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Lesson 1.1
Investigate • Place Value and
Patterns
Build on students’ understanding of
the base-ten system to develop sound
mathematical practices by asking
these questions.
• Why are base-ten blocks a good model
for understanding place value?
• What conclusions can you draw from
your model?
• How will you use the information from
the model?
• What happens when you move to the
left in place value positions?
Instructional Time: 1 day
Common Core Standard
CC.5.NBT.1 Recognize that in a multi-digit number, a digit in one
place represents 10 times as much as it represents in the place to
its right and 1_2 of what it represents in the place to its left.
Lesson Objective
Recognize the 10 to 1 relationship among
place-value positions.
Essential Question
Practice
3 PRACTICE
How can you describe the relationship
between two place-value positions?
Share and Show
Materials
• MathBoard
• base ten blocks
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
• Math Journal
• iTools: Base-Ten
Blocks
Engage Approximately 5 min.
1 ENGAGE
On Your Own
Approximately 10 min.
Students can begin independent practice
once they understand these place-value
concepts. Select exercises based on
students’ depth of understanding.
The exercises below require higher
order thinking skills and critical
reasoning, making them especially rich.
Exercises 13–18
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
© Houghton Mifflin Harcourt Publishing Company
Approximately 10 min.
Investigate • Activity to Build Conceptual
Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to recognize the
respective values of digits in a number
based on their place-value position.
As students work through Unlock
the Problem, gauge their level of
understanding to make better decisions
about how to progress through
instruction.
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How can you describe the relationship
between two place-value positions?
Any place value position is ten times
greater than the position to its right
1
and __
10 of the position to its left.
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Lesson 1.2
Place Value of Whole Numbers
• In what situations would it be better to
use word form or expanded form
instead of standard form?
• Do the numbers represent the same
value when written in different forms?
• How do you know which digit has the
greatest value in a number?
• What math vocabulary word describes
each set of three digits?
Instructional Time: 1 day
Common Core Standard
CC.5.NBT.1 Recognize that in a multi-digit number, a digit in one
place represents 10 times as much as it represents in the place to
its right and 1_2 of what it represents in the place to its left.
Lesson Objective
Essential Question
Practice
3 PRACTICE
How can you read, write, and represent whole
numbers through hundred millions?
Share and Show
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Materials
• MathBoard
• Math Journal
• HMH Mega Math
• iTools: Base-Ten
Blocks
• Animated Math Models
On Your Own
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Summarize Approximately 5 min.
4 SUMMARIZE
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to understand the
place value system for whole numbers
through hundred millions. As students
work through Unlock the Problem, gauge
their level of understanding to make
better decisions about how to progress
through instruction.
Build on students’ understanding of place
value to develop sound mathematical
practices by asking these questions.
28
Approximately 10 min.
Students can begin independent practice
once they understand these place value
concepts. Select exercises based on
students’ depth of understanding.
The exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 8, 14, 17 or 18–20
Engage Approximately 5 min.
1 ENGAGE
Teach and
Approximately
2 TEACH
andTalk
TALK
Approximately 10 min.
Essential Question
How can you read, write, and represent
whole numbers through hundred millions?
I identify the place value of each of the
digits within a period, name the number
and the period, and place a comma
between the periods.
Math Journal
Write Standard Form, Expanded Form, and
Word Form at the top of the page. Write
five numbers that are at least 8 digits long
under Standard Form. Write the expanded
form and the word form for each number
under the appropriated heading.
© Houghton Mifflin Harcourt Publishing Company
Read and write whole numbers through
hundred millions.
Chapter 1
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Lesson 1.3
Algebra • Properties
Instructional Time: 1 day
Common Core Standard
CC.5.NBT.6 Find whole-number quotients of whole numbers with
up to four-digit dividends and two-digit divisors, using strategies
based on place value, the properties of operations, and/or the
relationship between multiplication and division. Illustrate and
explain the calculation by using equations, rectangular arrays,
and/or area models.
Lesson Objective
Use properties of operations to solve
problems.
Essential Question
How can you use properties of operations
to solve problems?
Materials
• MathBoard
Models
• Math Journal
• Animated Math
• iTools: Counters
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Teach and
Approximately
2 TEACH
andTalk
TALK
© Houghton Mifflin Harcourt Publishing Company
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to use properties
of multiplication and addition to solve
problems. As students work through
Unlock the Problem, gauge their level of
understanding to make better decisions
about how to progress through
instruction.
Build on students’ understanding of
operations and properties to develop
sound mathematical practices by asking
these questions.
• What did you do first? Why?
• Will that method always work?
• What properties did you use to find
the answer?
• Why can you use that property for this
problem?
Practice
3 PRACTICE
Share and Show
Approximately 10 min.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
On Your Own
Approximately 10 min.
Students can begin independent practice
once they understand these addition
and multiplication properties. Select
exercises based on students’ depth of
understanding. The exercises below
require higher order thinking skills
and critical reasoning, making them
especially rich.
Exercises 10–12 or 13–16
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How can you use properties of operations
to solve problems?
I can use the Associative, Commutative,
Identity and Distributive Properties to
group numbers that are easier to add
or multiply.
Math Journal
Explain how you could mentally find
8 3 45 by using the Distributive Property.
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Lesson 1.4
Algebra • Powers of 10 and
Exponents
Build on students’ understanding of
modeling and place value to develop
sound mathematical practices by asking
these questions.
• Why are base-ten blocks a good model
for powers of ten?
• What conclusions can you draw from
your model?
• How would your model change if the
base number was not ten?
• What other patterns can you find?
Instructional Time: 1 day
Common Core Standard
CC.5.NBT.2 Explain patterns in the number of zeros of the product
when multiplying a number by powers of 10, and explain patterns in the
placement of the decimal point when a decimal is multiplied or divided
by a power of 10. Use whole-number exponents to denote powers of 10.
Lesson Objective
Essential Question
Practice
3 PRACTICE
How can you use an exponent to show powers
of 10?
Share and Show
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Materials
• MathBoard
• base-ten blocks
• Math Journal
• Animated Math
Models
• HMH Mega Math
• iTools: Base-Ten
Blocks
On Your Own
Teach and
Approximately
2 TEACH
andTalk
TALK
Summarize Approximately 5 min.
4 SUMMARIZE
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to use models and
repeated multiplication to understand
exponential form and powers of ten.
As students work through Unlock
the Problem, gauge their level of
understanding to make better decisions
about how to progress through
instruction.
30
Approximately 10 min.
Students can begin independent practice
once they understand these base-ten
concepts. Select exercises based on
students’ depth of understanding.
The exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 11, 13, 14
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Approximately 10 min.
Essential Question
How can you use an exponent to show
powers of 10?
I can count the number of times 10 is
used as a repeated factor and write that
number as the exponent.
Math Journal
Consider 7 3 103. Write a pattern to find
the value of the expression.
© Houghton Mifflin Harcourt Publishing Company
Write and evaluate repeated factors in
exponent form.
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Lesson 1.5
Algebra • Multiplication Patterns
Instructional Time: 1 day
Common Core Standard
CC.5.NBT.2 Explain patterns in the number of zeros of the product
when multiplying a number by powers of 10, and explain patterns in
the placement of the decimal point when a decimal is multiplied or
divided by a power of 10. Use whole-number exponents to denote
powers of 10.
Practice
3 PRACTICE
Lesson Objective
Use a basic fact and pattern to multiply
mentally by multiples of 10, 100, and 1,000.
Share and Show
Approximately 10 min.
How can you use a basic fact and a pattern to
multiply by a 2-digit number?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Materials
On Your Own
Essential Question
• MathBoard
• Animated Math
Models
• Math Journal
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
© Houghton Mifflin Harcourt Publishing Company
• Which operation did you use to
represent the situation? Why?
• How can you use a simpler problem to
help you find the answer?
• What property can you use to solve
this problem? Why?
• What other patterns did you find?
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to form two
generalizations based on patterns.
As students work through Unlock
the Problem, gauge their level of
understanding to make better
decisions about how to progress
through instruction.
Build on students’ understanding of
place value and patterns to develop
sound mathematical practices by asking
these questions.
Approximately 10 min.
Students can begin independent practice
once they understand the application
of these multiplication patterns. Select
exercises based on students’ depth of
understanding. The exercises below
require higher order thinking skills
and critical reasoning, making them
especially rich.
Exercises 20–23 or 24–26
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How can you use a basic fact and a
pattern to multiply by a 2-digit number?
I start with a basic fact, and then write
more equations with additional zeros in
factors until I find the product of the
original problem. I look for a pattern to
write the products.
Math Journal
Do the products 40 3 500 and 40 3 600
have the same number of zeros? Explain.
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Lesson 1.6
Multiply by 1-Digit Numbers
• What operation did you use to represent
the situation?
• Why does multiplication represent the
situation?
• What did you do first? Why?
• How do you know your answer is
reasonable?
Instructional Time: 1 day
Common Core Standard
CC.5.NBT.5 Fluently multiply multi-digit whole numbers using the
standard algorithm.
Lesson Objective
Essential Question
Practice
3 PRACTICE
How do you multiply by 1-digit numbers?
Share and Show
Materials
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
• MathBoard
• Math Journal
• Real World
Video, Ch. 1
• Animated Math
Models
• HMH Mega Math
• iTools: Base-Ten
Blocks
On Your Own
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Summarize Approximately 5 min.
4 SUMMARIZE
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to use the standard
algorithm to multiply by 1-digit numbers.
As students work through Unlock
the Problem, gauge their level of
understanding to make better
decisions about how to progress
through instruction.
Build on students’ understanding of
multiplication to develop sound
mathematical practices by asking
these questions.
32
Approximately 10 min.
Students can begin independent practice
once they understand how to multiply
using the standard algorithm Select
exercises based on students’ depth of
understanding. The exercises below
require higher order thinking skills
and critical reasoning, making them
especially rich.
Exercises 8–10 or 19
Engage Approximately 5 min.
1 ENGAGE
Teach and
Approximately
2 TEACH
andTalk
TALK
Approximately 10 min.
Essential Question
How do you multiply by 1-digit numbers?
I can use place value and regrouping.
I start by multiplying the ones, then the
tens, and so on, regrouping as necessary.
Math Journal
Show how to solve the problem 378 3 6
using place value with regrouping. Explain
how you knew when to regroup.
© Houghton Mifflin Harcourt Publishing Company
Multiply by 1-digit numbers.
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Lesson 1.7
Multiply by 2-Digit Numbers
Instructional Time: 1 day
Note: The instructional time for this lesson
can also be 2 days. Use the extra time to
complete some of the On Your Own exercises
as a class. Discuss how place value supports
the multiplication algorithm.
Common Core Standard
CC.5.NBT.5 Fluently multiply multi-digit whole numbers using
the standard algorithm.
Lesson Objective
Multiply by 2-digit numbers.
Practice
3 PRACTICE
Essential Question
How do you multiply by 2-digit numbers?
Share and Show
Materials
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
• MathBoard
• Math Journal
• Animated Math
Models
1
• HMH Mega Math
Engage Approximately 5 min.
ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
© Houghton Mifflin Harcourt Publishing Company
Build on students’ understanding of
multiplication and estimation to develop
sound mathematical practices by asking
these questions.
• Which operation did you use to
represent the situation?
• How does multiplication represent the
situation?
• Have you solved a problem similar to the
one given?
• How do you know your answer is
reasonable?
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to use place value
and regrouping to multiply by 2-digit
numbers. As students work through
Unlock the Problem, gauge their level
of understanding to make better
decisions about how to progress
through instruction.
On Your Own
Approximately 10 min.
Approximately 10 min.
Students can begin independent practice
once they understand these multiplication
concepts. Select exercises based on
students’ depth of understanding. The
exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 17–20
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How do you multiply by 2-digit numbers?
I multiply the first factor by the ones of the
second factor and regroup as necessary.
I multiply the first factor by the tens
of the second factor and regroup as
necessary. Then I add the two partial
products together.
Math Journal
Write a problem multiplying a 3-digit
number by a 2-digit number. Show all the
steps to solve it by using place value and
regrouping and by using partial products.
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Lesson 1.8
Relate Multiplication to Division
• Why does division represent the
situation?
• Why is a rectangular array a good model
for the given problem?
• What conclusions can you draw from
your model?
Instructional Time: 1 day
Common Core Standard
Lesson Objective
Practice
3 PRACTICE
Share and Show
Use multiplication to solve division problems.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Essential Question
How is multiplication used to solve a division
problem?
On Your Own
Materials
• MathBoard
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Summarize Approximately 5 min.
4 SUMMARIZE
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to use the
Distributive Property to relate
multiplication and division. As students
work through Unlock the Problem, gauge
their level of understanding to make
better decisions about how to progress
through instruction.
Build on students’ understanding of
multiplication and division to develop
sound mathematical practices by asking
these questions.
• Which operation did you use to
represent the situation?
34
Approximately 10 min.
Students can begin independent practice
once they understand the relationship
between multiplication and division.
Select exercises based on students’ depth
of understanding. The exercises below
require higher order thinking skills
and critical reasoning, making them
especially rich.
Exercises 8–10 or 11–14
• Math Journal
Teach and
Approximately
2 TEACH
andTalk
TALK
Approximately 10 min.
Essential Question
How is multiplication used to solve a
division problem?
First, I draw an area model, divide it into
two parts, and write the divisor on the left.
I write two multiples of the divisor whose
sum is equal to the dividend, divide those
numbers by the divisor, and write the
quotients. The sum of the quotients is the
answer.
Math Journal
For the problem 135 4 5, draw two
different ways to break apart the array.
Use the Distributive Property to write
products for each different way.
© Houghton Mifflin Harcourt Publishing Company
CC.5.NBT.6 Find whole-number quotients of whole numbers with
up to four-digit dividends and two-digit divisors, using strategies
based on place value, the properties of operations, and/or the
relationship between multiplication and division. Illustrate and
explain the calculation by using equations, rectangular arrays,
and/or area models.
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Lesson 1.9
Problem Solving • Multiplication
and Division
• What did you do first? Why?
• What strategy could you use to make
the calculation easier?
• What properties did you use to find
the answer?
• How do you know your answer is
reasonable?
Instructional Time: 1 day
Common Core Standard
CC.5.NBT.6 Find whole-number quotients of whole numbers with
up to four-digit dividends and two-digit divisors, using strategies
based on place value, the properties of operations, and/or the
relationship between multiplication and division. Illustrate and
explain the calculation by using equations, rectangular arrays,
and/or area models.
Lesson Objective
Share and Show
Use the strategy solve a simpler problem to
solve problems.
Essential Question
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
How can you use the strategy solve a simpler
problem to help you solve a division problem?
On Your Own
Materials
• MathBoard
• Math Journal
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
© Houghton Mifflin Harcourt Publishing Company
Practice
3 PRACTICE
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to solve division
problems by breaking difficult numbers
into numbers that are easier to divide.
As students work through Unlock
the Problem, gauge their level of
understanding to make better
decisions about how to progress
through instruction.
Build on students’ understanding of
multiples and properties to develop
sound mathematical practices by asking
these questions.
Approximately 10 min.
Approximately 10 min.
Students can begin independent
practice once they understand these
multiplication and division concepts.
Select exercises based on students’ depth
of understanding. The exercises below
require higher order thinking skills
and critical reasoning, making them
especially rich.
Exercises 6, 8, 9
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How can you use the strategy solve
a simpler problem to help you solve
a division problem?
I can use this strategy to break apart
a dividend into smaller numbers that are
simpler to divide to solve a problem.
Math Journal
Rewrite Exercise 4 with different numbers.
Solve the new problem and show your
work.
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Lesson 1.10
Algebra • Numerical Expressions
• How does that operation represent
the situation?
• How do you know?
• How do you decide which operation
to perform first?
Instructional Time: 1 day
Common Core Standard
Lesson Objective
Practice
3 PRACTICE
Write numerical expressions.
Share and Show
Essential Question
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
How can you use a numerical expression to
describe a situation?
Materials
• MathBoard
On Your Own
• Math Journal
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
20 min.
Summarize Approximately 5 min.
4 SUMMARIZE
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to translate words
into numerical expressions. As students
work through Unlock the Problem, gauge
their level of understanding to make
better decisions about how to progress
through instruction.
Build on students’ understanding of
operations and expressions to develop
sound mathematical practices by asking
these questions.
• Which operation did you use to
represent the situation?
36
Approximately 10 min.
Students can begin independent
practice once they understand how
to use numerical expressions. Select
exercises based on students’ depth
of understanding. The exercises below
require higher order thinking skills
and critical reasoning, making them
especially rich.
Exercises 9, 12, 13 or 14–17
Engage Approximately 5 min.
1 ENGAGE
Teach and
Approximately
2 TEACH
andTalk
TALK
Approximately 10 min.
Essential Question
How can you use a numerical expression
to describe a situation?
In the problem, I look for the language
that represents the operations. Then I
decide in which order the operations need
to be completed and write an expression.
If there is more than one operation, I put
parentheses around the first operation to
be completed.
Math Journal
Write a numerical expression. Then write
words to match the expression.
© Houghton Mifflin Harcourt Publishing Company
CC.5.OA.2 Write simple expressions that record calculations with
numbers, and interpret numerical expressions without evaluating
them.
Chapter 1
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Lesson 1.11
Algebra • Evaluate Numerical
Expressions
• What did you do first? Why?
• Have you solved a problem similar to
this one? Describe it.
• What do you think will happen if you
add before you multiply?
• How do you know your answer is
reasonable?
Instructional Time: 1 day
Common Core Standard
CC.5.OA.1 Use parentheses, brackets, or braces in numerical
expressions, and evaluate expressions with these symbols.
Lesson Objective
Practice
3 PRACTICE
Use the order operations to evaluate
numerical expressions.
Share and Show
Essential Question
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
In what order must operations be evaluated
to find the solution to a problem?
Materials
• MathBoard
• Math Journal
• Animated Math
Models
• HMH Mega Math
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Teach and
Approximately
2 TEACH
andTalk
TALK
© Houghton Mifflin Harcourt Publishing Company
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to learn the
fundamentals of the order of operations.
As students work through Unlock
the Problem, gauge their level of
understanding to make better
decisions about how to progress
through instruction.
Build on students’ understanding of
mathematical operations to develop
sound mathematical practices by asking
these questions.
Approximately 10 min.
On Your Own
Approximately 10 min.
Students can begin independent practice
once they understand how to apply the
order of operations to an expression.
Select exercises based on students’ depth
of understanding. The exercises below
require higher order thinking skills
and critical reasoning, making them
especially rich.
Exercises 12–14
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
In what order must operations be
evaluated to find the solution to a
problem?
1: perform operations in parentheses;
2: multiply and divide from left to right;
3: add and subtract from left to right.
Math Journal
Give two examples that show how using
parentheses can change the order in which
operations are performed in an expression.
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Lesson 1.12
Algebra • Grouping Symbols
• What did you do first? Why?
• Which operations did you use to
represent the situation? Why?
• What would happen if you did not
use parentheses?
Instructional Time: 1 day
Common Core Standard
CC.5.OA.1 Use parentheses, brackets, or braces in numerical
expressions, and evaluate expressions with these symbols.
Evaluate numerical expressions with
parentheses, brackets, and braces.
Practice
3 PRACTICE
Share and Show
Essential Question
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
In what order must operations be evaluated
to find a solution when there are parentheses
within parentheses?
On Your Own
Materials
• MathBoard
Engage Approximately 5 min.
1 ENGAGE
Teach and
Approximately
2 TEACH
andTalk
TALK
Summarize Approximately 5 min.
4 SUMMARIZE
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to extend their
understanding of the order of operations
to include grouping symbols. As students
work through Unlock the Problem, gauge
their level of understanding to make
better decisions about how to progress
through instruction.
Build on students’ understanding of the
order of operations to develop sound
mathematical practices by asking these
questions.
38
Approximately 10 min.
Students can begin independent practice
once they understand these algebra
concepts. Select exercises based on
students’ depth of understanding.
The exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 8, 10, 11
• Math Journal
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Approximately 10 min.
Essential Question
In what order must operations be
evaluated to find a solution when there
are parentheses within parentheses?
I must perform operations from the
innermost set of grouping symbols to the
outermost pair. The order is parentheses,
brackets, and then braces.
Math Journal
Explain how to use grouping symbols to
organize information appropriately.
© Houghton Mifflin Harcourt Publishing Company
Lesson Objective
Chapter 1
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Lesson 2.1
Place the First Digit
Instructional Time: 1 day
Common Core Standard
CC.5.NBT.6 Find whole-number quotients of whole numbers with up
to four-digit dividends and two-digit divisors, using strategies based
on place value, the properties of operations, and/or the relationship
between multiplication and division. Illustrate and explain the
calculation by using equations, rectangular arrays, and/or area models.
Lesson Objective
Place the first digit in the quotient by
estimating or using place value.
Essential Question
How can you tell where to place the first digit
quotient without dividing?
• Math Journal
• Real World
Video, Ch. 2
• Animated Math
Models
• HMH Mega Math
• iTools: Base-Ten
Blocks
Approximately 10 min.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
On Your Own
Approximately 10 min.
Students can begin independent practice
once they understand these division
concepts. Select exercises based on
students’ depth of understanding. The
exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 19, 23, 25
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Teach and
Approximately
2 TEACH
andTalk
TALK
Summarize Approximately 5 min.
4 SUMMARIZE
20 min.
© Houghton Mifflin Harcourt Publishing Company
Practice
3 PRACTICE
Share and Show
Materials
• MathBoard
Build on students’ understanding of
estimation and division to develop
sound mathematical practices by asking
these questions.
• How would estimation help you solve
this problem?
• What is another way to solve the
problem?
• How can you use math vocabulary in
your explanation?
• How do you know your answer is
reasonable?
Essential Question
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
evelopment is key. The goal of this activity
is for students to use estimation to place
the first digit in the quotient and to use
the division algorithm. As students work
through Unlock the Problem, gauge
their level of understanding to make
better decisions about how to progress
through instruction.
How can you tell where to place the first
digit quotient without dividing?
By using basic facts and compatible
numbers, I can estimate the value of the
quotient, which should allow me to place
the first digit of the quotient.
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Lesson 2.2
Divide by 1-Digit Divisors
Build on students’ understanding of
estimation and division to develop
sound mathematical practices by asking
these questions.
• What operation did you use to represent
the situation? Why?
• How would estimation help you solve
the problem?
• How do you know your answer is
reasonable?
Instructional Time: 1 day
Common Core Standard
CC.5.NBT.6 Find whole-number quotients of whole numbers with
up to four-digit dividends and two-digit divisors, using strategies
based on place value, the properties of operations, and/or the
relationship between multiplication and division. Illustrate and
explain the calculation by using equations, rectangular arrays,
and/or area models.
Lesson Objective
Essential Question
Practice
3 PRACTICE
Share and Show
How do you solve and check division
problems?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Materials
• MathBoard
• Math Journal
• HMH Mega Math
• iTools: Base-Ten
Blocks
On Your Own
Engage Approximately 5 min.
1 ENGAGE
Teach and
Approximately
2 TEACH
andTalk
TALK
Summarize Approximately 5 min.
4 SUMMARIZE
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to use the division
algorithm and to use inverse operations
to check their solutions. As students work
through Unlock the Problem, gauge their
level of understanding to make better
decisions about how to progress through
instruction.
42
Approximately 10 min.
Students can begin independent
practice once they understand these
multiplication and division concepts.
Select exercises based on students’ depth
of understanding. The exercises below
require higher order thinking skills
and critical reasoning, making them
especially rich.
Exercises 16–18 or 20–22
• Animated Math
Models
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Approximately 10 min.
Essential Question
How do you solve and check division
problems?
I multiply the quotient by the divisor, and
then add the remainder to the product. If
the result is identical to the dividend, the
problem checks.
Math Journal
Use a map to plan a trip in the United
States. Find the number of miles between
your current location and your destination,
and divide the mileage by the number of
days or hours that you wish to travel.
© Houghton Mifflin Harcourt Publishing Company
Divide 3- and 4-digit dividends by 1-digit
divisors.
Chapter 2
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Lesson 2.3
Investigate • Division with
2-Digit Divisors
mathematical practices by asking
these questions.
• Why are base-ten blocks a good model
for division?
• What conclusions can you draw from
your model?
• How would your model change if there
were 10 students in each row?
• How does the quick drawing support
your work?
Instructional Time: 1 day
Common Core Standard
CC.5.NBT.6 Find whole-number quotients of whole numbers with
up to four-digit dividends and two-digit divisors, using strategies
based on place value, the properties of operations, and/or the
relationship between multiplication and division. Illustrate and
explain the calculation by using equations, rectangular arrays,
and/or area models.
Lesson Objective
Practice
3 PRACTICE
Model division with 2-digit divisors using
base-ten blocks.
Share and Show
Essential Question
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Students can continue practice once they
understand these division models and
2-digit divisors. Select exercises based on
students’ depth of understanding. Use
the exercises below if you prefer to assign
fewer items.
Exercises 6, 8, 10
How can you use base-ten blocks to model
and understand division of whole numbers?
Materials
• MathBoard
• base-ten blocks
• Math Journal
• iTools: Base-Ten
Blocks
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
© Houghton Mifflin Harcourt Publishing Company
Approximately 20 min.
Investigate • Activity to Build Conceptual
Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to connect the area
model for multiplication to division with
2-digit divisors. As students work through
Unlock the Problem, gauge their level
of understanding to make better
decisions about how to progress
through instruction.
Build on students’ understanding of
modeling and division to develop sound
How can you use base-ten blocks to
model and understand division of whole
numbers?
First, I would use ones, tens and
hundreds blocks to model the dividend.
Then I would use one hundred block and
tens blocks to show 10 groups having the
same number as the divisor. I would use
the rest of the blocks to make more groups
of the same size. As I work, I may have to
regroup hundreds or tens.
Math Journal
Write a division problem that has 3-digit
dividend and a divisor between 10 and 20.
Show how to solve it by drawing a quick
picture.
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Lesson 2.4
Partial Quotients
• Which operation represents the
situation in the given problem? Why?
• What will you do first? Why?
• Will that method always work?
Instructional Time: 1 day
Common Core Standard
Practice
3 PRACTICE
Share and Show Approximately 10 min.
Lesson Objective
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Use partial quotients to divide by 2-digit
divisors.
Essential Question
On Your Own Approximately 10 min.
How can you use partial quotients to divide by
2-digit divisors?
Students can begin independent practice
once they understand division with partial
quotients. Select exercises based on
students’ depth of understanding. The
exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 14–17 or 18–21
Materials
• MathBoard
• Math Journal
• HMH Mega Math
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to learn a
different method (partial quotients) for
dividing with 2-digit divisors. As students
work through Unlock the Problem, gauge
their level of understanding to make
better decisions about how to progress
through instruction.
Build on students’ understanding of
division to develop sound mathematical
practices by asking these questions.
44
Essential Question
How can you use partial quotients to
divide by 2-digit divisors?
I multiply the divisor by ten and keep
subtracting that product from the dividend
until the result is less than that product.
Then I subtract other multiples of the
divisor until the result is less than the
divisor, or zero.
Math Journal
Explain how using a partial quotient to
divide is similar to using the Distributive
Property to multiply.
© Houghton Mifflin Harcourt Publishing Company
CC.5.NBT.6 Find whole-number quotients of whole numbers with
up to four-digit dividends and two-digit divisors, using strategies
based on place value, the properties of operations, and/or the
relationship between multiplication and division. Illustrate and
explain the calculation by using equations, rectangular arrays,
and/or area models.
Chapter 2
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Lesson 2.5
Estimate with 2-Digit Divisors
• What operation did you use to represent
the situation?
• What strategy could you use to help you
solve the problem?
• How did you discover the pattern?
• How do you know your answer is
reasonable?
Instructional Time: 1 day
Common Core Standard
CC.5.NBT.6 Find whole-number quotients of whole numbers with
up to four-digit dividends and two-digit divisors, using strategies
based on place value, the properties of operations, and/or the
relationship between multiplication and division. Illustrate and
explain the calculation by using equations, rectangular arrays,
and/or area models.
Practice
3 PRACTICE
Lesson Objective
Estimate quotients using compatible numbers.
Share and Show Approximately 10 min.
Essential Question
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
How can you use compatible numbers to
estimate quotients?
Materials
• MathBoard
• Math Journal
• Animated Math Models
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Teach and
Approximately
2 TEACH
andTalk
TALK
© Houghton Mifflin Harcourt Publishing Company
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to connect their
understanding of basic facts, patterns,
and compatible numbers to make an
estimate that helps them place the first
digit. As students work through
Unlock the Problem, gauge their level
of understanding to make better
decisions about how to progress
through instruction.
Build on students’ understanding of
number patterns and division to develop
sound mathematical practices by asking
these questions.
On Your Own Approximately 10 min.
Students can begin independent practice
once they understand these estimation and
division concepts. Select exercises based on
students’ depth of understanding.
The exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 21, 23, 24 or 25–27
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How can you use compatible numbers to
estimate quotients?
I round the divisor to a multiple of 10,
and I round the dividend to the nearest
multiple of the new divisor. Then I use a
basic fact pattern of zeros to complete
the estimate.
Math Journal
Create a division problem with a
2-digit divisor. Using more than 1 set
of compatible numbers, observe what
happens when you estimate using a
different divisor, a different dividend,
and when both are different. Using a
calculator, compare the estimates to the
answer and describe the differences.
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Lesson 2.6
Divide by 2-Digit Divisors
• Which operation did you use to
represent the situation? Why?
• What did you do first? Why?
• How do you know your answer is
reasonable?
Instructional Time: 1 day
Common Core Standard
Practice
3 PRACTICE
Share and Show Approximately 10 min.
Lesson Objective
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Divide by 2-digit divisors.
Essential Question
How can you divide by 2-digit divisors?
On Your Own Approximately 10 min.
Materials
• MathBoard
• Math Journal
Students can begin independent practice
once they understand how to use the
division algorithm. Select exercises based
on students’ depth of understanding.
The exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 16–21 or 22–24
• Animated Math
Models
• HMH Mega Math
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to use the division
algorithm to divide with 2-digit divisors.
As students work through Unlock
the Problem, gauge their level of
understanding to make better
decisions about how to progress
through instruction.
Build on students’ understanding of
estimation and division to develop
sound mathematical practices by asking
these questions.
46
Essential Question
How can you divide by 2-digit divisors?
First, I use compatible numbers and an
estimate to place the first digit. Then,
I repeat these steps: divide, multiply,
subtract and compare, and then regroup
when necessary.
Math Journal
Choose a problem that you solved in the
lesson, and solve the same problem using
the partial quotients method. Compare the
methods to solve the problems. Name the
method you like better, and explain why.
© Houghton Mifflin Harcourt Publishing Company
CC.5.NBT.6 Find whole-number quotients of whole numbers with
up to four-digit dividends and two-digit divisors, using strategies
based on place value, the properties of operations, and/or the
relationship between multiplication and division. Illustrate and
explain the calculation by using equations, rectangular arrays,
and/or area models.
Chapter 2
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Lesson 2.7
Interpret the Remainder
Instructional Time: 1 day
Common Core Standard
CC.5.NF.3 Interpret a fraction as division of the numerator by the
denominator ( _ba 5 a 4 b). Solve word problems involving division of
whole numbers leading to answers in the form of fractions or mixed
numbers, e.g., by using visual fraction models or equations to
represent the problem.
Also CC.5.NBT.6
Lesson Objective
Solve division problems and decide when to
write a remainder as a fraction.
Practice
3 PRACTICE
Essential Question
Share and Show Approximately 10 min.
When solving a division problem, when do
you write the remainder as a fraction?
Materials
• MathBoard
• Math Journal
• HMH Mega Math
• iTools: Base-Ten
Blocks
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Teach and
Approximately
2 TEACH
andTalk
TALK
© Houghton Mifflin Harcourt Publishing Company
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to solve division
problems and decide how to represent
the remainder. As students work
through Unlock the Problem, gauge their
level of understanding to make better
decisions about how to progress
through instruction.
Build on students’ understanding of
division and fractions to develop sound
mathematical practices by asking these
questions.
• What did you do first? Why?
• How do you know when to express the
remainder as a fraction?
• How do you know the answers are
equivalent?
• How can you use math vocabulary in
your explanation?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
On Your Own Approximately 10 min.
Students can begin independent practice
once they understand these division
concepts. Select exercises based on
students’ depth of understanding. The
exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 4, 6, 7
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
When solving a division problem, when do
you write the remainder as a fraction?
The remainder should be written as a
fraction when the remainder needs to
be part of the quotient. The context of
the problem determines whether the
remainder should be written as a fraction.
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Lesson 2.8
Adjust Quotients
• What did you do first? Why?
• What model could you use to help you
solve the problem?
• What would happen if you didn’t align
the place values?
Instructional Time: 1 day
Common Core Standard
Practice
3 PRACTICE
Share and Show Approximately 10 min.
Lesson Objective
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Adjust the quotient if the estimate is too high
or too low.
Essential Question
On Your Own Approximately 10 min.
How can you adjust the quotient if your estimate is too high or too low?
Students can begin independent practice
once they understand how to adjust
quotients. Select exercises based on
students’ depth of understanding. The
exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 22–24
Materials
• MathBoard
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is to familiarize students with
the conditions that are present when
an estimate is too high or too low.
As students work through Unlock
the Problem, gauge their level of
understanding to make better
decisions about how to progress
through instruction.
Build on students’ understanding of
division to develop sound mathematical
practices by asking these questions.
48
Essential Question
How can you adjust the quotient if your
estimate is too high or too low?
If the product is greater than the dividend,
decrease the estimate by 1. If the
difference is greater than or equal to
the divisor, increase the estimate by 1.
Math Journal
Explain the different ways that you can
use multiplication to estimate and solve
division problems.
© Houghton Mifflin Harcourt Publishing Company
CC.5.NBT.7 Find whole-number quotients of whole numbers with
up to four-digit dividends and two-digit divisors, using strategies
based on place value, the properties of operations, and/or the
relationship between multiplication and division. Illustrate and
explain the calculation by using equations, rectangular arrays,
and/or area models.
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Lesson 2.9
Problem Solving • Division
• Which operation did you use to
represent the situation?
• Why does division represent the
situation?
• What strategy could you use to help you
solve the problem?
• How does drawing a diagram support
your work?
Instructional Time: 1 day
Common Core Standard
CC.5.NBT.6 Find whole-number quotients of whole numbers with
up to four-digit dividends and two-digit divisors, using strategies
based on place value, the properties of operations, and/or the
relationship between multiplication and division. Illustrate and
explain the calculation by using equations, rectangular arrays,
and/or area models.
Lesson Objective
Practice
3 PRACTICE
Solve problems by using the strategy draw a
diagram.
Share and Show Approximately 10 min.
Essential Question
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
How can using the strategy draw a diagram
help you solve a division problem?
Materials
• MathBoard
• Math Journal
On Your Own Approximately 10 min.
• HMH Mega Math
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Teach and
Approximately
2 TEACH
andTalk
TALK
© Houghton Mifflin Harcourt Publishing Company
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to organize
information and use a strategy to solve
division problems. As students work
through Unlock the Problem, gauge
their level of understanding to make
better decisions about how to progress
through instruction.
Build on students’ understanding of
problem solving strategies and division to
develop sound mathematical practices by
asking these questions.
Students can begin independent practice
once they understand these division
concepts. Select exercises based on
students’ depth of understanding. The
exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 4–6
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How can using the strategy draw a
diagram help you solve a division
problem?
Drawing a diagram, such as a bar model,
helps me organize the information in a
way that I can understand.
Math Journal
Create a word problem that uses division.
Draw a bar model to help you write an
equation to solve the problem.
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Lesson 3.1
Investigate • Thousandths
• Why is a 10 3 10 grid a good model for
decimals?
• What conclusions can you draw from your
model?
• How would the model change to show
thousandths?
• How is this model similar to a base-ten
block model?
Instructional Time: 1 day
Common Core Standard
CC.5.NBT.1 Recognize that in a multi-digit number, a digit in one
place represents 10 times as much as it represents in the place to its
right and 1/10 of what it represents in the place to its left.
Also CC.5.NBT.3a
Lesson Objective
Practice
3 PRACTICE
Share and Show
Essential Question
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
How can you describe the relationship
between two decimal place-value positions?
Materials
• MathBoard
• color pencils
Problem Solving
• Math Journal
• Animated Math
Models
Engage Approximately 5 min.
1 ENGAGE
Teach and
Approximately
2 TEACH
andTalk
TALK
Summarize Approximately 5 min.
4 SUMMARIZE
20 min.
Investigate • Activity to Build Conceptual
Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to extend their
understanding of decimal place value to
thousandths. As students work through
Unlock the Problem, gauge their level
of understanding to make better
decisions about how to progress
through instruction.
Build on students’ understanding of
decimal place value to develop sound
mathematical practices by asking
these questions.
52
Approximately 10 min.
Students can begin independent practice
once they understand these decimal
place-value concepts. Select exercises based
on students’ depth of understanding. The
exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 17–20
• straightedge
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Approximately 10 min.
Essential Question
How can you describe the relationship
between two decimal place-value
positions?
The value of one place-value position is
10 times as much as the value of the
position to its right and 1/10 of the value
of the position to its left.
Math Journal
Write four decimals with the digit 4 in a
different place in each—ones, tenths,
hundredths, and thousandths. Then write
a statement that compares the value of
the digit 4 in the different decimals.
© Houghton Mifflin Harcourt Publishing Company
Model, read, and write decimals to
thousandths.
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Lesson 3.2
Place Value of Decimals
• Why is a place-value chart a helpful
model for this problem?
• What conclusions can you draw from the
place-value chart?
• How did you discover the pattern for
place value?
• What other patterns can you find?
Instructional Time: 1 day
Common Core Standard
CC.5.NBT.3a Read, write and compare decimals to
thousandths. Read and write decimals to thousandths
using base-ten numerals, number names, and expanded
form, e.g., 347.392 5 3 3 100 1 4 3 10 1 7 3 1 1 3 3
___
___
1
1
1
( __
10 ) 1 9 3 ( 100 ) 1 2 3 ( 1000 ).
Practice
3 PRACTICE
Also CC.5.NBT.1
Lesson Objective
Read and write decimals through thousandths.
Approximately 10 min.
How do you read, write, and represent
decimals through thousandths?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Materials
On Your Own
Essential Question
• MathBoard
• Math Journal
• Animated Math
Models
• HMH Mega Math
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
© Houghton Mifflin Harcourt Publishing Company
Share and Show
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to read, write,
and represent decimals through
thousandths. As students work through
Unlock the Problem, gauge their level
of understanding to make better
decisions about how to progress
through instruction.
Build on students’ understanding of
decimal place value to develop sound
mathematical practices by asking
these questions.
Approximately 10 min.
Students can begin independent
practice once they understand these
place value and decimal concepts. Select
exercises based on students’ depth
of understanding. The exercises below
require higher order thinking skills
and critical reasoning, making them
especially rich.
Exercises 12–14 or 15–18
SummarizeApproximately 5 min.
4 SUMMARIZE
Essential Question
How do you read, write, and represent
decimals through thousandths?
You can use a place-value chart to help
you see the value of each digit. Each place
is 10 times as much as the place to its right.
A decimal can be written in standard form,
word form, or expanded form. The last
digit determines the name of the decimal.
Math Journal
Write Standard Form, Expanded Form, and
Word Form at the top of the page. Under
Standard Form, write five decimals that
have at least 3 digits to the right of the
decimal point. Write the expanded form
and the word form for each number under
the appropriate heading.
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Lesson 3.3
Compare and Order Decimals
• What did you do first? Why?
• Have you solved a problem similar to the
given problem?
• What would happen if you did not line
up the decimal points?
• How do you know your answer is
reasonable?
Instructional Time: 1 day
Common Core Standard
CC.5.NBT.3b Read, write and compare decimals to thousandths.
Compare two decimals to thousandths based on meanings of the
digits in each place, using ., 5, and , symbols to record the results
of comparisons.
Compare and order decimals to thousandths
using place value.
Practice
3 PRACTICE
Share and Show
Essential Question
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
How can you use place value to compare and
order decimals?
Materials
• MathBoard
• Math Journal
On Your Own
• Animated Math
Models
• HMH Mega Math
Teach and
Approximately
2 TEACH
andTalk
TALK
Summarize Approximately 5 min.
4 SUMMARIZE
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to compare and
order decimals using place value or a
place-value chart. As students work
through Unlock the Problem, gauge their
level of understanding to make better
decisions about how to progress
through instruction.
Build on students’ understanding of
decimals and place value to develop
sound mathematical practices by asking
these questions.
54
Approximately 10 min.
Students can begin independent practice
once they understand these decimal and
place value concepts. Select exercises based
on students’ depth of understanding.
The exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 20–22 or 23–26
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Approximately 10 min.
Essential Question
How can you use place value to compare
and order decimals?
Line up the decimal points of the
numbers to be compared or ordered or use
a place-value chart. Compare the digits in
each place-value position, starting from
the greatest place-value position. The digit
that is greatest is the greatest number. If
the digits are the same, move to the next
lesser place-value position and compare
the digits.
Math Journal
Write a word problem that can be solved
by ordering three decimals to thousandths.
Include a solution.
© Houghton Mifflin Harcourt Publishing Company
Lesson Objective
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Lesson 3.4
Round Decimals
• What did you do first? Why?
• Have you solved a problem similar to
this one? Describe it.
• How can you use math vocabulary in
your explanation?
• What do you think will happen if the
last digit is a 5?
Instructional Time: 1 day
Common Core Standard
CC.5.NBT.4 Use place value understanding to round decimals
to any place.
Lesson Objective
Round decimals to any place.
Practice
3 PRACTICE
Essential Question
Share and Show Approximately 10 min.
How can you use place value to round
decimals to a given place?
Materials
• MathBoard
• Math Journal
• HMH Mega Math
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Teach and
Approximately
2 TEACH
andTalk
TALK
© Houghton Mifflin Harcourt Publishing Company
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to round decimals
to the nearest whole number, tenth or
hundredth using a place-value chart
and place value. As students work
through Unlock the Problem, gauge
their level of understanding to make
better decisions about how to progress
through instruction.
Build on students’ understanding of
decimals and place value to develop
sound mathematical practices by asking
these questions.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
On Your Own Approximately 10 min.
Students can begin independent practice
once they understand these decimal and
place value concepts. Select exercises based
on students’ depth of understanding.
The exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 11, 14, 17 or 20–23
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How can you use place value to round
decimals to a given place?
Find the digit in the place to which you
are rounding. Then, look at the digit to its
right. If that digit is greater than or equal
to 5, increase the digit in the place to
which you are rounding by 1 and drop the
digits to its right. If the digit to its right
is less than 5, keep the digit in the place
value you are rounding to the same and
drop the digits to its right.
Math Journal
Describe how to round 3.987 to the
nearest tenth.
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Lesson 3.5
Investigate • Decimal Addition
• Why are base-ten blocks a good model
for decimal addition?
• What conclusions can you make from
your model?
• Will this method always work for adding
decimals?
• How do you know?
Instructional Time: 1 day
Common Core Standard
CC.5.NBT.7 Add, subtract, multiply, and divide decimals to
hundredths, using concrete models or drawings and strategies based
on place value, properties of operations, and/or the relationship
between addition and subtraction; relate the strategy to a written
method and explain the reasoning used.
Model decimal addition using base-ten blocks.
Practice
3 PRACTICE
Share and Show Approximately 10 min.
Essential Question
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
How can you use base-ten blocks to model
decimal addition?
Materials
• MathBoard
• base-ten blocks
Problem Solving Approximately 10 min.
• Math Journal
Students can begin independent practice
once they understand these decimal and
addition concepts. Select exercises based
on students’ depth of understanding.
The exercise below requires higher order
thinking skills and critical reasoning,
making it especially rich.
Exercise 8
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Teach and
Approximately
2 TEACH
andTalk
TALK
Summarize Approximately 5 min.
4 SUMMARIZE
20 min.
Investigate • Activity to Build Conceptual
Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to use manipulatives
to model decimal addition. As students
work through Unlock the Problem, gauge
their level of understanding to make
better decisions about how to progress
through instruction.
Build on students’ understanding of
decimals and addition to develop sound
mathematical practices by asking
these questions.
56
Essential Question
How can you use base-ten blocks to model
decimal addition?
Model each addend using flats, longs, and
small cubes. Add the hundredths and, if
necessary, regroup every 10 hundredths as
1 tenth. Add the tenths and, if necessary,
regroup every 10 tenths as 1 one.
Math Journal
Explain why drawing a quick picture is
helpful when adding decimals.
© Houghton Mifflin Harcourt Publishing Company
Lesson Objective
Chapter 3
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Lesson 3.6
Investigate • Decimal Subtraction
Instructional Time: 1 day
Common Core Standard
CC.5.NBT.7 Add, subtract, multiply, and divide decimals to
hundredths, using concrete models or drawings and strategies based
on place value, properties of operations, and/or the relationship
between addition and subtraction; relate the strategy to a written
method and explain the reasoning used.
Lesson Objective
Practice
3 PRACTICE
Model decimal subtraction using base-ten
blocks.
Share and Show Approximately 10 min.
Essential Question
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
How can you use base-ten blocks to model
decimal subtraction?
Materials
• MathBoard
• base-ten blocks
Problem Solving Approximately 10 min.
• Math Journal
Students can begin independent
practice once they understand these
decimal and subtraction concepts. Select
exercises based on students’ depth of
understanding. The exercise below
requires higher order thinking skills and
critical reasoning, making it especially rich.
Exercise 8
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
Essential Question
20 min.
© Houghton Mifflin Harcourt Publishing Company
• Have you solved a problem similar to the
given problem?
• Why are base-ten blocks a good model
for decimal subtraction?
• What conclusions can you make from
your model?
• Will this method always work for
subtracting decimals?
Investigate • Activity to Build Conceptual
Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to use manipulatives
to model decimal subtraction. As students
work through Unlock the Problem, gauge
their level of understanding to make
better decisions about how to progress
through instruction.
Build on students’ understanding of
decimals and subtraction to develop
sound mathematical practices by asking
these questions.
How can you use base-ten blocks to model
decimal subtraction?
Model the first number using flats, longs
and small cubes. Then model the number
being subtracted by removing small cubes,
longs, and then flats that represent the
number. Regroup as needed.
Math Journal
Describe a problem involving decimals that
you would use a quick picture to solve.
Then solve the problem.
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Lesson 3.7
Estimate Decimal Sums and
Differences
• Which operation did you choose to
represent the situation?
• Why does addition represent the
situation in the given problem?
• What strategy could you use to make
the calculation easier?
• How do you know an estimate is a
reasonable answer?
Instructional Time: 1 day
Common Core Standard
Lesson Objective
Practice
3 PRACTICE
Make reasonable estimates of decimal sums
and differences.
Share and Show
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Essential Question
How can you estimate decimal sums and
differences?
On Your Own
Materials
Engage Approximately 5 min.
1 ENGAGE
Teach and
Approximately
2 TEACH
andTalk
TALK
Summarize Approximately 5 min.
4 SUMMARIZE
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to using rounding
and benchmarks to estimate decimal
sums and differences. As students work
through Unlock the Problem, gauge their
level of understanding to make better
decisions about how to progress
through instruction.
Build on students’ understanding of
decimals and estimation to develop
sound mathematical practices by asking
these questions.
58
Approximately 10 min.
Students can begin independent practice
once they understand these decimal and
estimation concepts. Select exercises based
on students’ depth of understanding.
The exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 13, 15, 16 or 17–18
• MathBoard
• Math Journal
• Animated Math Models
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Approximately 10 min.
Essential Question
How can you estimate decimal sums and
differences?
Rounding and number lines with
benchmarks can be used to estimate
decimal sums and differences.
Math Journal
Explain why estimation is an important
skill to know when adding and subtracting
decimals.
© Houghton Mifflin Harcourt Publishing Company
CC.5.NBT.7 Add, subtract, multiply, and divide decimals to
hundredths, using concrete models or drawings and strategies
based on place value, properties of operations, and/or the
relationship between addition and subtraction; relate the strategy
to a written method and explain the reasoning used.
Chapter 3
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Lesson 3.8
Add Decimals
• What did you do first? Why?
• What model could you use to help you
solve the problem?
• How does your drawing support your
answer?
• What would happen if you did not align
the place values?
Instructional Time: 1 day
Common Core Standard
CC.5.NBT.7 Add, subtract, multiply, and divide decimals to
hundredths, using concrete models or drawings and strategies
based on place value, properties of operations, and/or the
relationship between addition and subtraction; relate the strategy
to a written method and explain the reasoning used.
Practice
3 PRACTICE
Lesson Objective
Add decimals using place value.
Share and Show Approximately 10 min.
Essential Question
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
How can place value help you add decimals?
Materials
• MathBoard
• Math Journal
• HMH Mega Math
Approximately 10 min.
Students can begin independent practice
once they understand these decimal
addition concepts. Select exercises based
on students’ depth of understanding.
The exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 12–15
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Teach and
Approximately
2 TEACH
andTalk
TALK
SummarizeApproximately 5 min.
4 SUMMARIZE
20 min.
© Houghton Mifflin Harcourt Publishing Company
On Your Own
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to use place value
to add decimals. As students work through
Unlock the Problem, gauge their level
of understanding to make better
decisions about how to progress
through instruction.
Build on students’ understanding of
decimals and addition to develop sound
mathematical practices by asking
these questions.
Essential Question
How can place value help you add
decimals?
Aligning the place values of decimal
addends helps me add hundredths to
hundredths, tenths to tenths, ones to
ones, and so on.
Math Journal
Describe an addition problem that you
might need to regroup hundredths to
solve.
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Lesson 3.9
Subtract Decimals
• What did you do first? Why?
• What model could you use to help you
solve the problem?
• How does your drawing support your
work?
• What would happen if you did not start
with the least place value?
Instructional Time: 1 day
Common Core Standard
CC.5.NBT.7 Add, subtract, multiply, and divide decimals to
hundredths, using concrete models or drawings and strategies
based on place value, properties of operations, and/or the
relationship between addition and subtraction; relate the strategy
to a written method and explain the reasoning used.
Subtract decimals using place value.
Practice
3 PRACTICE
Share and Show
Essential Question
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
How can place value help you subtract
decimals?
Materials
On Your Own
• MathBoard
• Math Journal
• Animated Math Models
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
20 min.
Summarize Approximately 5 min.
4 SUMMARIZE
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to use place
value and regrouping to subtract
decimals. As students work through
Unlock the Problem, gauge their level
of understanding to make better
decisions about how to progress
through instruction.
Build on students’ understanding of
decimals and subtraction to develop
sound mathematical practices by asking
these questions.
60
Approximately 10 min.
Students can begin independent
practice once they understand these
decimal subtraction concepts. Select
exercises based on students’ depth of
understanding. The exercises below
require higher order thinking skills
and critical reasoning, making them
especially rich.
Exercises 13–17
Engage Approximately 5 min.
1 ENGAGE
Teach and
Approximately
2 TEACH
andTalk
TALK
Approximately 10 min.
Essential Question
How can place value help you subtract
decimals?
Aligning the place values helps me
subtract hundredths from hundredths,
tenths from tenths, ones from ones,
and so on.
Math Journal
Write a decimal subtraction problem that
requires regrouping to solve. Then solve
the problem.
© Houghton Mifflin Harcourt Publishing Company
Lesson Objective
Chapter 3
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Lesson 3.10
Algebra • Patterns with Decimals
Instructional Time: 1 day
Common Core Standard
CC.5.NBT.7 Add, subtract, multiply, and divide decimals to
hundredths, using concrete models or drawings and strategies
based on place value, properties of operations, and/or the
relationship between addition and subtraction; relate the
strategy to a written method and explain the reasoning used.
Lesson Objective
Identify, describe, and create numeric patterns
with decimals.
Practice
3 PRACTICE
Share and Show Approximately 10 min.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Essential Question
How can you use addition or subtraction to
describe a pattern or create a sequence with
decimals?
On Your Own
Materials
Approximately 10 min.
Students can begin independent practice
once they understand these decimal
pattern concepts. Select exercises based
on students’ depth of understanding. The
exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 11–15
• MathBoard
• Math Journal
• Animated Math Models
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
Essential Question
20 min.
© Houghton Mifflin Harcourt Publishing Company
• What did you do first? Why?
• How did you discover the pattern for
this problem?
• What rule did you make for this
pattern?
• How do you know if your answer is
reasonable?
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to identify patterns
in decimal number sequences and write
rules to define those patterns. As students
work through Unlock the Problem, gauge
their level of understanding to make
better decisions about how to progress
through instruction.
Build on students’ understanding of
decimals and numerical patterns to
develop sound mathematical practices by
asking these questions.
How can you use addition or subtraction
to describe a pattern or create a sequence
with decimals?
To describe a pattern, I need to analyze
the differences between one term and the
next. To create a sequence, I need to use
the pattern rule provided, which includes
the starting value.
Math Journal
Give an example of a rule describing the
pattern for a sequence. Then write the
terms of the sequence for your rule.
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Lesson 3.11
Problem Solving • Add and
Subtract Money
Build on students’ understanding of
decimals and problem solving to develop
sound mathematical practices by asking
these questions.
• What did you do first? Why?
• Which operations represent the given
situation?
• How does making a table support your
work?
• What would happen if you subtract
before adding?
Instructional Time: 1 day
Common Core Standard
CC.5.NBT.7 Add, subtract, multiply, and divide decimals to
hundredths, using concrete models or drawings and strategies
based on place value, properties of operations, and/or the
relationship between addition and subtraction; relate the
strategy to a written method and explain the reasoning used.
Lesson Objective
Essential Question
Practice
3 PRACTICE
Share and Show Approximately 10 min.
How can the strategy make a table help
you organize and keep track of your bank
account balance?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Materials
• MathBoard
• Math Journal
• Real World
Video, Ch. 3
On Your Own
• Animated Math
Models
• HMH Mega Math
• iTools:
Measurement
Students can begin independent practice
once they understand these decimal
concepts. Select exercises based on
students’ depth of understanding. The
exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 4–6
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
62
Approximately 10 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to organize
information to solve problems involving
money amounts. As students work
through Unlock the Problem, gauge their
level of understanding to make better
decisions about how to progress
through instruction.
Essential Question
How can the strategy make a table help
you organize and keep track of your bank
account balance?
I can use a table to record balances, add
deposits, and subtract checks.
Math Journal
Write a money problem that shows money
being added to and subtracted from a
bank account. Then solve the problem.
© Houghton Mifflin Harcourt Publishing Company
Solve problems using the strategy make a
table.
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Lesson 3.12
Choose a Method
Instructional Time: 1 day
Note: The instructional time for this lesson
can also be 2 days. Use the extra time to do
some of the On Your Own exercises as a class.
Discuss why place value is important when
adding or subtracting. Include Extend the
Math for additional practice and discussion.
Common Core Standard
CC.5.NBT.7 Add, subtract, multiply, and divide decimals to
hundredths, using concrete models or drawings and strategies
based on place value, properties of operations, and/or the
relationship between addition and subtraction; relate the
strategy to a written method and explain the reasoning used.
Lesson Objective
Choose a method to find a decimal sum or
difference.
Essential Question
Which method could you choose to find
decimal sums and difference?
Materials
• MathBoard
• Math Journal
• Animated Math
Models
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Teach and
Approximately
2 TEACH
andTalk
TALK
© Houghton Mifflin Harcourt Publishing Company
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to use different
methods when adding or subtracting
decimals. As students work through
Unlock the Problem, gauge their level
of understanding to make better
decisions about how to progress
through instruction.
Build on students’ understanding of
decimals and operations to develop
sound mathematical practices by asking
these questions.
• Have you solved a problem similar to the
one given? Describe its similarities.
• Will one of these methods always work
for a similar problem? Why?
• What properties did you use to find the
answer?
Practice
3 PRACTICE
Share and Show
Approximately 20 min.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Students can begin independent practice
once they understand these decimal
operation concepts. Select exercises based
on students’ depth of understanding.
The exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 27–29 or 30–33
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
Which method could you choose to find
decimal sums and difference?
I could choose to use mental math
and properties, paper and pencil, or a
calculator.
Math Journal
Write and solve a story problem for each
method you can use to find decimal sums
and differences.
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Lesson 4.1
Algebra • Multiplication Patterns
with Decimals
Build on students’ understanding of
decimals and patterns to develop
sound mathematical practices by asking
these questions.
• Which operation did you use to
represent the situation?
• Why does multiplication represent the
given situation?
• How did you discover the pattern of
adding a zero or moving the decimal
place?
Instructional Time: 1 day
Common Core Standard
CC.5.NBT.2 Explain patterns in the number of zeros of the product
when multiplying a number by powers of 10, and explain patterns in
the placement of the decimal point when a decimal is multiplied or
divided by a power of 10. Use whole-number exponents to denote
powers of 10.
Also CC.5.NBT.7
Find patterns in products when multiplying by
powers of 10.
Practice
3 PRACTICE
Share and Show
Essential Question
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
How can patterns help you place a decimal
point in a product?
Materials
• MathBoard
On Your Own Approximately 10 min.
• Math Journal
Students can begin independent practice
once they understand these decimal
concepts. Select exercises based on
students’ depth of understanding. The
exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 11–13 or 14
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual foundation for the lesson. Use evidence of
students’ understanding to decide how
deeply to discuss.
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Summarize Approximately 5 min.
4 SUMMARIZE
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to use place value
patterns when multiplying by powers
of 10. As students work through Unlock
the Problem, gauge their level of
understanding to make better
decisions about how to progress
through instruction.
66
Approximately 10 min.
Essential Question
How can patterns help you place a decimal
point in a product?
I can use a pattern to determine how many
places I need to move the decimal point.
For each increasing power of 10, I move
the decimal point one place to the right.
For each decreasing power of 10, I move
the decimal point one place to the left.
© Houghton Mifflin Harcourt Publishing Company
Lesson Objective
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Lesson 4.2
Investigate • Multiply Decimals
and Whole Numbers
sound mathematical practices by asking
these questions.
• What model could you use to help you
solve the problem?
• Why is a 10 3 10 grid a good model for
decimal operations?
• What conclusions can you draw from
your model?
• How do you know your answer is
reasonable?
Instructional Time: 1 day
Common Core Standard
CC.5.NBT.7 Add, subtract, multiply, and divide decimals to
hundredths, using concrete models or drawings and strategies
based on place value, properties of operations, and/or the
relationship between addition and subtraction; relate the strategy
to a written method and explain the reasoning used.
Lesson Objective
Practice
3 PRACTICE
Model multiplication of whole numbers and
decimals.
Essential Question
Share and Show Approximately 10 min.
How can you use a model to multiply a whole
number and a decimal?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Materials
• MathBoard
• color pencils
Problem Solving Approximately 10 min.
• Math Journal
• iTools: Base-Ten
Blocks
• Decimal Models
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide how
deeply to discuss.
Teach and
Approximately
2 TEACH
andTalk
TALK
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
20 min.
© Houghton Mifflin Harcourt Publishing Company
Students can begin independent
practice once they understand these
decimal concepts. Select exercises based
on students’ depth of understanding.
The exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 9–11
Investigate • Activity to Build Conceptual
Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to investigate
multiplication of whole numbers and
decimals. As students work through
Unlock the Problem, gauge their
level of understanding to make better
decisions about how to progress
through instruction.
Build on students’ understanding of
decimals and modeling to develop
How can you use a model to multiply a
whole number and a decimal?
I can model the decimal factor and then
repeat the model by the same number of
times as the whole-number factor. I can
find the product by renaming if necessary
and counting the number of each place
value that I have.
Math Journal
Explain how multiplying a whole number
and a decimal is similar to and different
from multiplying whole numbers.
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Lesson 4.3
Multiplication with Decimals and
Whole Numbers
• Have you solved a problem similar to
the one given?
• What model could you use to help you
solve the problem?
• How does your drawing support your
work?
• How do you know your answer is
reasonable?
Instructional Time: 1 day
Common Core Standard
Also CC.5.NBT.7
Lesson Objective
Practice
3 PRACTICE
Share and Show
Multiply a decimal and a whole number using
drawings and place value.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Essential Question
How can you use drawings and place value to
multiply a decimal and a whole number?
On Your Own Approximately 10 min.
Students can begin independent practice
once they understand these decimal
concepts. Select exercises based on
students’ depth of understanding.
The exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 17–20 or 21–23
Materials
• MathBoard
• Math Journal
• iTools: Base-Ten Blocks
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to use quick pictures
and place value to multiply a decimal
by a whole number. As students work
through Unlock the Problem, gauge their
level of understanding to make better
decisions about how to progress
through instruction.
Build on students’ understanding of
decimals and multiplication to develop
sound mathematical practices by asking
these questions.
68
Approximately 10 min.
Essential Question
How can you use drawings and place
value to multiply a decimal and a whole
number?
I can draw quick pictures using partial
products, renaming groups as necessary.
I can use place value to convert a decimal
multiplication to a whole number
multiplication, making sure I place the
decimal point correctly in the product.
Math Journal
Compare and contrast the methods you
can use to multiply a whole number and
a decimal.
© Houghton Mifflin Harcourt Publishing Company
CC.5.NBT.2 Explain patterns in the number of zeros of the product
when multiplying a number by powers of 10, and explain patterns in
the placement of the decimal point when a decimal is multiplied or
divided by a power of 10. Use whole-number exponents to denote
powers of 10.
Chapter 4
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Lesson 4.4
Multiply Using Expanded Form
Instructional Time: 1 day
Note: The instructional time for this lesson can
also be 2 days. Use the extra time to model
additional examples from On Your Own as a
class to strengthen understanding of why the
place-value method works.
Common Core Standard
CC.5.NBT.2 Explain patterns in the number of zeros of the product
when multiplying a number by powers of 10, and explain patterns in
the placement of the decimal point when a decimal is multiplied or
divided by a power of 10. Use whole-number exponents to denote
powers of 10.
Practice
3 PRACTICE
Also CC.5.NBT.7
Lesson Objective
Use expanded form and place value to
multiply a decimal and a whole number.
Essential Question
How can you use expanded form and place
value to multiply a decimal and a whole
number?
Materials
• MathBoard
• Math Journal
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
© Houghton Mifflin Harcourt Publishing Company
Build on students’ understanding of
decimals and problem solving strategies
to develop sound mathematical practices
by asking these questions.
• Which operation did you use to
represent the given situation?
• Why is an area model a good model for
the given problem?
• What conclusions can you draw from
your model?
• What is a different method for solving
this problem?
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to use models and
place value patterns to multiply decimals
by whole numbers. As students work
through Unlock the Problem, gauge their
level of understanding to make better
decisions about how to progress through
instruction.
Share and Show
Approximately 10 min.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
On Your Own
Approximately 10 min.
Students can begin independent practice
once they understand these decimal
concepts. Select exercises based on
students’ depth of understanding. The
exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 7, 9, 12
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How can you use expanded form and place
value to multiply a decimal and a whole
number?
I can use expanded form to draw an area
model and add the partial products. I can
use place value to convert a decimal
multiplication to a whole-number
multiplication. Then I can place the
decimal point correctly in the product.
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Lesson 4.5
Problem Solving • Multiply
Money
• What did you do first? Why?
• What model could you use to help you
solve the problem?
• How does your drawing support your
work?
• Why is a bar model a good model for
this problem?
Instructional Time: 1 day
Common Core Standard
Lesson Objective
Practice
3 PRACTICE
Share and Show
Solve problems using the strategy draw a
diagram to multiply money.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Essential Question
How can the strategy draw a diagram help
you solve a decimal multiplication problem?
On Your Own
• HMH Mega Math
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to organize
information to solve problems involving
money. As students work through
Unlock the Problem, gauge their
level of understanding to make better
decisions about how to progress
through instruction.
Build on students’ understanding of
decimals and problem solving strategies
to develop sound mathematical practices
by asking these questions.
70
Approximately 10 min.
Students can begin independent practice
once they understand these decimal
concepts. Select exercises based on
students’ depth of understanding. The
exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 5, 7, 8
Materials
• MathBoard
• Math Journal
Approximately 10 min.
Essential Question
How can the strategy draw a diagram
help you solve a decimal multiplication
problem?
Drawing a diagram, such as a bar model,
helps me organize the information in a
way that I can understand the steps I need
to take to solve the problem.
Math Journal
Create a word problem that uses
multiplication of money. Draw a bar
model to help you write equations to
solve the problem.
© Houghton Mifflin Harcourt Publishing Company
CC.5.NBT.7 Add, subtract, multiply, and divide decimals to
hundredths, using concrete models or drawings and strategies based
on place value, properties of operations, and/or the relationship
between addition and subtraction; relate the strategy to a written
method and explain the reasoning used.
Chapter 4
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Lesson 4.6
Investigate • Decimal
Multiplication
Instructional Time: 1 day
Note: The instructional time for this lesson
can also be 2 days. Use the extra time to
complete the entire lesson as a class. Consider
Extend the Math as an alternate model for
decimal multiplication.
Common Core Standard
CC.5.NBT.7 Add, subtract, multiply, and divide decimals to
hundredths, using concrete models or drawings and strategies
based on place value, properties of operations, and/or the
relationship between addition and subtraction; relate the
strategy to a written method and explain the reasoning used.
Practice
3 PRACTICE
Lesson Objective
Share and Show
Model multiplication of decimals.
How can you use a model to multiply
decimals?
Problem Solving
Materials
• Math Journal
• HMH Mega Math
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Approximately 10 min.
Students can begin independent practice
once they understand these decimal
concepts. Select exercises based on
students’ depth of understanding.
The exercise below requires higher order
thinking skills and critical reasoning,
making it especially rich.
Exercise 11
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
© Houghton Mifflin Harcourt Publishing Company
Approximately 10 min.
Use the checked exercises as a diagnotic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Essential Question
• MathBoard
• Decimal Models
• color pencils
Build on students’ understanding of
decimals and multiplication to develop
sound mathematical practices by asking
these questions.
• Which operation did you use to
represent the situation?
• Why is a decimal square a good model
for the given problem?
• What conclusions can you make from
your model?
• How can you use math vocabulary in
your explanation?
Investigate • Activity to Build Conceptual
Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to investigate using
models to multiply decimals. As students
work through Unlock the Problem, gauge
their level of understanding to make
better decisions about how to progress
through instruction.
How can you use a model to multiply
decimals?
I can shade columns of one or more
decimal squares with one color to
represent one factor. I can use another
color to shade rows of the shaded columns
to represent the other factor. Then I can
count or multiply to find how many small
squares are shaded twice.
Math Journal
Write a story problem that involves
multiplying a decimal less than 2 by a
decimal less than 1. Include the solution
and the work you did to find it.
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Lesson 4.7
Multiply Decimals
mathematical practices by asking these
questions.
• Which operation did you use to
represent the given situation?
• Have you solved a problem similar
to the one given? Describe it.
• What properties did you use to solve
the problem?
• How can estimation help you solve
the problem?
Instructional Time: 1 day
Common Core Standard
CC.5.NBT.2 Explain patterns in the number of zeros of the product
when multiplying a number by powers of 10, and explain patterns
in the placement of the decimal point when a decimal is multiplied
or divided by a power of 10. Use whole-number exponents to denote
powers of 10.
Also CC.5.NBT.7
Lesson Objective
Practice
3 PRACTICE
Essential Question
Share and Show
What strategies can you use to place
a decimal point in a product?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Materials
• MathBoard
• Math Journal
• HMH Mega Math
• iTools: Base-Ten
Blocks
• Animated Math Models
On Your Own
Teach and
Approximately
2 TEACH
andTalk
TALK
Summarize Approximately 5 min.
4 SUMMARIZE
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to use place value
or estimation to correctly place the
decimal point in a product. As students
work through Unlock the Problem, gauge
their level of understanding to make
better decisions about how to progress
through instruction.
Build on students’ understanding of
decimals and operations to develop sound
72
Approximately 10 min.
Students can begin independent practice
once they understand these decimal
concepts. Select exercises based on
students’ depth of understanding. The
exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 15–22 or 23–25
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Approximately 10 min.
Essential Question
What strategies can you use to place a
decimal point in a product?
I can multiply the same way I would
with whole numbers and then move the
decimal point one place to the left in
the product for each decimal place in
the factors; or, I could use estimation to
predict what the whole number should be
and use that number to place the decimal.
Math Journal
Write a problem that includes multiplying
decimals. Explain how you know where to
place the decimal in the product.
© Houghton Mifflin Harcourt Publishing Company
Place the decimal point in decimal
multiplication.
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Lesson 4.8
Zeros in the Product
Instructional Time: 1 day
Common Core Standard
CC.5.NBT.2 Explain patterns in the number of zeros of the product
when multiplying a number by powers of 10, and explain patterns in
the placement of the decimal point when a decimal is multiplied or
divided by a power of 10. Use whole-number exponents to denote
powers of 10.
Also CC.5.NBT.7
Practice
3 PRACTICE
Lesson Objective
Multiply decimals with zeros in the product.
Share and Show Approximately 10 min.
Essential Question
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
How do you know you have the correct
number of decimal places in your product?
Materials
• MathBoard
• Animated Math
Models
• Math Journal
• HMH Mega Math
• Real World Video, Ch. 4
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Teach and
Approximately
2 TEACH
andTalk
TALK
© Houghton Mifflin Harcourt Publishing Company
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to have the correct
number of decimal places in a product.
As students work through Unlock
the Problem, gauge their level of
understanding to make better
decisions about how to progress
through instruction.
Build on students’ understanding of
decimal multiplication to develop
sound mathematical practices by asking
these questions.
• Have you solved a problem similar to
this one? Describe the similarities.
• How can estimation help you solve the
problem?
• How do you know your answer is
reasonable?
• How can you use math vocabulary
in your explanation?
On Your Own Approximately 10 min.
Students can begin independent
practice once they understand these
decimal multiplication concepts. Select
exercises based on students’ depth of
understanding. The exercises below
require higher order thinking skills
and critical reasoning, making them
especially rich.
Exercises 15–17
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How do you know you have the correct
number of decimal places in your product?
I can count the number of decimal place
values in each factor and add to find the
correct number of place values the product
should have.
Math Journal
Explain how you write products when
there are not enough digits in the product
to place the decimal point.
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Lesson 5.1
Algebra • Division Patterns with
Decimals
• What is the problem asking?
• What patterns can you find in the given
problem?
• How can you use math vocabulary in
your explanation?
• How do you know your answer is
reasonable?
Instructional Time: 1 day
Common Core Standard
Lesson Objective
Practice
3 PRACTICE
Share and Show
Find patterns in quotients when dividing by
powers of 10.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Essential Question
How can patterns help you place the decimal
point in a quotient?
On Your Own
• MathBoard
• Math Journal
• Animated Math Models
Engage Approximately 5 min.
1 ENGAGE
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to use place value
patterns and exponents to place the
decimal point in quotients. As students
work through Unlock the Problem, gauge
their level of understanding to make
better decisions about how to progress
through instruction.
Build on students’ understanding of
decimals and place value to develop
sound mathematical practices by asking
these questions.
76
Approximately 10 min.
Students can begin independent practice
once they understand these decimal
concepts. Select exercises based on
students’ depth of understanding.
The exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 11–13 or 14–16
Materials
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Approximately 10 min.
Essential Question
How can patterns help you place the
decimal point in a quotient?
I can use a pattern of powers of ten. The
decimal moves one place to the left each
time the divisor increases by a power of 10.
Math Journal
Explain how to use a pattern to find
35.6 4 102.
© Houghton Mifflin Harcourt Publishing Company
CC.5.NBT.2 Explain patterns in the number of zeros of the product
when multiplying a number by powers of 10, and explain patterns
in the placement of the decimal point when a decimal is multiplied
or divided by a power of 10. Use whole-number exponents to denote
powers of 10.
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Lesson 5.2
Investigate • Divide Decimals by
Whole Numbers
Instructional Time: 1 day
Common Core Standard
CC.5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on
place value, properties of operations, and/or the relationship between
addition and subtraction; relate the strategy to a written method and
explain the reasoning used.
Lesson Objective
Practice
3 PRACTICE
Model division of decimals by whole numbers.
Share and Show Approximately 10 min.
Essential Question
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
How can you use a model to divide a decimal
by a whole number?
Materials
• MathBoard
• Decimal Models
• color pencils
Problem Solving Approximately 10 min.
• base-ten blocks
• Math Journal
Students can begin independent practice
once they understand these decimal
concepts. Select exercises based on
students’ depth of understanding.
The exercise below requires higher order
thinking skills and critical reasoning,
making it especially rich.
Exercise 12
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
Essential Question
20 min.
© Houghton Mifflin Harcourt Publishing Company
• Which operation did you use to
represent the situation?
• What model could you use to help
you solve the problem?
• Why did you decide to use base-ten
blocks?
• How do you know your answer is
reasonable?
Investigate • Activity to Build Conceptual
Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to use models
to divide decimals by whole numbers.
As students work through Unlock
the Problem, gauge their level of
understanding to make better
decisions about how to progress
through instruction.
Build on students’ understanding of
decimals and division to develop
sound mathematical practices by asking
these questions.
How can you use a model to divide a
decimal by a whole number?
I can use base-ten blocks or other decimal
models to show the dividend. Then I
can share the blocks equally among the
number of groups shown by the divisor.
I may need to regroup sometimes to share
equally. The number in each group is the
quotient.
Math Journal
Explain how you can use base-ten blocks
or other decimal models to find 3.15 4 3.
Include pictures to support your
explanation.
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Lesson 5.3
Estimate Quotients
• What do you remember about
compatible numbers?
• What is the problem asking?
• What strategy could you use to
solve the given problem?
• Why is using compatible numbers
a good strategy for this problem?
Instructional Time: 1 day
Common Core Standard
Lesson Objective
Estimate decimal quotients.
Practice
3 PRACTICE
Share and Show
Essential Question
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
How can you estimate decimal quotients?
Materials
• MathBoard
On Your Own
• Math Journal
Engage Approximately 5 min.
1 ENGAGE
20 min.
Summarize Approximately 5 min.
4 SUMMARIZE
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to use compatible
numbers and rounding to estimate
quotients. As students work through
Unlock the Problem, gauge their level
of understanding to make better
decisions about how to progress
through instruction.
Build on students’ understanding of
compatible numbers and decimals to
develop sound mathematical practices
by asking these questions.
78
Approximately 10 min.
Students can begin independent practice
once they understand these estimation
concepts. Select exercises based on
students’ depth of understanding.
The exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 10, 14, 17 or 18–20
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Teach and
Approximately
2 TEACH
andTalk
TALK
Approximately 10 min.
Essential Question
How can you estimate decimal quotients?
I can use compatible numbers to find an
estimate. I need to look at the whole
number part of the decimal dividend. If
the whole number is smaller than the
divisor, I need to rename the decimal as
tenths or hundredths first and then find
the compatible number.
Math Journal
Explain how to find an estimate for the
quotient 3.4 4 6.
© Houghton Mifflin Harcourt Publishing Company
CC.5.NBT.7 Add, subtract, multiply, and divide decimals to
hundredths, using concrete models or drawings and strategies
based on place value, properties of operations, and/or the
relationship between addition and subtraction; relate the
strategy to a written method and explain the reasoning used.
Chapter 5
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Lesson 5.4
Division of Decimals by Whole
Numbers
Instructional Time: 1 day
Note: The instructional time for this lesson
can also be 2 days. Use the extra time to have
students do some On Your Own examples
using both place value and estimation
methods. Discuss how they are similar and
the efficiency of each.
Common Core Standard
CC.5.NBT.2 Explain patterns in the number of zeros of the product
when multiplying a number by powers of 10, and explain patterns in
the placement of the decimal point when a decimal is multiplied or
divided by a power of 10. Use whole-number exponents to denote
powers of 10.
Also CC.5.NBT.7
Lesson Objective
How can you divide decimals by whole
numbers?
On Your Own
Materials
• HMH Mega Math
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
© Houghton Mifflin Harcourt Publishing Company
Approximately 10 min.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Essential Question
2
Practice
3 PRACTICE
Share and Show
Divide decimals by whole numbers.
• MathBoard
• Math Journal
• Animated Math
Models
Unlock the Problem, gauge their level
of understanding to make better
decisions about how to progress
through instruction.
Build on students’ understanding of
decimals and division to develop sound
mathematical practices by asking these
questions.
• What is the problem asking?
• How will you use that information?
• How can estimation help you solve
the problem?
• How do you know your answer is
reasonable?
Approximately 10 min.
Students can begin independent practice
once they understand these decimal
division concepts. Select exercises based
on students’ depth of understanding.
The exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 18–20
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
Teach and
Approximately
TEACH
andTalk
TALK
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to use place value
and an estimate to divide decimals by
whole numbers. As students work through
How can you divide decimals by whole
numbers?
I estimate the quotient first, then I divide
as I would with whole numbers. Finally,
I use my estimate to place my decimal in
the quotient.
Math Journal
Write a word problem involving money
that requires dividing a decimal by a
whole number. Include an estimate and
a solution.
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Lesson 5.5
Investigate • Decimal Division
• What did you do first? Why?
• How do base-ten blocks help you solve
this problem?
• What strategy could you use to make
the problem easier?
• What math vocabulary can you use in
your answer?
Instructional Time: 1 day
Common Core Standard
Lesson Objective
Model division by decimals.
Practice
3 PRACTICE
Share and Show
Essential Question
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
How can you use a model to divide
by a decimal?
Materials
• MathBoard
• Decimal Models
Problem Solving
• color pencils
• Math Journal
2
Teach and
Approximately
TEACH
andTalk
TALK
Summarize Approximately 5 min.
4 SUMMARIZE
20 min.
Investigate • Activity to Build Conceptual
Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to use decimal
models to divide by a decimal. As students
work through Unlock the Problem, gauge
their level of understanding to make
better decisions about how to progress
through instruction.
Build on students’ understanding of
modeling and decimal division to develop
sound mathematical practices by asking
these questions.
80
Approximately 10 min.
Students can begin independent practice
once they understand modeling decimal
division. Select exercises based on students’
depth of understanding. The exercises
below require higher order thinking
skills and critical reasoning, making them
especially rich.
Exercises 16, 18
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Approximately 10 min.
Essential Question
How can you use a model to divide
by a decimal?
I can shade decimal models to represent
the dividend. Then I can cut the model
apart into groups that are the same size
as the divisor. The number of same size
groups is the quotient.
Math Journal
Write a word problem that involves
dividing by a decimal. Include a picture
of the solution using a model.
© Houghton Mifflin Harcourt Publishing Company
CC.5.NBT.7 Add, subtract, multiply, and divide decimals to
hundredths, using concrete models or drawings and strategies
based on place value, properties of operations, and/or the
relationship between addition and subtraction; relate the
strategy to a written method and explain the reasoning used.
Chapter 5
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Lesson 5.6
Divide Decimals
Instructional Time: 1 day
Common Core Standard
CC.5.NBT.2 Explain patterns in the number of zeros of the product
when multiplying a number by powers of 10, and explain patterns in
the placement of the decimal point when a decimal is multiplied or
divided by a power of 10. Use whole-number exponents to denote
powers of 10.
Also CC.5.NBT.7
Practice
3 PRACTICE
Lesson Objective
Place the decimal point in decimal division.
Share and Show Approximately 10 min.
Essential Question
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
How can you place the decimal point in
the quotient?
Materials
• MathBoard
• Math Journal
• HMH Mega Math
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
On Your Own
Approximately 10 min.
Students can begin independent practice
once they understand these decimal
division concepts. Select exercises based
on students’ depth of understanding.
The exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 13–15 or 16–19
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
Essential Question
20 min.
© Houghton Mifflin Harcourt Publishing Company
• What method could you use to solve
the problem?
• Will another method work? Why or
why not?
• What strategy could you use to make
the calculations easier?
• How do you know that your answer
is reasonable?
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to multiply the
divisor by a power of 10 to change it to a
whole number before dividing. As students
work through Unlock the Problem, gauge
their level of understanding to make
better decisions about how to progress
through instruction.
Build on students’ understanding
of decimal division to develop sound
mathematical practices by asking
these questions.
How can place the decimal point in
the quotient?
I can multiply the dividend and the
divisor by the same power of ten so that
the divisor is a whole number. Then I can
place the decimal point directly above
the decimal point in the dividend.
Math Journal
Write and solve a division problem
involving decimals. Explain how you know
where to place the decimal point in the
quotient.
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Lesson 5.7
Write Zeros in the Dividend
• What is another way to solve the
problem?
• Will that method always work? How do
you know?
• Is your answer reasonable? How
do you know?
Instructional Time: 1 day
Common Core Standard
Also CC.5.NF.3
Practice
3 PRACTICE
Lesson Objective
Share and Show Approximately 10 min.
Write a zero in the dividend to find a
quotient.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Essential Question
When do you write a zero in the dividend
to find a quotient?
On Your Own
Students can begin independent practice
once they understand these decimal
division concepts. Select exercises based
on students’ depth of understanding. The
exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 25–27
Materials
• MathBoard
• Animated Math
Models
• Math Journal
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to know when
to write zeros in a decimal dividend.
As students work through Unlock
the Problem, gauge their level of
understanding to make better decisions
about how to progress through
instruction.
Build on students’ understanding of
decimal division and place value to
develop sound mathematical practices by
asking these questions.
82
Approximately 10 min.
Essential Question
When do you write a zero in the dividend
to find a quotient?
I write a zero in the dividend when there
aren’t enough digits in the dividend to
complete the division.
Math Journal
Solve 14.2 4 0.5. Show your work and
explain how you knew where to place
the decimal point.
© Houghton Mifflin Harcourt Publishing Company
CC.5.NBT.7 Add, subtract, multiply, and divide decimals to
hundredths, using concrete models or drawings and strategies based
on place value, properties of operations, and/or the relationship
between addition and subtraction; relate the strategy to a written
method and explain the reasoning used.
Chapter 5
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Lesson 5.8
Problem Solving • Decimal
Operations
Build on students’ understanding of
decimal division and problem solving
strategies to develop sound mathematical
practices by asking these questions.
• What strategy could you use to help you
solve the problem?
• Will the method of working backward
always work?
• How do you know?
• How is working backward like checking
your work?
Instructional Time: 1 day
Common Core Standard
CC.5.NBT.7 Add, subtract, multiply, and divide decimals to
hundredths, using concrete models or drawings and strategies
based on place value, properties of operations, and/or the
relationship between addition and subtraction; relate the
strategy to a written method and explain the reasoning used.
Lesson Objective
Solve multiple decimal problems using the
strategy work backward.
Practice
3 PRACTICE
Essential Question
Share and Show Approximately 10 min.
How do you use the strategy work backward
to solve multistep decimal problems?
Materials
• MathBoard
• Math Journal
• Real World Video,
Ch. 5
• HMH Mega Math
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Teach and
Approximately
2 TEACH
andTalk
TALK
On Your Own
Approximately 10 min.
Students can begin independent practice
once they understand these decimal
division concepts. Select exercises based on
students’ depth of understanding. The
exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 6–8
Summarize Approximately 5 min.
4 SUMMARIZE
20 min.
© Houghton Mifflin Harcourt Publishing Company
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Essential Question
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to organize
information and use a strategy to solve
decimal division problems. As students
work through Unlock the Problem, gauge
their level of understanding to make
better decisions about how to progress
through instruction.
How do you use the strategy work
backward to solve multistep decimal
problems?
I can work backward using a flowchart to
find the unknown information.
Math Journal
Write a problem that can be solved using
a flowchart and working backward. Then
draw the flowchart and solve the problem.
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Lesson 6.1
Investigate • Addition with
Unlike Denominators
Build on students’ understanding of
fractions and modeling to develop
sound mathematical practices by
asking these questions.
• Have you solved a problem similar to
the one given? Describe the similarities.
• Why are fraction strips a good model
for the given problem?
• What conclusions can you draw from
your model?
• How do you know your answer is
reasonable?
Instructional Time: 1 day
Common Core Standard
CC.5.NF.2 Solve word problems involving addition and subtraction
of fractions referring to the same whole, including cases of unlike
denominators, e.g., by using visual fraction models or equations
to represent the problem. Use benchmark fractions and number
sense of fractions to estimate mentally and assess the
reasonableness of answers.
Also CC.5.NBT.1
Lesson Objective
Use models to add fractions with unlike
denominators.
Practice
3 PRACTICE
Share and Show Approximately 10 min.
Essential Question
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
How can you use models to add fractions that
have different denominators?
Materials
Problem Solving Approximately 10 min.
• HMH Mega Math
• iTools: Fractions
Students can begin independent practice
once they understand these fraction
concepts. Select exercises based on
students’ depth of understanding. The
exercise below requires higher order
thinking skills and critical reasoning,
making it especially rich.
Exercise 15
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide how
deeply to discuss.
Teach and
Approximately
2 TEACH
andTalk
TALK
Summarize Approximately 5 min.
4 SUMMARIZE
20 min.
Investigate • Activity to Build Conceptual
Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to use fraction
strips to add fractions with unlike
denominators. As students work through
Unlock the Problem, gauge their
level of understanding to make
better decisions about how to progress
through instruction.
86
Essential Question
How can you use models to add fractions
that have different denominators?
Place fraction strips that have the same
denominators below the fraction strips
for the given fractions. Then add the
fractions that have like denominators.
Math Journal
Write a story problem that involves
adding fractions with unlike denominators.
Include the solution.
© Houghton Mifflin Harcourt Publishing Company
• MathBoard
• Fraction Strips
• Math Journal
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Lesson 6.2
Investigate • Subtract with
Unlike Denominators
Instructional Time: 1 day
Common Core Standard
CC.5.NF.2 Solve word problems involving addition and subtraction
of fractions referring to the same whole, including cases of unlike
denominators, e.g., by using visual fraction models or equations to
represent the problem. Use benchmark fractions and number sense
of fractions to estimate mentally and assess the reasonableness of
answers.
Also CC.5.NF.1
Lesson Objective
Practice
3 PRACTICE
Use models to subtract fractions with unlike
denominators.
Essential Question
Share and Show
How can you use models to subtract fractions
that have different denominators?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Students can continue practice once
they understand these fraction concepts
and modeling. Select exercises based on
students’ depth of understanding.
Materials
• MathBoard
• Fraction Strips
• Math Journal
• Animated Math
Models
• HMH Mega Math
• iTools: Fractions
Engage Approximately 5 min.
1 ENGAGE
Approximately 20 min.
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
© Houghton Mifflin Harcourt Publishing Company
Build on students’ understanding of
fractions and modeling to develop
sound mathematical practices by asking
these questions.
• Have you solved a problem similar to the
one given? Describe the similarities.
• Why are fraction strips a good model for
the given problem?
• What conclusions can you draw from
your model?
• How do you know your answer is
reasonable?
Investigate • Activity to Build Conceptual
Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to use fraction
strips to model subtraction of fractions
with unlike denominators. As students
work through Unlock the Problem, gauge
their level of understanding to make
better decisions about how to progress
through instruction.
How can you use models to subtract
fractions that have different
denominators?
I can use fraction strips to model the
fraction I am subtracting from and
place fraction strips below to show I am
subtracting. Then I find fractions strips
with the same denominator. Then I find
fraction strips with the same denominator
that fit exactly under the difference.
Math Journal
Explain how modeling subtraction with
fraction strips is different from adding
with fraction strips.
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Lesson 6.3
Estimate Fraction Sums and
Differences
Build on students’ understanding of
fractions and estimation to develop
sound mathematical practices by asking
these questions.
• How could you use a number line to
help you solve the problem?
• Will that method always work?
• How do you know your answer is
reasonable?
• How can you use math vocabulary in
your explanation?
Instructional Time: 1 day
Common Core Standard
CC.5.NF.2 Solve word problems involving addition and subtraction
of fractions referring to the same whole, including cases of unlike
denominators, e.g., by using visual fraction models or equations
to represent the problem. Use benchmark fractions and number sense
of fractions to estimate mentally and assess the reasonableness of
answers.
Lesson Objective
Practice
3 PRACTICE
Essential Question
Share and Show
How can you make reasonable estimates of
fraction sums and differences?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Materials
• MathBoard
• Animated Math
Models
• Math Journal
• HMH Mega Math
• Real World Video, Ch. 6
On Your Own
Teach and
2 TEACH
and Talk
TALKApproximately
Summarize Approximately 5 min.
4 SUMMARIZE
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to use benchmarks
on the number line and mental math to
estimate fraction sums and differences.
As students work through Unlock
the Problem, gauge their level of
understanding to make better
decisions about how to progress
through instruction.
88
Approximately 10 min.
Students can begin independent practice
once they understand these fraction and
estimation concepts. Select exercises based
on students’ depth of understanding.
The exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 17–19
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Approximately 10 min.
Essential Question
How can you make reasonable estimates
of fraction sums and differences?
I can round the fractions using benchmarks
of 0, 1_2 , and 1 on a number line, or I
can compare the numerator to the
denominator and round the fractions
to 0, 1_2 , or 1. Then I add or subtract the
rounded numbers.
Math Journal
What is an instance when you might want
to find an estimate for fraction sums or
differences rather than an exact answer?
© Houghton Mifflin Harcourt Publishing Company
Make reasonable estimates of fraction sums
and differences.
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Lesson 6.4
Common Denominator and
Equivalent Fractions
sound mathematical practices by asking
these questions.
• What do you remember about
multiples?
• What model could you use to help
solve the problem?
• How do you know those numbers are
equivalent?
• How could you use math vocabulary
in your explanation?
Instructional Time: 1 day
Common Core Standard
CC.5.NF.1 Add and subtract fractions with unlike denominators
(including mixed numbers) by replacing given fractions with
equivalent fractions in such a way as to produce an equivalent sum
or difference of fractions with like denominators.
Lesson Objective
Find a common denominator or a least
common denominator to write equivalent
fractions.
Practice
3 PRACTICE
Share and Show
Essential Question
How can you rewrite a pair of fractions so that
they have a common denominator?
Materials
• MathBoard
• Math Journal
• HMH Mega Math
• iTools: Number
Chart
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Teach and
Approximately
2 TEACH
andTalk
TALK
© Houghton Mifflin Harcourt Publishing Company
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to use a list or
multiply the denominators to find a
common denominator. As students
work through Unlock the Problem,
gauge their level of understanding
to make better decisions about how to
progress through instruction.
Build on students’ understanding of
fractions and multiples to develop
Approximately 10 min.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
On Your Own
Approximately 10 min.
Students can begin independent practice
once they understand these fraction
concepts. Select exercises based on
students’ depth of understanding.
The exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 19–21
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How can you rewrite a pair of fractions so
that they have a common denominator?
I can find a common denominator by
multiplying the two denominators or by
listing the multiples of each denominator
and finding a common multiple. Then
I can rewrite the fractions using the
common denominator.
Math Journal
Describe how you would rewrite the
fractions 1_6 and 1_4 with their least
common denominator.
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Lesson 6.5
Add and Subtract Fractions
Build on students’ understanding of
fractions to develop sound mathematical
practices by asking these questions.
• Have you solved a problem similar to the
given problem? Describe the similarities.
• What do you remember about common
denominators?
• Which operation did you choose to
represent the situation?
• Why does that operation represent
the situation?
Instructional Time: 1 day
Common Core Standard
CC.5.NF.1 Add and subtract fractions with unlike denominators
(including mixed numbers) by replacing given fractions with
equivalent fractions in such a way as to produce an equivalent
sum or difference of fractions with like denominators.
Also CC.5.NF.2
Lesson Objective
Use equivalent fractions to add and
subtract fractions.
How can you use a common denominator
to add and subtract fractions with unlike
denominators?
Practice
3 PRACTICE
Share and Show
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Materials
• MathBoard
• Math Journal
• Animated Math
Models
• HMH Mega Math
• iTools: Fractions
On Your Own
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Summarize Approximately 5 min.
4 SUMMARIZE
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to represent
problems with fraction symbols and
manipulate the symbols to solve problems.
As students work through Unlock
the Problem, gauge their level of
understanding to make better
decisions about how to progress
through instruction.
90
Approximately 10 min.
Students can begin independent
practice once they understand these
symbolic fraction concepts. Select
exercises based on students’ depth of
understanding. The exercises below
require higher order thinking skills
and critical reasoning, making them
especially rich.
Exercises 23–25 or 26–28
Engage Approximately 5 min.
1 ENGAGE
Teach and
2 TEACH
and Talk
TALKApproximately
Approximately 10 min.
Essential Question
How can you use a common denominator
to add and subtract fractions with unlike
denominators?
I can use the product of the denominators
to write equivalent fractions. Then I can
add or subtract and simplify.
Math Journal
How is 1_2 1 1_4 solved differently than 1_2 1 1_3 ?
© Houghton Mifflin Harcourt Publishing Company
Essential Question
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Lesson 6.6
Add and Subtract Mixed Numbers
Instructional Time: 1 day
Common Core Standard
CC.5.NF.1 Add and subtract fractions with unlike denominators
(including mixed numbers) by replacing given fractions with
equivalent fractions in such a way as to produce an equivalent
sum or difference of fractions with like denominators.
Also CC.5.NF.2
Lesson Objective
Add and subtract mixed numbers with
unlike denominators.
Essential Question
How can you add and subtract mixed numbers
with unlike denominators?
Materials
• MathBoard
• Math Journal
• Animated Math
Models
• HMH Mega Math
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Teach and
2 TEACH
and Talk
TALKApproximately
© Houghton Mifflin Harcourt Publishing Company
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to connect
their understanding of adding and
subtracting fractions with unlike
denominators to mixed numbers.
As students work through Unlock
the Problem, gauge their level of
understanding to make better
decisions about how to progress
through instruction.
Build on students’ understanding of
fractions and mixed numbers to
develop sound mathematical practices
by asking these questions.
• What do you remember about mixed
numbers?
• How would estimation help you solve
the given problem?
• Which operation did you choose to
represent the given situation?
• How do you know your answer is
reasonable?
Practice
3 PRACTICE
Share and Show
Approximately 10 min.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
On Your Own
Approximately 10 min.
Students can begin independent practice
once they understand these fractions
concepts. Select exercises based on
students’ depth of understanding.
The exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 25–28
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How can you add and subtract mixed
numbers with unlike denominators?
I find a common denominator and use
it to write equivalent fractions with like
denominators. Then I add or subtract the
fractions, and I add or subtract the whole
numbers. Finally, I make sure that the
sum or difference is in simplest form.
Math Journal
Write your own story problem using mixed
numbers. Show the solution.
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Lesson 6.7
Subtraction with Remaining
• What do you remember about
renaming fractions?
• How would estimation help you solve
the given problem?
• Which operation did you choose to
represent the situation?
• How do you know your answer is
reasonable?
Instructional Time: 1 day
Common Core Standard
CC.5.NF.1 Add and subtract fractions with unlike denominators
(including mixed numbers) by replacing given fractions with
equivalent fractions in such a way as to produce an equivalent
sum or difference of fractions with like denominators.
Also CC.5.NF.2
Rename to find the difference of two
mixed numbers.
Practice
3 PRACTICE
Share and Show
Essential Question
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
How can you use renaming to find the
difference of two mixed numbers?
Materials
On Your Own
• MathBoard
• Math Journal
• Animated Math Models
Teach and
2 TEACH
and Talk
TALKApproximately
Summarize Approximately 5 min.
4 SUMMARIZE
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to rename mixed
numbers when necessary to subtract.
As students work through Unlock
the Problem, gauge their level of
understanding to make better
decisions about how to progress
through instruction.
Build on students’ understanding of mixed
numbers to develop sound mathematical
practices by asking these questions.
92
Approximately 10 min.
Students can begin independent practice
once they understand these renaming
concepts. Select exercises based on
students’ depth of understanding.
The exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 11–18
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Approximately 10 min.
Essential Question
How can you use renaming to find the
difference of two mixed numbers?
First, I write equivalent fractions using
a common denominator. Next, I use
multiplication and addition to rename
each mixed number as a fraction greater
than 1. Then, I subtract the fractions and
write the difference in simplest form.
Math Journal
Write a subtraction problem that has
mixed numbers and requires renaming.
Draw a model illustrating the steps you
take to solve the problem.
© Houghton Mifflin Harcourt Publishing Company
Lesson Objective
Chapter 6
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Lesson 6.8
Algebra • Patterns with Fractions
Instructional Time: 1 day
Common Core Standard
CC.5.NF.1 Add and subtract fractions with unlike denominators
(including mixed numbers) by replacing given fractions with
equivalent fractions in such a way as to produce an equivalent
sum or difference of fractions with like denominators.
Practice
3 PRACTICE
Also CC.5.NF.2
Lesson Objective
Share and Show
Identify, describe, and create numerical
patterns with fractions.
How can you use addition or subtraction
to describe a pattern or create a sequence
with fractions?
On Your Own
Materials
• HMH Mega Math
• iTools: Fractions
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Teach and
2 TEACH
and Talk
TALKApproximately
© Houghton Mifflin Harcourt Publishing Company
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to use operations
with fractions to describe a pattern or
continue a sequence. As students work
through Unlock the Problem, gauge their
level of understanding to make better
decisions about how to progress through
instruction.
Build on students’ understanding of
fractions and patterns to develop sound
mathematical practices by asking these
questions.
Approximately 10 min.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Essential Question
• MathBoard
• Math Journal
• What do you remember about patterns?
• How did you discover the pattern for
this problem?
• What rule did you use to describe this
pattern?
• Will that method always work?
Approximately 10 min.
Students can begin independent practice
once they understand these fraction and
pattern concepts. Select exercises based
on students’ depth of understanding.
The exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 15–18
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How can you use addition or subtraction
to describe a pattern or create a sequence
with fractions?
To describe a pattern, I first write the
terms as equivalent fractions with a
common denominator. Then I find the
difference between consecutive terms
and write a rule. Finally, I can use the
rule to extend the sequence or to find
unknown terms. I can create a sequence
if I am given a starting term and a rule.
Math Journal
Make up your own sequence of 5 fractions
or mixed numbers. Offer the sequence to
another student to try and find the next
fraction in the sequence.
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Lesson 6.9
Problem Solving • Practice
Addition and Subtraction
Build on students’ understanding of
fractions and mixed numbers to develop
sound mathematical practices by asking
these questions.
• What strategy could you use to help
you solve the problem?
• Will that method always work?
• How do you know?
• How do you know your answer is
reasonable?
Instructional Time: 1 day
Common Core Standard
CC.5.NF.2 Solve word problems involving addition and subtraction
of fractions referring to the same whole, including cases of unlike
denominators, e.g., by using visual fraction models or equations
to represent the problem. Use benchmark fractions and number
sense of fractions to estimate mentally and assess the
reasonableness of answers.
Lesson Objective
Solve problems using the strategy
work backward.
Practice
3 PRACTICE
Share and Show
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Essential Question
How can the strategy work backward help
you solve a problem with fractions that
involves addition and subtraction?
On Your Own
Materials
• MathBoard
• Math Journal
Engage Approximately 5 min.
1 ENGAGE
Teach and
2 TEACH
and Talk
TALKApproximately
Summarize Approximately 5 min.
4 SUMMARIZE
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to organize
information and use a problem solving
strategy to solve fraction addition and
subtraction problems. As students work
through Unlock the Problem, gauge their
level of understanding to make better
decisions about how to progress through
instruction.
94
Approximately 10 min.
Students can begin independent
practice once they understand these
problem solving applications with
fractions. Select exercises based on
students’ depth of understanding. The
exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 5–7
• HMH Mega Math
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Approximately 10 min.
Essential Question
How can the strategy work backward help
you solve a problem with fractions that
involves addition and subtraction?
I can write an equation to represent the
problem, and then I can work backward
to solve for the unknown using the
inverse operation.
Math Journal
Write a word problem involving
fractions for which you would use
the work backward strategy and
addition to solve. Include your solution.
© Houghton Mifflin Harcourt Publishing Company
Also CC.5.NF.1
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Lesson 6.10
Algebra • Use Properties of
Addition
• Which operation did you choose to
represent the situation?
• What might be a shortcut for solving
this problem?
• What properties did you use to find
the answer?
• Will that method always work?
Instructional Time: 1 day
Common Core Standard
CC.5.NF.1 Add and subtract fractions with unlike denominators
(including mixed numbers) by replacing given fractions with
equivalent fractions in such a way as to produce an equivalent
sum or difference of fractions with like denominators.
Practice
3 PRACTICE
Lesson Objective
Share and Show
Add fractions and mixed numbers with
unlike denominators using the properties.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Essential Question
How can properties help you add fractions
with unlike denominators?
On Your Own
Materials
• MathBoard
• Math Journal
• HMH Mega Math
• iTools: Fractions
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Teach and
2 TEACH
and Talk
TALKApproximately
© Houghton Mifflin Harcourt Publishing Company
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to use addition
properties to add fractions and mixed
numbers with unlike denominators.
As students work through Unlock
the Problem, gauge their level of
understanding to make better
decisions about how to progress
through instruction.
Build on students’ understanding of
addition properties to develop sound
mathematical practices by asking
these questions.
Approximately 10 min.
Approximately 10 min.
Students can begin independent practice
once they understand these fraction
and mixed number concepts. Select
exercises based on students’ depth of
understanding. The exercises below
require higher order thinking skills
and critical reasoning, making them
especially rich.
Exercises 10–12
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How can properties help you add
fractions with unlike denominators?
I can use the Commutative Property
to rearrange the fractions so that the
fractions with like denominators are
next to each other. I can use the
Associative Property to group
fractions with like denominators.
Math Journal
Write Commutative Property and
Associative Property at the top of the
page. Underneath the name of each
property, write its definition and three
examples of its use.
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Lesson 7.1
Find Part of a Group
• Have you solved a problem similar to
given problem? Describe the similarities.
• Why are counters a good model for this
problem?
• What conclusions can you draw from
your model?
7
• How would your model change if __
10
of the stamps had been canceled?
Instructional Time: 1 day
Common Core Standard
CC.5.NF.4a Apply and extend previous understandings of
multiplication to multiply a fraction or whole number by a fraction.
Interpret the product ( _ba ) 3 q as a parts of a partition of q into
b equal parts; equivalently, as the result of a sequence of operations
a 3 q 4 b.
Model to find the fractional part of a group.
Practice
3 PRACTICE
Essential Question
Share and Show
How can you find a fractional part of a group?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Materials
• MathBoard
• Animated Math
Models
• counters
• HMH Mega Math
• Math Journal
• iTools: Fractions
• Real World Video, Ch. 7
On Your Own
Teach and
Approximately
2 TEACH
andTalk
TALK
Summarize Approximately 5 min.
4 SUMMARIZE
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to use manipulatives
and drawings to model fractional parts
of a group. As students work through
Unlock the Problem, gauge their level
of understanding to make better
decisions about how to progress
through instruction.
Build on students’ understanding of
fractions to develop sound mathematical
practices by asking these questions.
98
Approximately 10 min.
Students can begin independent practice
once they understand these fraction
concepts. Select exercises based on
students’ depth of understanding. The
exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 11–13
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Approximately 10 min.
Essential Question
How can you find a fractional part
of a group?
I can use the denominator to find how
many equal groups to make from the
whole number. Then I can use the
numerator to find how many equal groups
to count. I can count the number of items
in those groups.
Math Journal
Explain how to find 3_4 of 20 using a model.
Include a drawing.
© Houghton Mifflin Harcourt Publishing Company
Lesson Objective
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Lesson 7.2
Investigate • Multiply Fractions
and Whole Numbers
Instructional Time: 1 day
Common Core Standard
CC.5.NF.4a Apply and extend previous understandings of
multiplication to multiply a fraction or whole number by a fraction.
Interpret the product ( _ba ) 3 q as a parts of a partition of q into
b equal parts; equivalently, as the result of a sequence of operations
a 3 q 4 b.
Lesson Objective
Practice
3 PRACTICE
Model the product of a fraction and a
whole number.
Essential Question
Share and Show
How can you use a model to show the product
of a fraction and a whole number?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Materials
• MathBoard
• fraction strips
• Math Journal
• Animated Math
Models
• fraction circles
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
© Houghton Mifflin Harcourt Publishing Company
sound mathematical practices by asking
these questions.
• Have you solved a problem similar to the
given problem? Describe the similarities.
• Why are fraction strips a good model for
the given problem?
• What conclusions can you draw from
your model?
• How does your drawing support
your work?
In v e s t i g a t e • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to use models
to show the product of a fraction and
a whole number. As students work
through Unlock the Problem, gauge their
level of understanding to make better
decisions about how to progress through
instruction.
Build on students’ understanding of
fractions and multiplication to develop
Problem Solving
Approximately 10 min.
Approximately 10 min.
Students can begin independent practice
once they understand these fraction
modeling concepts. Select exercises based
on students’ depth of understanding.
The exercise below requires higher order
thinking skills and critical reasoning,
making it especially rich.
Exercise 13
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How can you use a model to show
the product of a fraction and a
whole number?
To find the fractional part of a
group, I would place the number of
same-size fraction strips indicated by
the denominator under the whole, and
then circle the number of same-size strips
indicated by the numerator to solve. To
find groups of a fractional part, I would
use fraction circles to model, and shade
the fractional part of each group to solve.
Math Journal
Explain how to use models to find 3 3 3_4
and 3_4 3 3. Include a picture of each model.
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Lesson 7.3
Fraction and Whole Number
Multiplication
sound mathematical practices by asking
these questions.
• Have you solved a problem similar to the
given problem? Describe the similarities.
• Which operation did you choose to
represent the given situation?
• How does your drawing support your
work?
• How do you know your answer is
reasonable?
Instructional Time: 1 day
Common Core Standard
CC.5.NF.4a Apply and extend previous understandings of
multiplication to multiply a fraction or whole number by a fraction.
Interpret the product ( _ba ) 3 q as a parts of a partition of q into
b equal parts; equivalently, as the result of a sequence of operations
a 3 q 4 b.
Lesson Objective
Essential Question
Practice
3 PRACTICE
Share and Show
How can you find the product of a fraction
and a whole number without using a model?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Materials
• MathBoard
• Math Journal
• Animated Math
Models
• iTools: Fractions
On Your Own
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
20 min.
Summarize Approximately 5 min.
4 SUMMARIZE
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to connect
modeling fraction and whole-number
multiplication to the algorithm. As
students work through Unlock the
Problem, gauge their level of
understanding to make better
decisions about how to progress
through instruction.
Build on students’ understanding of
fractions and multiplication to develop
100
Approximately 10 min.
Students can begin independent practice
once they understand these fraction
multiplication concepts. Select
exercises based on students’ depth of
understanding. The exercises below
require higher order thinking skills
and critical reasoning, making them
especially rich.
Exercises 14–16
Engage Approximately 5 min.
1 ENGAGE
Teach and
Approximately
2 TEACH
andTalk
TALK
Approximately 10 min.
Essential Question
How can you find the product of a
fraction and a whole number without
using a model?
Multiply the whole number and the
numerator. Then write the product over
the denominator and simplify if needed.
Math Journal
Write a word problem that can be solved
by multiplying a whole number and a
fraction. Include the solution.
© Houghton Mifflin Harcourt Publishing Company
Multiply fractions and whole numbers.
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Lesson 7.4
Investigate • Multiply Fractions
• Which operation did you choose to
represent the given situation?
• Why is an area model a good model for
the given problem?
• What conclusions can you draw from
your model?
• How would your model change is you
were finding 1_2 of 34_ ?
Instructional Time: 1 day
Common Core Standard
CC.5.NF.4b Apply and extend previous understandings of
multiplication to multiply a fraction or whole number by a fraction.
Find the area of a rectangle with fractional side lengths by tilting it
with unit squares of the appropriate unit fraction side lengths, and
show that the area is the same as would be found by multiplying
the side lengths. Multiply fractional side lengths to find areas of
rectangles, and represent fraction products as rectangular areas.
Practice
3 PRACTICE
Lesson Objective
Multiply fractions using models.
Share and Show
Essential Question
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
How can use an area model to show the
product of two fractions?
Materials
• MathBoard
• HMH Mega Math
• Math Journal
• iTools: Fractions
• Animated Math Models
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Students can begin independent practice
once they understand these fraction
concepts. Select exercises based on
students’ depth of understanding. The
exercise below requires higher order
thinking skills and critical reasoning,
making it especially rich.
Exercise 9
Essential Question
20 min.
© Houghton Mifflin Harcourt Publishing Company
Problem Solving Approximately 10 min.
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
Investigate • Activity to Build Conceptual
Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to use an area
model to show the product of two
fractions. As students work through
Unlock the Problem, gauge their level
of understanding to make better
decisions about how to progress
through instruction.
Build on students’ understanding of
fractions and modeling to develop sound
mathematical practices by asking
these questions.
5_MNYCETS222724_C07RML04.indd 101
Approximately 10 min.
How can use an area model to show
the product of two fractions?
When finding 2_3 3 1_4 , for example, I divide
a whole into 4 equal parts. I shade 1_4 of
the parts yellow. Then I divide each of
the four equal parts into thirds. I shade 2_3
of the yellow area. I count the number
of equal parts shaded twice, 2. This is
the numerator of the product, and the
denominator is the total number of equal
parts in the whole, 12. Then I simplify. So,
2
2 or 1
_ 3 1_ = __
_.
4
3
12
6
Math Journal
There is 5_8 of a pizza left. Josh eats 1_4 of the
leftover pizza. How much pizza does Josh
eat? Describe how to solve the problem
using an area model. Include a picture of
your model.
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Lesson 7.5
Compare Fraction Factors
and Products
to develop sound mathematical practices
by asking these questions.
• Why is a rectangle a good model for
the given problem?
• What conclusions can you draw from
your model?
• How would your model change if you
were working with thirds?
• How do you know your answer is
reasonable?
Instructional Time: 1 day
Common Core Standard
CC.5.NF.5a Interpret multiplication as scaling (resizing), by:
Comparing the size of a product to the size of one factor on
the basis of the size of the other factor, without performing the
indicated multiplication.
Also CC.5.NF.5b
Relate the size of the product compared
to the size of one factor when multiplying
fractions.
Practice
3 PRACTICE
Share and Show Approximately 10 min.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Essential Question
How does the size of the product compare
to the size of one factor when multiplying
fractions?
On Your Own Approximately 10 min.
Materials
• MathBoard
• Math Journal
Students can begin independent practice
once they understand these fraction
concepts. Select exercises based on
students’ depth of understanding.
The exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 7, 9, 10 or 12–13
• iTools: Fractions
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to use models to
compare the size of the product to the
size of a factor when multiplying fractions.
As students work through Unlock
the Problem, gauge their level of
understanding to make better
decisions about how to progress
through instruction.
Build on students’ understanding of
fraction multiplication and modeling
102
Essential Question
How does the size of the product
compare to the size of one factor
when multiplying fractions?
The product of 1 and any fraction will be
equal to that fraction. The product of a
number less than 1 and any fraction will
be less than either factor. The product of
a number greater than 1 and any fraction
will be greater than the fraction and less
than the number greater than 1.
Math Journal
Explain how you can compare the size
of a product to the size of a factor when
multiplying fractions, without actually
doing the multiplication. Include a model.
© Houghton Mifflin Harcourt Publishing Company
Lesson Objective
Chapter 7
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Lesson 7.6
Fraction Multiplication
Instructional Time: 1 day
Common Core Standard
CC.5.NF.4a Apply and extend previous understandings of
multiplication to multiply a fraction or whole number by a fraction.
Interpret the product ( _ba ) 3 q as a parts of a partition of q into
b equal parts; equivalently, as the result of a sequence of operations
a 3 q 4 b.
Also CC.5.NF.5a, CC.5.NF.5b
Practice
3 PRACTICE
Lesson Objective
Multiply fractions.
Share and Show
Essential Question
Materials
• MathBoard
• HMH Mega Math
• Math Journal
• iTools: Fractions
• Animated Math Models
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Teach and
Approximately
2 TEACH
andTalk
TALK
© Houghton Mifflin Harcourt Publishing Company
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to use models to
develop the reasoning behind the
algorithm for fraction multiplication.
As students work through Unlock
the Problem, gauge their level of
understanding to make better
decisions about how to progress
through instruction.
Build on students’ understanding of
fractions and modeling to develop
sound mathematical practices by asking
these questions.
Approximately 10 min.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
How do you multiply fractions?
Engage Approximately 5 min.
1 ENGAGE
• Have you solved a problem similar to the
given problem? Describe the similarities.
• Why is a rectangle a good model for this
problem?
• What conclusions can you draw from
your model?
• How do you know your answer is
reasonable?
On Your Own
Approximately 10 min.
Students can begin independent practice
once they understand these fraction and
modeling concepts. Select exercises based
on students’ depth of understanding.
The exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 19–21
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How do you multiply fractions?
I multiply the numerators together, and
I multiply the denominators together.
Then I write the product in simplest form.
Math Journal
Explain how multiplying fractions is similar
to multiplying whole numbers and how it
is different.
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Lesson 7.7
Investigate • Area and Mixed
Numbers
• What do you remember about finding
the area of rectangles?
• Why is a grid a good model for this
problem?
• What conclusions can you draw from
your model?
• How does your diagram support your
answer?
Instructional Time: 1 day
Common Core Standard
Practice
3 PRACTICE
Also CC.5.NF.5b
Share and Show
Lesson Objective
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response to
Intervention).
Use a model to multiply two mixed numbers
and find the area of a rectangle.
Essential Question
Problem Solving Approximately 10 min.
How can you use a unit tile to find the area of
a rectangle with fractional side lengths?
Students can begin independent practice
once they understand these fraction and
area concepts. Select exercises based on
students’ depth of understanding. The
exercise below requires higher order
thinking skills and critical reasoning,
making it especially rich.
Exercise 8
Materials
• MathBoard
• Math Journal
Engage Approximately 5 min.
1 ENGAGE
•
Teacher Edition, p. 317
Teach and
Approximately
2 TEACH
andTalk
TALK
Summarize Approximately 5 min.
4 SUMMARIZE
20 min.
Investigate • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to investigate
the relationship between area and
multiplication of mixed numbers.
As students work through Unlock
the Problem, gauge their level of
understanding to make better
decisions about how to progress
through instruction.
Build on students’ understanding of
fractions and area to develop sound
mathematical practices by asking
these questions.
104
Approximately 10 min.
Essential Question
How can you use a unit tile to find the
area of a rectangle with fractional side
lengths?
I can cover the rectangle with fractional
unit tiles and then multiply the number of
tiles by the area of each tile to find
the total area.
Math Journal
Draw a shape with fractional side lengths.
Describe how you will find its area.
© Houghton Mifflin Harcourt Publishing Company
CC.5.NF.4b Apply and extend previous understandings of
multiplication to multiply a fraction or whole number by a fraction.
Find the area of a rectangle with fractional side lengths by tilting it
with unit squares of the appropriate unit fraction side lengths, and
show that the area is the same as would be found by multiplying
the side lengths. Multiply fractional side lengths to find areas of
rectangles, and represent fraction products as rectangular areas.
Chapter 7
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Lesson 7.8
Compare Mixed Number Factors
and Products
Instructional Time: 1 day
Common Core Standard
CC.5.NF.5a Interpret multiplication as scaling (resizing), by:
Comparing the size of a product to the size of one factor on
the basis of the size of the other factor, without performing the
indicated multiplication.
Also CC.5.NF.5b
Lesson Objective
Relate the size of the product to the factors
when multiplying fractions greater than 1.
Practice
3 PRACTICE
Essential Question
Share and Show
How does the size of the product compare
to the size of one factor when multiplying
fractions greater than one?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Materials
• MathBoard
• Math Journal
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
© Houghton Mifflin Harcourt Publishing Company
Build on students’ understanding of
fraction multiplication and modeling to
develop sound mathematical practices by
asking these questions.
• Have you solved a problem similar to the
given problem? Describe the similarities.
• What did you do first? Why?
• Why is shading a rectangle a good
model for the given problem?
• What conclusions can you draw from
your model?
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to use models to
understand the size of the product
relative to the size of fractional factors.
As students work through Unlock
the Problem, gauge their level of
understanding to make better
decisions about how to progress
through instruction.
On Your Own
Approximately 10 min.
Approximately 10 min.
Students can begin independent practice
once they understand these fractional
scaling concepts. Select exercises based
on students’ depth of understanding.
The exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 7–9 or 10–12
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How does the size of the product compare
to the size of one factor when multiplying
fractions greater than one?
When multiplying a fraction greater than
1 by a fraction less than 1, the product will
be less than the factor that is greater than
1 and greater than the factor that is less
than 1.
Math Journal
Explain how scaling a mixed number by _12
will affect the size of the number.
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Lesson 7.9
Multiply Mixed Numbers
• What do you remember about
multiplying fractions?
• Why is a grid a good model for the
given problem?
• What conclusions can you draw from
your model?
• What properties could you use to help
solve this problem?
Instructional Time: 1 day
Common Core Standard
CC.5.NF.6 Solve real world problems involving multiplication
of fractions and mixed numbers, e.g., by using visual fraction
models or equations to represent the problem.
Lesson Objective
Multiply mixed numbers.
Practice
3 PRACTICE
How do you multiply mixed numbers?
Share and Show
Materials
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
• MathBoard
• Math Journal
• iTools: Fractions
Engage Approximately 5 min.
1 ENGAGE
On Your Own
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
106
Approximately 10 min.
Students can begin independent practice
once they understand these fraction
multiplication concepts. Select
exercises based on students’ depth of
understanding. The exercises below
require higher order thinking skills
and critical reasoning, making them
especially rich.
Exercises 16–18
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to multiply a mixed
number by a fraction, a whole number,
or another mixed number. As students
work through Unlock the Problem, gauge
their level of understanding to make
better decisions about how to progress
through instruction.
Build on students’ understanding of
fraction multiplication and modeling to
develop sound mathematical practices by
asking these questions.
Approximately 10 min.
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How do you multiply mixed numbers?
Change the mixed numbers to fractions
greater than 1. Then multiply the
numerators and multiply the
denominators.
Math Journal
Write and solve a word problem that
involves multiplying by a mixed number.
© Houghton Mifflin Harcourt Publishing Company
Essential Question
Chapter 7
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Lesson 7.10
Problem Solving • Find Unknown
Lengths
Instructional Time: 1 day
Common Core Standard
CC.5.NF.5b Interpret multiplication as scaling (resizing), by:
Explaining why multiplying a given number by a fraction greater
than 1 results in a product greater than the given number
(recognizing multiplication by whole numbers greater than 1 as
a familiar case); explaining why multiplying a given number by
a fraction less than 1 results in a product smaller than the given
3 a)
_____
number; and relating the principle of fraction equivalence _ba = (n
(n 3 b)
to the effect of multiplying _ba by 1.
Also CC.5.NF.6
Lesson Objective
Essential Question
How can you use the strategy guess, check,
and revise to solve problems with fractions?
• MathBoard
• Math Journal
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Teach and
2 TEACH
and Talk
TALKApproximately
© Houghton Mifflin Harcourt Publishing Company
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to organize
information and use a strategy to solve
fractional measurement problems.
As students work through Unlock
the Problem, gauge their level of
understanding to make better
decisions about how to progress
through instruction.
Practice
3 PRACTICE
Share and Show
Solve problems using the strategy guess,
check, and revise.
Materials
Build on students’ understanding of
fractions and measurement to develop
sound mathematical practices by asking
these questions.
• What did you do first? Why?
• What strategy could you use to help
you solve the given problem?
• Will that method always work?
• How can estimation help you solve
the problem?
Approximately 10 min.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
On Your Own
Approximately 10 min.
Students can begin independent practice
once they understand these fraction
concepts. Select exercises based on
students’ depth of understanding. The
exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 4–6
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How can you use the strategy guess,
check, and revise to solve problems with
fractions?
I can guess the fraction I need to replace
the unknown number and then increase
or decrease my guess until the results
are correct.
Math Journal
Explain how you can use the strategy
guess, check, and revise to solve problems
that involve a given area when the
relationship between the side lengths
is given, too.
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Lesson 8.1
Investigate • Divide Fractions
and Whole Numbers
Build on students’ understanding of
fractions and division to develop
sound mathematical practices by
asking these questions.
• What is the given problem asking?
• How can you use math vocabulary in
your explanation?
• What conclusions can you draw from
using the fraction strip model?
• How do you know your answer is
reasonable?
Instructional Time: 1 day
Common Core Standard
CC.5.NF.7a Apply and extend previous understandings of division
to divide unit fractions by whole numbers and whole numbers by unit
fractions. Interpret division of a unit fraction by a non-zero whole
number, and compute such quotients.
Also CC.5.NF.7b, CC.5.NF.7c
Lesson Objective
Practice
3 PRACTICE
Essential Question
Share and Show
How do you divide a whole number by
a fraction and divide a fraction by a
whole number?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Materials
• MathBoard
• Fraction Strips
• Math Journal
Problem Solving
• Animated Math
Models
• HMH Mega Math
• iTools: Fractions
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Investigate • Activity to Build Conceptual
Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to model division
with fractions two ways to open a
pathway to the division algorithm.
As students work through Unlock
the Problem, gauge their level of
understanding to make better
decisions about how to progress
through instruction.
110
Approximately 10 min.
Students can begin independent practice
once they understand these fraction
concepts. Select exercises based on
students’ depth of understanding. The
exercise below requires higher order
thinking skills and critical reasoning,
making it especially rich.
Exercise 13
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Approximately 10 min.
Essential Question
How do you divide a whole number
by a fraction and divide a fraction by
a whole number?
Model the problem using fraction strips
or a number line.
Math Journal
Explain how you could use a model to find
the quotient 4 4 1_3 .
© Houghton Mifflin Harcourt Publishing Company
Divide a whole number by a fraction and
divide a fraction by a whole number.
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Lesson 8.2
Problem Solving • Use
Multiplication
Instructional Time: 1 day
Common Core Standard
CC.5.NF.7b Apply and extend previous understandings of division to
divide unit fractions by whole numbers and whole numbers by unit
fractions. Interpret division of a whole number by a unit fraction, and
compute such quotients.
Lesson Objective
Practice
3 PRACTICE
Solve a problem using the strategy
draw a diagram.
Share and Show
Essential Question
Approximately 10 min.
How can the strategy draw a diagram help
you solve division problems by writing a
multiplication sentence?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Materials
On Your Own
• MathBoard
• Math Journal
• Animated Math Models
Approximately 10 min.
Students can begin independent practice
once they understand these fraction
and problem solving concepts. Select
exercises based on students’ depth of
understanding. The exercises below
require higher order thinking skills
and critical reasoning, making them
especially rich.
Exercises 6–8
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Teach and
2 TEACH
and Talk
TALKApproximately
Summarize Approximately 5 min.
4 SUMMARIZE
20 min.
© Houghton Mifflin Harcourt Publishing Company
• What do you remember about the
relationship between multiplication
and division?
• What strategy can you use to solve
the given problem?
• What operation did you use to solve
the given problem?
• How do you know your answer is
reasonable?
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to organize
information and use a strategy to solve
fractional division problems. As students
work through Unlock the Problem, gauge
their level of understanding to make
better decisions about how to progress
through instruction.
Build on students’ understanding of
fractions, division, and problem solving to
develop sound mathematical practices by
asking these questions.
How can the strategy draw a diagram help
you solve division problems by writing a
multiplication sentence?
I can draw a circle or rectangle to
represent each whole unit in the
problem. Then I can use the fraction
to divide each circle or rectangle into
equal size pieces. Finally, I can write a
multiplication sentence that represents
the diagram to solve.
Math Journal
Draw a diagram and explain how you can
use it to find 3 4 1_5 .
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Lesson 8.3
Connect Fractions to Division
• What do you remember about
representing remainders in division
problems?
• What can you share about the given
method of expressing division as a
fraction?
• How do you check your answer?
• How do you know your answer is
reasonable?
Instructional Time: 1 day
Common Core Standard
CC.5.NF.3 Interpret a fraction as division of the numerator by the
denominator ( _ba 5 a 4 b). Solve word problems involving division
of whole numbers leading to answers in the form of fractions or
mixed numbers, e.g., by using visual fraction models or equations to
represent the problem.
Lesson Objective
Practice
3 PRACTICE
Share and Show
Essential Question
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
How does a fraction represent division?
Materials
• MathBoard
• Math Journal
• HMH Mega Math
On Your Own
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
20 min.
Summarize Approximately 5 min.
4 SUMMARIZE
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to understand how
a fraction represents division. As students
work through Unlock the Problem, gauge
their level of understanding to make
better decisions about how to progress
through instruction.
Build on students’ understanding of
fractions and division to develop sound
mathematical practices by asking these
questions.
112
Approximately 10 min.
Students can begin independent practice
once they understand these fraction and
division concepts. Select exercises based
on students’ depth of understanding.
The exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 9–11
Engage Approximately 5 min.
1 ENGAGE
Teach and
2 TEACH
and Talk
TALKApproximately
Approximately 10 min.
Essential Question
How does a fraction represent division?
The numerator of a fraction shows the
number of items being divided. The
denominator shows the number of equal
pieces the item is being divided into.
Both the fraction and the quotient of the
numerator express the size or amount of
each piece after division.
Math Journal
Jason divides 8 pounds of dog food
equally among 6 dogs. Draw a diagram
and explain how you can use it to find
the amount of food each dog receives.
© Houghton Mifflin Harcourt Publishing Company
Interpret a fraction as division and solve
whole-number division problems that
result in a fraction or mixed number.
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Lesson 8.4
Fraction and Whole-Number
Division
Instructional Time: 1 day
Note: The instructional time for this lesson
can also be 2 days. Use the extra time to have
students use models for extra support when
completing the On Your Own exercises.
Common Core Standard
CC.5.NF.7c Apply and extend previous understandings of division
to divide unit fractions by whole numbers and whole numbers by
unit fractions. Solve real world problems involving division of unit
fractions by non-zero whole numbers and division of whole numbers
by unit fractions, e.g., by using visual fraction models and equations
to represent the problem.
Also CC.5.NF.7a, CC.5.NF.7b
Lesson Objective
Practice
3 PRACTICE
Divide a whole number by a fraction and
divide a fraction by a whole number.
Share and Show
Essential Question
Materials
• Animated Math
Models
• HMH Mega Math
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
© Houghton Mifflin Harcourt Publishing Company
Approximately 10 min.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
How can you divide fractions by solving
a related multiplication sentence?
• MathBoard
• Math Journal
• Real World
Video, Ch. 8
Unlock the Problem, gauge their level
of understanding to make better
decisions about how to progress
through instruction.
Build on students’ understanding of
fractions and modeling to develop sound
mathematical practices by asking these
questions.
• What is the given problem asking?
• What model could you use to help solve
the problem?
• Why is a rectangular model a good
model for this problem?
• What might be a shortcut for solving
this problem?
On Your Own
Approximately 10 min.
Students can begin independent practice
once they understand these fraction
concepts. Select exercises based on
students’ depth of understanding.
The exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 8, 12, 14
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
Essential Question
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to relate a fraction
division expression to a multiplication
expression. As students work through
How can you divide fractions by solving a
related multiplication sentence?
If you are dividing a fraction by a whole
number, multiply the fraction by the
1 . If you are dividing a whole
fraction ___
number by a fraction, multiply the whole
number by the denominator of the
fraction.
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Tell whether the quotient is greater than
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Lesson 8.5
Interpret Division with Fractions
• What equation could represent this
situation?
• Why did you choose that operation?
• What model did you use to represent
the given problem? Why was this a good
choice?
Instructional Time: 1 day
Common Core Standard
CC.5.NF.7c Apply and extend previous understandings of division
to divide unit fractions by whole numbers and whole numbers by
unit fractions. Solve real world problems involving division of unit
fractions by non-zero whole numbers and division of whole numbers
by unit fractions, e.g., by using visual fraction models and equations
to represent the problem.
Also CC.5.NF.7a, CC.5.NF.7b
Practice
3 PRACTICE
Share and Show Approximately 10 min.
Lesson Objective
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Represent division by drawing diagrams and
writing story problems and equations.
Essential Question
On Your Own
How can you use diagrams, equations, and
story problems to represent division?
Students can begin independent practice
once they understand these fraction and
division concepts. Select exercises based
on students’ depth of understanding.
The exercise below requires higher order
thinking skills and critical reasoning,
making it especially rich.
Exercise 7
Materials
• Math Journal
• Animated Math
Models
• HMH Mega Math
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to represent
division in different ways. As students
work through Unlock the Problem, gauge
their level of understanding to make
better decisions about how to progress
through instruction.
Build on students’ understanding of
fractions and division to develop sound
mathematical practices by asking these
questions.
114
Essential Question
How can you use diagrams, equations, and
story problems to represent division?
Students’ answers should refer to
the dividends and divisors they are
representing with diagrams, equations
and story problems.
Math Journal
Write and solve a story problem to
represent 1_3 4 4.
© Houghton Mifflin Harcourt Publishing Company
• MathBoard
Approximately 10 min.
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Lesson 9.1
Line Plots
Instructional Time: 1 day
Common Core Standard
CC.5.MD.2 Make a line plot to display a data set of measurements
in fractions of a unit ( 1_2 , 1_4 , _18 ). Use operations on fractions for this
grade to solve problems involving information presented in line plots.
Also CC.5.OA.1, CC.5.NF.7a
Practice
3 PRACTICE
Lesson Objective
Share and Show
Make and use line plots with fractions to
solve problems.
How can a line plot help you find an
average with data given fraction?
On Your Own
Materials
• Animated Math
Models
• iTools: Graphs
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual foundation for the lesson. Use evidence of
students’ understanding to decide how
deeply to discuss.
2
Teach and
Approximately
TEACH
andTalk
TALK
20 min.
© Houghton Mifflin Harcourt Publishing Company
Approximately 10 min.
Use the checked exercises as a diagnostic assessment. If students answer either
exercise incorrectly, use RtI (Response to
Intervention).
Essential Question
• MathBoard
• Math Journal
• What is the given problem asking?
• What do you do first? Why?
• Why is the line plot a good model for
this problem?
• What do you remember about the order
of operations?
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to make and use
line plots that display a set of data that
is measured in fractional amounts.
As students work through Unlock
the Problem, gauge their level
of understanding to make better
decisions about how to progress
through instruction.
Build on students’ understanding of
multiplication and estimation to develop
sound mathematical practices by asking
these questions.
Approximately 10 min.
Students can begin independent practice
once they understand these multiplication
concepts. Select exercises based on
students’ depth of understanding. The
exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 8–10
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How can a line plot help you find an
average with data given in fractions?
I can find how many times the fraction is
recorded on the line plot, find the total
amount for each fraction, and then find
the total amount for all. Then I can divide
the total by the total number of data to
find the average.
Math Journal
Describe the steps you can use to find
an average of fractional amounts.
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Lesson 9.2
Ordered Pairs
Build on students’ understanding of
number lines to develop sound
mathematical practices by asking
these questions.
• What is the given problem asking?
• What vocabulary can you use to
describe the process of solving the
given problem?
• What happens when you are given
different points to plot? How do you
know where to move on the coordinate
plane?
• How do you know your answer is
reasonable?
Instructional Time: 1 day
Common Core Standard
CC.5.G.1 Use a pair of perpendicular number lines, called axes, to
define a coordinate system, with the intersection of the lines (the
origin) arranged to coincide with 0 on each line and given a point
in the plane located by using an ordered pair of numbers, called its
coordinates. Understand that the first number indicates how far to
travel from the origin in the direction of one axis, and the second
number indicates how far to travel in the direction of the second
axis, with the convention that the names of the two axes and the
coordinates correspond (e.g., x-axis and x- coordinate, y-axis and
y-coordinate).
Lesson Objective
Essential Question
Practice
3 PRACTICE
Share and Show
How can you identify and plot points on a
coordinate grid?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Materials
• MathBoard
• Math Journal
• Real World
Video, Ch. 9
• Animated Math
Models
• HMH Mega Math
• iTools: Algebra
On Your Own
Teach and
Approximately
2 TEACH
andTalk
TALK
Summarize Approximately 5 min.
4 SUMMARIZE
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to use ordered
pairs to plot and locate points on a
coordinate grid. As students work
through Unlock the Problem, gauge
their level of understanding to make
better decisions about how to progress
through instruction.
118
Approximately 10 min.
Students can begin independent practice
once they understand these graphing
concepts. Select exercises based on
students’ depth of understanding. The
exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 33–36
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Approximately 10 min.
Essential Question
How can you identify and plot points on a
coordinate grid?
I can use the x- and y-coordinates to find
or describe the distance from a point to
the origin.
Math Journal
What is a situation in which you might
locate points on a coordinate grid?
© Houghton Mifflin Harcourt Publishing Company
Graph and name points on a coordinate grid
using ordered pairs.
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Lesson 9.3
Investigate • Graph Data
Instructional Time: 1 day
Common Core Standard
CC.5.G.2 Represent real world and mathematical problems by
graphing points in the first quadrant of the coordinate plane, and
interpret coordinate values of points in the context of the situation.
Lesson Objective
Collect and graph data on a coordinate grid.
Essential Question
How can you use a coordinate grid to display
data collected in an experiment?
Materials
•
•
•
•
MathBoard
paper cup
water
Fahrenheit
thermometer
• ice cubes
• stopwatch
• Math Journal
• Animated Math
Models
• HMH Mega Math
• iTools: Algebra
Practice
3 PRACTICE
Share and Show
Approximately 10 min.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Problem Solving Approximately 10 min.
Students can begin independent practice
once they understand these graphing
concepts. Select exercises based on
students’ depth of understanding. The
exercise below requires higher order
thinking skills and critical reasoning,
making it especially rich.
Exercise 3
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Teach and
Approximately
2 TEACH
andTalk
TALK
Summarize Approximately 10 min.
4 SUMMARIZE
20 min.
© Houghton Mifflin Harcourt Publishing Company
instruction.
Build on students’ understanding of data
collection and display to develop sound
mathematical practices by asking these
questions.
• In the experiment, what did you do
first? Why?
• What do you think will happen if
we measure the temperature more
frequently? Less frequently?
• How can you use math vocabulary in
your explanation?
Investigate • Activity to Build Conceptual
Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to understand
the relationship between the x- and
y-coordinates, and how changes in the two
data sets are related. As students work
through Unlock the Problem, gauge their
level of understanding to make better
decisions about how to progress through
Essential Question
How can you use a coordinate grid to
display data collected in an experiment?
If my data are measured in two ways such
as time and temperature, I can write my
recorded data as ordered pairs and then
graph them.
Math Journal
Give an example of some data you could
collect and display on a coordinate grid.
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Lesson 9.4
Line Graphs
Build on students’ understanding of
data and data displays to develop
sound mathematical practices by asking
these questions.
• What is the problem asking?
• What do you remember about ordered
pairs?
• How might your graph change if the
labels on the x- and y-axis were
changed?
Instructional Time: 1 day
Note: The instructional time for this lesson
can also be 2 days. Use the extra time to
have students display data they collect as
homework (e.g., high/low temperatures).
Have students interpret and compare graphs
as a class.
Common Core Standard
Practice
3 PRACTICE
Lesson Objective
Share and Show
Analyze and display data in a line graph.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Essential Question
How can you use a line graph to display and
analyze real-word data?
On Your Own
Materials
• MathBoard
• Math Journal
• Animated Math
Models
Engage Approximately 5 min.
1 ENGAGE
Exercises 6, 7, 9
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to display and
analyze data in a line graph. As students
work through Unlock the Problem, gauge
their level of understanding to make
better decisions about how to progress
through instruction.
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Approximately 10 min.
Students can begin independent practice
once they understand these graphing
concepts. Select exercises based on
students’ depth of understanding. The
exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
• HMH Mega Math
• iTools: Graphs
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Approximately 10 min.
Essential Question
How can you use a line graph to display
and analyze real-word data?
Organize the data in related pairs.
Choose a title, labels, an interval and
a scale for the graph. Plot the points.
Draw line segments to connect the
consecutive points.
Math Journal
Give an example of a situation in which
you could use a line graph. Describe how
you would set up your graph; what labels
would you use for the x-axis? The y-axis?
© Houghton Mifflin Harcourt Publishing Company
CC.5.G.2 Represent real world and mathematical problems by
graphing points in the first quadrant of the coordinate plane, and
interpret coordinate values of points in the context of the situation.
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Lesson 9.5
Numerical Patterns
Instructional Time: 1 day
Common Core Standard
CC.5.OA.3 Generate two numerical patterns using two given rules.
Identify apparent relationships between corresponding terms. Form
ordered pairs consisting of corresponding terms from the two
patterns, and graph the ordered pairs on a coordinate plane.
Lesson Objective
Use two rules to generate a numerical pattern
and identify the relationship between the
corresponding terms in the pattern.
Essential Question
How can you identify a relationship between
two numerical patterns?
Materials
• MathBoard
• Math Journal
• iTools: Number
Lines
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Practice
3 PRACTICE
Share and Show
Approximately 10 min.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
On Your Own
Approximately 10 min.
Students can begin independent practice
once they understand these sequence and
rule concepts. Select exercises based on
students’ depth of understanding. The
exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 4–6 or 7–9
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
Essential Question
20 min.
© Houghton Mifflin Harcourt Publishing Company
• What operation did you use to solve the
given problem?
• Is there a pattern you can see? How did
you discover it?
• What would happen if Joel bought only
2 songs each week?
• How would your graph change?
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to generate two
numerical sequences using two different
rules and find a relationship between
the terms. As students work through
Unlock the Problem, gauge their level
of understanding to make better
decisions about how to progress
through instruction.
Build on students’ understanding of
numerical patterns to develop sound
mathematical practices by asking
these questions.
How can you identify a relationship
between two numerical patterns?
I can find a rule to write the first few
terms in each sequence. Using the two
sequences, I can write number pairs
and then find a rule that relates to one
sequence or the other.
Math Journal
Give an example using the subject of time
to describe how two number patterns are
related.
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Lesson 9.6
Problem Solving • Find a Rule
Build on students’ understanding of
patterns and problem solving to develop
sound mathematical practices by asking
these questions.
• What is the given problem asking?
• Is there another way to solve this
problem?
• How did you discover the pattern?
• What rule did you use to solve the given
problem?
Instructional Time: 1 day
Common Core Standard
CC.5.OA.3 Generate two numerical patterns using two given rules.
Identify apparent relationships between corresponding terms. Form
ordered pairs consisting of corresponding terms from the two
patterns, and graph the ordered pairs on a coordinate plane.
Lesson Objective
Essential Question
Practice
3 PRACTICE
Share and Show
How can you use the strategy solve a simpler
problem to help you solve a problem with
patterns?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Materials
• MathBoard
• Math Journal
• HMH Mega Math
• iTools: Algebra
On Your Own
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. U se evidence
of students’ understanding to decide
how deeply to discuss.
20 min.
Summarize Approximately 5 min.
4 SUMMARIZE
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to organize
information and use a problem solving
strategy to solve pattern problems.
As students work through Unlock
the Problem, gauge their level of
understanding to make better decisions
about how to progress through
instruction.
122
Approximately 10 min.
Students can begin independent practice
once they understand these pattern
and problem solving concepts. Select
exercises based on students’ depth of
understanding. The exercises below
require higher order thinking skills
and critical reasoning, making them
especially rich.
Exercises 4–6
Engage Approximately 5 min.
1 ENGAGE
Teach and
Approximately
2 TEACH
andTalk
TALK
Approximately 10 min.
Essential Question
How can you use the strategy solve a
simpler problem to help you solve a
problem with patterns?
I can find a pattern using simple numbers
and then use the pattern that I found to
predict results with greater numbers to
solve the problem.
Math Journal
You have a table that shows a pattern.
Describe two ways that you could find the
15th entry in the table.
© Houghton Mifflin Harcourt Publishing Company
Solve problems using the strategy solve a
simpler problem.
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Lesson 9.7
Graph and Analyze Relationships
Instructional Time: 1 day
Common Core Standard
CC.5.OA.3 Generate two numerical patterns using two given rules.
Identify apparent relationships between corresponding terms. Form
ordered pairs consisting of corresponding terms from the two
patterns, and graph the ordered pairs on a coordinate plane.
Also CC.5.G.2
Lesson Objective
Practice
3 PRACTICE
Graph the relationship between two
numerical patterns on a coordinate grid.
Share and Show
Essential Question
Approximately 10 min.
How can you write and graph ordered pairs
on a coordinate grid using two numerical
patterns?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Materials
On Your Own
• MathBoard
• Math Journal
• Animated Math
Models
• HMH Mega Math
• iTools: Algebra
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Approximately 10 min.
Students can begin independent practice
once they understand these pattern and
graphing concepts. Select exercises based
on students’ depth of understanding.
The exercise below requires higher order
thinking skills and critical reasoning,
making it especially rich.
Exercise 5
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
© Houghton Mifflin Harcourt Publishing Company
mathematical practices by asking these
questions.
• What do you remember about ordered
pairs?
• Do you see a pattern? What rule is being
used?
• What happens when the numbers
continue to grow? Could you predict
what would happen?
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction for this
lesson, in which conceptual development is
key. The goal of this activity is for students to
extend their understanding of relationships
in numerical patterns by graphing ordered
pairs. As students work through Unlock the
Problem, gauge their level of understanding
to make better decisions about how to
progress through instruction.
Build on students’ understanding of
patterns and graphing to develop sound
How can you write and graph ordered
pairs on a coordinate grid using two
numerical patterns?
Use the given rule to generate the first few
terms in each pattern. Write the number
pairs that represent the relationship
between the patterns as ordered pairs.
Graph and label the ordered pairs. If a line
can be drawn from the origin through all the
points, then the pattern between the two
relationships can be found by multiplying.
Math Journal
A fathom is 6 inches. Describe how you
can write and graph ordered pairs on a
coordinate grid to show this relationship.
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Lesson 10.1
Customary Length
Build on students’ understanding of
measurement to develop sound
mathematical practices by asking
these questions.
• What do you remember about
measuring length?
• Why is a bar model a good model for
the given problem?
• What conclusions can you draw from
your model?
Instructional Time: 1 day
Common Core Standard
CC.5.MD.1 Convert among different-sized standard measurement
units within a given measurement system (e.g., convert
5 cm to 0.05 m), and use these conversions in solving multi-step,
real world problems.
Lesson Objective
Essential Question
Practice
3 PRACTICE
Share and Show
How can you compare and convert customary
units of length?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Materials
• MathBoard
• Math Journal
• Animated Math
Models
• HMH Mega Math
• iTools: Base-Ten
Blocks
On Your Own
2
Teach and
Approximately
TEACH
andTalk
TALK
Summarize • Approximately 5 min.
4 SUMMARIZE
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to compare and
convert customary units of length.
As students work through Unlock
the Problem, gauge their level of
understanding to make better
decisions about how to progress
through instruction.
126
Approximately 10 min.
Students can begin independent practice
once they understand these measurement
concepts. Select exercises based on
students’ depth of understanding. The
exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 16–19
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Approximately 10 min.
Essential Question
How can you compare and convert
customary units of length?
First, I use division to convert the smaller
unit to the larger unit, or I use multiplication
to convert the larger unit to the smaller
unit. Then I use a ,, ., or 5 to compare.
Math Journal
Explain how to compare two lengths that
are measured in different-sized units.
© Houghton Mifflin Harcourt Publishing Company
Compare, contrast, and convert customary
units of length.
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Lesson 10.2
Customary Capacity
Instructional Time: 1 day
Common Core Standard
CC.5.MD.1 Convert among different-sized standard measurement
units within a given measurement system (e.g., convert
5 cm to 0.05 m), and use these conversions in solving multi-step,
real world problems.
Lesson Objective
Practice
3 PRACTICE
Compare, contrast, and convert customary
units of capacity.
Share and Show
Essential Question
How can you compare and convert customary
units of capacity?
Materials
• MathBoard
• Math Journal
• Animated Math
Models
• HMH Mega Math
• iTools:
Measurement
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishin\g a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Approximately 10 min.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
On Your Own
Approximately 10 min.
Students can begin independent practice
once they understand these measurement
concepts. Select exercises based on
students’ depth of understanding. The
exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 24–26
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
• Approximately
2 TEACH
andTalk
TALK
20 min.
© Houghton Mifflin Harcourt Publishing Company
these questions.
• What do you remember about liquid
volume?
• Why is a bar model a good model for
this problem?
• What conclusions can you draw from
your model?
• Will that method always work?
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to compare and
convert customary units of capacity.
As students work through Unlock the
Problem, gauge their level of
understanding to make better decisions
about how to progress through instruction.
Build on students’ understanding of
measurement to develop sound
mathematical practices by asking
Essential Question
How can you compare and convert
customary units of capacity?
First, I use division to convert the
smaller unit to the larger unit, or I use
multiplication to convert the larger unit to
the smaller unit. Then I use a ,, ., or 5 to
compare.
Math Journal
Give some examples of when you would
measure capacity in each of the units of
capacity shown in the table on page 410.
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Lesson 10.3
Weight
Build on students’ understanding of
measurement to develop sound
mathematical practices by asking
these questions.
• Which operation did you choose to
represent the situation? Why?
• Why is a bar model a good model for
this problem?
• What conclusions can you draw from
your model?
Instructional Time: 1 day
Common Core Standard
CC.5.MD.1 Convert among different-sized standard measurement
units within a given measurement system (e.g., convert
5 cm to 0.05 m), and use these conversions in solving multi-step,
real world problems.
Lesson Objective
Essential Question
Practice
3 PRACTICE
Share and Show
How can you compare and convert customary
units of weight?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Materials
• MathBoard
• Math Journal
• Real World
Video, Ch. 10
• Animated Math
Models
• HMH Mega Math
• iTools:
Measurement
On Your Own
Teach and
Approximately
2 TEACH
andTalk
TALK
Summarize Approximately 10 min.
4 SUMMARIZE
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to compare and
convert customary units of weight.
As students work through Unlock
the Problem, gauge their level of
understanding to make better
decisions about how to progress
through instruction.
128
Approximately 10 min.
Students can begin independent practice
once they understand these measurement
concepts. Select exercises based on
students’ depth of understanding. The
exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 23, 25
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Approximately 10 min.
Essential Question
How can you compare and convert
customary units of weight?
First, I use division to convert the
smaller unit to the larger unit, or I use
multiplication to convert the larger unit to
the smaller unit. Then I use a ,, ., or 5 to
compare.
Math Journal
Give two examples of items that weigh less
than 1 ounce and two examples of items
that weigh more than 1 ton.
© Houghton Mifflin Harcourt Publishing Company
Compare, contrast, and convert customary
units of weight.
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Lesson 10.4
Multistep Measurement Problems
Instructional Time: 1 day
Common Core Standard
CC.5.MD.1 Convert among different-sized standard measurement
units within a given measurement system (e.g., convert 5 cm to
0.05 m), and use these conversions in solving multi-step, real world
problems.
Lesson Objective
Convert measurement units to solve multistep
problems.
Practice
3 PRACTICE
Essential Question
Share and Show
How can you solve multistep problems that
include measurement conversions?
Use the checked exercises as a diagnostic assessment. If students answer either
exercise incorrectly, use RtI (Response to
Intervention).
Materials
• MathBoard
• Math Journal
• Animated Math
Models
• HMH Mega Math
• iTools:
Measurement
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
On Your Own
Approximately 10 min.
Approximately 10 min.
Students can begin independent practice
once they understand these measurement
and problem solving concepts. Select
exercises based on students’ depth of
understanding. The exercises below
require higher order thinking skills
and critical reasoning, making them
especially rich.
Exercises 5, 6, 9
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
Essential Question
20 min.
© Houghton Mifflin Harcourt Publishing Company
Build on students’ understanding of
measurement and problem solving to
develop sound mathematical practices by
asking these questions.
• What did you do first? Why?
• Which operation did you choose to
represent the situation? Why?
• How do you know your answer is
reasonable?
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to organize
information to solve multistep problems
involving measurement conversion.
As students work through Unlock
the Problem, gauge their level of
understanding to make better decisions
about how to progress through instruction.
How can you solve multistep problems that
include measurement conversions?
First, record the information you are given.
Next, convert one of the units you are
given to one of the units you are looking
for. Finally, convert the second unit you
are given to the second unit you are
looking for.
Math Journal
An object moves on a conveyor belt at a
speed of 60 inches per second. Explain how
you could convert the speed to feet per
minute.
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Lesson 10.5
Metric Measures
Build on students’ understanding of place
value and multiplication patterns to
develop sound mathematical practices by
asking these questions.
• What do you remember about the
metric system?
• How could you use a diagram to help
you solve this problem?
• How does the diagram support your
work?
• Will that method always work?
Instructional Time: 1 day
Common Core Standard
CC.5.MD.1 Convert among different-sized standard measurement
units within a given measurement system (e.g., convert
5 cm to 0.05 m), and use these conversions in solving multi-step,
real world problems.
Lesson Objective
Compare, contrast and convert metric units.
How can you compare and convert metric
units?
Practice
3 PRACTICE
Share and Show
Materials
• MathBoard
• Math Journal
• Animated Math
Models
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response to
Intervention).
• HMH Mega Math
• iTools:
Measurement
On Your Own
Engage Approximately 5 min.
1 ENGAGE
Teach and Talk
Approximately
Summarize Approximately 5 min.
4 SUMMARIZE
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to find two possible
addends for each sum given. As students
work through Listen and Draw, gauge
their level of understanding to make
better decisions about how to progress
through instruction.
130
Approximately 10 min.
Students can begin independent practice
once they understand these measurement
concepts. Select exercises based on
students’ depth of understanding. The
exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 15–19
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
2 20TEACH
and TALK
min.
Approximately 10 min.
Essential Question
How can you compare and convert metric
units?
Possible answer: I have to decide if I am
converting a smaller unit to a larger unit,
or a larger unit to a smaller unit. Once
I know that, I convert by multiplying or
dividing by the appropriate power of ten.
© Houghton Mifflin Harcourt Publishing Company
Essential Question
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Lesson 10.6
Problem Solving • Customary and
Metric Conversions
Instructional Time: 1 day
Common Core Standard
CC.5.MD.1 Convert among different-sized standard measurement
units within a given measurement system (e.g., convert
5 cm to 0.05 m), and use these conversions in solving multi-step,
real world problems.
Lesson Objective
Solve problems about customary and metric
conversions using the strategy make a table.
Essential Question
How can use the strategy make a table to
help you solve problems about customary and
metric conversions?
Materials
• MathBoard
• Math Journal
• Animated Math
Models
• HMH Mega Math
• iTools: Number
Charts
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide how
deeply to discuss.
Teach and
Approximately
2 TEACH
andTalk
TALK
Practice
3 PRACTICE
Share and Show
Approximately 10 min.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response to
Intervention).
On Your Own
Approximately 10 min.
Students can begin independent practice
once they understand these measurement
concepts. Select exercises based on
students’ depth of understanding. The
exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 5, 6, 7
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
20 min.
© Houghton Mifflin Harcourt Publishing Company
Build on students’ understanding
of measurement conversion and
problem-solving strategies to develop
sound mathematical practices by asking
these questions.
• What do you remember about tables?
• How could you use a table to help you
solve the given problem?
• What did you do first? Why?
• How do you know your answer is
reasonable?
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to organize
information to solve problems involving
unit conversions. As students work
through Unlock the Problem, gauge their
level of understanding to make better
decisions about how to progress through
instruction.
How can use the strategy make a table to
help you solve problems about customary
and metric conversions?
Use the table to find the correct
conversion factor. Then multiply or
divide the given number of units by the
conversion factor.
Math Journal
Explain how you could use the
conversion table on page 428 to
convert 700 centimeters to meters.
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Lesson 10.7
Elapsed Time
Build on students’ understanding of the
number line and time to develop sound
mathematical practices by asking these
questions.
• What do you remember about telling
time?
• How could the number line help you
solve the problem?
• What is another method for solving the
given problem?
• Will that method always work?
Instructional Time: 1 day
Common Core Standard
CC.5.MD.1 Convert among different-sized standard measurement
units within a given measurement system (e.g., convert
5 cm to 0.05 m), and use these conversions in solving multi-step,
real world problems.
Lesson Objective
Convert units of time to solve elapsed time
problems.
How can you solve elapsed time problems by
converting units of time?
Practice
3 PRACTICE
Share and Show
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response to
Intervention).
Materials
• MathBoard
• Math Journal
• Animated Math
Models
1
• HMH Mega Math
• iTools:
Measurement
On Your Own
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
20 min.
Summarize Approximately 5 min.
4 SUMMARIZE
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to use the
number line or a clock to find elapsed
time and solve problems by converting
units. As students work through
Unlock the Problem, gauge their level
of understanding to make better
decisions about how to progress through
instruction.
132
Approximately 10 min.
Students can begin independent
practice once they understand these
time measurement concepts. Select
exercises based on students’ depth of
understanding. The exercises below require
higher order thinking skills and critical
reasoning, making them especially rich.
Exercises 12–14
Engage Approximately 5 min.
ENGAGE
Teach and
Approximately
2 TEACH
andTalk
TALK
Approximately 10 min.
Essential Question
How can you solve elapsed time problems
by converting units of time?
To convert, I use multiplication or division
and a relationship like 1 hour 5 sixty
minutes. Then I add or subtract units
of time.
Math Journal
Write a real-world word problem that can
be solved using elapsed time. Include the
solution.
© Houghton Mifflin Harcourt Publishing Company
Essential Question
Chapter 10
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Lesson 11.1
Polygons
Build on students’ understanding of
geometry to develop sound mathematical
practices by asking these questions.
• What do you remember about
geometric figures?
• When would a figure not be a polygon?
• How can you use math vocabulary in
your explanation?
Instructional Time: 1 day
Common Core Standard
CC.5.G.3 Understand that attributes belonging to a category of
two-dimensional figures also belong to all subcategories of that
category.
Lesson Objective
Identify and classify polygons.
Practice
3 PRACTICE
Essential Question
How can you identify and classify polygons?
Materials
• MathBoard
• Math Journal
• Animated Math
Models
• HMH Mega Math
• iTools: Geometry
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide how
deeply to discuss.
Teach and
Approximately
2 TEACH
andTalk
TALK
Approximately 10 min.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response to
Intervention).
On Your Own
Engage Approximately 5 min.
1 ENGAGE
Approximately 10 min.
Students can begin independent practice
once they understand these geometry
concepts. Select exercises based on students’
depth of understanding. The exercises
below require higher order thinking
skills and critical reasoning, making them
especially rich.
Exercises 11–14
Summarize Approximately 5 min.
4 SUMMARIZE
20 min.
© Houghton Mifflin Harcourt Publishing Company
Share and Show
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to use geometric
properties to classify polygons. As students
work through Unlock the Problem, gauge
their level of understanding to make
better decisions about how to progress
through instruction.
Essential Question
How can you identify and classify
polygons?
I name polygons based on the number of
sides and angles it has. I classify polygons
as regular polygons if all the sides are
congruent and all of the angles are
congruent.
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Lesson 11.2
Triangles
Build on students’ understanding of
geometry and measurement to develop
sound mathematical practices by asking
these questions.
• What do you remember about triangles?
• How could you use math vocabulary in
your explanation?
• What do you remember about measuring
length?
• What other information do you need?
Instructional Time: 1 day
Common Core Standard
CC.5.G.3 Understand that attributes belonging to a category of
two-dimensional figures also belong to all subcategories of that
category.
Also CC.5.G.4
Lesson Objective
Essential Question
Practice
3 PRACTICE
Share and Show
How can you classify triangles?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response to
Intervention).
Materials
•
•
•
•
MathBoard
centimeter ruler
protractor
Math Journal
• Animated Math
Models
• HMH Mega Math
• iTools: Geometry
On Your Own
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide how
deeply to discuss.
Summarize Approximately 5 min.
4 SUMMARIZE
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to classify triangles
by side lengths and angle measures.
As students work through Unlock
the Problem, gauge their level of
understanding to make better
decisions about how to progress
through instruction.
136
Approximately 10 min.
Students can begin independent practice
once they understand these geometry
concepts. Select exercises based on
students’ depth of understanding. The
exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 9–11
Engage Approximately 5 min.
1 ENGAGE
Teach and
Approximately
2 TEACH
andTalk
TALK
Approximately 10 min.
Essential Question
How can you classify triangles?
I can classify triangles by the number
of congruent sides or congruent angles
they have.
© Houghton Mifflin Harcourt Publishing Company
Classify and draw triangles using their
properties.
Chapter 11
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Lesson 11.3
Quadrilaterals
Instructional Time: 1 day
Common Core Standard
CC.5.G.4 Classify two-dimensional figures in a hierarchy based on
properties.
Lesson Objective
Classify and compare quadrilaterals using their
properties.
Essential Question
Practice
3 PRACTICE
How can you classify and compare
quadrilaterals?
Share and Show
Materials
•
•
•
•
MathBoard
Quadrilaterals
scissors
Math Journal
• Animated Math
Models
• HMH Mega Math
• iTools: Geometry
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide how
deeply to discuss.
Teach and
Approximately
2 TEACH
andTalk
TALK
Approximately 10 min.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response to
Intervention).
On Your Own
Approximately 10 min.
Students can begin independent practice
once they understand these geometry
concepts. Select exercises based on
students’ depth of understanding. The
exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 4–7 or 8–10
Summarize Approximately 5 min.
4 SUMMARIZE
20 min.
© Houghton Mifflin Harcourt Publishing Company
Build on students’ understanding of
addends to develop sound mathematical
practices by asking these questions.
• What do you remember about
quadrilaterals?
• How could you use math vocabulary in
your explanation?
• What do you remember about
measuring length?
• What other information do you need?
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this activity
is for students to use side lengths and
angle measures to classify quadrilaterals.
As students work through Unlock
the Problem, gauge their level of
understanding to make better
decisions about how to progress
through instruction.
Essential Question
How can you classify and compare
quadrilaterals?
The properties I use include the number
of sides, the types of angles, and the
relationship shared by opposite sides and
opposite angles.
Math Journal
All rectangles are parallelograms. Are all
parallelograms rectangles? Explain.
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Lesson 11.4
Problem Solving • Properties of
Two-Dimensional Figures
Build on students’ understanding of
geometry and problem-solving strategies
to develop sound mathematical practices
by asking these questions.
• What did you do first? Why?
• How can tracing the figure help you
solve the problem?
• How do you know your answer is
reasonable?
Instructional Time: 1 day
Common Core Standard
CC.5.G.3 Understand that attributes belonging to a category of
two-dimensional figures also belong to all subcategories of that
category.
Solve problems using the strategy act it out.
Practice
3 PRACTICE
Essential Question
Share and Show
How can you use the strategy act it out to
approximate whether the sides of a figure are
congruent?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response to
Intervention).
Materials
• MathBoard
• tracing paper
• scissors
On Your Own
• Math Journal
• iTools: Geometry
Teach and
Approximately
2 TEACH
andTalk
TALK
Summarize Approximately 5 min.
4 SUMMARIZE
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this activity
is for students to organize information and
use models to solve problems involving
geometric properties. As students work
through Unlock the Problem, gauge their
level of understanding to make better
decisions about how to progress through
instruction.
138
Approximately 10 min.
Students can begin independent practice
once they understand these geometry
concepts. Select exercises based on
students’ depth of understanding. The
exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 5, 7, 8
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual foundation for the lesson. Use evidence of
students’ understanding to decide how
deeply to discuss.
Approximately 10 min.
Essential Question
How can you use the strategy act it out to
approximate whether the sides of a figure
are congruent?
I can fold the figure as needed to see if the
sides are the same length.
Math Journal
Explain how you can check to see if a
polygon’s sides are congruent without
measuring.
© Houghton Mifflin Harcourt Publishing Company
Lesson Objective
Chapter 11
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Lesson 11.5
Three-Dimensional Figures
Build on students’ understanding of
geometry to develop sound mathematical
practices by asking these questions.
• What do you remember about
three-dimensional figures?
• What information do you need to
classify the figures?
• What properties did you use to answer
the question?
Instructional Time: 1 day
Common Core Standard
CC.5.MD.3 Recognize volume as a attribute of solid figures and
understand concepts of volume measurement.
Also CC.5.G.4
Lesson Objective
Identify, describe, and classify threedimensional figures.
Practice
3 PRACTICE
Essential Question
Share and Show
How can you identify, describe, and classify
three-dimensional figures?
Materials
• MathBoard
• Math Journal
• Real World
Video, Ch. 11
• Animated Math
Models
• HMH Mega Math
• iTools: Geometry
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide how
deeply to discuss.
Teach and
Approximately
2 TEACH
andTalk
TALK
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
On Your Own
Approximately 10 min.
Students can begin independent practice
once they understand these geometry
concepts. Select exercises based on
students’ depth of understanding. The
exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 16–17
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
20 min.
© Houghton Mifflin Harcourt Publishing Company
Approximately 10 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to use geometric
properties to classify three-dimensional
figures. As students work through
Unlock the Problem, gauge their level
of understanding to make better
decisions about how to progress through
instruction.
How can you identify, describe, and classify
three-dimensional figures?
First, I look at the surfaces and decide if
they are flat and polygons. If they are,
I know the solid figure is a polyhedron.
If any surface is curved, I know it is not a
polyhedron. If it is a polyhedron, I look at
the base and lateral faces to decide if it is a
prism or a pyramid. Finally, I use the shape
of the base to name the polyhedron.
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Lesson 11.6
Investigate • Unit Cubes and
Solid Figures
Build on students’ understanding of
geometry to develop sound mathematical
practices by asking these questions.
• What do you remember about unit
squares?
• What tools could you use to help you
solve the given problem?
• How can you use math vocabulary in
your explanation?
• How many rectangular prisms could you
build with 12 cubes?
Instructional Time: 1 day
Common Core Standard
CC.5.MD.3a Recognize volume as an attribute of solid figures and
understand concepts of volume measurement. A cube with side
length 1 unit, called a “unit cube” is said to have “one cubic unit”
of volume, and can be used to measure volume.
Lesson Objective
Essential Question
Practice
3 PRACTICE
Share and Show
What is a unit cube and how can you use it to
build a solid figure?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Students can begin independent practice
once they understand these geometry
concepts. Select exercises based on
students’ depth of understanding. The
exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 8–10
Materials
• MathBoard
• centimeter cubes
• Math Journal
• iTools: Geometry
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide how
deeply to discuss.
Teach and
Approximately
2 TEACH
andTalk
TALK
Summarize Approximately 5 min.
4 SUMMARIZE
20 min.
Investigate • Activity to Build Conceptual
Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to use the unit cube
to build rectangular prisms and figures
composed of unit cubes. As students work
through Unlock the Problem, gauge their
level of understanding to make better
decisions about how to progress through
instruction.
140
Approximately 20 min.
Essential Question
What is a unit cube and how can you use it
to build a solid figure?
A unit cube is a rectangular prism that is
1 unit long, 1 unit wide, and 1 unit high.
It has 6 square faces and 12 edges. You can
use unit cubes to build rectangular prisms
and other solid figures by joining the unit
cubes.
Math Journal
Draw and label examples of all rectangular
prisms built with 16 unit cubes.
© Houghton Mifflin Harcourt Publishing Company
Understand unit cubes and how they can be
used to build a solid figure.
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Lesson 11.7
Investigate • Understand Volume
Instructional Time: 1 day
Common Core Standard
CC.5.MD.3b Recognize volume as an attribute of solid figures and
understand concepts of volume measurement. A solid figure which
can be packed without gaps or overlaps using n unit cubes is said to
have a volume of n cubic units.
Also CC.5.MD.4
Lesson Objective
Count unit cubes that fill a solid figure to find
volume.
Practice
3 PRACTICE
Essential Question
Share and Show
How can you use unit cubes to find the
volume of a rectangular prism?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Materials
• MathBoard
• Rectangular
Prism Net A
• centimeter cubes
• Math Journal
• HMH Mega Math
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide how
deeply to discuss.
Teach and
Approximately
2 TEACH
andTalk
TALK
On Your Own
Approximately 10 min.
Approximately 10 min.
Students can begin independent practice
once they understand these geometry and
modeling concepts. Select exercises based
on students’ depth of understanding.
The exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 7–9
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
20 min.
© Houghton Mifflin Harcourt Publishing Company
Build on students’ understanding of
geometry and modeling to develop sound
mathematical practices by asking these
questions.
• What do you remember about volume?
• Why is a rectangular prism net a good
tool for this problem?
• What might be a shortcut for solving the
given problem?
• Will that shortcut method always work?
Investigate • Activity to Build Conceptual
Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to count unit
cubes to determine the volume of
rectangular prisms. As students work
through Unlock the Problem, gauge their
level of understanding to make better
decisions about how to progress through
instruction.
How can you use unit cubes to find the
volume of a rectangular prism?
I can find the number of unit cubes it takes
to fill the base of the rectangular prism
without any gaps or overlaps, and then
multiply that number by the number of
layers that make up its height. Then I can
write the volume in cubic units.
Math Journal
Explain how to find the volume of a
rectangular prism in cubic inches that is
4 inches long, 3 inches wide, and 2 inches
high. Include a drawing in your solution.
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Lesson 11.8
Investigate • Understand Volume
• What do you remember about finding
the volume?
• What tools could you use to help you
solve the problem?
• What is another method to solve the
problem?
• How do you know your answer is
reasonable?
Instructional Time: 1 day
Common Core Standard
CC.5.MD.4 Measure volumes by counting unit cube, using cubic cm,
cubic in., and cubic ft, and improvised units.
Also CC.5.MD.3b
Estimate the volume of a rectangular prism.
Practice
3 PRACTICE
Essential Question
Share and Show
How can you use an everyday object to
estimate the volume of a rectangular prism?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Materials
• MathBoard
• Rectangular
Prism Net B
• 2 different-sized
boxes
• Math Journal
• HMH Mega Math
On Your Own
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Investigate • Activity to Build Conceptual
Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to estimate the
volume of a rectangular prism by using
improvised units. As students work
through Unlock the Problem, gauge their
level of understanding to make better
decisions about how to progress through
instruction.
Build on students’ understanding of
geometry and estimation to develop
sound mathematical practices by asking
these questions.
142
Approximately 10 min.
Students can begin independent practice
once they understand these geometry and
estimation concepts. Select exercises based
on students’ depth of understanding.
The exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 6–8
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide how
deeply to discuss.
Approximately 10 min.
Essential Question
How can you use an everyday object to estimate the volume of a rectangular prism?
I can use a small rectangular prism that I
know the volume of as a tool to estimate
the volume of a larger rectangular prism.
I can find about how many of the smaller
prisms fit in the base, and about how
many make up the height. I can multiply
these numbers and the volume of the
smaller rectangular prism to estimate the
volume of the larger rectangular prism.
Math Journal
Explain how you can estimate the volume
of a large container that holds 5 rows of
4 snack-sized boxes of cereal in its bottom
layer and is 3 layers high. Each cereal box
has a volume of 16 cubic inches.
© Houghton Mifflin Harcourt Publishing Company
Lesson Objective
Chapter 11
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Lesson 11.9
Volume of Rectangular Prisms
Instructional Time: 1 day
Common Core Standard
CC.5.MD.5a Relate volume to the operations of multiplication and
addition and solve real world and mathematical problems involving
volume. Find the volume of a right rectangular prism with wholenumber side lengths by packing it with unit cubes, and show that
the volume is the same as would be found by multiplying the edge
lengths, equivalently by multiplying the height by the area of the
base. Represent threefold whole-number products as volumes, e.g.,
to represent the associative property of multiplication.
Practice
3 PRACTICE
Lesson Objective
Find the volume of a rectangular prism.
Share and Show
Essential Question
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
How can you find the volume of a rectangular
prism?
Materials
• MathBoard
• Math Journal
• HMH Mega Math
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide how
deeply to discuss.
Teach and
Approximately
2 TEACH
andTalk
TALK
On Your Own
Approximately 10 min.
Approximately 10 min.
Students can begin independent practice
once they understand these geometry
concepts. Select exercises based on
students’ depth of understanding. The
exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 5, 6, 7
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
20 min.
© Houghton Mifflin Harcourt Publishing Company
Build on students’ understanding of
geometry to develop sound mathematical
practices by asking these questions.
• What do you remember about finding
volume?
• What might be a shortcut for finding
the volume?
• Will that method always work?
• How do you know?
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to find volume
of rectangular prisms by breaking the
prism’s base into width and height and
multiplying. As students work through
Unlock the Problem, gauge their level of
understanding to make better decisions
about how to progress through instruction.
How can you find the volume of a
rectangular prism?
I multiply the area of the base by the
height of the prism, and write the volume
using cubic units.
Math Journal
Write a word problem that involves
finding the volume of a box. Draw the
box, solve the problem, and explain how
you found your answer.
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Lesson 11.10
Algebra • Apply Volume Formulas
Build on students’ understanding of
geometry to develop sound mathematical
practices by asking these questions.
• What do you remember about formulas?
• What did you do first? Why?
• Will that method always work?
• How do you know your answer is
reasonable?
Instructional Time: 1 day
Common Core Standard
CC.5.MD.5b Relate volume to the operations of multiplication and
addition and solve real world and mathematical problems involving
volume. Apply the formulas V 5 I × w × h and V 5 b × h for
rectangular prisms to find volumes of right rectangular prisms with
whole-number edge lengths in the context of solving real world and
mathematical problems.
Use a formula to find the volume of a
rectangular prism.
Practice
3 PRACTICE
Share and Show
Approximately 10 min.
How can you use a formula to find the volume
of a rectangular prism?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
Materials
On Your Own
Essential Question
• MathBoard
• Math Journal
• Animated Math
Models
• HMH Mega Math
Students can begin independent practice
once they understand these geometry
concepts. Select exercises based on
students’ depth of understanding. The
exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 7, 8, 11
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide how
deeply to discuss.
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to use a formula
to find the volume of a rectangular
prism. As students work through Unlock
the Problem, gauge their level of
understanding to make better decisions
about how to progress through instruction.
144
Approximately 10 min.
Essential Question
How can you use a formula to find the
volume of a rectangular prism?
If I know the dimensions of the
rectangular prism, I can use those
dimensions in the formula V 5 B 3 H, or
V 5 L 3 W 3 H to find its volume quickly
and efficiently. I write the volume using
cubic units.
Math Journal
Explain how you would find the height
of a rectangular prism if you know that
the volume is 60 cubic centimeters and
that the area of the base is 10 square
centimeters.
© Houghton Mifflin Harcourt Publishing Company
Lesson Objective
Chapter 11
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Lesson 11.11
Problem Solving • Compare
Volumes
Instructional Time: 1 day
Common Core Standard
CC.5.MD.5b Relate volume to the operations of multiplication and
addition and solve real world and mathematical problems involving
volume. Apply the formulas V 5 I × w × h and V 5 b × h for
rectangular prisms to find volumes of right rectangular prisms with
whole-number edge lengths in the context of solving real world and
mathematical problems.
Practice
3 PRACTICE
Lesson Objective
Use the strategy make a table to compare
volumes.
Share and Show
Essential Question
How can you use the strategy make a table to
compare different rectangular prisms with the
same volume?
Materials
• MathBoard
• Math Journal
• Animated Math
Models
• HMH Mega Math
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide how
deeply to discuss.
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
© Houghton Mifflin Harcourt Publishing Company
Build on students’ understanding of
geometry and problem solving strategies
to develop sound mathematical practices
by asking these questions.
• What did you do first? Why?
• What strategy could you use to help you
solve the problem?
• Will that method always work?
• Why is a table a good model for this
problem?
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to organize
information in a table to find the
number of rectangular prisms that
have a given volume. As students work
through Unlock the Problem, gauge their
level of understanding to make better
decisions about how to progress through
instruction.
Approximately 10 min.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
On Your Own
Approximately 10 min.
Students can begin independent practice
once they understand these geometry
concepts. Select exercises based on
students’ depth of understanding. The
exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 4, 6, 7
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How can you use the strategy make a table
to compare different rectangular prisms
with the same volume?
I can make a table to find all the
combinations of three factors whose
product equals a given volume, and have
different-sized bases.
Math Journal
Using drawings of rectangular prisms,
define in your own words perimeter,
area, and volume. Use colored pencils to
highlight what each term refers to.
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Lesson 11.12
Find Volume of Composed Figures
Build on students’ understanding of
geometry to develop sound mathematical
practices by asking these questions.
• What do you remember about
composite figures?
• Which operation did you choose to
represent the situation? Why?
• What is another method for solving the
given problem?
Instructional Time: 1 day
Common Core Standard
CC.5.MD.5c Relate volume to the operations of multiplication and
addition and solve real world and mathematical problems involving
volume. Recognize volume as additive. Find volumes of solid figures
composed of two non-overlapping right rectangular prisms by adding
the volume of the non-overlapping parts, applying this technique to
solve real world problems.
Find the volume of the combined rectangular
prisms.
Practice
3 PRACTICE
Share and Show
Essential Question
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response
to Intervention).
How can you find the volume of rectangular
prisms that are combined?
Materials
• MathBoard
• Math Journal
• Animated Math
Models
On Your Own
• HMH Mega Math
2
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
TEACH
andTalk
TALK
20 min.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
activity is for students to develop different
methods for finding the volume of
composite figures. As students work
through Unlock the Problem, gauge their
level of understanding to make better
decisions about how to progress through
instruction.
146
Approximately 10 min.
Students can begin independent practice
once they understand these geometry
concepts. Select exercises based on
students’ depth of understanding. The
exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 5, 7, 8 or 9–11
Engage Approximately 5 min.
1 ENGAGE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide how
deeply to discuss.
Approximately 10 min.
Essential Question
How can you find the volume of
rectangular prisms that are combined?
I can break apart the prisms and add each
of their volumes, or I can find the greatest
possible volume and subtract the volume
of the empty space.
Math Journal
Draw a composite figure and label its
dimensions. Find the volume of the
composite figure.
© Houghton Mifflin Harcourt Publishing Company
Lesson Objective
Chapter 11
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