Groton Public Schools
Curriculum Map
INTRODUCTION
Course Title: Math
Curriculum Area and Grade: Math – Grade 5
Course Purpose:
The purpose of this course is to provide a means to implement meaningful methods to understand mathematical concepts, approach problem solving
and learn computation at the fifth grade level. The course incorporates best practices of both traditional and reform mathematics curricula and strikes
a balance between promoting children’s natural solution methods and introducing new and effective mathematical practices. In order to promote and
implement natural and new methods, as well as to encourage students to become reflective and resourceful problem solvers, the course will assist
teachers in developing lessons that create a progressive and logical mathematical environment.
The Learner at this Level:
The Fifth Grade Child:
 Likes order and a harmonious environment.
 Finds comfort in themselves, their parents and siblings and teachers.
 Learns factual information easily.
 Knows the rules.
 Works well with others.
 Enjoys group games and projects.
 Concentrates on completing projects and tasks.
 Needs breaks and rest periods.
 Is a good problem solver.
Major Learning Goals and Understandings:
Algebraic Reasoning: The Fifth Grade Child:
 Performs complex classification and seriation tasks.
 Thinks based on rules and logic.
 Can articulate the rules embedded in a function, relationship, or pattern.
 Represents patterns in words, tables, graphs and equations.
 Describes how the change in one variable affects another variable in everyday situations.
 Models equivalence and solves one step equations using manipulatives .
Numerical and Proportional Reasoning: The Fifth Grade Child:
 Selects, uses, and explains various meanings and models for multiplication and division.
Grade 5 Page | 1
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Computes efficiently and accurately in all four operations.
Solves computation problems using the order of operations.
Comprehends the relationship between fractions, decimals and percentage.
Realizes that a percent means part of 100.
Identifies and represents decimals, fractions, mixed numbers, and positive and negative integers on a number line.
Uses drawings, number patterns or models to explain solutions for fraction and decimal problems.
Converts improper fractions to mixed numbers.
1. Fact Fluency Review
3. Perimeter and Area
5. Circles, Polygons, and Angles
7. Volume, Capacity, Weight and Time
9. Algebra, Functions and Graphs
11. Patterns and Transformations
13. Three-Dimensional Figures
Grade 5 Page | 2
Units/Concepts for the Year
2. Multiplication and Division Word Problems
4. Addition and Subtraction of Whole Numbers and Decimals
6. Addition and Subtraction of Fractions
8. Multiplication and Division of Whole Numbers and Decimals
10. Multiplication and Division w/Fractions
12. Ratio,, Proportion, and Percent
Grade:
5
Part 1 – Unit 1
Course:
Fact Fluency Review
Subject:
Math
Length of Unit:
About 16 days
Essential Questions and Big Ideas
EQ -What strategies can be used to increase fluency for multiplication and division facts?
BI- Focusing on number patterns increases fluency with multiplication and division facts.
BI- An array is a visual representation of both multiplication and division.
BI-Understanding the inverse relationship between multiplication and division increases fact fluency.
Part 2 – Standards
Algebraic Reasoning: Patterns and Functions
1.1 Understand and describe patterns and functional relationships.
Geometry and Measurement
3.1 Use properties and characteristics of two- and three- dimensional shapes and geometric theorems to describe relationships,
communicate ideas, and solve problems.
Numerical and Proportional Reasoning
2.1 Understand that variety of numerical representations can be used to describe quantitative relationships.
2.2 Use numbers and their properties flexibly and fluently and to reasonably estimate measures and quantities.
Students will be able to:
CMT Correlations
Grade Level Expectations
1.1.1 Represent, extend and compare
geometric and numeric patterns using
words, tables, graphs and equations.
2.1.5 Classify numbers as prime,
composite or perfect squares and
identify factor pairs using rectangular
arrays.
2.2.12 Develop and use strategies
involving place value relationships,
inverse operations and algebraic
properties (commutative, associative
and distributive to simplify addition,
subtraction and multiplication
problems with three-, four – and five
– digit numbers and money amounts
Grade 5 Page | 3
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Develop, find, and solve formulas for
area of rectangles.
Identify factor pairs using arrays, by
exploring multiplication tables, and by
using multiplication strategies.
Represent extend and compare
multiplication number patterns.
Describe multiplication and division as
inverse operations and use relationship
between quantities.
6A. Multiply and divide facts.
16B. Measure and determine perimeters and areas.
22A. Identify the missing terms in a pattern, or identify rules
for a given pattern using whole numbers and attributes.
22B. Extend or complete patterns and state rules for given
patterns using whole numbers and attributes.
and division by one-digit factors.
3.1.2 Develop formulas for finding
the perimeter and area of squares,
rectangles and triangles and use them
to solve problems.
Part 3 – Common Unit Assessment
Pre Assessment:
Math Expressions Assessment Guide
Unit 1 Test Form B (multiple choice)
Post Assessment:
Math Expressions Assessment Guide
Unit 1 Test Form A (short response)
Weekly Math Review Quiz
Part 4 – Common/Assured Learning Experiences
Promethean Board Activity: Student Work
FASTTMATH: 3 times a week
Study Island: Reinforcement of CMT basic skills
Common Vocabulary:
combination, factor, product, comparison, area, combination, equal groups, array comparison, factor, product, function, variable, equation, parentheses,
misleading, commutative property, associative property, distributive property, expression, example, counterexample
Daily Math Review (Computational review)
Math Journaling (End of Unit)
Grade 5 Page | 4
Part 5-Teacher Notes
Teacher Resources
Differentiated Instruction
LESSON PLANS
FLIP CHARTS
Electronic Resources:
http://prometheanplanet.com
http://thinkcentral.com
Grade 5 Page | 5
Part 1 – Unit 2
Grade:
5
Subject:
Math
Course:
Multiplication and
Division Word
Problems
Length of Unit:
About 16 days
Essential Questions and Big Idea
EQ –How are numbers classified?
BI - Numbers can be classified by identifying their factor pairs.
EQ - What is a variable?
BI - Variables are symbols that take the place of an unknown quantity.
EQ - How can relationships between quantities be represented?
BI - An expression and equation can be written to represent a relationship between quantities.
EQ - What is a function?
BI –A function is a consistent relationship between two sets of numbers.
Part 2 – Standards and State Frameworks
Algebraic Reasoning
1.2 Represent and analyze quantitative relationship in a variety of ways.
1.3 Use operations, properties and algebraic symbols to determine equivalence and solve problems.
Numerical and Proportional Reasoning
2.1 Understand that a variety of numerical representations can be used to describe quantitative relationships.
Grade Level Expectations
Students will be able to:
1.2.3 Represent and describe
 Represent and describe by making combinations,
mathematical relationships using
understanding comparisons, by writing and solving
variables or symbols in expressions,
problems and by using the math process.
equations and inequalities.
 Classify properties of numbers by writing word
problems.
1.2.4 Describe how a change in one  Describe how change in one variable affects another.
variable relates to a change in a
 Describe, evaluate, simplify by using the properties
second variable in context. For
of multiplication.
Example: If a recipe requires two
cups of flour for eight servings, the
four must be doubled for 1.
CMT Correlations
5 A. Identify the appropriate operation or number
sentence to solve a story problem.
1.3.5 Replace variables or symbols
in algebraic expressions with given
values and evaluate or simplify the
9B. Solve two-step story problems involving
whole numbers and money amounts with or
without extraneous information.
Grade 5 Page | 6
5B. Write story problems from multiplication or
division number sentences, using one- and twodigit numbers.
9A. Solve one-step story problems involving
whole numbers and money amounts with or
without extraneous information. Use all
operations.
expression e.g., If x =5, find the
value of 4x+7.
10A. Identify the best expression to find an
estimate.
1.3.6 Model, write and solve onestep equations by using appropriate
concrete materials that model
equivalence. For example: If 4 x Δ
= 36, then Δ equals 9.
11 A. Identify a reasonable estimate to a problem,
including estimating change.
22A. Extend or complete patterns, or identify
rules using numbers and attributes.
2.1.5 Classify numbers as prime,
composite or perfect squares and
identify factor pairs using
rectangular arrays.
22B. Extend or complete patterns and state rules
using numbers and attributes.
23 A. Solve simple one-step algebraic equations
involving addition, subtraction, multiplication
and fact families.
25A. Solve extended numerical and statistical
problems.
Part 3 – Common Unit Assessments
Pre Assessment:
Math Expressions Assessment Guide
Unit 2 Test Form B (multiple choice)
Post Assessment:
Math Expressions Assessment Guide
Unit 2 Test Form A (short response)
Weekly Math Review Quiz
Grade 5 Page | 7
Part 4 – Common/Assured Learning Experiences
Promethean Board Activity: Student Work
FASTTMATH: 3 times per week
Study Island: Reinforcement of CMT basic skills
Common Vocabulary:
combination, factor, product, comparison, area, combination, equal groups, array comparison, factor, product, function, variable, equation,
parentheses, misleading, commutative property, associative property, distributive property, expression, example, counterexample
Daily Math Review (Computational review)
Math Journaling (End of Unit)
Part 5-Teacher Notes
Teacher Resources
Differentiated Instruction
LESSON PLANS
FLIP CHARTS
Electronic Resources:
http://prometheanplanet.com
http://thinkcentral.com
Grade 5 Page | 8
Part 1 – Unit 3
Grade:
5
Subject:
Math
Course:
Perimeter and Area
Length of Unit:
About 10 days
Perimeter and Area
Essential Questions and Big Ideas
EQ – When and why is estimation used?
BI - Estimation is used to recognize when an answer is or is not reasonable, and to predict results.
EQ - What is perimeter?
BI - Perimeter is the distance around a geometric figure and is measured in units of length.
EQ - What is area?
BI - Area is measured by covering a geometric figure and is measured in square units.
Part 2 – Standards and State Frameworks
Numerical and Proportional Reasoning
2.2 Use numbers and their properties to compute flexibly and fluently and to reasonably estimate measures and quantities.
Geometry and Measurement
3.1. Use properties and characteristics for two and three dimensional shapes and geometric theorems to describe relationships, communicate
ideas and solve problems.
3.2 Use spatial reasoning, location, and geometric relationships to solve problems.
3.3 Develop and apply units, systems, formulas, and appropriate tools to estimate and measure.
Grade Level Expectations
2.2.19 Use estimation to predict
results and to recognize when an
answer is or is not reasonable, or
will result in an over estimate or
under estimate and explain the
reasoning used orally and in
writing.
Students will be able to:
3.1.2 Develop formulas for finding
the perimeter and area of squares,
rectangles and triangles and use
them to solve problems.
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3.1.3 Use the attributes of parallel
sides, perpendicular sides,
congruent sides/angles, number and
length of sides or faces, and number
Grade 5 Page | 9
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Develop and find the perimeter of polygons.
Find perimeter and area of complex figures.
Estimate and measure to solve a variety of problems
that involve length and area in customary and metric
units.
Use estimation to predict results and to recognize
when an answer is or is not reasonable or will result
in an over or underestimation.
Solve length problems involving conversions of
measure within the customary or metric systems.
Use different kinds of angles to identify different
kinds of triangles.
CMT Correlations
9A. Solve one-step story problems involving
whole numbers and money amounts with or
without extraneous information. Use all
operations.
9B. Solve two-step story problems involving
whole numbers and money amounts with or
without extraneous information.
10A. Identify the best expression to find an
estimate.
10B. Identify whether and why a particular
strategy will result in an overestimate or an
underestimate.
11A. Identify a reasonable estimate to a
problem, including estimating change.
and kinds of angles (right, acute and
obtuse) to describe, classify and
sort polygons and solids (cube,
prism, pyramid and sphere).
15A. Estimate lengths and areas.
16A. Measure lengths to the nearest quarter-inch
or half-centimeter.
16B. Measure and determine perimeters and
areas.
3.2.6 Analyze and describe the
effect that changing the dimensions
(perimeter) of a polygon has on its
area and vice versa.
16C. Identify appropriate customary or metric
units of measure (length, capacity and mass) for
a given situation.
3.3.8 Estimate and measure to solve
a variety of problems that involve
angles, length, area, weight, mass,
temperature, capacity and volume
in either metric or customary units
explain the reasoning used orally
and in writing.
16D. Solve problems involving conversions of
measures of length.
18D. Locate points on grids.
19A. Identify correct information from tables,
bar graphs, pictographs and charts.
23A. Solve simple one-step algebraic equations
involving addition, subtraction, multiplication
and fact families.
3.3.10 Solve length problems
involving conversions of measure
within the customary (inches, feet,
yards, miles) or metric systems
(millimeters, centimeters, meters,
and kilometers).
25A. Solve extended numerical and statistical
problems.
Part 3 – Common Unit Assessments
Pre Assessment:
Math Expressions Assessment Guide
Unit 3 Test Form B (multiple choice)
Post Assessment:
Math Expressions Assessment Guide
Unit 3 Test Form A (short response)
Weekly Math Review Quiz
Grade 5 Page | 10
Part 4 – Common/Assured Learning Experiences
Promethean Board Activity: Student Work
FASTTMATH : 3 times per week
Study Island: Reinforcement of CMT basic skills
Common Vocabulary:
meter, decimeter, centimeter, perimeter, area, square centimeter, square unit, base height, acute angle, right angle, obtuse angle, triangle, rectangle,
dimensions, complex figures, hexagon, pentagon, right triangle, acute triangle, obtuse triangle, equilateral triangle, isosceles triangle, scalene
triangle, inch, foot, yard, square inch, square foot, square yard
Daily Math Review (Computational review)
Math Journaling (End of Unit)
Part 5-Teacher Notes
Teacher Resources
Differentiated Instruction
LESSON PLANS
FLIP CHARTS
Electronic Resources:
http://prometheanplanet.com
http://thinkcentral.com
Grade 5 Page | 11
Part 1 – Unit 4
Grade:
5
Subject:
Math
Course:
Addition &
Subtraction of Whole
Numbers and
Decimals
Length of Unit:
About 31 days
Essential Questions and Big Ideas
EQ – What properties can be used to solve a problem?
BI – The Commutative, Associative, and Distributive Properties of our number system can be used to solve problems.
EQ -How and why do we use estimation?
BI - Estimation is used to recognize when an answer is or is not reasonable, and to predict results.
EQ - How do you know the value of a digit?
BI - The value of a digit is determined by its position.
EQ - How is each place value in our number system related to each other?
BI - The place value system is based on groups of ten.
EQ - How can you represent data?
BI – Graphs are the visual representation of data.
Part 2 – Standards and State Frameworks
Algebraic Reasoning
1.1Understand and describe patterns and functional relationships.
1.2 Represent and analyze quantitative relationships in a variety of ways.
Numerical and Proportional Reasoning
2.1 Understand that a variety of numerical representations can be used to describe quantitative relationships.
2.2 Use numbers and their properties to compute flexibly and fluently and to reasonably estimate measures and quantities.
Geometry and Measurement
3.1 Use properties and characteristics of two and three dimensional shapes and geometric theorems to describe relationships, communicate ideas
and solve problems.
Working with Data
4.1 Collect, organize and display data using appropriate statistical and graphical methods.
4.2 Analyze data sets to form hypotheses and make predictions.
Grade Level Expectations
1.1.2 Analyze patterns and data to
make generalizations, make
predictions and to identify trends.
Grade 5 Page | 12
Students will be able to:
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Compare, and represent whole numbers to 1,000,000
place.
Represent data in different kinds of plots and graphs
and mathematic relationships using variables and
CMT Correlations
1A. Solve problems involving 100 more/less or
1,000 more/less than a given number.
1B. Identify alternative forms of expressing
1.2.3 Represent and describe
mathematical relationships using
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variables or symbols in expressions, 
equations and inequalities.
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2.1.1 Compare, order and round
whole numbers to 1,000,000 using
number patterns, number lines and
diagrams.
2.1.2 Represent whole numbers up
to 1,000,000 in expanded and
regrouped forms and use the forms
to support computation.
2.1.3 Construct and use models,
number patterns and pictorial
representations to extend place
value concepts and patterns to
decimals. For example: 0.1 is onetenth of one and 0.01 is onehundredth of one and one-tenth of
one-tenth.
2.1.4 Investigate negative integers
(values less than zero) using place
value models, diagrams and number
lines; represent negative integers in
practical applications such as
temperatures, money and locations
below sea level.
2.2.10 Solve practical problems
involving 10, 100, 1,000 and 10,000
more or less than a number.
2.2.12 Develop and use strategies
involving place value relationships,
inverse operations and algebraic
Grade 5 Page | 13
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symbols, expressions, equations and inequalities.
Compare different representations of the same data.
Add and subtract whole numbers and decimals.
Develop strategies involving place value,
relationships, inverse operations, algebraic properties,
commutative, associative and distributive to simplify
subtraction and addition.
Use estimation to predict results and to recognize
when an answer is or is not reasonable, or will result
in an overestimate or underestimate.
Analyze patterns and data to make generalizations,
make predictions and identify trends.
Write and solve multistep problems for all four
operations involving multidigit whole numbers.
Design and conduct surveys of a representative
sample of a population and use the data collected to
begin to make inferences about the general
population.
whole numbers less than 10,000 using expanded
notation.
1C. Identify alternative forms of expressing
whole numbers less than 10,000 using
regrouping.
1D. Use place value concepts to identify and
compare the magnitude and value of digits in
numbers.
9A. Solve one-step story problems involving
whole numbers and money amounts with or
without extraneous information. Use all
operations.
9B. Solve two-step story problems involving
whole numbers and money amounts with or
without extraneous information.
10A. Identify the best expression to find an
estimate.
10B. Identify whether and why a particular
strategy will result in an over estimate or an
underestimate.
11A. Identify a reasonable estimate to a problem,
including estimating change.
18D. Locate points on grids.
19A. Identify correct information from tables, bar
graphs, pictographs and charts.
20A. Draw reasonable conclusions from data in
tables, bar graphs, pictographs, circle graphs and
charts.
20B. State a conclusion and explain why a claim
is or is not reasonable, based on the data.
22A. Identify the missing terms in a pattern, or
properties (commutative,
associative and distributive) to
simplify addition, subtraction and
multiplication problems with three,
four and five digit numbers and
money amounts and division by one
digit factors.
2.2.14 Write and solve multistep
problems for all four operations
involving multidigit whole numbers
and money amounts and explain
how answers were determined,
orally and in writing.
2.2.16 Add and subtract fractions,
decimals and mixed numbers using
a variety of strategies e.g., models,
mental math, equivalence and
substitutions: 1/2 +3/4 can also be
solved using 0.5 +0.75.
2.2.19 Use estimation to predict
results and to recognize when an
answer is or is not reasonable, or
will result in an overestimate or
underestimate and explain the
reasoning used orally and in
writing.
3.1.2 Develop formulas for finding
the perimeter and area of squares,
rectangles and triangles and use
them to solve problems.
4.1.1 Represent sets of data using
line plots, bar graphs, double bar
graphs, pictographs, simple circle
graphs, stem and leaf plots and
Grade 5 Page | 14
identify rules for a given pattern using whole
numbers and attributes.
22B. Extend or complete patterns and state rules
for given patterns using whole numbers and
attributes.
scatter plots.
4.1.2 Compare different
representations of the same data set
and evaluate how well each kind of
display represents the features of
the data.
4.2.3 Design and conduct surveys
of a representative sample of a
population and use the data
collected to begin to make
inferences about the general
population.
Part 3 – Common Unit Assessments
Pre Assessment:
Math Expressions Assessment Guide
Unit 4 Test Form B (multiple choice)
Post Assessment:
Math Expressions Assessment Guide
Unit 4 Test Form A (short response)
Weekly Math Review Quiz
Part 4 – Common/Assured Learning Experiences
Promethean Board Activity: Student Work
FASTTMATH: 3 times per week
Study Island: Reinforcement of CMT basic skills
Common Vocabulary:
meter, decimeter, centimeter, millimeter, standard from , word form, short from, short word form, expanded form, bar graph, double bar graph,
discrete data, continuous data, Commutative Property of Addition, Associative Property of Addition, Distributive Property, scale, estimate, front end
estimation, situation equation, solution equation, range, median, mode, yard
Grade 5 Page | 15
Daily Math Review (Computational review)
Math Journaling (End of Unit)
Part 5-Teacher Notes
Teacher Resources
Differentiated Instruction
LESSON PLANS
FLIP CHARTS
Electronic Resources:
http://prometheanplanet.com
http://thinkcentral.com
Grade 5 Page | 16
Part 1 – Unit 5
Grade:
5
Subject:
Math
Course:
Circles, Polygons, and
Angles
Length of Unit:
About 9 Days
Essential Questions and Big Ideas
EQ – What are the attributes of geometric figures?
BI – Attributes of geometric figures include parallel sides, perpendicular sides, congruent sides/angles, number of sides, number and kind of
angles.
EQ -What are graphs?
BI - Graphs are the visual representation of data.
Part 2 – Standards and State Frameworks
Algebraic Reasoning
1.1 Understand and describe patterns and functional relationships.
Numerical and Proportional Reasoning
2.2 Use numbers and their properties to compute flexibly and fluently and to reasonably estimate measures and quantities.
Geometry and Measurement
3.1 Use properties and characteristics of two and three dimensional shapes and geometric theorems to describe relationships, communicate ideas
and solve problems.
3.3 Develop and apply units, systems, formulas and appropriate tools to estimate and measure.
Working with Data
4.1 Collect, organize and display data using appropriate statistical and graphical methods.
Grade Level Expectations
1.1.2 Analyze patterns and data to
make generalizations, make
predictions and to identify trends.
Students will be able to:
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Grade 5 Page | 17
Measure and identify angles.
Find the measure of an unknown angle of a
polygon.
Identify congruent figures by using attributes of
CMT Correlations
10A. Identify the best expression to find an
estimate.
10B. Identify whether and why a particular
2.2.14 Write and solve multistep
problems for all four operations
involving multi-digit whole numbers
and money amounts and explain how
answers were determined, orally and
in writing.
2.2.15 Find fractional parts of a set by
using estimation counting, grouping of
objects, number patterns, equivalent
ratios and division.
2.2.16 Add and subtract fractions,
decimals and mixed numbers using a
variety of strategies, e.g., models
mental math, equivalence and
substitution: ½ +3/4 can also be solved
using 0.5+0.75.
3.1.3 Use the attributes of parallel
sides, perpendicular sides, congruent
sides/angles, number and length of
sides or faces and number and kinds of
angles (right, acute or obtuse) to
describe, classify and sort polygons
and solids (cube, prism, pyramid and
sphere).
3.1.4 Make and test conjectures about
polygons using geometric
relationships.
3.3.8 Estimate and measure to solve a
variety of problems that involve
angles, length, area, weight, mass,
temperature, capacity and volume in
either metric or customary units and
explain the reasoning used orally and
in writing.
Grade 5 Page | 18
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polygons.
Define, describe, sort and classify polygons.
Identify the position of an object after it has been
turned.
Represent, analyze and read circle graphs to solve
problems.
Discuss and explain the measurement of angles
orally and in writing.
strategy will result in an overestimate or an
underestimate.
Use information about geometric relationships to
identify, classify and form polygons.
17A. Identify, describe and/or classify twodimensional geometric shapes and figures.
11A. Identify a reasonable estimate to a problem,
including estimating change.
15A. Estimate lengths and areas.
16B. Measure and determine perimeters and
areas.
17B. Draw, describe and/or classify twodimensional geometric shapes and figures.
18A. Identify lines of symmetry.
18B. Draw lines of symmetry.
18C. Identify congruent figures.
19A. Identify correct information from tables, bar
graphs, pictographs and charts.
19B. Create bar graphs and pictographs from data
in tables and charts.
20 A. Draw reasonable conclusions from data in
tables, bar graphs, pictographs, circle graphs and
charts.
20B. State a conclusion and explain why a claim
is or is not reasonable, based on the data.
22A. Identify the missing terms in a pattern, or
identify rules for a given pattern using whole
numbers and attributes.
22B. Extend or complete patterns and state rules
for given patterns using whole numbers and
attributes.
24A. Solve logic, counting and classification
problems involving the organization of data.
24B. Sort or classify objects, and draw logical
conclusions from data including Venn diagrams
and transitive reasoning questions.
4.1.1 Represent sets of data using line
plots, bar graphs, double bar graphs,
pictographs, simple circle graphs, stem
and leaf plots and scatter plots.
25A. Solve extended numerical and statistical
problems.
Part 3 – Common Unit Assessments
Pre Assessment:
Math Expressions Assessment Guide
Unit 5 Test Form B (multiple choice)
Post Assessment:
Math Expressions Assessment Guide
Unit 5 Test Form A (short response)
Weekly Math Review Quiz
Part 4 – Common/Assured Learning Experiences
Promethean Board Activity: Student Work
FASTTMATH: 3 times per week
Study Island: Reinforcement of CMT basic skills
Common Vocabulary:
line, ray, angle, parallel, perpendicular, oblique, protractor, degree, right angle, straight angle, intersect, opposite angle, vertical angle,
complementary, supplementary, proof, polygon, congruent, isosceles triangle, equilateral triangle, scalene triangle, acute triangle, obtuse triangle,
right triangle, right trapezoid, reflex angle, circle, turn, line symmetry, line of symmetry, rotational symmetry, quarter turn, half turn, circle graph,
area, circumference, radius, diameter, pi
Daily Math Review (Computational review)
Math Journaling (End of Unit)
Grade 5 Page | 19
Part 5-Teacher Notes
Teachers Resources
Differentiated Instruction
LESSON PLANS
FLIP CHARTS
Electronic Resources:
http://prometheanplanet.com
http://thinkcentral.com
Grade 5 Page | 20
Part 1 – Unit 6
Grade:
5
Subject:
Math
Course:
Addition and
Subtraction of
Fractions
Length of Unit:
About 29 Days
Essential Questions and Big Ideas
EQ – What is a fraction?
BI – Fractional parts are equal shares or equal sized portions of a whole or a set.
EQ - How are fractions, decimals and mixed numbers placed on a number line or coordinate grid?
BI - Fractions, mixed numbers and decimals can be placed on a number line or coordinate to grid according to their relative size.
EQ- What are equivalent fractions?
BI - Two equivalent fractions are 2 ways of describing the same amount by using different sized fractional parts.
EQ - How are fractions added or subtracted?
BI – Fractions, decimals and mixed numbers can be added and subtracted using a variety of strategies (mental math, equivalence, substitution).
EQ – What is the probability of an event? How is it expressed?
The probability of an event is a number between 0 and 1 that is a measure of the chance that a given event will occur.
Part 2 – Standards and State Frameworks
Algebraic Reasoning
1.1 Understand and describe patterns and functional relationships.
Numerical and Proportional Reasoning
2.1 Understand that a variety of numerical representations can be used to describe quantitative relationships.
2.2 Use numbers and their properties to compute flexibly and fluently and to reasonably estimate measures and quantities.
Working with Data
4.3 Understand and apply basic concepts of probability.
Grade Level Expectations
The students will be able to:
CMT Correlations
1.1.2 Analyze pattern and data to
make generalizations, make
predictions and to identify trends.
Grade 5 Page | 21
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
Add and subtract fractions and mixed number with
like and unlike denominators.
Compare and order fractions and mixed numbers.
2A. Relate decimals (0.01-2.99) to pictorial
representations and vice versa.
2.1.1 Compare, order and round
whole numbers to 1,000,000 using
number patterns, number lines and
diagrams.
2.1.6 Represent equivalent
fractions, decimals, ratios and
percents using models, pictures,
number patterns and common
factors.
2.1.7 Choose and use benchmarks
to approximate locations, of
fractions, mixed numbers and
decimals, on number lines and
coordinate grids.
2.2.14 Write and solve multistep
problems for all four operations
involving multi-digit whole
numbers and money amounts and
explain how answers were
determined, orally and in writing.
2.2.15 Find fractional parts of a set
by using estimation counting,
grouping of objects, number
patterns, equivalent ratios and
division.
2.2.16 Add and subtract fractions,
decimals and mixed numbers using
a variety of strategies, e.g., models
mental math, equivalence and
substitution: ½ +3/4 can also be
solved using 0.5+0.75.
2.2.18 Use ratios and proportions to
Grade 5 Page | 22








Relate fractions and wholes.
Find equivalent fractions.
Conduct experiments, and express the probability of
an event as a fraction to solve problems.
Solve problems involving fractions.
Find fractional parts of a set or a whole.
Place fractions accurately on a number line.
Determine and describe possible outcomes of
permutations.
Conduct a survey and use the information to make
generalizations about a population.
2B. Relate fractions and mixed numbers to
pictures and vice versa.
2C. Identify and/or shade fractional parts of
regions, sets or mixed numbers in pictures.
3A. Rename equivalent fractions.
3B. Rename equivalent mixed numbers as
improper fractions and vice versa.
4B. Order mixed numbers, fractions and
decimals.
5A. Identify the appropriate operation or number
sentence to solve a story problem.
8A. Add and subtract fractions and mixed
numbers with like denominators.
21A. Identify correct solutions to problems
involving elementary notions of probability.
21B. Solve problems involving elementary
notions of probability and fairness, including
justifying solutions.
24A. Solve logic, counting and classification
problems involving the organization of data.
24B. Sort or classify objects, and draw logical
conclusions from data including Venn diagrams
and transitive reasoning questions.
25A. Solve extended numerical and statistical
problems.
solve practical problems, e.g.,
interpreting scale drawings and
maps and determining the
probability of an event.
4.3.5 Design and conduct
probability experiments and simple
games of chance to test predictions
about outcomes and fairness.
4.3.6 Determine and describe
possible outcomes and express the
likelihood of events as a fraction.
4.3.7 Determine and describe
possible outcomes using
permutations, where order does
matter, e.g., when there is a choice
of vanilla (V), chocolate (C) or
strawberry (S) ice cream for a three
scoop cone, there are two possible
ways to have the chocolate scoop
on top CVS or CSV.
Part 3 – Common Unit Assessments
Pre Assessment:
Math Expressions Assessment Guide
Unit 6 Test Form B (multiple choice)
Post Assessment:
Math Expressions Assessment Guide
Unit 6 Test Form A (short response)
Weekly Math Review Quiz
Grade 5 Page | 23
Part 4 – Common/Assured Learning Experiences
Promethean Board Activity: Student Work
FASTTMATH: 3 times per week
Study Island: Reinforcement of CMT basic skills
Common Vocabulary:
unit fraction, non-unit fraction, numerator, denominator, addend, sum, improper fraction, mixed number, ungroup, add on, subtract, equivalent
fractions, multiplier, simplify, unsimplify, multiplication table, equivalent, common denominator, least common denominator, probability, likely,
unlikely, certain, impossible, frequency table, line plot, benchmark
Daily Math Review (Computational review)
Math Journaling (End of Unit)
Part 5-Teacher Notes
Teacher Resources
Differentiated Instruction
LESSON PLANS
FLIP CHARTS
Electronic Resources:
http://prometheanplanet.com
http://thinkcentral.com
Grade 5 Page | 24
Part 1 – Unit 7
Grade:
5
Subject:
Math
Course:
Volume, Capacity,
Weight and Time
Length of Unit:
About 5 days
Essential Questions and Big Ideas
EQ – What is volume?
BI – Volume is the amount of space an object occupies and is measured in cubic units.
EQ - What is capacity?
BI - Capacity measures the amount a container can hold.
EQ - What is mass?
BI - Mass is the amount of matter in an object and is measured using units of weight.
EQ - How are elapsed time problems solved?
BI –There are a variety of strategies that can be used to solve elapsed time problems (conversion, counting up, etc.).
Part 2 – Standards
Geometry and Measurement
3.2 Use properties and characteristics of two and three-dimensional shapes and geometric theorems to describe relationships, communicate ideas
and solve problems.
3.3 Develop and apply units, systems, formulas and appropriate tools to estimate and measure.
Grade Level Expectations
3.1.1 Represent the surface of threedimensional solids using twodimensional nets.
3.3.7 Use calendars and clocks to
plan and sequence events and to
solve problems involving the
conversion of measures of time and
elapsed time using days, hours,
Grade 5 Page | 25
Students will be able to:





Find volume of a rectangular prism.
Solve problems involving capacity, mass and weight.
Solve problems involving elapsed time.
Estimate and solve problems involving area,
perimeter, temperature, and volume.
Measure in metric and customary units and convert
measurements.
CMT Correlations
15A. Estimate lengths and areas.
16A. Measure lengths to the nearest quarter-inch
or half-centimeter.
16B. Measure and determine perimeters and areas.
16C. Identify appropriate customary or metric
units of measure (length, capacity and mass) for a
minutes and seconds.
given situation.
3.3.8 Estimate and measure to solve
a variety of problems that involve
angles, length, area, weight, mass
temperature, capacity and volume
in either metric or customary units
and explain the reasoning used
orally and in writing.
16D. Solve problems involving conversions of
measures of length.
17A. Identify, describe and/or classify twodimensional geometric shapes and figures.
17B. Draw, describe and/or classify twodimensional geometric shapes and figures.
25A. Solve extended numerical and statistical
problems.
3.3.9 Use cubic inch or cubic
centimeter models to find the
volume of rectangular solids.
Part 3 – Common Unit Assessments
Pre Assessment:
Math Expressions Assessment Guide
Unit 7 Test Form B (multiple choice)
Post Assessment:
Math Expressions Assessment Guide
Unit 7 Test Form A (short response)
Weekly Math Review Quiz
Part 4 – Common/Assured Learning Experiences
Promethean Board Activity: Student Work
FASTTMATH: 3 times per week
Study Island: Reinforcement of CMT basic skills
Common Vocabulary:
capacity, cubic unit, mass, three-dimensional, volume, weight, face, edge, vertex, rectangular prism, one-dimensional, two-dimensional, liter,
kiloliter, milliliter, cup, pint, quart, gallon, kilogram, gram, milligram, ounce, pound, ton, degree Fahrenheit degree, Celsius, stem and leaf plot,
analog clock, digital clock
Daily Math Review (Computational review)
Grade 5 Page | 26
Math Journaling (End of Unit)
Part 5-Teacher Notes
Teacher Resources
Differentiated Instruction
LESSON PLANS
FLIP CHARTS
Electronic Resources:
http://prometheanplanet.com
http://thinkcentral.com
Grade 5 Page | 27
Part 1 – Unit 8
Grade:
5
Subject:
Math
Course:
Multiplication and
Division of Whole
numbers and Decimals
Length of Unit:
About 32 Days
Essential Questions and Big Ideas
EQ – What properties can be used to solve a problem?
BI - The Commutative, Associative, and Distributive Properties of our number system can be used to solve problems.
EQ – When and why is estimation used?
BI - Estimation is used to recognize when an answer is or is not reasonable and to predict results.
EQ - How are multiplication and division problems solved?
BI - There are a variety of strategies for solving multiplication and division problems.
EQ - What are measures of central tendency? How are they used?
BI - Measures of central tendency (mean, median, mode) are used to analyze data.
Part 2 – Standards
Algebraic Reasoning
1.1 Understand and describe patterns and functional relationships.
Numerical and Proportional Reasoning
2.1 Understand that a variety of numerical representations can be used to describe quantitative relationships.
2.2 Use numbers and their properties to compute flexibly and fluently and to reasonably estimate measures and quantities.
Working with Data
4.2 Analyze data sets to form hypotheses and make predictions.
Grade Level Expectations
Students will be able to:
CMT Correlations
1.1.1 Represent, extend, and
1A. Solve problems involving 100 more/less or
 Use patterns to enhance skills in multiplying and
compare geometric and numeric
1,000 more/less than a given number.
dividing whole numbers and decimals.
patterns using words, tables, graphs,  Solve multi-digit multiplication problems using
1B. Identify alternative forms of expressing
and equations.
various methods.
whole numbers less than 10,000 using expanded
Grade 5 Page | 28

1.1.2 Analyze patterns and data to
make generalizations, make
predictions and to identify trends.


2.1.2 Represent whole numbers up
to 1,000,000 in expanded and
regrouped forms and use the forms
to support computation.
2.1.9 Use models and pictures to
identify and compare ratios and
represent ratios in equivalent
fraction and decimal forms.
2.2.11 Estimate products and
missing factors using multiples of
10, 100 and 1,000.

Solve word problems involving multiplication of
larger numbers.
Solve multi-digit multiplication problems when one
or both factors are decimal numbers.
Round numbers to the nearest ten or hundred, and
round decimal numbers to the nearest tenth or
hundredth.
Solve problems in which over estimating or under
estimating requires adjustments.
notation.
1C. Identify alternative forms of expressing
whole numbers less than 10,000 using
regrouping.
1D. Use place value concepts to identify and
compare the magnitude and value of digits in
numbers.
2A. Relate decimals (0.01-2.99) to pictorial
representations and vice versa.
2B. Relate fractions and mixed numbers to
pictures and vice versa.
2C. Identify and/or shade fractional parts of
regions, sets or mixed numbers in pictures.
3A. Rename equivalent fractions.
3B. Rename equivalent mixed numbers as
improper fractions and vice versa.
4A. Order whole numbers less than 100,000.
2.2.12 Develop and use strategies
involving place value relationships,
inverse operations and algebraic
properties (commutative,
associative, and distributive) to
simplify addition, subtraction and
multiplication problems with three-,
four-and five-digit numbers and
money amounts and division by
one-digit factors.
2.2.13 Multiply and divide decimals
and money amounts by whole
numbers.
2.2.14 Write and solve multistep
problems for all four operations
involving multidigit whole numbers
and money amounts and explain
Grade 5 Page | 29
4B. Order mixed numbers, fractions and
decimals.
4C. Describe magnitude of whole numbers less
than 100,000 and decimals.
4D. Describe magnitude of mixed numbers and
fractions.
4E. Round whole numbers in context.
4F. Round decimals.
4G. Locate points (fractions, decimals and whole
numbers) on number lines and scales.
17A. Identify, describe and/or classify twodimensional geometric shapes and figures.
19A. Identify correct information from tables, bar
graphs, pictographs and charts.
20 A. Draw reasonable conclusions from data in
how answers were determined,
orally and in writing.
tables, bar graphs, pictographs, circle graphs and
charts.
22A. Identify the missing terms in a pattern, or
identify rules for a given pattern using whole
numbers and attributes.
2.2.19 Use estimation to predict
results and to recognize when an
answer is or is not reasonable, or
will result in an overestimate or
underestimate and explain the
reasoning used orally and in
writing.
22B. Extend or complete patterns and state rules
for given patterns using whole numbers and
attributes.
24A. Solve logic, counting and classification
problems involving the organization of data.
4.2.4 Determine the mean, mode
and median of a data set and
explain in writing, how they are
affected by a change in the data set.
25A. Solve extended numerical and statistical
problems.
Part 3 – Common Unit Assessments
Pre Assessment:
Math Expressions Assessment Guide
Unit 8 Test Form B (multiple choice)
Post Assessment:
Math Expressions Assessment Guide
Unit 8 Test Form A (short response)
Weekly Math Review Quiz
Part 4 – Common/Assured Learning Experiences
Promethean Board Activity: Student Work
FASTTMATH: 3 times per week
Study Island: Reinforcement of CMT basic skills
Common Vocabulary:
partial product, rectangle sections, expanded notation, rectangle rows, short cut, round, remainder, estimate, digit-by-digit, under-estimate, over estimate, adjusted estimate, divisible, even, odd, operation, mean, median, mode, range, maximum, minimum, outlier, stem-and-leaf plot
Grade 5 Page | 30
Daily Math Review (Computational review)
Math Journaling (End of Unit)
Part 5-Teacher Notes
Teacher Resources
Differentiated Instruction
LESSON PLANS
FLIP CHARTS
Electronic Resources:
http://prometheanplanet.com
http://thinkcentral.com
Grade 5 Page | 31
Part 1 – Unit 9
Grade:
5
Subject:
Math
Course:
Algebra, Functions
and Graphs
Length of Unit:
About 5 Days
Essential Questions and Big Ideas
EQ – How can relationships between quantities be represented?
BI - An expression and equation can be written to represent a relationship between quantities.
EQ - What is a function?
BI - Functions are a special relationship or rule between 2 related sets of numbers.
EQ - What is a graph?
BI - Graphs are the visual representation of data.
Part 2 – Standards and State Frameworks
Algebraic Reasoning
1.1 Understand and describe patterns and functional relationships.
1.2 Represent and analyze quantitative relationships in a variety of ways.
1.3 Use operations, properties and algebraic symbols to determine equivalence and solve problems.
Numerical and Proportional Reasoning
2.1 Understand that a variety of numerical representations can be used to describe quantitative relationships.
2.2 Use numbers and their properties to compute flexibly and fluently and to reasonably estimate measures and quantities.
Geometry and Measurement
3.2 Use spatial reasoning, location and geometric relationships to solve problems.
Grade Level Expectations
Students will able to:
CMT Correlations
1.1.1 Represent, extend and
1A. Solve problems involving 100 more/less or
 Find the prime factorization of composite numbers.
compare geometric and numeric
1,000 more/less than a given number.
 Use exponents and order of operations to simplify
patterns using words, tables, graphs
expressions and solve equations.
1B. Identify alternative forms of expressing
and equations.
 Use all operations to solve story problems involving
whole numbers less than 10,000 using expanded
whole numbers and money amounts.
Grade 5 Page | 32
1.1.2 Analyze patterns and data to
make generalizations, make
predictions and to identify trends.


1.2.3 Represent and describe

mathematical relationships using
variables or symbols in expressions, 
equations and inequalities.
1.2.4 Describe how a change in one
variable relates to a change in a
second variable in context. For
example: If a recipe requires two
cups of flour for eight servings, the
flour must be doubled for 16
servings or increased by one-half
for 12 servings.
1.3.5 Replace variables or symbols
in algebraic expressions with given
values and evaluate or simplify the
expressions, e.g., if p = 5, find the
value of 4 x p + 7.
1.3.6 Model, write and solve onestep equations by using appropriate
concrete materials that model
equivalence, e.g., if 4 x r = 36, then
r equals 9.
2.1.5 Classify numbers as prime,
composite or perfect squares and
identify factor pairs using
rectangular arrays.
2.1.7 Choose and use benchmarks
to approximate locations, of
fractions, mixed numbers and
decimals, on number lines and
Grade 5 Page | 33


Use what they know about equalities to find the value
of a variable.
Evaluate and use expressions, equations and
inequalities to represent real-world situations.
Represent functions with tables, rules and equations
and use them to solve real-world problems.
Identify the missing terms in a pattern, or identify
rules for a given pattern using whole numbers and
attributes.
Read and plot points of the coordinate system.
Solve problems involving grids and paths.
notation.
1C. Identify alternative forms of expressing
whole numbers less than 10,000 using
regrouping.
1D. Use place value concepts to identify and
compare the magnitude and value of digits in
numbers.
2A. Relate decimals (0.01-2.99) to pictorial
representations and vice versa.
2B. Relate fractions and mixed numbers to
pictures and vice versa.
2C. Identify and/or shade fractional parts of
regions, sets or mixed numbers in pictures.
3A. Rename equivalent fractions.
3B. Rename equivalent mixed numbers as
improper fractions and vice versa.
4A. Order whole numbers less than 100,000.
4B. Order mixed numbers, fractions and
decimals.
4C. Describe magnitude of whole numbers less
than 100,000 and decimals.
4D. Describe magnitude of mixed numbers and
fractions.
4E. Round whole numbers in context.
4F. Round decimals.
4G. Locate points (fractions, decimals and whole
numbers) on number lines and scales.
5 A. Identify the appropriate operation or number
sentence to solve a story problem.
5B. Write story problems from multiplication or
division number sentences, using one- and twodigit numbers.
9A. Solve one-step story problems involving
coordinate grids.
whole numbers and money amounts with or
without extraneous information. Use all
operations.
9B. Solve two-step story problems involving
whole numbers and money amounts with or
without extraneous information.
10A. Identify the best expression to find an
estimate.
11 A. Identify a reasonable estimate to a problem,
including estimating change.
17A. Identify, describe and/or classify twodimensional geometric shapes and figures.
2.2.19 Use estimation to predict
results and to recognize when an
answer is or is not reasonable, or
will result in an overestimate or
underestimate and explain the
reasoning used orally and in
writing.
3.2.5 Use an x, y coordinate system
to plot points, to estimate the
distance between points and to
determine the horizontal or vertical
distance between two points.
18D. Locate points on grids.
19A. Identify correct information from tables, bar
graphs, pictographs and charts.
20 A. Draw reasonable conclusions from data in
tables, bar graphs, pictographs, circle graphs and
charts.
22A. Extend or complete patterns, or identify
rules using numbers and attributes.
22B. Extend or complete patterns and state rules
using numbers and attributes.
23 A. Solve simple one-step algebraic equations
involving addition, subtraction, multiplication
and fact families.
24A. Solve logic, counting and classification
problems involving the organization of data.
25A. Solve extended numerical and statistical
problems.
Part 3 – Common Unit Assessments
Pre Assessment:
Math Expressions Assessment Guide
Unit 9 Test Form B (multiple choice)
Post Assessment:
Math Expressions Assessment Guide
Grade 5 Page | 34
Unit 9 Test Form A (short response)
Weekly Math Review Quiz
Part 4 – Common/Assured Learning Experiences
Promethean Board Activity: Student Work
FASTTMATH: 3 times per week
Study Island: Reinforcement of CMT basic skills
Common Vocabulary:
exponent, base, square root, prime factorization, order of operations, equation, variable, inverse operations, expression, evaluate, inequality, input,
function, output, coordinate plane, x-axis, y-axis, ordered pair, origin
Daily Math Review (Computational review)
Math Journaling (End of Unit)
Part 5-Teacher Notes
Teacher Resources
Differentiated Instruction
LESSON PLANS
FLIP CHARTS
Electronic Resources:
http://prometheanplanet.com
http://thinkcentral.com
Grade 5 Page | 35
Part 1 – Unit 10
Grade:
5
Subject:
Math
Course:
Multiplication and
Division w/Fractions
Length of Unit:
About 8 Days
Essential Questions and Big Idea
EQ – How are fractions multiplied or divided?
BI - Multiplying and dividing fractions can be solved using manipulatives, number lines and algorithms.
Part 2 – Standards and State Frameworks
Numerical and Proportional Reasoning
2.2 Use numbers and their properties to compute flexibly and fluently and to reasonably estimate measures and quantities.
Grade Level Expectations
Students will be able to:
CMT Correlations
2.2.17 Construct and use models
and pictorial representations to
multiply common fractions and
mixed numbers by whole
numbers.
2.2.18 Write division problems in
fraction form and round the
fraction form to estimate an
answer to a division problem. For
example: 14/3 = 4.5.






Multiply a whole number or a fraction by a fraction.
Divide fractions and whole numbers.
Change fractions to equivalent decimals.
Compare operations of fractions to operations with
whole numbers.
Solve problems with fractions and mixed operations.
Estimate the answer to a multiplication or division
question.
6A. Multiply and divide facts.
7A. Add and subtract two-, three- and four-digit
whole numbers and money amounts less than
$100.
7B. Multiply and divide multiples of 10 and 100
by 10 and 100.
7C. Multiply and divide two- and three-digit
whole numbers and money amounts less than $10
by one-digit numbers.
8A. Add and subtract fractions and mixed
numbers with like denominators.
17A. Identify, describe and/or classify twodimensional geometric shapes and figures.
Grade 5 Page | 36
19A. Identify correct information from tables, bar
graphs, pictographs and charts.
20 A. Draw reasonable conclusions from data in
tables, bar graphs, pictographs, circle graphs and
charts.
22A. Identify the missing terms in a pattern, or
identify rules for a given pattern using whole
numbers and attributes.
22B. Extend or complete patterns and state rules
for given patterns using whole numbers and
attributes.
24A. Solve logic, counting and classification
problems involving the organization of data.
25A. Solve extended numerical and statistical
problems.
Part 3 – Common Unit Assessments
Pre Assessment:
Math Expressions Assessment Guide
Unit 10 Test Form B (multiple choice)
Post Assessment:
Math Expressions Assessment Guide
Unit 10 Test Form A (short response)
Weekly Math Review Quiz
Part 4 – Common/Assured Learning Experiences
Promethean Board Activity: Student Work
FASTTMATH: 3 times per week
Study Island: Reinforcement of CMT basic skills
Common Vocabulary:
repeating pattern, term, growing pattern, shrinking pattern, function, rotation, reflection, translation, transformation, congruent, image, pre-image
Grade 5 Page | 37
Daily Math Review (Computational review)
Math Journaling (End of Unit)
Part 5-Teacher Notes
Teacher Resources
Differentiated Instruction
LESSON PLANS
FLIP CHARTS
Electronic Resources:
http://prometheanplanet.com
http://thinkcentral.com
Grade 5 Page | 38
Part 1 – Unit 11
Grade:
5
Subject:
Math
Course:
Patterns and
Transformations
Length of Unit:
About 5 Days
Essential Questions and Big Ideas
EQ – What kinds of patterns exist in mathematics?
BI - In math there are both number patterns and geometric patterns.
EQ - What are transformations and transitions?
BI -Patterns may repeat, grow, shrink, or involve transformations.
BI -Transformations include rotations and reflections.
BI -Translations are slides.
EQ - How can they be represented?
BI -They can be represented on a coordinate plane.
Part 2 – Standards and State Standards
Algebraic Reasoning
1.1 Understand and describe patterns and functional relationships.
Geometry and Measurement
3.2 Use special reasoning, location and geometric relationships to solve problems.
Grade Level Expectations
Students will be able to:
1.1.1 Represent, extend and compare
geometric and numeric patterns
using words, tables, graphs and
equations.
Grade 5 Page | 39



Extend repeating, growing, and shrinking geometric
and numerical patterns.
Describe and draw transformations.
Translate and reflect figures in the coordinate plane.
CMT Correlations
17A. Identify, describe and/or classify twodimensional geometric shapes and figures.
19A. Identify correct information from tables, bar
graphs, pictographs and charts.
1.1.2 Analyze patterns and data to
make generalizations, make
predictions and to identify trends.
20 A. Draw reasonable conclusions from data in
tables, bar graphs, pictographs, circle graphs and
charts.
22A. Identify the missing terms in a pattern, or
identify rules for a given pattern using whole
numbers and attributes.
3.2.5 Use an x, y coordinate system
to plot points, to estimate the
distance between points and to
determine the horizontal or vertical
distance between two points.
22B. Extend or complete patterns and state rules
for given patterns using whole numbers and
attributes.
24A. Solve logic, counting and classification
problems involving the organization of data.
25A. Solve extended numerical and statistical
problems.
Part 3 – Common Unit Assessments
Pre Assessment:
Math Expressions Assessment Guide
Unit 11 Test Form B (multiple choice)
Post Assessment:
Math Expressions Assessment Guide
Unit 11 Test Form A (short response)
Weekly Math Review Quiz
Part 4 – Common/Assured Learning Experiences
Promethean Board Activity: Student Work
FASTTMATH: 3 times per week
Study Island: Reinforcement of CMT basic skills
Common Vocabulary:
repeating pattern, term, growing pattern, shrinking pattern, function, rotation, reflection, translation, transformation, congruent, image, pre-image
Daily Math Review (Computational review)
Grade 5 Page | 40
Math Journaling (End of Unit)
Part 5-Teacher Notes
Teacher Resources
Differentiated Instruction
LESSON PLANS
FLIP CHARTS
Electronic Resources:
http://prometheanplanet.com
http://thinkcentral.com
Grade 5 Page | 41
Part 1 – Unit 12
Grade:
5
Subject:
Math
Course:
Ratio, Proportion and
Percent
Length of Unit:
About 4 days
Essential Questions and Big Ideas
EQ – What is a ratio?
BI - A ratio describes the relationship between two quantities.
EQ - What is a proportion?
BI - A proportion is an equation that shows two equivalent ratios.
EQ - What is percent?
BI -Percent is per hundred and is a number compared to a hundred.
Part 2 – Standards and State Frameworks
Algebraic Reasoning
1.1 Understand and describe patterns and functional relationships.
Numerical and Proportional Reasoning
2.1 Understand that a variety of numerical representations can be used to describe quantitative relationships.
2.2 Use numbers and their properties to compute flexibly and fluently and to reasonably estimate measures and quantities.
Geometry and Measurement
3.1 Use properties and characteristics of two-and three-dimensional shapes and geometric theorems to describe relationships, communicate idea
and solve problems.
Working with Data
4.3 Understand and apply basic concepts of probability.
Grade Level Expectations
Students will be able to:
CMT Correlations
1.1.1 Represent, extend and compare
geometric and numeric patterns
using words, tables, graphs and
equations.


1.1.2 Analyze patterns and data to
make generalizations, make
predictions and to identify trends.




Grade 5 Page | 42

Find basic ratios.
See relationships among fractions, decimals, and
percents.
Understand that a ratio describes a relationship
between two quantities.
Solve numeric proportion problems.
Apply unit rates to all multiplication situations.
Write and solve proportion word problems.
Solve problems using percents.
3A. Rename equivalent fractions.
3B. Rename equivalent mixed numbers as
improper fractions and vice versa.
4A. Order whole numbers less than 100,000.
4B. Order mixed numbers, fractions and
decimals.
4C. Describe magnitude of whole numbers less
than 100,000 and decimals.
2.1.5 Classify numbers as prime,
composite or perfect squares and
identify factor pairs using
rectangular arrays.



Express the probability of an event as a percent
Identify similar figures and use similarity to find
missing measurements.
Use a scale to find a distance on a map or a length on
a scale drawing.
4D. Describe magnitude of mixed numbers and
fractions.
4E. Round whole numbers in context.
4F. Round decimals.
2.1.6 Represent equivalent fractions,
decimals, ratios and percents using
models, pictures, number patterns
and common factors.
4G. Locate points (fractions, decimals and whole
numbers) on number lines and scales.
2.1.9 Use models and pictures to
identify and compare ratios and
represent ratios in equivalent
fraction and decimal forms.
5B. Write story problems from multiplication or
division number sentences, using one- and twodigit numbers.
2.2.14 Write and solve multistep
problems for all four operations
involving multidigit whole numbers
and money amounts and explain how
answers were determined, orally and
in writing.
2.2.18 Use ratios and proportions to
solve practical problems, e.g.,
interpreting scale drawings and maps
and determining the probability of an
event.
2.2.19 Use estimation to predict
results and to recognize when an
answer is or is not reasonable, or
will result in an overestimate or
underestimate and explain the
reasoning used orally and in writing.
3.1.4 Make and test conjectures
about polygons using geometric
relationships.
Grade 5 Page | 43
5A. Identify the appropriate operation or number
sentence to solve a story problem.
10A. Identify the best expression to find an
estimate.
17A. Identify, describe and/or classify twodimensional geometric shapes and figures.
19A. Identify correct information from tables, bar
graphs, pictographs and charts.
20 A. Draw reasonable conclusions from data in
tables, bar graphs, pictographs, circle graphs and
charts.
21A. Identify correct solutions to problems
involving elementary notions of probability.
21 B. Solve problems involving elementary
notions of probability and fairness, including
justifying solutions
22A. Identify the missing terms in a pattern, or
identify rules for a given pattern using whole
numbers and attributes.
22B. Extend or complete patterns and state rules
for given patterns using whole numbers and
attributes.
24A. Solve logic, counting and classification
problems involving the organization of data.
4.3.5 Design and conduct probability
experiments and simple games of
chance to test predictions about
outcomes and fairness.
24B. Sort or classify objects, and draw logical
conclusions from data including Venn diagrams
and transitive reasoning questions.
25A. Solve extended numerical and statistical
problems.
Part 3 – Common Unit Assessments
Pre Assessment:
Math Expressions Assessment Guide
Unit 12 Test Form B (multiple choice)
Post Assessment:
Math Expressions Assessment Guide
Unit 12 Test Form A (short response)
Weekly Math Review Quiz
Part 4 – Common/Assured Learning Experiences
Promethean Board Activity: Student Work
FASTTMATH: 3 times per week
Study Island: Reinforcement of CMT basic skills
Common Vocabulary:
unit, linked multiplication, column table, ratio, ratio table, proportion, basic ratio, factor puzzle, percent, similar, scale, scale drawing, key, floor
plan
Daily Math Review (Computational review)
Math Journaling (End of Unit)
Grade 5 Page | 44
Part 5-Teacher Notes
Teacher Resources
Differentiated Instruction
LESSON PLANS
FLIP CHARTS
Electronic Resources:
http://prometheanplanet.com
http://thinkcentral.com
Grade 5 Page | 45
Part 1 – Unit 13
Grade:
5
Subject:
Math
Course:
Three-Dimensional
Figures
Length of Unit:
About 5 Days
Essential Questions and Big Ideas
EQ – What are attributes of three-dimensional geometric shapes?
BI – Attributes of three-dimensional figures include congruent faces, number and shape of faces, number of edges and vertices.
EQ - How can the surface of a three-dimensional figure be represented?
BI – The surface of a three-dimensional solid can be represented using a two-dimensional net.
Part 2 – Standards and State Frameworks
Numerical and Proportional Reasoning
2.1 Understand that a variety of numerical representations can be used to describe quantitative relationships.
2.2 Use numbers and their properties to compute flexibly and fluently and to reasonably estimate measures and quantities.
Geometry and Measurement
3.1 Develop and apply units, systems, formulas and appropriate tools to estimate and measure.
Grade Level Expectations
Students will be able to:
CMT Correlations
2.1.9 Use models and pictures to
Grade
Expectations
identifyLevel
and compare
ratios and
represent ratios in equivalent,
fractional and decimal forms.


2.2.18 Use ratios and proportions to
solve practical problems, e.g.,
interpreting scale drawings and
maps and determining the
probability of an event.



3.1.1 Represent the surface of threedimensional solids using twodimensional nets.
3.1.3 Use the attributes of parallel
sides, perpendicular sides,
congruent sides/angles, number and
length of sides or faces and number
Grade 5 Page | 46

Identify three-dimensional figures.
Compare and contrast properties of three-dimensional
figures.
Recognize, use and create nets for three-dimensional
figures.
Find the surface area of prisms and pyramids.
Solve problems about the volume of prisms.
Describe three-dimensional rotations and rotational
symmetry.
2A. Relate decimals (0.01-2.99) to pictorial
representations and vice versa.
2B. Relate fractions and mixed numbers to
pictures and vice versa.
2C. Identify and/or shade fractional parts of
regions, sets or mixed numbers in pictures.
3A. Rename equivalent fractions.
3B. Rename equivalent mixed numbers as
improper fractions and vice versa.
4A. Order whole numbers less than 100,000.
4B. Order mixed numbers, fractions and
decimals.
4C. Describe magnitude of whole numbers less
than 100,000 and decimals.
4D. Describe magnitude of mixed numbers and
fractions.
and kinds of angles (right, acute or
obtuse) to describe, classify and
sort polygons and solids (cube,
prism, pyramid and sphere).
4E. Round whole numbers in context.
4F. Round decimals.
4G. Locate points (fractions, decimals and whole
numbers) on number lines and scales.
8A. Add and subtract fractions and mixed
numbers with like denominators.
9A. Solve one-step story problems involving
whole numbers and money amounts with or
without extraneous information. Use all
operations.
9B. Solve two-step story problems involving
whole numbers and money amounts with or
without extraneous information.
15A. Estimate lengths and areas.
16B. Measure and determine perimeters and
areas.
17A. Identify, describe and/or classify twodimensional geometric shapes and figures.
17B. Draw, describe and/or classify twodimensional geometric shapes and figures.
18A. Identify lines of symmetry.
18B. Draw lines of symmetry.
18C. Identify congruent figures.
18D. Locate points on grids.
24A. Solve logic, counting and classification
problems involving the organization of data.
24B. Sort or classify objects, and draw logical
conclusions from data including Venn diagrams
and transitive reasoning questions.
25A. Solve extended numerical and statistical
problems.
Grade 5 Page | 47
Part 3 – Common Unit Assessments
Pre Assessment:
Math Expressions Assessment Guide
Unit 13 Test Form B (multiple choice)
Post Assessment:
Math Expressions Assessment Guide
Unit 13 Test Form A (short response)
Weekly Math Review Quiz
Part 4 – Common/Assured Learning Experiences
Promethean Board Activity: Student Work
FASTTMATH: 3 times per week
Study Island: Reinforcement of CMT basic skills
Common Vocabulary:
rectangular prism, face, base, prism, cylinder, net, circumference, surface area, cube, edge, pyramid, cone, apex, view, rotation, axis of rotation,
clockwise, counterclockwise, rotational symmetry
Daily Math Review (Computational review)
Math Journaling (End of Unit)
Part 5-Teacher Notes
Teacher Resources
Differentiated Instruction
LESSON PLANS
FLIP CHARTS
Electronic Resources:
http://prometheanplanet.com
Grade 5 Page | 48
http://thinkcentral.com
Grade 5 Page | 49