Understand and solve        Terra Nova        SIOP      representation                  Success Maker      Highlighted texts (clue words
strategy to solve                                            In what ways can I communicate     problems using mental       Quarterly                   *act it out; draw a picture;    Mountain Math      and/or phrases)
mathematical and real      A sense of number is necessary    the reasoning used in problem      math and estimation.        Assessment                  guess and check; find a                            Functional level materials
world problems.            to solve problems and             solving situations?                                                                        pattern; partners; charts and
communicate the reasoning used    What makes a quality solution?                                                             tables; build a model; choose
in problem solving.               What essential components are                                                              an operation
needed to solve problems?                                                                  *Choose an appropriate
strategy

Standard 2: Students apply algebraic and/or other mathematical methods to understand and explore models, data, graphs, patterns, functions, and spatial relationships.

BENCHMARK 2.1: Reproduce, extend, create, and describe patterns and sequences using a variety of materials (for example, beans, toothpicks, pattern blocks, calculators, unifix cubes, colored tiles).

Enduring Understanding                                                                         Assessment        Key        Suggested Instructional                               Differentiation-             Quarter
State Frameworks                                                Essential Questions              Essential Skills                                                                           Resources
Conceptual Vocabulary                                                                           Methods        Strategy           Practice                                     Adaptations/Extensions          Taught

2.1b Use a pattern to find                                                                      PATTERNS AND                Quarterly        McREL      McREL Nonlinguistic             Math Text          Visual demonstrations                  2
missing elements (for                                                                           ALGEBRA                     Assessment        SIOP      representations                 Success Maker      Utilization of visual or multi-
example, multiples of 2, 3,                                                                     Use patterns to find        "Chick-a-dee-               *patterning                     Mountain Math      sensory materials
4, 5, 10)                                                    What is a pattern?                 missing elements (e.g.      dee Problem"                *multiple representations                          Emphasis on success
Recognizing patterns helps us
How do we find patterns?           multiples of 2,3,4,5,10)    Exemplar                                                                       experiences
make sense of our world.
What can patterns reveal?
Terra Nova

BENCHMARK 2.3: Recognize when a pattern exists and use that information to solve a problem.

2.3b Given numbers in a                                                                         PATTERNS AND                Quarterly        McREL      McREL Nonlinguistic             Math Text          Visual demonstrations                  2
table, extend the table.                                                                        FUNCTIONS                   Assessment        SIOP      representations                 Success Maker      Utilization of visual or multi-
What is a pattern?                 Numeric patterns on a       "Pet Survey"                *patterning                     Mountain Math      sensory materials
Recognizing patterns helps us                                        given table (Input/Output   Puddles                     *charts, tables, and lists                         Emphasis on success
How do we find patterns?
make sense of our world.                                             Table)                                                                                                     experiences
What can patterns reveal?
Terra Nova

District Indicator: Use                                                                         PATTERNS AND                Quarterly        McREL      McREL Nonlinguistic             Math Text          Visual demonstrations
tools such as tables and                                                                        FUNCTIONS                   Assessment        SIOP      representations                 Success Maker      Utilization of visual or multi-
graphs to analyze and                                        What is a pattern?                 Use tables and graphs to    "Pet Survey"                *graphing                       Mountain Math      sensory materials
record patterns.           Recognizing patterns helps us                                        analyze and record data     Puddles                     *multiple representations                          Emphasis on success
How do we find patterns?                                                                                                                                                             2
make sense of our world.                                                                                                     *Personal connections-SOP                          experiences
What can patterns reveal?
Terra Nova

Revised 4-26-2006/jkw                                                                                                                                                                                                               14
BY TEACHERS FOR TEACHERS                                                                                                 2nd Quarter
MATH CURRICULUM GUIDE

Standard 2: Students apply algebraic and/or other mathematical methods to understand and explore models, data, graphs, patterns, functions, and spatial relationships.

BENCHMARK 2.4: Observe and explain how a change in one quantity can produce a change in another (for example, the relationship between the number of bicycles and the number of wheels).

Enduring Understanding                                                                     Assessment       Key        Suggested Instructional                              Differentiation-             Quarter
State Frameworks                                              Essential Questions             Essential Skills                                                                        Resources
Conceptual Vocabulary                                                                       Methods       Strategy           Practice                                    Adaptations/Extensions          Taught

2.4a Using whole                                                                             PATTERNS AND               "Chick-a-dee-   McREL      McREL Nonlinguistic             Math Text         Visual demonstrations                  2
numbers, determine how                                                                       FUNCTIONS                  dee Problem"     SIOP      representations                 Success Maker     Utilization of visual or multi-
the change in one quantity                                                                   Use charts and tables to   Exemplar                   *patterning                     Mountain Math     sensory materials
affects the change in the                                                                    extend an increasing or                               *draw a picture                                   Emphasis on success
other by addition or                                                                         decreasing pattern         Terra Nova                 Cooperative learning                              experiences
subtraction (for example,                               What is a pattern?                                              Quarterly
one bicycle has 2 wheels, Recognizing patterns helps us How do we find patterns?                                        Assessment
2 bicycles have 4 wheels, make sense of our world.      What can patterns reveal?
and 3 bicycles have 6
wheels. How many
wheels do 4 bicycles
have? The solution could
be presented in chart or
picture form)
Standard 7: Students communicate the reasoning used in problem-solving situations.

BENCHMARK B: Communicate the use of PATTERNS AND FUNCTIONS needed to model real-world situations and solve appropriate problems.

Enduring Understanding                                                                     Assessment       Key        Suggested Instructional                              Differentiation-             Quarter
District Indicators                                           Essential Questions             Essential Skills                                                                        Resources
Conceptual Vocabulary                                                                       Methods       Strategy           Practice                                    Adaptations/Extensions          Taught

District Indicator: 7b2-                                                                     PROBLEM SOLVING                            McREL      McREL Nonlinguistic             Math Text         Visual demonstrations                  2
Choose and apply a                                                                           Understand and solve       Terra Nova       SIOP      representation                  Success Maker     Utilization of visual or multi-
strategy to solve                                           In what ways can I communicate   problems using             Quarterly                  *act it out; draw a picture;    Mountain Math     sensory materials
mathematical and real      A sense of number is necessary   the reasoning used in problem    patterning                 Assessment                 guess and check; find a                           Emphasis on success
world problems.            to solve problems and            solving situations?                                                                    pattern; partners; charts and                     experiences
communicate the reasoning used   What makes a quality solution?                                                         tables; build a model; choose                     Extended time for
in problem solving.               What essential components are                                                         an operation                                      assignment completion
needed to solve problems?                                                              *Choose an appropriate
strategy

Revised 4-26-2006/jkw                                                                                                                                                                                                         15
BY TEACHERS FOR TEACHERS                                                                                                    2nd Quarter
MATH CURRICULUM GUIDE

Standard 3: Students use mathematical strategies, data collection and analysis, statistics, and probability in everyday situations.

BENCHMARK 3.1: Construct, read, and interpret displays of data including tables, charts, pictographs, and bar graphs.

Enduring Understanding                                                                               Assessment           Key        Suggested Instructional                           Differentiation-             Quarter
State Frameworks                                                      Essential Questions                Essential Skills                                                                           Resources
Conceptual Vocabulary                                                                                 Methods           Strategy           Practice                                 Adaptations/Extensions          Taught

3.1a Organize and                                                                                       DATA AND GRAPHS              Quarterly           McREL      McREL Nonlinguistic          Math Text         Functional level materials             2
display data using tallies,                                                                             Collect & organize data      Assessment           SIOP      representations              Success Maker     Small group
bar graphs, pictographs,      Graphics are tools used to clarify                                        in graphs                    "Pet Survey"                   *graphing                    Mountain Math     Utilization of visual or multi-
What are the tools used to clarify
and tables using a given      data.                                                                                                  Puddles                        Cooperative learning                           sensory materials
data, and when do we use them?
set of data.                  Analyzing data displays allows                                                                         "Typical objects"
How do we analyze data?
us to interpret and explain data                                                                       Exemplars
How do probability and statistics
and make predictions based on
help us to make predictions?
probability and statistics..                                                                           Terra Nova

3.1a Organize and                                                                                     DATA AND GRAPHS                Quarterly           McREL      McREL Cooperative learning ; Math Text         Functional level materials             2
display data using tallies,   Graphics are tools used to clarify                                      Interpret and evaluate         Assessment           SIOP      Identifying similarities and Success Maker     Small group
bar graphs, pictographs,                                           What are the tools used to clarify data, graphs, tables, lists,   "Pet Survey"                   differences                  Mountain Math     Utilization of visual or multi-
data.
and tables using a given                                           data, and when do we use them? etc.                               Puddles                        *compare/contrast                              sensory materials
Analyzing data displays allows
set of data.                                                       How do we analyze data?                                                                          *Personal connections-SOP
us to interpret and explain data
How do probability and statistics                                 Terra Nova
and make predictions based on
help us to make predictions?
probability and statistics..

BENCHMARK 3.2: Interpret data using the concepts of largest, smallest, most often, and middle.

3.2 a Given a set of                                                                                    DATA AND GRAPHS              Quarterly           McREL      McREL Nonlinguistic          Math Text         Functional level materials             2
numbers, determine the        Graphics are tools used to clarify                                        Determine which values       Assessment           SIOP      representations              Success Maker     Small group
mode                                                               What are the tools used to clarify                                Classroom                                                   Mountain Math     Utilization of visual or multi-
data.                                                                     occur most often                                            *ordering numbers
data, and when do we use them?                                    Evidence                       *listing numbers                               sensory materials
Analyzing data displays allows
How do we analyze data?
us to interpret and explain data
How do probability and statistics
and make predictions based on
help us to make predictions?
probability and statistics..

BENCHMARK 3.3: Generate, analyze, and make predictions based on data obtained from surveys and chance devices.

3.3 a Determine what is                                                                               DATA AND GRAPHS                Quarterly           McREL      McREL Cooperative learning   Math Text         Functional level materials             2
the most likely, least        Graphics are tools used to clarify                                      Define, understand, apply      assessments          SIOP      *games                       Success Maker     Small group
likely, or equally likely                                          What are the tools used to clarify and interpret concepts of      "Is It Fair?"                  *Technology (Math Keys)      Mountain Math     Utilization of visual or multi-
data.
outcome from using a                                               data, and when do we use them? probability (Most likely,          Puddles                                                                       sensory materials
Analyzing data displays allows
chance device (for                                                 How do we analyze data?            least likely & likely)
us to interpret and explain data
example, spinners).                                                How do probability and statistics                                 Terra Nova
and make predictions based on
help us to make predictions?
probability and statistics..

Revised 4-26-2006/jkw                                                                                                                                                                                                                       16
BY TEACHERS FOR TEACHERS                                                                                              2nd Quarter
MATH CURRICULUM GUIDE

Standard 7: Students communicate the reasoning used in problem-solving situations.

BENCHMARK C: Communicate the use of PROBABILITY AND STATISTICS needed to represent and solve problems involving uncertainty.

Enduring Understanding                                                                     Assessment     Key         Suggested Instructional                             Differentiation-             Quarter
District Indicators                                              Essential Questions             Essential Skills                                                                     Resources
Conceptual Vocabulary                                                                       Methods     Strategy            Practice                                   Adaptations/Extensions          Taught

District Indicator: 7c2-                                                                         PROBLEM SOLVING                          McREL     McREL Nonlinguistic             Math Text         Highlighted texts (clue words          2
Choose and apply a                                                                               Understand and solve       Terra Nova     SIOP     representation                  Success Maker     and/or phrases)
strategy to solve                                              In what ways can I communicate    problems related to        Quarterly               *act it out; draw a picture;    Mountain Math     Small group
mathematical and real         A sense of number is necessary   the reasoning used in problem     probability, data, graphs, Assessment              guess and check; find a                           Manipulation of materials in
world problems.               to solve problems and            solving situations?               and tables                                         pattern; partners; charts and                     small steps
communicate the reasoning used   What makes a quality solution?                                                       tables; build a model; choose
in problem solving.               What essential components are                                                       an operation
needed to solve problems?                                                            *Choose an appropriate
strategy

Standard 4: Students use geometric reasoning to gather evidence, build an argument, and make conjectures in one-, two-, and three-dimensional problem solving situations.

BENCHMARK 4.1: Recognize shapes and their relationships (for example, symmetry, congruence) using a variety of materials (for example, pasta, boxes, pattern blocks).

Enduring Understanding                                                                     Assessment     Key         Suggested Instructional                             Differentiation-             Quarter
State Frameworks                                                  Essential Questions             Essential Skills                                                                     Resources
Conceptual Vocabulary                                                                       Methods     Strategy            Practice                                   Adaptations/Extensions          Taught

4.1a Identify figures which                                                                      GEOMETRY                   Quarterly     McREL     McREL Nonlinguistic             Math Text         Functional level materials             2
are congruent                                                                                    Identify congruent figures Assessment     SIOP     representations                 Success Maker     Small group
Classroom               *concrete models                Mountain Math     Utilization of visual or multi-
What is geometry?                                            Evidence                Identifying similarities and                      sensory materials
Geometry builds our world.       How do we use geometry in every                                                      differences
day life?                                                                            *compare/contrast

4.1c Create a figure with                                                                      GEOMETRY                                   McREL     McREL Nonlinguistic             Math Text         Functional level materials             2
at least one line of                                                                           Create a figure with at    Classroom        SIOP     representations                 Success Maker     Small group
symmetry                                                       What is geometry?               least 1 line of symmetry   Evidence                  *build a model                  Mountain Math     Utilization of visual or multi-
Geometry builds our world.       How do we use geometry in every in regular polygons                                  *multiple representations                         sensory materials
day life?

BENCHMARK 4.2: Identify, describe, draw, compare, classify, and build physical models of geometric figures.

4.2b Identify points, lines, Geometry builds our world.        What is geometry?               GEOMETRY                                   McREL     McREL Nonlinguistic             Math Text         Functional level materials             2
and line segments                                              How do we use geometry in every Identify points, lines, and Quarterly       SIOP     representations                 Success Maker     Small group
day life?                       line segments.              Assessment               *concrete models                Mountain Math     Utilization of visual or multi-
Classroom                Identifying similarities and                      sensory materials
Evidence                 differences
*compare/contrast

Revised 4-26-2006/jkw                                                                                                                                                                                                          17
BY TEACHERS FOR TEACHERS                                                                                              2nd Quarter
MATH CURRICULUM GUIDE

Standard 4: Students use geometric reasoning to gather evidence, build an argument, and make conjectures in one-, two-, and three-dimensional problem solving situations.

BENCHMARK 4.1: Recognize shapes and their relationships (for example, symmetry, congruence) using a variety of materials (for example, pasta, boxes, pattern blocks).

Enduring Understanding                                                                     Assessment     Key         Suggested Instructional                             Differentiation-             Quarter
State Frameworks                                                 Essential Questions              Essential Skills                                                                     Resources
Conceptual Vocabulary                                                                       Methods     Strategy            Practice                                   Adaptations/Extensions          Taught

4.2c Identify three-     Geometry builds our world.            What is geometry?               GEOMETRY                                   McREL     McREL Nonlinguistic             Math Text         Functional level materials             2
dimensional figures (for                                       How do we use geometry in every Identify and list the       Terra Nova      SIOP     representations                 Success Maker     Small group
example, cubes, spheres,                                       day life?                       characteristics of 2D       Quarterly                *multiple representations       Mountain Math     Utilization of visual or multi-
cylinders, cones, and                                                                          shapes and basic 3D         Assessment               Identifying similarities and                      sensory materials
pyramids).                                                                                     shapes (cubes, spheres,     "Geometry"               differences
cylinders)                  Exemplar                 *compare/contrast
*Vocabulary-graphic
organizers-SOP

4.2d Identify right angles.                                                                      GEOMETRY                                 McREL                                     Math Text         Functional level materials             2
Identify rays and right                   SIOP                                     Success Maker     Small group
angles.                                                                            Mountain Math     Utilization of visual or multi-
What is geometry?
sensory materials
Geometry builds our world.       How do we use geometry in every
day life?

BENCHMARK 4.3: Relate geometric ideas to measurement and number sense.

4.3a Find the perimeter of                                                                       GEOMETRY                                 McREL     McREL Nonlinguistic             Math Text         Functional level materials             2
a polygon.                                                                                       Find perimeter of a       Terra Nova      SIOP     representations                 Success Maker     Small group
What is geometry?                 polygon                   Quarterly                *concrete models                Mountain Math     Utilization of visual or multi-
Geometry builds our world.       How do we use geometry in every                             Assessment               Homework and practice                             sensory materials
day life?

Standard 7: Students communicate the reasoning used in problem-solving situations.

BENCHMARK D: Communicate the use of GEOMETRIC CONCEPTS needed to model real-world situations and solve appropriate problems.

Enduring Understanding                                                                     Assessment     Key         Suggested Instructional                             Differentiation-             Quarter
District Indicators                                              Essential Questions              Essential Skills                                                                     Resources
Conceptual Vocabulary                                                                       Methods     Strategy            Practice                                   Adaptations/Extensions          Taught

District Indicator: 7d2-                                                                         PROBLEM SOLVING                          McREL     McREL Nonlinguistic             Math Text         Highlighted texts (clue words          2
Explain clearly the                                                                              Understand and solve      Terra Nova      SIOP     representation                  Success Maker     and/or phrases)
strategy used and the                                          In what ways can I communicate    problems related to       Quarterly                *act it out; draw a picture;    Mountain Math     Small group
solution to mathematical      A sense of number is necessary   the reasoning used in problem     geometric concepts        Assessments              guess and check; find a                           Manipulation of materials in
and real-world problems       to solve problems and            solving situations?                                         Exemplars                pattern; partners; charts and                     small steps
through written and/or oral   communicate the reasoning used   What makes a quality solution?                                                       tables; build a model; choose
communication.                in problem solving.               What essential components are                                                       an operation
needed to solve problems?                                                            *Choose an appropriate
strategy

Revised 4-26-2006/jkw                                                                                                                                                                                                          18
BY TEACHERS FOR TEACHERS                                                                                                     2nd Quarter
MATH CURRICULUM GUIDE

Standard 5: Students use a variety of tools and techniques to measure and use measurement in problems and in everyday situations.

BENCHMARK 5.1: Know, use, describe, and estimate measures of length, perimeter, capacity, weight, time, and temperature.

Enduring Understanding                                                                      Assessment        Key        Suggested Instructional                               Differentiation-             Quarter
State Frameworks                                                 Essential Questions           Essential Skills                                                                            Resources
Conceptual Vocabulary                                                                        Methods        Strategy           Practice                                     Adaptations/Extensions          Taught

5.1c Choose the                                                                               MEASUREMENT                                   McREL      McREL Cooperative learning; Math Text              Functional level materials             2
appropriate tool to                                                                           Select correct tools to      Terra Nova        SIOP      Generating and testing      Success Maker          Small group
measure familiar objects                                       Why measure?                   measure length, weight,      Quarterly                   hypotheses;                 Mountain Math          Utilization of visual or multi-
Appropriate tools and units are
in situations that contain                                     In measuring situations what   temp., time                  Assessment                  *Vocabulary-graphic                                sensory materials
needed to measure.
length, weight,                                                tool(s) would you use?                                      "The Puddle                 organizers-SOP                                     Visual demonstrations
Recognize and communicate
temperature, or time.                                          What are the units used to                                  Problem"
measurement relationships.
communicate a measurement?                                  Puddles

BENCHMARK 5.2: Compare and order objects according to measurable attributes (for example, longest to shortest, lightest to heaviest)

5.2a Compare objects                                                                          MEASUREMENT                  Terra Nova       McREL      McRel                 Identifying Math Text        Functional level materials             2
according to the                                                                              Select correct tools to      Quarterly         SIOP      similarities and differences      Success Maker    Small group
measurable attributes of                                       Why measure?                   measure length, weight,      Assessment                                                    Mountain Math    Utilization of visual or multi-
Appropriate tools and units are
length, capacity, weight, or                                   In measuring situations what   temp., time                                                                                                 sensory materials
needed to measure.
temperature                                                    tool(s) would you use?                                                                                                                     Visual demonstrations
Recognize and communicate
What are the units used to
measurement relationships.
communicate a measurement?

BENCHMARK 5.3: Demonstrate the process of measuring and explaining the concepts related to units of measurement.

5.3a Measure the length                                                                       MEASUREMENT                  "Wrist           McREL      McREL Nonlinguistic            Math Text           Functional level materials             2
of objects including the                                                                      Measure objects              Circumference"    SIOP      representations                Success Maker       Small group
sides of rectangles and                                                                       accurately to nearest inch   Exemplar                    *concrete models               Mountain Math       Utilization of visual or multi-
squares to the nearest                                         Why measure?                   and centimeter               Classroom                   Homework and practice                              sensory materials
Appropriate tools and units are
inch and centimeter.                                           In measuring situations what                                evidence                                                                       Visual demonstrations
needed to measure.
tool(s) would you use?
Recognize and communicate
What are the units used to                                  Terra Nova
measurement relationships.
communicate a measurement?                                  Quarterly
Assessment

BENCHMARK 5.5: Select and use appropriate standard and non-standard units of measurement in problem-solving situations.

District Indicator: 5B2-                                                                      MEASUREMENT                                   McREL      McREL Cooperative learning; Math Text              Functional level materials             2
Select appropriate units                                                                      Measure accurately to        Terra Nova        SIOP      Homework and practice       Success Maker          Small group
and tools to measure to                                        Why measure?                   the nearest inch/cm,         Classroom                   *concrete models)           Mountain Math          Utilization of visual or multi-
the degree of accuracy     Appropriate tools and units are                                    lb/oz, degree F/C,           Evidence                                                                       sensory materials
In measuring situations what
required in a particular   needed to measure.                                                 hour/minute                                                                                                 Visual demonstrations
tool(s) would you use?
problem-solving situation. Recognize and communicate           What are the units used to
measurement relationships.
communicate a measurement?

Revised 4-26-2006/jkw                                                                                                                                                                                                              19
BY TEACHERS FOR TEACHERS                                                                                              2nd Quarter
MATH CURRICULUM GUIDE

Standard 7: Students communicate the reasoning used in problem-solving situations.

BENCHMARK E: Communicate the use of APPROPRIATE MEASUREMENT TECHNIQUES needed to solve problems, and determine whether the report the degree of accuracy required.

Enduring Understanding                                                                          Assessment      Key        Suggested Instructional                              Differentiation-            Quarter
District Indicators                                                  Essential Questions              Essential Skills                                                                       Resources
Conceptual Vocabulary                                                                            Methods      Strategy           Practice                                    Adaptations/Extensions         Taught

District Indicator: 7e2-                                                                              PROBLEM SOLVING           Classroom       McREL      McREL Nonlinguistic             Math Text         Highlighted texts (clue words         2
Choose and apply a                                                                                    Understand and solve      Evidence         SIOP      representation                  Success Maker     and/or phrases)
strategy to solve                                                  In what ways can I communicate     problems using            Exemplars                  *act it out; draw a picture;    Mountain Math     Small group
mathematical and real                                                                                 appropriate                                          guess and check; find a                           Manipulation of materials in
A sense of number is necessary      the reasoning used in problem
world problems.                                                                                       measurement tools                                    pattern; partners; charts and                     small steps
to solve problems and               solving situations?
communicate the reasoning used      What makes a quality solution?                                                          tables; build a model; choose
an operation
in problem solving.                  What essential components are
*Choose an appropriate
needed to solve problems?
strategy

Standard 6: Students understand, develop, and use computational skills and techniques, including estimation, mental math, paper and pencil, calculators, and computers in problem-solving situations.

BENCHMARK 6.2: Add and subtract commonly-used fractions and decimals using physical models (for example, 1/3, 3/4, 0.5, 0.75)

Enduring Understanding                                                                          Assessment      Key        Suggested Instructional                              Differentiation-            Quarter
State Frameworks                                                     Essential Questions              Essential Skills                                                                       Resources
Conceptual Vocabulary                                                                            Methods      Strategy           Practice                                    Adaptations/Extensions         Taught

6.2b Using money                                                                                     COMPUTATION                Terra Nova      McREL      McREL Nonlinguistic             Math Text         Time for repeated review/drill        2
notation, add and subtract                                         What strategies are used to solve Adds & subtracts using     Quarterly        SIOP      representation                  Success Maker     Functional level materials
commonly used decimals                                             problems?                         money notation up to       Assessment                 *patterning                     Mountain Math     Visual demonstrations
in which sums and           A sense of number is necessary         How are computation skills and    \$10.00                                                Homework and practice
differences should not     to communicate the reasoning            strategies used daily?
exceed \$10.00.             used in problem solving.                Why be fluent at computation?
Estimation and computation are          How do you use estimation to
vital tools.                            determine whether your solution
is reasonable?

BENCHMARK 6.3: Demonstrate understanding of and proficiency with basic addition, subtraction, multiplication, and division facts without the use of a calculator.

6.3 a Demonstrate                                                                                     COMPUTATION                               McREL      McREL Nonlinguistic             Math Text         Time for repeated review/drill        2
understanding of basic                                                                                Knows basic                  Terra Nova    SIOP      representation                  Success Maker     Functional level materials
multiplication facts of 1's,   Estimation and computation are       What strategies are used to       multiplication facts for     Quarterly               *patterning                     Mountain Math     Visual demonstrations
2's, 3's, 5's, and 10's        vital tools. A sense of number is   solve problems?                    1's, 2's, 3's, 5's, and 10's Assessment              Homework and practice
necessary to communicate the         be fluent at computation?
reasoning used in problem           How are computation skills and
solving.                            strategies used daily?

District Indicator: 6B1-                                                                             COMPUTATION                Classroom       McREL      McREL Nonlinguistic             Math Text         Time for repeated review/drill        2
Create and use                                                     What strategies are used to solve Create and use             Evidence         SIOP      representation                  Success Maker     Functional level materials
multiplication tables                                              problems?                         multiplication tables                                 *patterning                     Mountain Math     Visual demonstrations
Estimation and computation are      How are computation skills and
vital tools. A sense of number is   strategies used daily?
necessary to communicate the        Why be fluent at computation?
reasoning used in problem           How do you use estimation to
is reasonable?

Revised 4-26-2006/jkw                                                                                                                                                                                                               20
BY TEACHERS FOR TEACHERS                                                                                              2nd Quarter
MATH CURRICULUM GUIDE

Standard 6: Students understand, develop, and use computational skills and techniques, including estimation, mental math, paper and pencil, calculators, and computers in problem-solving situations.

BENCHMARK 6.4: Construct, use, and explain procedures to compute and estimate with whole numbers.

Enduring Understanding                                                                        Assessment     Key        Suggested Instructional                                   Differentiation-         Quarter
State Frameworks                                                   Essential Questions               Essential Skills                                                                   Resources
Conceptual Vocabulary                                                                          Methods     Strategy           Practice                                         Adaptations/Extensions      Taught

6.4a Use estimation                                                                                 COMPUTATION               "The Tower    McREL      McREL Generating and testing Math Text              Time for repeated review/drill        2
strategies with whole                                         What strategies are used to solve     Use rounding and          Problem"       SIOP      hypotheses                    Success Maker         Functional level materials
numbers prior to                                              problems?                             estimation of whole       Exemplar                 *guess and check              Mountain Math         Visual demonstrations
performing on operation        A sense of number is necessary How are computation skills and        numbers to make                                    Nonlinguistic representations
(+,-); (for example, front-   to communicate the reasoning    strategies used daily?                predictions before        Terra Nova               *concrete models
end estimation, estimation    used in problem solving.        Why be fluent at computation?         computation               Quarterly
by rounding, friendly         Estimation and computation are How do you use estimation to                                     Assessment
numbers, flexible             vital tools.                    determine whether your solution
rounding, clustering).                                        is reasonable?

Standard 6: Students understand, develop, and use computational skills and techniques, including estimation, mental math, paper and pencil, calculators, and computers in problem-solving situations.

BENCHMARK 6.5: Select and use appropriate methods for computing with whole numbers in problem-solving situations from among mental arithmetic, estimation, paper-and-pencil, calculator and computer methods.

Enduring Understanding                                                                        Assessment     Key        Suggested Instructional                                   Differentiation-         Quarter
State Frameworks                                                   Essential Questions               Essential Skills                                                                   Resources
Conceptual Vocabulary                                                                          Methods     Strategy           Practice                                         Adaptations/Extensions      Taught

6.5 a Given a real world                                                                         COMPUTATION                                McREL      McREL Nonlinguistic          Math Text              Highlighted texts (clue words         2
problem-solving situation,                                     What strategies are used to solve Select and use               Terra Nova     SIOP      representation               Success Maker          and/or phrases)
use addition, subtraction,                                     problems?                         appropriate method to        Quarterly                *draw a picture              Mountain Math          Small group
or multiplication to solve                                                                       solve problems.              Assessment               *Choose an operation                                Manipulation of materials in
How are computation skills and
the problem.                                                                                                                                                                                               small steps
A sense of number is necessary   strategies used daily?
to communicate the reasoning     Why be fluent at computation?
used in problem solving.         How do you use estimation to
is reasonable?

District Indicator: 6C2-                                                                            COMPUTATION               Classroom     McREL      McREL Generating and testing Math Text              Highlighted texts (clue words         2
Use estimation to                                               What strategies are used to solve   Use estimation to         Evidence       SIOP      hypotheses                   Success Maker          and/or phrases)
determine whether the                                           problems?                           determine whether the                              *estimating                  Mountain Math          Small group
results of a problem are      Estimation and computation are How are computation skills and         results of an addition,                            *guess and check                                    Manipulation of materials in
reasonable.                   vital tools. A sense of number is strategies used daily?              subtraction, or                                                                                        small steps
necessary to communicate the      Why be fluent at computation?       multiplication problem
reasoning used in problem         How do you use estimation to        are reasonable
is reasonable?

Revised 4-26-2006/jkw                                                                                                                                                                                                              21
BY TEACHERS FOR TEACHERS                                                                                              2nd Quarter
MATH CURRICULUM GUIDE

Standard 7: Students communicate the reasoning used in problem-solving situations.

BENCHMARK F: Communicate the use of APPROPRIATE COMPUTATIONAL TECHNIQUES needed to solve problems, and determine whether the results are reasonable.

Enduring Understanding                                                                     Assessment     Key        Suggested Instructional                              Differentiation-           Quarter
District Indicators                                           Essential Questions             Essential Skills                                                                      Resources
Conceptual Vocabulary                                                                       Methods     Strategy           Practice                                    Adaptations/Extensions        Taught

District Indicator: 7f 2-                                                                     PROBLEM SOLVING                          McREL      McREL Nonlinguistic             Math Text         Highlighted texts (clue words        2
Evaluate the                                                                                  Understand and solve       Terra Nova     SIOP      representation                  Success Maker     and/or phrases)
solutions/arguments of                                                                        problems using             Quarterly                *act it out; draw a picture;    Mountain Math     Small group
mathematical and real-                                       In what ways can I communicate                              Assessment                                                                 Manipulation of materials in
appropriate                                         guess and check; find a
world problems for          A sense of number is necessary   the reasoning used in problem    computational techniques   Exemplars                pattern; partners; charts and                     small steps
reasonableness.             to solve problems and            solving situations?                                                                  tables; build a model; choose
communicate the reasoning used   What makes a quality solution?                                                       an operation
in problem solving.               What essential components are                                                       *Choose an appropriate
needed to solve problems?                                                            strategy

Revised 4-26-2006/jkw                                                                                                                                                                                                      22
BY TEACHERS FOR TEACHERS                                                                                                                3rd Quarter
MATH CURRICULUM GUIDE

Standard 1: Students utilize language, symbolism, and technology to develop number sense and to communicate those mathematical ideas.

BENCHMARK 1.1: Demonstrate meanings for whole numbers, and commonly-used fractions decimals (for example, 1/3, 3/4, 0.5, 0.75) and represent equivalent forms of the same number through the use of physical models, drawings, calculators, and
computers.

Enduring Understanding                                                                 Assessment      Key         Suggested Instructional                                    Differentiation-                 Quarter
State Frameworks                                                 Essential Questions            Essential Skills                                                                     Resources
Conceptual Vocabulary                                                                   Methods      Strategy            Practice                                          Adaptations/Extensions              Taught

1.1c Using concrete                                                                              NUMBERS AND                              McREL     McREL Nonlinguistic            Math Text                 Visual demonstration                     3
materials or pictures identify                                                                   NUMBER                   Terra Nova       SIOP     representation                 Success Maker             Small group
What is number sense, and how
different combinations of                                                                        RELATIONSHIPS            Quarterly                 *multiple representations      Math Exemplars            Utilization of visual or multi-
is it used in problem solving?
coins up to \$0.99.                                                                               Money combinations       Assessment                *Personal connections-SIOP     Mountain Math             sensory materials
How many different ways can
Mathematics is dependent on                                     and make change up to    Classroom
you write this number ____?
place value.                                                    \$5.00                    Evidence
Why do numbers have
A sense of number is necessary
designated places?
to communicate the reasoning
What mathematics vocabulary
used in problem solving.
do you need to communicate
mathematical ideas?

BENCHMARK 1.2: Reading and writing whole numbers and knowing place-value concepts and numeration through their relationships to counting, ordering, and grouping.

1.2a Read, write, and order                                                                      NUMBERS AND              Classroom       McREL     McREL Nonlinguistic            Math Text                 Visual demonstration                     3
numerals from zero to 9,999.                                                                     NUMBER                   Evidence         SIOP     representation                 Success Maker             Small group
What is number sense, and how                                                       *patterning                    Math Exemplars            Utilization of visual or multi-
RELATIONSHIPS
is it used in problem solving?                                                      *charts, tables, and lists     Mountain Math             sensory materials
How many different ways can
Mathematics is dependent on                                     orders numbers to
you write this number ____?
place value.                                                    1,000,000
Why do numbers have
A sense of number is necessary
designated places?
to communicate the reasoning
What mathematics vocabulary
used in problem solving.
do you need to communicate
mathematical ideas?

1.2c Identify place value                                                                      NUMBERS AND                Classroom       McREL     McREL Nonlinguistic            Math Text                 Visual demonstration                     3
through ten-thousands (I.e.                                                                    NUMBER                     Evidence         SIOP     representation                 Success Maker             Small group
86,243, "6" is in the                                           What is number sense, and how                                                       *patterning                    Math Exemplars            Utilization of visual or multi-
RELATIONSHIPS
thousands place).                                               is it used in problem solving?                                                      *ordering numbers              Mountain Math             sensory materials
Place value- Identify to
How many different ways can
Mathematics is dependent on                                   1,000,000
you write this number ____?
place value.
Why do numbers have
A sense of number is necessary
designated places?
to communicate the reasoning
What mathematics vocabulary
used in problem solving.
do you need to communicate
mathematical ideas?

BENCHMARK 1.5: Using number sense to estimate and justify the reasonableness of solutions to problems involving whole numbers and commonly-used fractions and decimals (for example, 1/3, 3/4, 0.5, 0.75)
1.5a Use estimation                                                                              NUMBERS AND                              McREL     McREL Generating and testing   Math Text                 Visual demonstration                     3
strategies to determine the                                                                      NUMBER                   Terra Nova       SIOP     hypotheses                     Success Maker             Small group
What is number sense, and how
reasonableness of solutions                                                                      RELATIONSHIPS            Quarterly                 *guess and check               Math Exemplars            Utilization of visual or multi-
is it used in problem solving?
to problems                                                                                      Use reasonable           Assessment                Homework and practice          Mountain Math             sensory materials
How many different ways can
Mathematics is dependent on                                     estimation to solve      Classroom
you write this number ____?
place value.                                                    problems                 Evidence
Why do numbers have
A sense of number is necessary
designated places?
to communicate the reasoning
What mathematics vocabulary
used in problem solving.
do you need to communicate
mathematical ideas?

Revised 4-26-2006/jkw                                                                                                                                                                                                                                   23
BY TEACHERS FOR TEACHERS                                                                                                                  3rd Quarter
MATH CURRICULUM GUIDE

Standard 1: Students utilize language, symbolism, and technology to develop number sense and to communicate those mathematical ideas.

BENCHMARK 1.5: Using number sense to estimate and justify the reasonableness of solutions to problems involving whole numbers and commonly-used fractions and decimals (for example, 1/3, 3/4, 0.5, 0.75)

Enduring Understanding                                                                  Assessment        Key         Suggested Instructional                                   Differentiation-                 Quarter
State Frameworks                                              Essential Questions            Essential Skills                                                                        Resources
Conceptual Vocabulary                                                                    Methods        Strategy            Practice                                         Adaptations/Extensions              Taught

District Indicator: ID1                                                                       NUMBERS AND                                 McREL     McREL Generating and testing    Math Text               Visual demonstration                     3
Develop a process for                                        What is number sense, and how    NUMBER                    Classroom          SIOP     hypotheses                      Success Maker           Small group
estimating quantities which                                  is it used in problem solving?   RELATIONSHIPS             Evidence                    *guess and check                Math Exemplars          Utilization of visual or multi-
includes testing a previous                                  How many different ways can      Develop a process for                                 Nonlinguistic representation    Mountain Math           sensory materials
Mathematics is dependent on
estimation and revising the                                  you write this number ____?      estimation and revision                               *charts
place value.
estimation.                                                  Why do numbers have              of that estimate
A sense of number is necessary
designated places?
to communicate the reasoning
What mathematics vocabulary
used in problem solving.
do you need to communicate
mathematical ideas?

Standard 7: Students communicate the reasoning used in problem-solving situations.

BENCHMARK A: Communicate the use of NUMBER SENSE, INCLUDING ESTIMATIONS AND MENTAL MATH , needed to solve problems, and determine the reasonableness of the solution.

Quarter
Enduring Understanding                                                                  Assessment        Key         Suggested Instructional                                   Differentiation-                 Taught
State Frameworks                                              Essential Questions            Essential Skills                                                                        Resources
Conceptual Vocabulary                                                                    Methods        Strategy            Practice                                         Adaptations/Extensions

District Indicator: 7A3-                                                                    PROBLEM SOLVING                               McREL     McREL Nonlinguistic             Math Text               Highlighted texts (clue words            3
Evaluate the                                                 What is number sense, and how Understand and solve         Terra Nova         SIOP     representation                  Success Maker           and/or phrases)
solutions/arguments of                                       is it used in problem solving? problems using mental       Quarterly                   *act it out; draw a picture;    Math Exemplars          Small group
mathematical and real-world                                  How many different ways can    math and estimation.        Assessment                  guess and check; find a         Mountain Math           Manipulation of materials in
Mathematics is dependent on
problems for                                                 you write this number ____?                                Exemplars                   pattern; partners; charts and                           small steps
place value.
reasonableness.                                              Why do numbers have                                        Classroom                   tables; build a model; choose
A sense of number is necessary
designated places?                                         Evidence                    an operation
to communicate the reasoning
What mathematics vocabulary                                                            *Choose an appropriate
used in problem solving.
do you need to communicate                                                             strategy
mathematical ideas?

Revised 4-26-2006/jkw                                                                                                                                                                                                                                  24
BY TEACHERS FOR TEACHERS                                                                                                         3rd Quarter
MATH CURRICULUM GUIDE

Standard 2: Students apply algebraic and/or other mathematical methods to understand and explore models, data, graphs, patterns, functions, and spatial relationships.

BENCHMARK 2.3: Recognize when a pattern exists and using that information to solve a problem.

Quarter
Enduring Understanding                                                                Assessment      Key         Suggested Instructional                             Differentiation-                 Taught
State Frameworks                                             Essential Questions           Essential Skills                                                                     Resources
Conceptual Vocabulary                                                                  Methods      Strategy            Practice                                   Adaptations/Extensions

2.3a Identify a rule using                                                                  PATTERNS                                 McREL     McREL Nonlinguistic             Math Text         Visual demonstration                     3
addition or subtraction                                                                     Identify, describe, and   Terra Nova      SIOP     representations                 Success Maker     Small group
patterns and solve a new                                                                    extend, increasing and Quarterly                   *patterning                     Math Exemplars    Utilization of visual or multi-
What is a pattern?
problem using the rule.      Recognizing patterns helps us                                  decreasing, patterns      Assessment               *draw a picture                 Mountain Math     sensory materials
How do we find patterns?
make sense of our world.                                       (What's my rule (+, -, x)                          *charts and tables
What can patterns reveal?
)

Standard 7: Students communicate the reasoning used in problem-solving situations.

BENCHMARK B: Communicate the use of PATTERNS AND FUNCTIONS needed to model real-world situations and solve appropriate problems.

Quarter
Enduring Understanding                                                                Assessment      Key         Suggested Instructional                             Differentiation-                 Taught
State Frameworks                                             Essential Questions           Essential Skills                                                                     Resources
Conceptual Vocabulary                                                                  Methods      Strategy            Practice                                   Adaptations/Extensions

District Indicator: 7b 3-                                                                   PROBLEM SOLVING                          McREL     McREL Nonlinguistic             Math Text         Highlighted texts (clue words            3
Evaluate the                                                                                Understand and solve    Terra Nova        SIOP     representation                  Success Maker     and/or phrases)
solutions/arguments of                                                                      problems using          Quarterly                  *act it out; draw a picture;    Math Exemplars    Small group
mathematical and real-world                                  In what ways can I communicate patterning              Assessment                 guess and check; find a         Mountain Math     Manipulation of materials in
problems for                                                 the reasoning used in problem                          Exemplars                  pattern; partners; charts and                     small steps
A sense of number is
reasonableness.                                              solving situations?                                    Classroom                  tables; build a model; choose
necessary to solve problems
What makes for a quality                               Evidence                   an operation
and communicate the reasoning
solution?                                                                         *Choose an appropriate
used in problem solving.
What essential components are                                                     strategy
needed to solve problems?

Revised 4-26-2006/jkw                                                                                                                                                                                                                       25
BY TEACHERS FOR TEACHERS                                                                                                            3rd Quarter
MATH CURRICULUM GUIDE

Standard 3: Students use mathematical strategies, data collection and analysis, statistics, and probability in everyday situations.

BENCHMARK 3.2: Interpret data using the concepts of largest, smallest, most often, and middle.

Quarter
Enduring Understanding                                                                             Assessment     Key        Suggested Instructional                              Differentiation-                 Taught
State Frameworks                                                   Essential Questions                Essential Skills                                                                        Resources
Conceptual Vocabulary                                                                               Methods     Strategy           Practice                                    Adaptations/Extensions

3.2a Given a set of numbers,                                                                         DATA AND GRAPHS                Quarterly     McREL      McREL Nonlinguistic             Math Text         Visual demonstration                     3
determine the mode.                                                                                  Determine mode and             Assessment     SIOP      representation                  Success Maker     Small group
Graphics are tools used to         What are the tools used to clarify median given a set of          Classroom                *ordering numbers               Math Exemplars    Utilization of visual or multi-
clarify data.                      data, and when do we use           numbers                        Evidence                                                 Mountain Math     sensory materials
Analyzing data displays allows     them?
us to interpret and explain data   How do we analyze data?
and make predictions based on      How do probability and statistics
probability and statistics..       help us to make predictions?

BENCHMARK 3.4: Solve problems using various strategies for making combinations (for example, determining the number of different outfits that can be made using two blouses).
3.4a Given pictures,                                                                                   DATA AND GRAPHICS                          McREL      McREL Nonlinguistic             Math Text         Visual demonstration                     3
determine all the possible                                                                             Finding possible  Classroom                 SIOP      representation                  Success Maker     Small group
combinations of matching a                                                                             combinations      Evidence                            *draw a picture                 Math Exemplars    Utilization of visual or multi-
Graphics are tools used to         What are the tools used to clarify
set containing three                                                                                                                                         *concrete models                Mountain Math     sensory materials
clarify data.                      data, and when do we use
elements.                                                                                                                                                    *act it out
Analyzing data displays allows     them?
Generating and testing
us to interpret and explain data   How do we analyze data?
hypotheses *guess and check
and make predictions based on      How do probability and statistics
probability and statistics..       help us to make predictions?

Standard 7: Students communicate the reasoning used in problem-solving situations.

BENCHMARK C: Communicate the use of PROBABILITY AND STATISTICS needed to represent and solve problems involving uncertainty.

Quarter
Enduring Understanding                                                                             Assessment     Key        Suggested Instructional                              Differentiation-                 Taught
State Frameworks                                                   Essential Questions                Essential Skills                                                                        Resources
Conceptual Vocabulary                                                                               Methods     Strategy           Practice                                    Adaptations/Extensions

District Indicator: 7c 3-                                                                              PROBLEM SOLVING                            McREL      McREL Nonlinguistic             Math Text         Highlighted texts (clue words            3
Evaluate the                                                                                           Understand and solve         Terra Nova     SIOP      representation                  Success Maker     and/or phrases)
solutions/arguments of                                                                                 problems related to          Quarterly                *act it out; draw a picture;    Math Exemplars    Small group
mathematical and real-world                                        In what ways can I                  probability, data, graphs,   Assessment               guess and check; find a         Mountain Math     Manipulation of materials in
problems for                                                      communicate the reasoning            and tables                   Exemplars                pattern; partners; charts and                     small steps
reasonableness.                 A sense of number is              used in problem solving                                           Classroom                tables; build a model; choose
necessary to solve problems        situations?                                                       Evidence                 an operation
and communicate the reasoning      What makes for a quality                                                                   *Choose an appropriate
used in problem solving.           solution?                                                                                  strategy
What essential components are
needed to solve problems?

Revised 4-26-2006/jkw                                                                                                                                                                                                                                     26
BY TEACHERS FOR TEACHERS                                                                                                     3rd Quarter
MATH CURRICULUM GUIDE

Standard 4: Students use geometric reasoning to gather evidence, build an argument, and make conjectures in one-, two-, and three-dimensional problem solving situations.

BENCHMARK 4.2: Identify, describe, draw, compare, classify, and build physical models of geometric figures.

Quarter
Enduring Understanding                                                                 Assessment     Key         Suggested Instructional                             Differentiation-                 Taught
State Frameworks                                               Essential Questions            Essential Skills                                                                  Resources
Conceptual Vocabulary                                                                   Methods     Strategy            Practice                                   Adaptations/Extensions

4.2 c Identify three-                                                                          GEOMETRY                             McREL      McREL Nonlinguistic             Math Text         Visual demonstration                     3
dimensional figures (for                                                                       Identify 3-D shapes    Terra Nova     SIOP      representation                  Success Maker     Small group
example, cubes, spheres,                                                                       Review Quarter 1 and   Quarterly                *concrete models                Math Exemplars    Utilization of visual or multi-
cylinders, cones, and                                                                          Quarter 2 e-skills     Assessment               Identifying similarities and    Mountain Math     sensory materials
pyramids).                                                    What is geometry?                                                                differences
Geometry builds our world.       How do we use geometry in                                                        *compare/contrast
every day life?                                                                  *Vocabulary-graphic
organizers-SIOP

Standard 7: Students communicate the reasoning used in problem-solving situations.

BENCHMARK D: Communicate the use of GEOMETRIC CONCEPTS needed to model real-world situations and solve appropriate problems.

Enduring Understanding                                                                 Assessment     Key         Suggested Instructional                             Differentiation-                 Quarter
State Frameworks                                               Essential Questions            Essential Skills                                                                  Resources
Conceptual Vocabulary                                                                   Methods     Strategy            Practice                                   Adaptations/Extensions              Taught

District Indicator: 7d 3-                                                                      PROBLEM SOLVING                      McREL      McREL Nonlinguistic             Math Text         Highlighted texts (clue words            3
Evaluate the                                                                                   Understand and solve   Terra Nova     SIOP      representation                  Success Maker     and/or phrases)
solutions/arguments of                                         In what ways can I              problems related to    Quarterly                *act it out; draw a picture;    Math Exemplars    Small group
mathematical and real-world                                   communicate the reasoning        geometric concepts     Assessment               guess and check; find a         Mountain Math     Manipulation of materials in
problems for                 A sense of number is             used in problem solving                                 Exemplars                pattern; partners; charts and                     small steps
reasonableness.             necessary to solve problems       situations?                                             Classroom                tables; build a model; choose
and communicate the reasoning     What makes for a quality                                Evidence                 an operation
used in problem solving.          solution?                                                                        *Choose an appropriate
What essential components are                                                    strategy
needed to solve problems?

Revised 4-26-2006/jkw                                                                                                                                                                                                                       27
BY TEACHERS FOR TEACHERS                                                                                                       3rd Quarter
MATH CURRICULUM GUIDE

Standard 5: Students use a variety of tools and techniques to measure and use measurement in problems and in everyday situations.

BENCHMARK 5.1: Know, use, describe, and estimate measures of length, perimeter, capacity, weight, time, and temperature.

Enduring Understanding                                                                  Assessment     Key        Suggested Instructional                             Differentiation-                 Quarter
State Frameworks                                                 Essential Questions           Essential Skills                                                                   Resources
Conceptual Vocabulary                                                                    Methods     Strategy           Practice                                   Adaptations/Extensions              Taught

5.1b Read and interpret                                                                         MEASUREMENT                            McREL      McREL Cooperative learning;    Math Text         Visual demonstration                     3
pictorial representations of                                                                    Read/interpret           Terra Nova     SIOP      Identifying similarities and   Success Maker     Small group
measurements of length,                                          Why measure?                   representations of       Quarterly                differences ;                  Math Exemplars    Utilization of visual or multi-
weight, temperature, and       Appropriate tools and units are                                  length, weight,          Assessment               *compare/contrast              Mountain Math     sensory materials
In measuring situations what
capacity                       needed to measure.                                               temperature                                       *Vocabulary-graphic
tool(s) would you use?
Recognize and communicate                                                                                          organizers-SIOP
What are the units used to
measurement relationships.
communicate a measurement?

District Indicator: 5A2-                                                                        MEASUREMENT            Classroom       McREL      McREL Nonlinguistic            Math Text         Visual demonstration                     3
Determine elapsed time                                                                          Determine elapsed time Evidence         SIOP      representation                 Success Maker     Small group
Why measure?                                                                     *concrete model                Math Exemplars    Utilization of visual or multi-
Appropriate tools and units are                                                                                    Homework and practice          Mountain Math     sensory materials
In measuring situations what
needed to measure.
tool(s) would you use?
Recognize and communicate
What are the units used to
measurement relationships.
communicate a measurement?

District Indicator: 5C1- Read                                                                   MEASUREMENT                            McREL      McREL Nonlinguistic            Math Text         Visual demonstration                     3
and interpret various scales                                                                    Read and interpret       Terra Nova     SIOP      representation                 Success Maker     Small group
including those based on                                         Why measure?                   number lines, graphs,    Quarterly                *concrete models               Math Exemplars    Utilization of visual or multi-
Appropriate tools and units are
number lines, graphs, and                                        In measuring situations what   and maps                 Assessment               *charts and tables             Mountain Math     sensory materials
needed to measure.
maps.                                                            tool(s) would you use?                                  Classroom                *patterns
Recognize and communicate
What are the units used to                              Evidence
measurement relationships.
communicate a measurement?

District Indicator: 5D2-                                                                        MEASUREMENT              Classroom     McREL      McREL Nonlinguistic            Math Text         Visual demonstration                     3
Measure distance between                                                                        Measure distance         Evidence       SIOP      representation                 Success Maker     Small group
locations using map scale                                                                       between locations on a                            *concrete models               Math Exemplars    Utilization of visual or multi-
Why measure?
and create simple scale        Appropriate tools and units are                                  map                                               Cooperative learning           Mountain Math     sensory materials
In measuring situations what
drawings.                      needed to measure.
tool(s) would you use?
Recognize and communicate
What are the units used to
measurement relationships.
communicate a measurement?

Revised 4-26-2006/jkw                                                                                                                                                                                                                         28
BY TEACHERS FOR TEACHERS                                                                                                            3rd Quarter
MATH CURRICULUM GUIDE

Standard 7: Students communicate the reasoning used in problem-solving situations.

BENCHMARK E: Communicate the use of APPROPRIATE MEASUREMENT TECHNIQUES needed to solve problems, and determine whether the report the degree of accuracy required.

Enduring Understanding                                                                      Assessment      Key        Suggested Instructional                              Differentiation-                 Quarter
State Frameworks                                                     Essential Questions             Essential Skills                                                                        Resources
Conceptual Vocabulary                                                                        Methods      Strategy           Practice                                    Adaptations/Extensions              Taught

District Indicator: 7e3-                                                                              PROBLEM SOLVING                            McREL      McREL Nonlinguistic             Math Text         Highlighted texts (clue words            3
Evaluate the                                                                                          Understand and solve      Terra Nova        SIOP      representation                  Success Maker     and/or phrases)
solutions/arguments of                                               In what ways can I               problems using            Quarterly                   *act it out; draw a picture;    Math Exemplars    Small group
mathematical and real-world                                         communicate the reasoning         appropriate               Assessment                  guess and check; find a         Mountain Math     Manipulation of materials in
problems for                 A sense of number is                   used in problem solving           measurement tools         Exemplars                   pattern; partners; charts and                     small steps
reasonableness.             necessary to solve problems             situations?                                                 Classroom                   tables; build a model; choose
and communicate the reasoning           What makes for a quality                                    Evidence                    an operation
used in problem solving.                solution?                                                                               *Choose an appropriate
What essential components are                                                           strategy
needed to solve problems?

Standard 6: Students understand, develop, and use computational skills and techniques, including estimation, mental math, paper and pencil, calculators, and computers in problem-solving situations.

BENCHMARK 6.2: Adding and subtracting commonly-used fractions and decimals using physical models (for example, 1/3, 3/4, 0.5, 0.75)

Enduring Understanding                                                                      Assessment      Key        Suggested Instructional                              Differentiation-                 Quarter
State Frameworks                                                     Essential Questions             Essential Skills                                                                        Resources
Conceptual Vocabulary                                                                        Methods      Strategy           Practice                                    Adaptations/Extensions              Taught

6.2 a Using pictures,                                                                               COMPUTATION              Classroom           McREL      McREL Nonlinguistic             Math Text         Visual demonstration                     3
demonstrate addition and                                                                            Addition/subtraction of Evidence              SIOP      representation                  Success Maker     Small group
subtraction of proper                                               What strategies are used to     common fractions using                                  *concrete models                Math Exemplars    Utilization of visual or multi-
fractions with common                                               solve problems?                 pictures (denominator of                                *draw a picture                 Mountain Math     sensory materials
denominators                         Estimation and computation are How are computation skills and 4 of less)
vital tools.                    strategies used daily?
A sense of number is necessary Why be fluent at computation?
to communicate the reasoning    How do you use estimation to
used in problem solving.        determine whether your solution
is reasonable?

BENCHMARK 6.3: Demonstrating understanding of and proficiency with basic addition, subtraction, multiplication, and division facts without the use of a calculator.

6.3 a Demonstrate                                                                                     COMPUTATION                                McREL      McREL Nonlinguistic             Math Text         Visual demonstration                     3
understanding of basic                                                                                Knows basic                   Terra Nova    SIOP      representation                  Success Maker     Small group
multiplication facts of 1's, 2's,                                   What strategies are used to       multiplication facts of       Quarterly               *patterns                       Math Exemplars    Utilization of visual or multi-
3's, 5's, and 10's                                                  solve problems?                   1's, 2's, 3's, 4's, 5's, 9's, Assessment              Homework and practice           Mountain Math     sensory materials
Estimation and computation are How are computation skills and    and 10's                                                                                                Time for repeated review/drill
vital tools.                    strategies used daily?
A sense of number is necessary Why be fluent at computation?
to communicate the reasoning    How do you use estimation to
used in problem solving.        determine whether your solution
is reasonable?

Revised 4-26-2006/jkw                                                                                                                                                                                                                                    29
BY TEACHERS FOR TEACHERS                                                                                                      3rd Quarter
MATH CURRICULUM GUIDE

Standard 6: Students understand, develop, and use computational skills and techniques, including estimation, mental math, paper and pencil, calculators, and computers in problem-solving situations.

BENCHMARK 6.4: Construct, use, and explain procedures to compute and estimate with whole numbers.

Enduring Understanding                                                                 Assessment     Key        Suggested Instructional                                 Differentiation-             Quarter
State Frameworks                                                 Essential Questions            Essential Skills                                                                 Resources
Conceptual Vocabulary                                                                   Methods     Strategy           Practice                                       Adaptations/Extensions          Taught

6.4 b Demonstrate three                                                                           COMPUTATION                           McREL      McREL Nonlinguistic          Math Text               Visual demonstration                 3
basic operations of whole                                                                         Use 3 basic operations Terra Nova      SIOP      representations              Success Maker           Small group
What strategies are used to
numbers (for example,                                                                             to compute using whole Quarterly                 *multiple representations    Math Exemplars          Utilization of visual or multi-
solve problems?
addition and subtraction of                                                                       numbers (+, -, x)        Assessment              Homework and practice        Mountain Math           sensory materials
Estimation and computation are How are computation skills and
three digit numbers, and                                                                          Subtract 4 digit numbers                                                                              Time for repeated review/drill
vital tools.                   strategies used daily?
multiplication of multiples of                                                                    with regrouping
A sense of number is necessary Why be fluent at computation?
ten by 1, 2, 3, and 5)                                                                            Add 4 digit numbers
to communicate the reasoning   How do you use estimation to
with regrouping
used in problem solving.       determine whether your solution
is reasonable?

District Indicator: 6B3-                                                                        COMPUTATION              Classroom      McREL      McREL Cooperative learning   Math Text               Visual demonstration                 3
Analyze and create                                              What strategies are used to     Create algorithms for    Evidence        SIOP      *Vocabulary-graphic          Success Maker           Small group
algorithms for addition,                                        solve problems?                 addition, subtraction,                             organizers-SIOP              Math Exemplars          Utilization of visual or multi-
subtraction, multiplication,     Estimation and computation are How are computation skills and and multiplication                                  *Choose an operation         Mountain Math           sensory materials
and division of whole            vital tools.                   strategies used daily?                                                                                                                  Time for repeated review/drill
numbers.                         A sense of number is necessary Why be fluent at computation?
to communicate the reasoning   How do you use estimation to
used in problem solving.       determine whether your solution
is reasonable?

Revised 4-26-2006/jkw                                                                                                                                                                                                                          30
BY TEACHERS FOR TEACHERS                                                                                                           3rd Quarter
MATH CURRICULUM GUIDE

Standard 6: Students understand, develop, and use computational skills and techniques, including estimation, mental math, paper and pencil, calculators, and computers in problem-solving situations.

BENCHMARK 6.5: Select and use appropriate methods for computing with whole numbers in problem-solving situations from among mental arithmetic, estimation, paper-and-pencil, calculator and computer methods.

Enduring Understanding                                                                   Assessment     Key        Suggested Instructional                                      Differentiation-           Quarter
State Frameworks                                                Essential Questions            Essential Skills                                                                      Resources
Conceptual Vocabulary                                                                     Methods     Strategy           Practice                                            Adaptations/Extensions        Taught

6.5 a Given a real world                                                                         COMPUTATION                             McREL      McREL Cooperative learning      Math Text               Visual demonstration                 3
problem-solving situation,                                     What strategies are used to       Select and use            Terra Nova     SIOP      *Vocabulary-graphic             Success Maker           Small group
use addition, subtraction, or                                  solve problems?                   appropriate method to     Quarterly                organizers-SIOP                 Math Exemplars          Utilization of visual or multi-
multiplication to solve the     Estimation and computation are How are computation skills and    solve problems(+,-, x).   Assessment               *Choose an operation            Mountain Math           sensory materials
problem.                        vital tools.                   strategies used daily?            Determine from real-      Classroom                                                                        Time for repeated review/drill
A sense of number is necessary Why be fluent at computation?     world problems, whether   evidence
to communicate the reasoning   How do you use estimation to      an estimated or exact
used in problem solving.       determine whether your solution   sum, difference, or
is reasonable?                    product is acceptable.

Standard 7: Students communicate the reasoning used in problem-solving situations.

BENCHMARK F: Communicate the use of APPROPRIATE COMPUTATIONAL TECHNIQUES needed to solve problems, and determine whether the results are reasonable.

Enduring Understanding                                                                   Assessment     Key        Suggested Instructional                                      Differentiation-           Quarter
State Frameworks                                                Essential Questions            Essential Skills                                                                      Resources
Conceptual Vocabulary                                                                     Methods     Strategy           Practice                                            Adaptations/Extensions        Taught

District Indicator: 7f 3-                                                                        PROBLEM SOLVING                         McREL      McREL Nonlinguistic             Math Text               Highlighted texts (clue words        3
Evaluate the                                                                                     Understand and solve      Terra Nova     SIOP      representation                  Success Maker           and/or phrases)
solutions/arguments of                                          In what ways can I               problems using            Quarterly                *act it out; draw a picture;    Math Exemplars          Small group
mathematical and real-world                                    communicate the reasoning         appropriate               Assessment               guess and check; find a         Mountain Math           Manipulation of materials in
problems for                 A sense of number is              used in problem solving           computational             Classroom                pattern; partners; charts and                           small steps
reasonableness.             necessary to solve problems        situations?                       techniques                Evidence                 tables; build a model; choose
and communicate the reasoning      What makes for a quality                                    Exemplars                an operation
used in problem solving.           solution?                                                                            *Choose an appropriate
What essential components are                                                        strategy
needed to solve problems?

Revised 4-26-2006/jkw                                                                                                                                                                                                                              31
BY TEACHERS FOR TEACHERS                                                                                                  4th Quarter
MATH CURRICULUM GUIDE

Standard 1: Students utilize language, symbolism, and technology to develop number sense and to communicate those mathematical ideas.

BENCHMARK 1.2: Read and write whole numbers and know place-value concepts and numeration through their relationships to counting, ordering, and grouping.

Enduring Understanding                                                                    Assessment         Key         Suggested Instructional                             Differentiation-             Quarter
State Frameworks                                                Essential Questions             Essential Skills                                                                           Resources
Conceptual Vocabulary                                                                      Methods         Strategy             Practice                                  Adaptations/Extensions          Taught

1.2a Read, write and order                                                                     NUMBERS AND NUMBER          Classroom           McREL      McREL Nonlinguistic           Math Text          Use colored chalk for                 4
numerals from zero to 9, 999                                    What is number sense, and how RELATIONSHIPS                evidence             SIOP      representation                Success Maker      emphasis Use visual aids and
is it used in problem solving? Reads, writes, & orders                                    *patterning                   Math Exemplars     media        Time for repeated
How many different ways can    numbers to 1,000,000                                       *charts, tables, and lists    Mountain Math      review/drill
Mathematics is dependent on
you write this number ____?
place value.
Why do numbers have
A sense of number is necessary
designated places?
to communicate the reasoning
What mathematics vocabulary
used in problem solving.
do you need to communicate
mathematical ideas?

1.2c Identify place value                                                                      NUMBERS AND NUMBER          Classroom           McREL      McREL Nonlinguistic           Math Text          Use colored chalk for                 4
through ten-thousands (i.e. in                                  What is number sense, and how RELATIONSHIPS                evidence             SIOP      representation                Success Maker      emphasis Use visual aids and
86,243, "6" is in the                                           is it used in problem solving? Place value-identify to                                    *patterning                   Math Exemplars     media        Time for repeated
thousands place).                                               How many different ways can    1,000,000                                                  *ordering numbers             Mountain Math      review/drill
Mathematics is dependent on
you write this number ____?
place value.
Why do numbers have
A sense of number is necessary
designated places?
to communicate the reasoning
What mathematics vocabulary
used in problem solving.
do you need to communicate
mathematical ideas?

1.2e Compare whole                                                                             NUMBERS AND NUMBER          Classroom           McREL      McREL Nonlinguistic           Math Text          Use colored chalk for                 4
numbers as greater than,                                        What is number sense, and how RELATIONSHIPS                evidence             SIOP      representation                Success Maker      emphasis Use visual aids and
less than, or equal to on                                       is it used in problem solving? Compares numbers to                                        *patterning                   Math Exemplars     media        Time for repeated
another using words or                                          How many different ways can    1,000,000                                                  *ordering numbers             Mountain Math      review/drill
symbols.                         Mathematics is dependent on
you write this number ____?
place value.
Why do numbers have
A sense of number is necessary
designated places?
to communicate the reasoning
What mathematics vocabulary
used in problem solving.
do you need to communicate
mathematical ideas?

BENCHMARK 1.5: Use number sense to estimate and justify the reasonableness of solutions to problems involving whole numbers and commonly-used fractions and decimals (for example, 1/3, 3/4, 0.5, 0.75)
1.5a Use estimation                                                                            NUMBERS AND NUMBER Classroom                    McREL      McREL Generating and          Math Text          Use colored chalk for                 4
strategies to determine the                                     What is number sense, and how RELATIONSHIPS                 Evidence            SIOP      testing hypotheses            Success Maker      emphasis Use visual aids and
reasonableness of solutions                                     is it used in problem solving? Use reasonable estimation to                               *guess and check              Math Exemplars     media        Time for repeated
to problems                                                     How many different ways can    solve problems                                                                           Mountain Math      review/drill
Mathematics is dependent on
you write this number ____?
place value.
Why do numbers have
A sense of number is necessary
designated places?
to communicate the reasoning
What mathematics vocabulary
used in problem solving.
do you need to communicate
mathematical ideas?

Revised4-26-2006/jkw                                                                                                                                                                                                               32
BY TEACHERS FOR TEACHERS                                                                                                    4th Quarter
MATH CURRICULUM GUIDE

Standard 7: Students communicate the reasoning used in problem-solving situations.

BENCHMARK A: Communicate the use of NUMBER SENSE, INCLUDING ESTIMATIONS AND MENTAL MATH , needed to solve problems, and determine the reasonableness of the solution.

Enduring Understanding                                                                      Assessment          Key        Suggested Instructional                               Differentiation-              Quarter
State Frameworks                                              Essential Questions               Essential Skills                                                                            Resources
Conceptual Vocabulary                                                                        Methods          Strategy            Practice                                    Adaptations/Extensions           Taught

District Indicator: 7A4-                                                                      PROBLEM SOLVING                                 McREL      McREL Nonlinguistic             Math Text          Highlighted texts (clue words          4
Explain clearly the strategy                                                                  Understand and solve       Terra Nova            SIOP      representation                  Success Maker      and/or phrases)
used and the solution to                                      In what ways can I              problems using mental math Exemplars                       *act it out; draw a picture;    Math Exemplars     Small group
mathematical and real-world A sense of number is necessary   communicate the reasoning        and estimation.            Classroom                       guess and check; find a         Mountain Math      Manipulation of materials in
problems through written                                     used in problem solving                                     Evidence                        pattern; partners; charts and                      small steps
to solve problems and
and/or oral communication. communicate the reasoning         situations?                                                                                 tables; build a model; choose
What makes a quality solution?                                                              an operation
used in problem solving.
What essential components are                                                               *Choose an appropriate
needed to solve problems?                                                                   strategy

Standard 2: Students apply algebraic and/or other mathematical methods to understand and explore models, data, graphs, patterns, functions, and spatial relationships.

BENCHMARK 2.3: Recognize when a pattern exists and use that information to solve a problem.

Enduring Understanding                                                                      Assessment          Key        Suggested Instructional                               Differentiation-              Quarter
State Frameworks                                              Essential Questions               Essential Skills                                                                            Resources
Conceptual Vocabulary                                                                        Methods          Strategy            Practice                                    Adaptations/Extensions           Taught

2.3a Identify a rule using                                                                    PATTERNS AND ALGEBRA                            McREL      McREL Nonlinguistic             Math Text          Visual demonstrations                  4
addition or subtraction                                                                       Identify, describe and extend Terra Nova         SIOP      representation                  Success Maker      Utilization of visual or multi-
patterns and solve a new                                     What is a pattern?               patterns (What's my rule :)   Quarterly                    *patterning                     Math Exemplars     sensory materials
problem using the rule       Recognizing patterns helps us   How do we find patterns?         increasing and decreasing     Assessment                   *charts, tables, and lists      Mountain Math      Small group
make sense of our world.        What can patterns reveal?                                                                   *draw a picture                                    Time for repeated review/drill

BENCHMARK 2.4: Observe and explain how a change in one quantity can produce a change in another (for example, the relationship between the number of bicycles and the number of wheels).

2.4a Using whole numbers,                                                                     PATTERNS AND ALGEBRA Classroom                  McREL      McREL Nonlinguistic             Math Text          Visual demonstrations                  4
determine how the change in                                                                   Explain how patterns are Evidence                SIOP      representation                  Success Maker      Utilization of visual or multi-
one quantity affects the                                     What is a pattern?               generated                                                  *charts, tables, and lists      Math Exemplars     sensory materials
change in the other by      Recognizing patterns helps us    How do we find patterns?                                                                    *draw a picture                 Mountain Math      Small group
addition or subtraction.    make sense of our world.         What can patterns reveal?                                                                                                                      Time for repeated review/drill

Revised4-26-2006/jkw                                                                                                                                                                                                                 33
BY TEACHERS FOR TEACHERS                                                                                                    4th Quarter
MATH CURRICULUM GUIDE

Standard 7: Students communicate the reasoning used in problem-solving situations.

BENCHMARK B: Communicate the use of PATTERNS AND FUNCTIONS needed to model real-world situations and solve appropriate problems.

Enduring Understanding                                                                            Assessment          Key        Suggested Instructional                               Differentiation-              Quarter
State Frameworks                                                   Essential Questions                  Essential Skills                                                                            Resources
Conceptual Vocabulary                                                                              Methods          Strategy            Practice                                    Adaptations/Extensions           Taught

District Indicator: 7b 4-                                                                             PROBLEM SOLVING                                 McREL      McREL Nonlinguistic             Math Text          Highlighted texts (clue words          4
Explain clearly the strategy                                                                          Understand and solve        Terra Nova           SIOP      representation                  Success Maker      and/or phrases)
used and the solution to                                                                              problems using patterning   Quarterly                      *act it out; draw a picture;    Math Exemplars     Small group
mathematical and real-world                                        In what ways can I                                             Assessment                     guess and check; find a         Mountain Math      Manipulation of materials in
problems through written                                          communicate the reasoning                                       Exemplars                      pattern; partners; charts and                      small steps
A sense of number is necessary
and/or oral communication. to solve problems and                  used in problem solving                                         Classroom                      tables; build a model; choose
situations?                                                     Evidence                       an operation
communicate the reasoning
What makes a quality solution?                                                                 *Choose an appropriate
used in problem solving.
What essential components are                                                                  strategy
needed to solve problems?

Standard 3: Students use mathematical strategies, data collection and analysis, statistics, and probability in everyday situations.

BENCHMARK 3.1: Construct, read, and interpret displays of data including table, charts, pictographs, and bar graphs.

Enduring Understanding                                                                            Assessment          Key        Suggested Instructional                               Differentiation-              Quarter
State Frameworks                                                   Essential Questions                  Essential Skills                                                                            Resources
Conceptual Vocabulary                                                                              Methods          Strategy            Practice                                    Adaptations/Extensions           Taught

3.1a Organize and display                                                                             DATA AND GRAPHS             Quarterly           McREL      McREL Nonlinguistic             Math Text          Visual demonstrations                  4
data using tallies, bar                                                                               Collect & organize data     Assessment           SIOP      representation                  Success Maker      Utilization of visual or multi-
graphs, pictographs, and       Graphics are tools used to         What are the tools used to                                      "Pet Survey"                   *charts, tables, and graphs     Math Exemplars     sensory materials
tables using a given set of    clarify data.                      clarify data, and when do we                                    Puddles                                                        Mountain Math      Small group
data                           Analyzing data displays allows     use them?                                                       "Typical objects"                                                                 Time for repeated review/drill
us to interpret and explain data   How do we analyze data?                                         Exemplars
and make predictions based on      How do probability and statistics
probability and statistics..       help us to make predictions?                                    Terra Nova

BENCHMARK 3.2: Interpret data using the concepts of largest smallest, most often, and middle.

3.2a Given a set of numbers,                                                                          DATA AND GRAPHS           Quarterly             McREL      McREL Nonlinguistic             Math Text          Visual demonstrations                  4
determine the mode.                                                                                   Determine mode and median Assessment             SIOP      representation                  Success Maker      Utilization of visual or multi-
Graphics are tools used to         What are the tools used to          given a set of numbers.   Classroom                        *ordering numbers               Math Exemplars     sensory materials
clarify data.                      clarify data, and when do we                                  evidence                                                         Mountain Math      Small group
Analyzing data displays allows     use them?                                                                                                                                         Time for repeated review/drill
us to interpret and explain data   How do we analyze data?
and make predictions based on      How do probability and statistics
probability and statistics..       help us to make predictions?

3.2b Using various displays                                                                           DATA AND GRAPHS             Quarterly           McREL      McREL Cooperative learning Math Text               Visual demonstrations                  4
of data, interpret and draw                                                                           Interpret/analyze data      Assessment           SIOP      *Personal connections-SIOP Success Maker           Utilization of visual or multi-
conclusions                 Graphics are tools used to            What are the tools used to                                      "Pet Survey"                                              Math Exemplars          sensory materials
clarify data.                         clarify data, and when do we                                    Puddles                                                   Mountain Math           Small group
Analyzing data displays allows        use them?                                                       "Typical objects"                                                                 Time for repeated review/drill
Exemplars
us to interpret and explain data      How do we analyze data?
and make predictions based on         How do probability and statistics
Terra Nova
probability and statistics..          help us to make predictions?

Revised4-26-2006/jkw                                                                                                                                                                                                                         34
BY TEACHERS FOR TEACHERS                                                                                                  4th Quarter
MATH CURRICULUM GUIDE

Standard 7: Students communicate the reasoning used in problem-solving situations.

BENCHMARK C: Communicate the use of PROBABILITY AND STATISTICS needed to represent and solve problems involving uncertainty.

Enduring Understanding                                                                        Assessment     Key        Suggested Instructional                               Differentiation-              Quarter
State Frameworks                                              Essential Questions               Essential Skills                                                                          Resources
Conceptual Vocabulary                                                                          Methods     Strategy            Practice                                    Adaptations/Extensions           Taught

District Indicator: 7c 4-                                                                     PROBLEM SOLVING                                McREL      McREL Nonlinguistic             Math Text          Highlighted texts (clue words          4
Explain clearly the strategy                                                                  Understand and solve             Terra Nova     SIOP      representation                  Success Maker      and/or phrases)
used and the solution to                                      In what ways can I              problems related to              Quarterly                * act it out; draw a picture;   Math Exemplars     Small group
mathematical and real-world A sense of number is necessary   communicate the reasoning        probability, data, graphs, and   Assessment               guess and check; find a         Mountain Math      Manipulation of materials in
problems through written                                     used in problem solving          tables                           Exemplars                pattern; partners; charts and                      small steps
to solve problems and
and/or oral communication. communicate the reasoning         situations?                                                       Classroom                tables; build a model; choose
What makes a quality solution?                                    Evidence                 an operation
used in problem solving.
What essential components are                                                              *Choose an appropriate
needed to solve problems?                                                                  strategy

Standard 4: Students use geometric reasoning to gather evidence, build an argument, and make conjectures in one-, two-, and three-dimensional problem solving situations.

BENCHMARK 4.2: Identify, describe, draw, compare, classify, and build physical models of geometric figures.

Enduring Understanding                                                                        Assessment     Key        Suggested Instructional                               Differentiation-              Quarter
State Frameworks                                              Essential Questions               Essential Skills                                                                          Resources
Conceptual Vocabulary                                                                          Methods     Strategy            Practice                                    Adaptations/Extensions           Taught

4.2 e Create and identify the                                                                 GEOMETRY                    Classroom          McREL      McREL Nonlinguistic             Math Text          Visual demonstrations                  4
results of combining or                                                                       Explore & create new shapes Evidence            SIOP      representation                  Success Maker      Utilization of visual or multi-
subdividing given geometric                                                                   using manipulatives ( for                                 *concrete models                Math Exemplars     sensory materials
shapes (for example,                                         What is geometry?                example, tangrams, pattern                                Identifying similarities and    Mountain Math      Small group
patterns blocks, tangrams) Geometry builds our world.        How do we use geometry in        blocks).                                                  differences                                        Time for repeated review/drill
every day life?                                                                            *compare/contrast

4.2d Recognize common                                                                         GEOMETRY                         Classroom     McREL      McREL Nonlinguistic             Math Text          Visual demonstrations                      4
attributes of squares and                                                                     Compare and contrast             evidence       SIOP      representation                  Success Maker      Utilization of visual or multi-
rectangles. (introduction to                                                                  attributes of squares and                                 *concrete models                Math Exemplars     sensory materials
4th grade standard)                                          What is geometry?                                                                          Identifying similarities and    Mountain Math      Small group
rectangles.
Geometry builds our world.    How do we use geometry in                                                                  differences                                        Time for repeated review/drill
every day life?                                                                            *compare/contrast

Revised4-26-2006/jkw                                                                                                                                                                                                                35
BY TEACHERS FOR TEACHERS                                                                                               4th Quarter
MATH CURRICULUM GUIDE

Standard 7: Students communicate the reasoning used in problem-solving situations.

BENCHMARK D: Communicate the use of GEOMETRIC CONCEPTS needed to model real-world situations and solve appropriate problems.

Enduring Understanding                                                                        Assessment     Key        Suggested Instructional                               Differentiation-              Quarter
State Frameworks                                                    Essential Questions               Essential Skills                                                                       Resources
Conceptual Vocabulary                                                                          Methods     Strategy            Practice                                    Adaptations/Extensions           Taught

District Indicator: 7d 4-                                                                            PROBLEM SOLVING                            McREL      McREL Nonlinguistic             Math Text          Highlighted texts (clue words          4
Explain clearly the strategy                                                                         Understand and solve         Terra Nova     SIOP      representation                  Success Maker      and/or phrases)
used and the solution to                                                                             problems related to          Quarterly                *act it out; draw a picture;    Math Exemplars     Small group
mathematical and real-world                                          In what ways can I              geometric concepts           Assessment               guess and check; find a         Mountain Math      Manipulation of materials in
problems through written                                            communicate the reasoning                                     Exemplars                pattern; partners; charts and                      small steps
A sense of number is necessary
and/or oral communication.                                          used in problem solving                                       Classroom                tables; build a model; choose
to solve problems and
situations?                                                   Evidence                 an operation
communicate the reasoning
What makes a quality solution?                                                         *Choose an appropriate
used in problem solving.
What essential components are                                                          strategy
needed to solve problems?

Standard 5: Students use a variety of tools and techniques to measure and use measurement in problems and in everyday situations.

BENCHMARK 5.1: Know, use, describe, and estimate measures of length, perimeter, capacity, weight, time, and temperature.

Enduring Understanding                                                                        Assessment     Key        Suggested Instructional                               Differentiation-              Quarter
State Frameworks                                                    Essential Questions               Essential Skills                                                                       Resources
Conceptual Vocabulary                                                                          Methods     Strategy            Practice                                    Adaptations/Extensions           Taught

5.1a Using an analog and                                                                             MEASUREMENT                   Classroom    McREL      McREL Nonlinguistic             Math Text          Visual demonstrations                  4
digital clock, tell time to the                                                                      Tell time to nearest 5 minute evidence      SIOP      representations                 Success Maker      Utilization of visual or multi-
nearest five minutes                                                Why measure?                     (digital and analog)                                  *concrete models                Math Exemplars     sensory materials
Appropriate tools and units are
In measuring situations what                                   Terra Nova              Homework and practice           Mountain Math      Small group
needed to measure.
tool(s) would you use?                                         Quarterly                                                                  Time for repeated review/drill
Recognize and communicate
What are the units used to                                     Assessment
measurement relationships.
communicate a measurement?

BENCHMARK 5.3: Demonstrate the process of measuring and explaining the concepts related to units of measurement.

5.3a Measure the length of                                                                           MEASUREMENT                                McREL      McREL Nonlinguistic             Math Text          Visual demonstrations                  4
objects including the sides of                                                                       Measure objects accurately   Terra Nova     SIOP      representation                  Success Maker      Utilization of visual or multi-
rectangles and squares to                                           Why measure?                                                  Quarterly                *concrete models                Math Exemplars     sensory materials
Appropriate tools and units are
the nearest inch and                                                In measuring situations what                                  Assessment               Homework and practice           Mountain Math      Small group
needed to measure.
centimeter                                                          tool(s) would you use?                                                                                                                    Time for repeated review/drill
Recognize and communicate
What are the units used to
measurement relationships.
communicate a measurement?

Revised4-26-2006/jkw                                                                                                                                                                                                                  36
BY TEACHERS FOR TEACHERS                                                                                                   4th Quarter
MATH CURRICULUM GUIDE

Standard 7: Students communicate the reasoning used in problem-solving situations.

BENCHMARK E: Communicate the use of APPROPRIATE MEASUREMENT TECHNIQUES needed to solve problems, and determine whether the report the degree of accuracy required.

Enduring Understanding                                                                            Assessment        Key           Suggested Instructional                             Differentiation-             Quarter
State Frameworks                                                    Essential Questions                Essential Skills                                                                            Resources
Conceptual Vocabulary                                                                              Methods        Strategy               Practice                                  Adaptations/Extensions          Taught

District Indicator: 7e 4-                                                                            PROBLEM SOLVING                                 McREL      McREL Nonlinguistic             Math Text          Highlighted texts (clue words         4
Explain clearly the strategy                                                                         Understand and solve         Terra Nova          SIOP      representation                  Success Maker      and/or phrases)
used and the solution to                                            In what ways can I               problems using appropriate   Quarterly                     *act it out; draw a picture;    Math Exemplars     Small group
mathematical and real-world A sense of number is necessary         communicate the reasoning         measurement tools            Assessment                    guess and check; find a         Mountain Math      Manipulation of materials in
problems through written                                           used in problem solving                                        Exemplars                     pattern; partners; charts and                      small steps
to solve problems and
and/or oral communication.                                         situations?                                                    Classroom                     tables; build a model; choose
communicate the reasoning
What makes a quality solution?                                 Evidence                      an operation
used in problem solving.
What essential components are                                                                *Choose an appropriate
needed to solve problems?                                                                    strategy

Standard 6: Students understand, develop, and use computational skills and techniques, including estimation, mental math, paper and pencil, calculators, and computers in problem-solving situations.

BENCHMARK 6.2: Adding and subtracting commonly-used fractions and decimals using physical models (for example, 1/3, 3/4, 0.5, 0.75)

Enduring Understanding                                                                            Assessment        Key           Suggested Instructional                             Differentiation-             Quarter
State Frameworks                                                    Essential Questions                Essential Skills                                                                            Resources
Conceptual Vocabulary                                                                              Methods        Strategy               Practice                                  Adaptations/Extensions          Taught

6.2 a Using pictures,                                                                         COMPUTATION                         Classroom          McREL      McREL Nonlinguistic             Math Text          Mnemonic aids/review                  4
demonstrate addition and                                      What strategies are used to     Addition/subtraction of             Evidence            SIOP      representation                  Success Maker      instruction of mnemonic
subtraction of proper                                         solve problems?                 common fractions using                                            *draw a picture                 Math Exemplars     devices
fractions with common          Estimation and computation are How are computation skills and pictures                                                           *concrete models                Mountain Math      Visual demonstrations
denominators of four of less   vital tools.                   strategies used daily?                                                                                                                               Time for repeated review/drill
A sense of number is necessary Why be fluent at computation?
to communicate the reasoning   How do you use estimation to
used in problem solving.       determine whether your solution
is reasonable?

BENCHMARK 6.3: Demonstrate understanding of and proficiency with basic addition, subtraction, multiplication, and division facts without the use of a calculator.

6.3a Demonstrate                                                                                     COMPUTATION                    Classroom        McREL      McREL Nonlinguistic             Math Text          Mnemonic aids/review                  4
understanding of basic                                             What strategies are used to       Demonstrate understanding Evidence               SIOP      representation                  Success Maker      instruction of mnemonic
multiplication facts of 1's, 2's,                                  solve problems?                   of 1s, 2s, 3s, 5s, and 10,s                                 *patterns                      Math Exemplars     devices
3's, 5's, and 10's                Estimation and computation are   How are computation skills and    and extended facts for                                     Homework and practice           Mountain Math      Visual demonstrations
vital tools.                     strategies used daily?            multiples of 10 for 1,2,3, and                                                                                Time for repeated review/drill
A sense of number is necessary   Why be fluent at computation?     5
to communicate the reasoning     How do you use estimation to
used in problem solving.         determine whether your solution
is reasonable?

Revised4-26-2006/jkw                                                                                                                                                                                                                       37
BY TEACHERS FOR TEACHERS                                                                                                           4th Quarter
MATH CURRICULUM GUIDE

Standard 6: Students understand, develop, and use computational skills and techniques, including estimation, mental math, paper and pencil, calculators, and computers in problem-solving situations.

BENCHMARK 6.4: Construct, use, and explain procedures to compute and estimate with whole numbers.

Enduring Understanding                                                                          Assessment     Key        Suggested Instructional                                      Differentiation-              Quarter
State Frameworks                                                 Essential Questions               Essential Skills                                                                          Resources
Conceptual Vocabulary                                                                            Methods     Strategy            Practice                                           Adaptations/Extensions           Taught

6.4b Demonstrate three                                                                            COMPUTATION                                   McREL      McREL Nonlinguistic             Math Text                 Visual demonstrations                  4
basic operations of whole                                                                         Demonstrate math fact           Terra Nova     SIOP      representation *base ten        Success Maker             Utilization of visual or multi-
numbers (for example,                                           What strategies are used to       fluency in addition and         Quarterly                blocks                          Math Exemplars            sensory materials
addition and subtraction of                                     solve problems?                   subtraction                     Assessment               *Demonstration modeling)-       Mountain Math             Small group
three digit numbers, and         Estimation and computation are How are computation skills and    Add 4-digit numbers with        Classroom                SIOP                                                      Time for repeated review/drill
multiplication of multiples of   vital tools.                   strategies used daily?            regrouping                      Evidence
ten by 1, 2, 3, and 5).          A sense of number is necessary Why be fluent at computation?     Subtract 4-digit numbers with
to communicate the reasoning   How do you use estimation to      regrouping
used in problem solving.       determine whether your solution
is reasonable?

BENCHMARK 6.5: Selecting and using appropriate methods for computing with whole numbers in problem-solving situations from among mental arithmetic, estimation, paper-and-pencil, calculator and computer methods.

6.5a Given a real world                                                                         COMPUTATION                       Classroom     McREL      McRel Generating and testing Math Text                    Utilization of visual or multi-        4
problem-solving situation,                                      What strategies are used to     Select and use appropriate        evidence       SIOP      hypotheses                   Success Maker                sensory materials
use addition, subtraction, or                                   solve problems?                 method to solve problems.                                  Strategies: GIST             Math Exemplars               Highlighted texts
multiplication to solve the      Estimation and computation are How are computation skills and                                                                                          Mountain Math                Small group
problem.                         vital tools.                   strategies used daily?
A sense of number is necessary Why be fluent at computation?
to communicate the reasoning   How do you use estimation to
used in problem solving.       determine whether your solution
is reasonable?

Standard 7: Students communicate the reasoning used in problem-solving situations.

BENCHMARK F: Communicate the use of APPROPRIATE COMPUTATIONAL TECHNIQUES needed to solve problems, and determine whether the results are reasonable.

Enduring Understanding                                                                          Assessment     Key        Suggested Instructional                                      Differentiation-              Quarter
State Frameworks                                                 Essential Questions               Essential Skills                                                                          Resources
Conceptual Vocabulary                                                                            Methods     Strategy            Practice                                           Adaptations/Extensions           Taught

District Indicator: 7f 4-                                                                         PROBLEM SOLVING                               McREL      McREL Nonlinguistic             Math Text                 Highlighted texts (clue words          4
Explain clearly the strategy                                                                      Understand and solve            Terra Nova     SIOP      representation                  Success Maker             and/or phrases)
used and the solution to                                         In what ways can I               problems using appropriate      Quarterly                *act it out; draw a picture;    Math Exemplars            Small group
mathematical and real-world A sense of number is necessary      communicate the reasoning         computational techniques        Assessment               guess and check; find a         Mountain Math             Manipulation of materials in
problems through written                                        used in problem solving                                           Exemplars                pattern; partners; charts and                             small steps
to solve problems and
and/or oral communication.                                      situations?                                                       Classroom                tables; build a model; choose
communicate the reasoning
What makes a quality solution?                                    Evidence                 an operation
used in problem solving.
What essential components are                                                              *Choose an appropriate
needed to solve problems?                                                                  strategy

Revised4-26-2006/jkw                                                                                                                                                                                                                         38

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