GRADE
5 OHIO ACADEMIC CONTENT STANDARDS
MATHEMATICS CURRICULUM GUIDE
Fifth Grade – Number, Number Sense and Operations Standard
Students demonstrate number sense, including an understanding of number systems and operations and how they relate to one another. Students
compute fluently and make reasonable estimates using paper and pencil, technology-supported and mental methods.
BENCHMARKS GRADE LEVEL INDICATORS STRATEGIES/RESOURCES
Represent and compare Meaning of Operations 6. Blast Off: CH 6-9
numbers less than 0 Represent and compare numbers less
through familiar that 0 by extending the number line
applications and and using familiar applications; such
extending the number as, temperature, owing money. (6)
line. (A) -3 -2 -1 0 1 2 3
Number and Number Systems B1. Ratios are used to compare quantities. Ratios are usually set up initially as a fraction and can be
Compare, order and Use models and visual expressed in several ways.
convert among fractions, representations to develop the ex. 2 : 4, 2
decimals and percents. concept of ratio as part-to-part and 4
(B) part-to-whole, and the concept of Though ratios can be expressed as a fraction, ratios are not like fractions when computing.
percent as part-to-whole. (1)
www.pbs.org/teachersource/mathline/lessonplans/msmp/somethingfishy/somethingfishy_procedure.
Use various forms of “one” to
demonstrate the equivalence of
fractions; such as, 18/24 = 9/12 x 2/2
=3/4 x 6/6. (2)
Adapted From Summit County ESC Course of Study 2003 Revised by Trumbull County ESC 1
Identify and generate equivalent 3. When generating equivalent decimals, zeros in the places to the right of the decimal is a shortcut.
forms of fractions, decimals and ex. 0.2 = 0.20 = 0.200
percents. (3)
www.filer.weblogger.com/earlyalgebraManilaWebsite/classes/Lesson12.pdf
www.math.rice.edu/~lanius/fractions/index.html
D1. Given a fraction, students should be able to identify an equivalent percent or decimal.
Use models and pictures
to relate concepts of www.illuminations.nctm.org/lessonplans/6-8/percent/index.html
ratio, proportion and Number and Number Systems
percent. (D) Use models and visual ex.
representations to develop the Fraction Decimal Percent
concept of ratio as part-to-part and 1 0.50 50%
part-to-whole, and the concept of 2
percent as part-to-whole. (1) 1 0.10 10%
10
2 0.40 40%
5
8. A mnemonic devise can be used for order of operations. Please Excuse My Dear Aunt Sally:
Use order of operations, Meaning of Operations 1) do operations inside Parenthesis first;
including use of Identify and use relationships 2) rewrite numbers in Exponential;
parenthesis and between operations to solve 3) Multiply and Divide from left to right;
exponents to solve multi- problems. (8) 4) Add and Subtract from left to right.
step problems, and verify
and interpret the results. Use order of operations, including Blast Off p 19-20
(E) use of parentheses, to simplify
numerical expressions. (9)
Note: There are instances when a grade-
level indicator for one standard is linked
to a benchmark for a different standard.
See also correlation for Patterns, 7. commutative property
Functions and Algebra for indicator 8. 9x4=4x9
associative property
(6x4) x 2 24 x 2 = 48
Apply number system
properties when Meaning of Operations distributive property
performing computations. Use commutative, associative, 3 x (4+5) = (3x4) + (3x5)
(F) distributive, identity and inverse 3 x 9 = 12 + 15
properties to simplify and perform 27 = 27
computations. (7)
Adapted From Summit County ESC Course of Study 2003 Revised by Trumbull County ESC 2
identity property of multiplication – if you multiply the number by 1, the product is the same as
the given number
Blast Off p 17-18
www.nces.ed.gov/nationsreportcard/itmrls/qtab.asp?listarr=%221992-4m5+01%22
5. perfect square – product of a number multiplied by itself
ex. 16 is a perfect square because 4 x 4 = 16
Blast Off p 14
Apply and explain the
use of prime www.illuminations.nctm.org/lessonplans/6-8/factorgame/index.html
factorizations, Number and Number Systems
common factors, and Recognize and identify perfect
common multiples in squares and their roots. (5)
problem situations. (G)
Adapted From Summit County ESC Course of Study 2003 Revised by Trumbull County ESC 3
Use and analyze the steps in Meaning of Operations 10. To add or subtract fractions with unlike denominators, a common
standard Justify why fractions need common denominator needs to be determined so that like values are being compared.
and non-standard denominators to be added or subtracted. (10)
algorithms for
computing with fractions, Explain how place value is related to addition 11. A decimal point always separates the units from tenths.
decimals and integers. (H) and subtraction of decimals; such as, 0.2 + 0.14; ex. 6 3 . 7 4
two tenths are added to the one tenth because
they are both tenths. (11) tens ones tenths hundredths
Use a variety of strategies, Number and Number Systems 4. Decimals are often rounded to the nearest selected place.
including Round decimals to a given place value and round ex. 0.44 0.4
proportional reasoning, to fractions (including mixed numbers) to the
20.76 20.8
estimate, compute, nearest half. (4)
solve and explain 181.30 181.3
solutions to problems Computation and Estimation
involving integers, Use physical models, points of reference, and www.filer.weblogger.com/earlyalgebraManilaWebsite/classes/Lesson12.pdf
fractions, decimals and equivalent forms to add and subtract commonly
percents. (I) used fractions with like and unlike
12. Physical Model Ex.
denominators and decimals. (12)
¼
Estimate the results of computations involving ¼ + ½ = 3/4
whole numbers, fractions and decimals, using a
variety of strategies. (13) ½
Provide experiences using a number line to add and subtract fractions.
Note: There are instances where a grade-level
indicator is linked to a benchmark for a grade www.illuminations.nctm.org/lessonplans/6-8/mango/index.html
band that does not include the grade level of the
indicator. See Grade 8 for indicator 5.
Related Literature:
Fraction Action – L. Leedy
Adapted From Summit County ESC Course of Study 2003 Revised by Trumbull County ESC 4
Fifth Grade – Measurement Standard
Students estimate and measure to a required degree of accuracy and precision by selecting and using appropriate units, tools and technologies.
BENCHMARKS GRADE LEVEL INDICATORS STRATEGIES/RESOURCES
Select appropriate units to Measurement Units www.figurethis.org/challenges/c10/challenge.htm
measure angles, Identify and select appropriate units to measure
circumference, surface area, angles; such as, degrees. (1)
mass and volume, using:
U.S. customary units;
such as, degrees, square
feet, pounds, and other
units as appropriate;
Metric units; such as,
square meters, kilograms
and other units as
appropriate. (A)
5. Conversions
Convert units of length, area, Length – customary- inch, feet, yard, mile
volume, mass and time within Use Measurement Techniques and Tools metric – centimeter. decimeter, meter,
the same measurement system. Make simple unit conversions within a kilometer
(B) measurement system; such as, inches to feet, Area – customary – square inches, square foot
kilograms to grams, quarts to gallons. (5) metric – square centimeters, square
meters
(Grade 4)
Volume – customary – cubic inch, cubic foot
metric – cubic centimeter, cubic meter
Make conversions within the same Capacity – customary – cup, pint, quart, gallon
measurement system while performing metric – milliliter, liter
computations. (5) Mass - metric – gram, kilogram
Time – customary – second, minute, hour
www.filer.weblogger.com/earlyalgebraManilaWebsite/classes/Lesson12.pdf
Adapted From Summit County ESC Course of Study 2003 Revised by Trumbull County ESC 5
Identify appropriate Use Measurement Techniques and Tools 6. Provide a number of polygons for students to measure the sides to the nearest centimeter.
tools and apply Use strategies to develop formulas 2 3 2
appropriate techniques for determining perimeter and area
for measuring angles, of triangles, rectangles and 1 1
parallelograms, and volume of 4 2
perimeter or
circumference and area rectangular prisms. (6)
of triangles, Encourage students to write an explanation of what perimeter is – distance around a shape.
quadrilaterals, circles,
and composite shapes, Grid paper can be used for students to explain area.
and surface area
and volume of prisms illuminations.nctm.org/lessonplans/3-5/collectrays/index.html
and
cylinders. (C)
7. Benchmark angles provide a reference point to determine if an angles measure is > or <
than 45o, 90o or 120o.
Use benchmark angles (such as,
45o, 90o, 120o) to estimate the www.figurethis.org/challenges/c10/challenge.htm
measure of angles, and use a tool to
measure and draw angles. (7)
Use Measurement Techniques and Tools
Use problem solving Write, solve and verify solutions to
techniques and multi-step
technology as needed problems involving measurement. (6) 2. When identifying points in a coordinate plane, ordered pairs are in order (x, then y axis).
to solve problems (Grade 4)
involving length, Maps are useful tools for students to use in determining lengths of paths.
weight, perimeter, area, Measurement Units
volume, time and Identify paths between points on a Blast Off p 139-140
grid or www.pbs.org/teachersource/mathline/lessonplans/atmp/newheights/newheights_procedure.shtm
temperature. (E)
coordinate plane and compare the
lengths of
the paths; such as, shortest path, paths
of
equal length. (2)
Adapted From Summit County ESC Course of Study 2003 Revised by Trumbull County ESC 6
Analyze and explain what Measurement Units
happens to area and perimeter Demonstrate and describe the differences between
or surface area and volume covering the faces (surface area) and filling the
when the interior (volume) of three-dimensional objects. (3)
dimensions of an object are
changed. (F) Demonstrate understanding of the differences among
linear units, square units and cubic units. (4) 4. Customary Units of Volume
-cubic inch
-cubic foot
Metric Units of Volume
-cubic centimeter
-cubic meter
Surface area of a figure is the sum of all the faces.
Use geometric models to solve problems in other
areas of mathematics, such as number Vocabulary flashcards
(multiplication/division) and measurement (area,
perimeter, border). (8) Geometry and Spatial Sense
(Grade 4)
Understand and demonstrate Measurement Units
the Demonstrate and describe the differences between
independence of perimeter and covering the faces (surface area) and filling the
area for two-dimensional interior (volume) of three-dimensional objects. (3) 3. Provide hands on experiences for students to determine volume of a figure
shapes and of surface area and – volume is always measured in cubic units (lines on each edge).
volume for three- Demonstrate understanding of the differences among
dimensional shapes. (G) linear units, square units and cubic units. (4) Students construct a box from a net and layer cm. cubes inside the box to
determine its volume. (See Math Resources page xxx for net templates for
Note: There are instances when a grade-level indicator class use).
for one standard is linked to a benchmark for a different
standard. See correlation for Patterns, Functions and 4. Review the symbols for square and cubic units: in2, cm2, in3, cm3, etc.
Algebra for indicator 6.
Adapted From Summit County ESC Course of Study 2003 Revised by Trumbull County ESC 7
Fifth Grade – Geometry and Spatial Sense Standard
Students identify, classify, compare and analyze characteristics, properties and relationships of one-, two- and three-dimensional geometric
figures and objects. Students use spatial reasoning, properties of geometric objects, and transformations to analyze mathematical situations and
solve problems.
BENCHMARKS GRADE LEVEL INDICATORS STRATEGIES/RESOURCES
Identify and label angle parts Characteristics and Properties 2. line – infinite set of points that form a straight
and the regions defined Use standard language to describe line, segment, line
within the plane where the ray, angle, skew, parallel and perpendicular. (2) segment – part of a line that is defined by two
angle resides. (A) endpoints
ray – part of a line that has one endpoint and
extends indefinitely in one direction
angle – two rays that share an endpoint
skew – two or more lines that have no
intersection but are not parallel
skew
perpendicular – lines that intersect at one
point (forming 90o)
parallel – lines in the same plane and
maintains a constant distance from
each other
Blast Off Chapter 10
Label vertex, rays, interior and exterior for an
angle. (3) 3. label angle
vertex – plural: vertices Blast Off CH 10
Adapted From Summit County ESC Course of Study 2003 Revised by Trumbull County ESC 8
Draw circles, and identify Characteristics and Properties
and determine the Draw circles, and identify and determine
relationships among the relationships among the radius, diameter, center
radius, diameter, center and and circumference; such as, radius is half the
circumference. (B) diameter, the ratio of the circumference of a circle
to its diameter is an approximation of. (1)
Spatial Relationship
Extend understanding of coordinate system to
include points whose x or y values may be Blast Off p 130-131
Specify locations and plot negative numbers. (6)
ordered pairs on a coordinate
plane. (C) www.learner.org/teacherlab/math/geometry/shape/taxicab/index.html
Adapted From Summit County ESC Course of Study 2003 Revised by Trumbull County ESC 9
Identify, describe and classify Characteristics and Properties 2. line – infinite set of points that form a straight
types of line pairs, angles, two- Use standard language to describe line, segment, line
dimensional segment – part of a line that is defined by two endpoints l
ray, angle, skew, parallel and perpendicular. (2)
figures and three-dimensional ray – part of a line that has one endpoint and
extends indefinitely in one direction
objects using their properties.
(D)
Use physical models to determine the sum of the angle – two rays that share an endpoint
interior angles of triangles and quadrilaterals. (5) skew – two or more lines that have no
intersection but are not parallel
skew
perpendicular – lines that intersect at one
point (forming 90o)
parallel – lines in the same plane and
maintains a constant distance from
each other
Blast Off Chapter 10
www.illuminations.nctm.org/lessonplans/3-5/rectangles/index.htm
Visualization and Geometric Models www.illumination.nctm.org/lmathlets/IGD_lines/index.html
Understand that the measure of an angle is
determined by the degree of rotation of a angle 7. Use pattern blocks or same-tile tessellations for students to explore sum of interior angles.
Students draw, with a straightedge, a number of polygons on paper. Students measure the angles
side rather than the length of either side. (7) of each polygon (using their knowledge that the sum of angles in a triangle measures 180 o).
www.figurethis.org/challenges/c10/challenge.htm
Describe and use the concepts
Characteristics and Properties 4. congruent figures – are exact copies of each other (same size, same shape)
of congruence,
similarity and symmetry to Describe and use properties of congruent figures Students can prove that a figure is congruent to another figure by cutting out one figure and
placing it on top of the original.
solve problems. (F) to solve problems. (4)
www.illuminations.nctm.org/lessonplans/PreK-2/tangram/index.html
www.illuminations.nctm.org/lesonplans/6-8/tiles/index.html
Describe and use properties of Characteristics and Properties
triangles to solve problems Use physical models to determine the sum of the 5. geometry tools:
involving angle measures and interior angles of triangles and quadrilaterals. (5) - geometry template
side lengths of right triangles. - straightedge
- compass
(G)
Adapted From Summit County ESC Course of Study 2003 Revised by Trumbull County ESC 10
Identify and draw three- Visualization and Geometric Models 8. nets – a two-dimensional shape that can be folded into a three-dimensional
dimensional objects from Predict what three-dimensional object will result figure. (See Math Resources page xxx, for net templates for class use).
different views (top, side, front from folding a two-dimensional net, and then Present templates to students. In groups of 2, students predict what
and perspective). (I) confirm the prediction by folding the net. (8) three-dimensional shape would be made by folding each net. Students note
their predictions and verbally (or in writing) tell why. Next day, students cut
out each net and build three-dimensional models. Students determine if their
predictions were correct.
Note: If using net resouces within this document, cover the names of the
three-dimensional objects for student predictions.
www,learner.org/teacherslab/math/geometry/space/plotplan/index.html
www.illuminations.nctm.org/index_o.aspx?id=122
Apply properties of equality Characteristics and Properties
and proportionality to solve Describe and use properties of congruent figures to
problems involving congruent solve problems. (4)
or similar figures; such as,
create a scale drawing. (J)
Adapted From Summit County ESC Course of Study 2003 Revised by Trumbull County ESC 11
Fifth Grade – Patterns, Functions and Algebra
Students use patterns, relations and functions to model, represent and analyze problem situations that involve variable quantities.
Students analyze, model and solve problems using various representations such as, tables, graphs and equations
BENCHMARKS GRADE LEVEL INDICATORS STRATEGIES/RESOURCES
Describe, extend and Use Patterns, Relations and Functions 1. Students need to be provided practice in writing a rule for various patterns.
determine the rule for Justify a general rule for a pattern or a .
patterns and relationships function by using physical materials, wwww.pbs.org/teachersourcr/mathline/lessonplans/atmp/newheights/newheights_procedure.shtm
occurring in numeric visual representations, words, tables or www.thirteen.org/edonline/lessons/patterns/index.html
patterns, computation, graphs. (1)
geometry, graphs and
other applications. (A) Use calculators or computers to in out
develop patterns, and generalize them 2 9
using tables and graphs. (2) 3 13
4
21
6 25
Compare results of problems using algebraic and non-algebraic calculators.
Provide a number of ways to present patterns to students.
Represent, analyze and 3. After students have had numerous opportunities to describe a rule in writing, students may
generalize a variety of Use Algebraic Representation then rewrite the rule as an equation.
patterns and functions Use variables as unknown quantities in
with tables, graphs, words general rules when describing patterns www.pbs.org/teachersourcr/mathline/lessonplans/atmp/newheights/newheights_procedure.shtm
and symbolic rules. (B) and other relationships. (3) www.pbs.org/teachersource/mathline/lessonplans/atmp/hoptoit/hoptoit_procedure.shtm
Use variables to create 4.Provide real-world problems for students to solve using equations.
and solve equations and Use Algebraic Representation
inequalities representing Create and interpret the meaning of www.illuminations.nctm,org/lessonplans/6-8/squares/index.html
problem situations. (C) equations and inequalities representing www.filer.weblogger.com/earlyalgebraManilaWebsite/classes/Lesson28.pbs
problem situations. (4)
Materials to develop algebraic thinking:
-algebraic tiles
-hands-on equations
Blast Off p 97
Adapted From Summit County ESC Course of Study 2003 Revised by Trumbull County ESC 12
Use rules and variables to
describe patterns, Use Algebraic Representation
functions and other Use variables as unknown quantities in
relationships. (E) general rules when describing patterns and
other relationships. (3)
Adapted From Summit County ESC Course of Study 2003 Revised by Trumbull County ESC 13
Use representations, such Use Algebraic Representation 5. Students use color tiles to make a pattern. The pattern is continued. Students represent their
as tables, graphs and Model problems with physical materials pattern in multiple ways – use graph, table and algebraic equations.
equations, to model and visual representations, and use
situations and to solve models, graphs and tables to draw www.pbs.org/teachersourcr/mathline/lessonplans/atmp/newheights/newheights_procedure.shtm
problems, especially those conclusions and make predictions. (5) www.pbs.org/teachersource/mathline/lessonplans/atmp/snake/snake_procedure.shtm
that involve linear www.filer.weblogger.com/earlyalgebraManilaWebsite/classes/Lesson28.pbs
relationships. (F)
Write, simplify and Use Algebraic Representation 3. Variables in equations should be represented in a variety of ways.
evaluate algebraic Use variables as unknown quantities in ex. Tyler weighs 10 pounds less than Andrew. If A = Andrew‟s weight, then A – 10 = T
expressions. (G) general rules when describing patterns (Tyler‟s weight)
and other relationships. (3)
www.filer.weblogger.com/earlyalgebraManilaWebsite/classes/Lesson28.pbs
www.pbs.org/teachersource/mathline/lessonplans/atmp/hoptoit/hoptoit_procedure.shtm
Explain how inverse Identify and use relationships between
operations are used to operations to solve problems. (8)
solve linear equations. (I) Number, Number Sense and Operations
Use formulas in problem- Use strategies to develop formulas for
solving situations. (J) determining perimeter and area of
triangles, rectangles and parallelograms,
and volume of
rectangular prisms. (6) Measurement
Adapted From Summit County ESC Course of Study 2003 Revised by Trumbull County ESC 14
Graph linear equations and Use Algebraic Representation www.filer.webloger.com/earlyalgebraManilaWebsite/classes/Lesson01.pdf
inequalities. (K) Model problems with physical materials and visual
representations, and use models, graphs and tables to
draw conclusions and make predictions. (5)
Analyze Change
Describe how the quantitative change in a variable
affects the value of a related variable; such as,
Analyze functional describe how the rate of growth varies over time, 6. www.illuminations.nctm.org/lessonplans/6-8/topspeed/index.html
relationships, and explain how based upon data in a table or graph. (6) www.math.rice.edu/~lanius/Algebra/rentacar.html
a change in one
quantity results in a change in
the other. (L)
Students make predictions and draw conclusions based on information
obtained from a graph or table.
Adapted From Summit County ESC Course of Study 2003 Revised by Trumbull County ESC 15
Fifth Grade – Data Analysis & Probability Standard
Students pose questions and collect, organize, represent, interpret and analyze data to answer those questions. Students develop and evaluate
inferences, predictions and arguments that are based on data.
BENCHMARKS GRADE LEVEL INDICATORS STRATEGIES/RESOURCES
Read, create and use line Data Collection 1. Frequency charts can be used for counting responses. Tally marks are
graphs, histograms, circle Read, construct and interpret frequency tables, circle usually used for this type of frequency table.
graphs, box and whisker plots, graphs and line graphs. (1)
stem-and-leaf plots, and other Data can be grouped into intervals or ranges.
representations This frequency table is referred to as a grouped frequency table.
when appropriate. (A)
Line graphs are often used to evaluate if data is increasing, decreasing or
remaining the same every time,
Blast Off p 161-177
www.illuminations.nctm.org/lessonplans/3-5/statistics/index.html
www.illuminations.nctm.org/lessonplans/3-5/picture/index.html
Evaluate interpretations and Data Collection
conclusions as Modify initial conclusions, propose and justify new
additional data are interpretations and predictions as additional data are
collected, modify conclusions collected. (5)
and predictions, and justify
new findings. (C)
Compare increasingly complex Data Collection
displays of data, such as Read and interpret increasingly complex displays of data, 3. Double bar graphs are often used to compare sets of data.
multiple sets of data on the such as double bar graphs. (3)
same graph. (D) *See Math, Social Studies, Science text
Blast Off p 174
Adapted From Summit County ESC Course of Study 2003 Revised by Trumbull County ESC 16
Collect, organize, display, and Data Collection 2. Provide experiences for students to determine the kind of graph that best
interpret data for a specific Select and use a graph that is appropriate for the type represents a set of data.
purpose or need. (E) of data to be displayed; such as, numerical vs. circle graph – used to show information that
categorical data, discrete vs. continuous data. (2) is part of a whole
line graph – used to show changes over time
Determine appropriate data to be collected to answer pictograph – often used when data is
questions posed by students or teacher, collect and expressed in multiples
display data, and clearly communicate findings. (4) bar graph – used when the data can be
counted
www.sciencenetlinks.com/lessons.cfm?DocID=254
www.illuminations.nctm.org/lessonplans/3-5/statistics/index.html
Determine and use the range, Statistical Methods 6. range – difference between the highest value
mean, median and mode to Determine and use the range, mean, median and and the lowest value
analyze and compare data, and mode, and explain what each does and does not
explain what each indicate about the set of data. (6) mean – a type of average (add all numbers
indicates about the data. (F) in a set and divide by the number
of values)
The mean is a good measure to utilize when the data doesn‟t include
unusually high or low numbers.
median – number that falls exactly in the middle of the data – best to
arrange data from least to greatest to determine the median number. The
median number will be the number in the middle if there is an odd number of
data pieces: when there are an even number of data pieces, there are two
middle numbers that would be designated as the median. The measure is used
when there are outliers in the data.
mode – is the number that occurs most often in a set of numbers: there can
be more than one mode in a set of numbers or there may be no mode at all.
This measure is used often when several data pieces are the same.
www.hsor.org/modules.cfm?name=Torn_Shirts_Inc
www.illuminations.nctm.org/lessonplans/3-5/statistics/index.html
NOTE: It is mathematically unclear to use the term „average‟ when referring
to the mean, median, or mode class – the term „average‟ can refer to any of
these measures.
Adapted From Summit County ESC Course of Study 2003 Revised by Trumbull County ESC 17
Find all possible outcomes Probability 7. Brittany went to the ice cream store. She can have a sugar cone, waffle
of simple List and explain all possible outcomes in a given cone or dish. She can have vanilla, chocolate or strawberry frozen yogurt.
experiments or problem situation. (7) How many combinations are possible?
situations, using methods
List
such as lists, arrays and
sugar cone + vanilla yogurt
tree diagrams. (H) sugar cone + chocolate yogurt
sugar cone + strawberry yogurt
waffle cone + vanilla yogurt
etc.
Tree Diagram
vanilla
sugar cone chocolate
strawberry
vanilla
waffle cone chocolate
strawberry
vanilla
dish chocolate
strawberry
www.illuminations.nctm.org/index_o.aspx?id=75
Adapted From Summit County ESC Course of Study 2003 Revised by Trumbull County ESC 18
Describe the Probability 8. probability notations
probability of an event Identify the probability of events Fraction Decimal Ratio Percent
using ratios, within a simple experiment, such as ½ 0.5 1:2 50%
including fractional three chances out of eight. (8)
notation. (I) www.hsor.org/modules.cfm?name=Torn_Shirts_Inc
Use 0, 1 and ratios between 0 and 1 to 9. A probability line or a number line can be used to represent the outcome of an event (with
represent the probability of outcomes notations of 0 to 1).
for an event, and associate the ratio
with the likelihood of the outcome. (9) probability line
0 equally likely certain
event event
www.hsor.org/modules.cfm?name=Torn_Shirts_Inc
www.pbs.org/teachersource/mathline/lessonplans/esmp/chances/chances_procedure.shtm
Probability
Compare experimental Compare what should happen 10. Note: If a probability experiment is conducted with few attempts or data results, the results may
and theoretical results (theoretical/expected results) with be deceptive. With an increase in data information, probability results may prove to be more
for a variety of simple what did happen (experimental/actual accurate.
experiments. (J) results) in a simple experiment. (10)
www.hsor.org/modules.cfm?name=Torn_Shirts_Inc
www.pbs.org/teachersource/mathline/lessonplans/msmp/somethingfishy/somethingfishy_procedure.
shtm
Probability
Make and justify Make predictions based on
predictions based on experimental and theoretical
experimental and probabilities. (11) Related Literature:
theoretical Back in the Beforetime: Tales of the California Indians – J. Curry
probabilities. (K) Do You Wanna Bet?: Your Chance to Find Out About Probability – J. Cushman
Adapted From Summit County ESC Course of Study 2003 Revised by Trumbull County ESC 19
Fifth Grade – Mathematical Processes Standard
Students use mathematical processes and knowledge to solve problems. Students apply problem-solving and decision-making techniques, and
communicate mathematical ideas. The benchmarks for mathematical processes articulate what students should demonstrate in problem-solving,
representation, communication, reasoning and connections at key points in their mathematics program.
BENCHMARKS GRADE LEVEL INDICATORS STRATEGIES/RESOURCES
Clarify problem-solving compare: to determine how two things are alike and/or different; the
situation and identify potential common/critical attributes must be identified.
solution processes; such as,
consider different strategies Compare is involved in ALL of the following:
and approaches to a problem,
restate problem from various analyze: to investigate by breaking it down so as to more clearly understand
perspectives. (A) Specific grade-level indicators have not been the impact to the situation
included for the mathematical processes standard
Apply and adapt problem- because content and processes should be describe: to analyze into its parts but less detailed than explain
solving strategies to solve a interconnected at the indicator level. Therefore,
variety of problems, including mathematical processes have been embedded within identify: to show or prove the sameness of
unfamiliar and non-routine the grade-level indicators for the five content
problem situations. (B) Other Stated Verbs in the Indicators:
standards. communicate predict
Use more than one strategy to construct interpret
solve a problem, and recognize create model
there are advantages associated use select
with various methods. (C) generate modify
recognize list
Recognize whether an estimate represent identify
or an exact solution is simplify compare
appropriate for a given perform
problem situation. (D) justify
estimate
Use deductive thinking to select
construct informal arguments demonstrate
to support reasoning and to label
justify solutions to problems. extend
(E)
Use inductive thinking to
generalize a pattern of
observations for particular
cases, make conjectures, and
provide supporting arguments
for conjectures. (F)
Adapted From Summit County ESC Course of Study 2003 Revised by Trumbull County ESC 20
Relate mathematical ideas to Explain is the most frequently stated verb in short and extended response
one another and to other questions.
content areas; such as, use area
models for adding fractions, Explain means to:
interpret graphs in reading, make plain or clear; understandable
science and social studies. (G) give reasons for.
Specific grade-level indicators have not been included for
Use representations to the mathematical processes standard because content and Explain requires the application of prior knowledge.
organize and communicate processes should be interconnected at the indicator level. Students will need to communicate their responses with concise but
mathematical thinking and Therefore, mathematical processes have been embedded complete information.
problem solutions. (H) within the grade-level indicators for the five content In order to do that, students must provide details and go beyond just a
standards. “telegram style response” that leaves the reader making too many
Select, apply, and translate inferences.
among mathematical The written response must include sufficient quality information and
representations to solve proof.
problems; such as,
representing a number as a Explain requires more details than describe. Explain is at the analysis level
fraction, decimal or percent as or above for problem solving.
appropriate for a problem. (I)
Technique Suggestion: Each time “explain” is in a prompt, students must
Communicate mathematical cross out the word and replace it with - Give Specific Details.
thinking to others and analyze This raises the first awareness of what is required.
the mathematical thinking and
strategies of others. (J)
Recognize and use
mathematical language and
symbols when reading, writing
and conversing with others.
(K)
Adapted From Summit County ESC Course of Study 2003 Revised by Trumbull County ESC 21
Fifth Grade Student Vocabulary
Number, Number Sense Measurement Standard Geometry and Spatial Patterns, Functions and Data Analysis &
and Operations Standard Sense Standard Algebra Standard Probability Standard
percent as part-to-whole degrees ray quantitative change in a frequency tables
equivalent forms of - formulas for- angle variable circle graphs
percents determining perimeter skew MEPCV* double bar graphs
ratio as part-to-part area of triangles radius numerical data
properties area of rectangles diameter categorical data
identity area of parallelograms center discrete data
inverse volume of rectangular circumference continuous data
perfect squares prisms net range
roots benchmark angles MEPCV* mean
common denominators paths between points on a theoretical/expected
MEPCV* grid or coordinate plane results
surface area experimental/actual
volume results
units MEPCV*
linear
square
cubic
border
MEPCV*
*MEPCV – Maintain and Enhance Previous Content Vocabulary – Previous Content Vocabulary is now enhanced to the current grade appropriate indicators.
Adapted From Summit County ESC Course of Study 2003 Revised by Trumbull County ESC 22