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Lesson 1.1
Algebra • Use Pictures to Add To
Build on students’ understanding of
putting together to develop sound
mathematical practices by asking these
questions.
• What does it mean “to join” when you
add?
• Why is drawing pictures a good model
to use?
• What does our model show?
Instructional Time: 1 day
Common Core Standard
CC.1.OA.1 Use addition and subtraction within 20 to solve word
problems involving situations of adding to, taking from, putting
together, taking apart, and comparing, with unknowns in all
positions, e.g., by using objects, drawings, and equations with a
symbol for the unknown number to represent the problem.
Lesson Objective
Practice
3 PRACTICE
Use pictures to “add to” and find sums.
Essential Question
Share and Show
How do pictures show adding to?
Materials
• MathBoard
• Math Journal
• Animated Math
Models
• HMH Mega Math
• iTools: Counters
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 how to use pictures
to add. Select exercises based on students’
depth of understanding. The exercises
below require higher order thinking skills
and critical reasoning, making them
especially rich.
Exercises 3, 4, 5, or 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
Essential Question
20 min.
© Houghton Mifflin Harcourt Publishing Company
Approximately 10 min.
Listen and Draw • 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 addition
problems by drawing pictures. As students
work through Listen and Draw, gauge
their level of understanding to make
better decisions about how to progress
through instruction.
How do pictures show adding to?
Possible answer: I show how many there
are in the first picture. Then I show how
many more in the second picture.
Math Journal
Use pictures and numbers to show 4 dogs
and 1 more dog. Then write how many
dogs there are.
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Lesson 1.2
Hands On • Model Adding To
Build on students’ understanding of
adding to to develop sound mathematical
practices by asking these questions.
• How else can you model the problem?
• What will you join together?
• What will you do first?
Instructional Time: 1 day
Common Core Standard
Also CC.1.OA.7
Practice
3 PRACTICE
Share and Show
Lesson Objective
Approximately 10 min.
Essential Question
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
How do you model adding to a group?
On Your Own
Materials
Students can begin independent practice
once they understand the concept of
adding to a group. 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, or 10–13
Use concrete objects to solve “adding to”
addition problems.
• MathBoard
• connecting cubes
• Math Journal
• Animated Math
Models
• HMH Mega 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.
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Listen and Draw • 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 addition. As students work through
Listen and Draw, gauge their level of
understanding to make better decisions
about how to progress through
instruction.
26
Approximately 10 min.
Essential Question
How do you model adding to a group?
Possible answer: I can use cubes to show
the number I start with. Then I can add
more cubes to show the number being
added.
Math Journal
Use cubes to show how to add 1 turtle to
5 turtles. Draw the cubes.
© Houghton Mifflin Harcourt Publishing Company
CC.1.OA.1 Use addition and subtraction within 20 to solve word
problems involving situations of adding to, taking from, putting
together, taking apart, and comparing, with unknowns in all
positions, e.g., by using objects, drawings, and equations with a
symbol for the unknown number to represent the problem.
Chapter 1
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Lesson 1.3
Hands On • Model Putting
Together
Build on students’ understanding of
putting together to develop sound
mathematical practices by asking these
questions.
• What does the problem ask you to do?
• What is the first thing you will do?
• How else could you model the problem?
Instructional Time: 1 day
Common Core Standard
CC.1.OA.1 Use addition and subtraction within 20 to solve word
problems involving situations of adding to, taking from, putting
together, taking apart, and comparing, with unknowns in all
positions, e.g., by using objects, drawings, and equations with a
symbol for the unknown number to represent the problem.
Practice
3 PRACTICE
Lesson Objective
Share and Show
Use concrete objects to solve “putting
together” addition problems.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
Essential Question
How do you model putting together?
On Your Own
Materials
• MathBoard
• HMH Mega Math
• two-color counters • iTools: Counters
• 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
© Houghton Mifflin Harcourt Publishing Company
20 min.
Listen and Draw • 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 counters to
show addition. As students work through
Listen and Draw, gauge their level of
understanding to make better decisions
about how to progress through
instruction.
Approximately 10 min.
Approximately 10 min.
Students can begin independent practice
once they understand these 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 3, 5, 6, or 7–8
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How do you model putting together?
Possible answer: I use counters to show the
numbers in the problem. Then I draw the
counters and count how many to write an
addition sentence.
Math Journal
Write your own addition problem. Draw
counters to help you solve.
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Lesson 1.4
Problem Solving • Model Addition
their level of understanding to make
better decisions about how to progress
through instruction.
Build on students’ understanding of
putting together to develop sound
mathematical practices by asking these
questions.
• Why is 4 the first number in the bar
model?
• What is being put together in the
problem?
• What does the 6 stand for?
Instructional Time: 1 day
Note: The instructional time for this lesson
can also be 2 days. On Day 1, have students
solve Unlock the Problem with connecting
cubes to make a bar model. Then discuss and
compare models. Have students solve Try
Another Problem with counting cubes and bar
models, relating the models. On Day 2, model
the Share and Show problems with connecting
cubes. Then have students redo the problems
independently with bar models.
CC.1.OA.1 Use addition and subtraction within 20 to solve word
problems involving situations of adding to, taking from, putting
together, taking apart, and comparing, with unknowns in all
positions, e.g., by using objects, drawings, and equations with a
symbol for the unknown number to represent the problem.
Practice
3 PRACTICE
Share and Show
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
Have students work on exercise 6 based on
their depth of understanding. The exercise
requires higher order thinking skills and
critical reasoning, making it especially rich.
Lesson Objective
Solve adding to and putting together
situations using the strategy make a model.
Essential Question
How do you solve addition problems by
making a model?
Materials
• MathBoard
Summarize Approximately 5 min.
4 SUMMARIZE
• 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.
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 addition
problems by using models. As students
work through Unlock the Problem, gauge
28
Approximately 10 min.
Essential Question
How do you solve addition problems by
making a model?
Possible answer: When I make a model,
it helps me see the parts or whole that
are given. Then I can find the other part
or the whole.
Math Journal
Write a problem that has two parts. Then
solve it by finding the whole.
© Houghton Mifflin Harcourt Publishing Company
Common Core Standard
Chapter 1
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Lesson 1.5
Algebra • Add Zero
Build on students’ understanding of the
Additive Identity Property to develop
sound mathematical practices by asking
these questions.
• What is the problem asking you to do?
• How does adding zero change your
answer?
• How else can you solve the problem?
Instructional Time: 1 day
Common Core Standard
CC.1.OA.3 Apply properties of operations as strategies to add and
subtract.
Lesson Objective
Understand and apply the Additive Identity
Property for Addition.
Practice
3 PRACTICE
Essential Question
What happens when you add 0 to a number?
Materials
• MathBoard
• Animated Math
Models
• two-color counters • iTools: Counters
• 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
© Houghton Mifflin Harcourt Publishing Company
20 min.
Listen and Draw • 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 add zero to a
given number. As students work through
Listen and Draw, 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, see RtI (Response to
Intervention).
On Your Own
Approximately 10 min.
Students can begin independent practice
once they understand how to use pictures
to add zero. 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, 11, 17, or 18–20
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
What happens when you add 0 to a
number?
Possible answer: The sum is the number
that zero is added to.
Math Journal
Use pictures and numbers to show 8 1 0.
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Lesson 1.6
Hands On: Algebra • Add in
Any Order
Build on students’ understanding of
addition to develop sound mathematical
practices by asking these questions.
• What information will you use to solve
the problem?
• How else can you model the problem?
• How do you know that your answer
makes sense?
Instructional Time: 1 day
Common Core Standard
CC.1.OA.3 Apply properties of operations as strategies to add and
subtract.
Explore the Commutative Property of
Addition.
Practice
3 PRACTICE
Share and Show
Essential Question
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
Why can you add addends in any order?
Materials
• MathBoard
• red and
blue crayons
• red and blue
connecting cubes
• Math Journal
On Your Own
• iTools: Counters
Engage Approximately 5 min.
1 ENGAGE
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Listen and Draw • 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 adding in
any order. As students work through
Listen and Draw, 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 the Commutative
Property of Addition. 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, or 10–12
• 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
Why can you add addends in any order?
Possible answer: You are still adding the
same parts, so you get the same whole.
Math Journal
Use pictures and numbers to show how to
add 3 1 1 in any order.
© Houghton Mifflin Harcourt Publishing Company
Lesson Objective
Chapter 1
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Lesson 1.7
Hands On: Algebra • Put Together
Numbers to 10
Instructional Time: 1 day
Common Core Standard
CC.1.OA.1 Use addition and subtraction within 20 to solve word
problems involving situations of adding to, taking from, putting
together, taking apart, and comparing, with unknowns in all
positions, e.g., by using objects, drawings, and equations with a
symbol for the unknown number to represent the problem.
Lesson Objective
Model and record all the ways to put together
numbers within 10.
Practice
3 PRACTICE
Share and Show
Approximately 10 min.
How can you show all the ways to make a
number?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
Materials
On Your Own
Essential Question
• MathBoard
• red and blue
crayons
• Math Journal
• Animated Math
Models
• red and blue
connecting cubes
• 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
20 min.
© Houghton Mifflin Harcourt Publishing Company
Build on students’ understanding of
putting together to develop sound
mathematical practices by asking these
questions.
• What is the problem asking you to do?
• Why should you use two different
colors to model?
• How many answers are you looking
for?
Listen and Draw • 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 putting
together numbers. As students work
through Listen and Draw, gauge their
level of understanding to make better
decisions about how to progress through
instruction.
Approximately 10 min.
Students can begin independent practice
once they understand the ways to make
a number up to 10. 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, 17, 21, or 22
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How can you show all the ways to make a
number?
Possible answer: I can use different
numbers of red and blue cubes in each
cube train.
Math Journal
Use pictures and numbers to show all the
ways to make 3.
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Lesson 1.8
Addition to 10
• What numbers will you use to solve the
first problem?
• How did you model the problem?
• What is alike about the two ways to
add?
• What is different?
Instructional Time: 1 day
Common Core Standard
Lesson Objective
Practice
3 PRACTICE
Share and Show
Build fluency for addition within 10.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
Essential Question
Why are some addition facts easy to add?
Materials
• MathBoard
• crayons
• Math Journal
On Your Own
• HMH Mega Math
• iTools: Counters
Teach and
Approximately
2 TEACH
andTalk
TALK
Summarize Approximately 5 min.
4 SUMMARIZE
20 min.
Listen and Draw • 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 draw and
understand addition up to 10. As students
work through Listen and Draw, gauge
their level of understanding to make
better decisions about how to progress
through instruction.
Build on students’ understanding of
addition facts to develop sound
mathematical practices by asking these
questions.
32
Approximately 10 min.
Students can begin independent practice
once they understand these basic addition
facts. 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, 20, 23, or 24–25
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
Why are some addition facts easy to add?
Possible answer: When addition facts have
0 as an addend, I know the sum is the
other number. If I know the sum of one
addition fact and I see another addition
fact with the same addends in a different
order, I know the sums are the same.
Math Journal
Explain how knowing 1 1 7 helps you find
the sum for 7 1 1.
© Houghton Mifflin Harcourt Publishing Company
CC.1.OA.6 Add and subtract within 20, demonstrating fluency for
addition and subtraction within 10. Use strategies such as counting
on; making ten; decomposing a number leading to a ten; using the
relationship between addition and subtraction; and creating
equivalent but easier or known sums.
Chapter 1
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Lesson 2.1
Use Pictures to Show Taking From
Instructional Time: 1 day
•
Common Core Standard
CC.1.OA.1 Use addition and subtraction within 20 to solve word
problems involving situations of adding to, taking from, putting
together, taking apart, and comparing, with unknowns in all
positions, e.g., by using objects, drawings, and equations with
a symbol for the unknown number to represent the problem.
•
What happens when you take from
something or someone?
How can a picture show when you are
“taking from”?
What is the problem asking you to do?
Practice
3 PRACTICE
Share and Show
Lesson Objective
Approximately 10 min.
Essential Question
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
How can you show taking from with pictures?
On Your Own
Materials
Students can begin independent practice
once they understand these 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 3, 4, 6, or 7–9
Use pictures to show “taking from” and find
differences.
• MathBoard
• HMH Mega Math
• Math Journal
• iTools: Counters
• 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.
2
Teach and
Approximately
TEACH
andTalk
TALK
20 min.
© Houghton Mifflin Harcourt Publishing Company
•
Listen and Draw • 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 pictures
to show subtraction. As students work
through Listen and Draw, gauge their
level of understanding to make better
decisions about how to progress through
instruction.
Build on students’ understanding of
“adding to” to develop sound
mathematical practices by asking these
questions.
Approximately 10 min.
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How can you show taking from with
pictures?
Possible answer: I can draw the number of
animals I start with. Then I can cross out
how many I take from the whole.
Math Journal
Draw a picture to show the problem. There
are 9 turtles. 3 turtles walk away. How
many turtles are there now?
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Lesson 2.2
Hands On • Model Taking From
• What is the first thing you would do?
Why?
• What numbers do you need to know?
• How else can you solve the problem?
Instructional Time: 1 day
Common Core Standard
Practice
3 PRACTICE
Share and Show
Lesson Objective
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
Use concrete objects to solve “taking from”
subtraction problems.
Essential Question
On Your Own
How do you model taking from a group?
• connecting cubes
• Math Journal
• Animated Math
Models
• HMH Mega 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.
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Listen and Draw • 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
subtraction problems. As students work
through Listen and Draw, gauge their
level of understanding to make better
decisions about how to progress through
instruction.
Build on students’ understanding of
“taking from” to develop sound
mathematical practices by asking these
questions.
36
Approximately 10 min.
Students can begin independent practice
once they understand how to use concrete
objects to model and solve subtraction
problems. 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, or 8–10
Materials
• MathBoard
Approximately 10 min.
Essential Question
How do you model taking from a group?
Possible answer: I take some cubes from
the rest of the group and I count to see
how many there are now. Then I draw the
cubes I started with and I circle and cross
out the cubes I take away.
Math Journal
Use pictures and numbers to model 9 2 2.
© Houghton Mifflin Harcourt Publishing Company
CC.1.OA.1 Use addition and subtraction within 20 to solve word
problems involving situations of adding to, taking from, putting
together, taking apart, and comparing, with unknowns in all
positions, e.g., by using objects, drawings, and equations with
a symbol for the unknown number to represent the problem.
Chapter 2
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Lesson 2.3
Hands On • Model Taking Apart
• What words in the problem help you
know what to do?
• How will you use the numbers?
• How else can you model the problem?
Instructional Time: 1 day
Common Core Standard
CC.1.OA.1 Use addition and subtraction within 20 to solve word
problems involving situations of adding to, taking from, putting
together, taking apart, and comparing, with unknowns in all
positions, e.g., by using objects, drawings, and equations with a
symbol for the unknown number to represent the problem.
Practice
3 PRACTICE
Share and Show
Lesson Objective
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
Use concrete objects to solve “taking apart”
subtraction problems.
Essential Question
On Your Own
How do you model taking apart?
Materials
• MathBoard
• HMH Mega Math
• two-color counters • iTools: Counters
• Math Journal
Engage Approximately 5 min.
1 ENGAGE
Approximately 10 min.
Students can begin independent practice
once they understand the concept “taking
apart.” Select exercises based on students’
depth of understanding. The exercises
below require higher order thinking skills
and critical reasoning, making them
especially rich.
Exercises 3, 4, 5, or 7–9
Summarize Approximately 5 min.
4 SUMMARIZE
This activity reviews prerequisite skills,
establishing a common conceptual
foundation for the lesson. Use evidence
of students’ understanding to decide
how deeply to discuss.
Essential Question
How do you model taking apart?
Possible answer: I use counters to show the
whole. I count the part I know. Then I turn
over the rest of the counters and count
those.
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
© Houghton Mifflin Harcourt Publishing Company
Approximately 10 min.
Listen and Draw • 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 taking apart. As students work
through Listen and Draw, gauge their level
of understanding to make better decisions
about how to progress through
instruction.
Build on students’ understanding of
“taking from” to develop sound
mathematical practices by asking these
questions.
Math Journal
Use pictures and numbers to find 8 2 3.
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Lesson 2.4
Problem Solving • Model
Subtraction
development is key. The goal of this
activity is for students to use models to
show subtraction situations. 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
“taking from” and “taking apart” to
develop sound mathematical practices by
asking these questions.
• What is the problem asking?
• What will you do first? Why?
• How can you tell if your answer makes
sense?
Instructional Time: 1 day
Note: The instructional time for this lesson
can also be 2 days. On Day 1, introduce using
bar models to show subtraction. Then model
Unlock the Problem using connecting cubes
and bar models. Then do Try Another Problem
using bar models only. On Day 2, guide
students through the Share and Show
problems. Spend extra time on the Go Deeper
by having students made bar models showing
different scenarios.
Common Core Standard
Practice
3 PRACTICE
Share and Show
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
Lesson Objective
Solve taking from and taking apart
subtraction problems using the strategy
make a model.
On Your Own
Essential Question
Materials
• MathBoard
• HMH Mega Math
• Math Journal
• iTools: Counters
• Animated Math Models
Summarize Approximately 5 min.
4 SUMMARIZE
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.
Unlock the Problem • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
38
Approximately 10 min.
Students can begin independent practice
once they understand the concept of
solving subtraction problems with models.
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, or 8
How do you solve subtraction problems by
making a model?
Engage Approximately 5 min.
1 ENGAGE
Approximately 10 min.
Chapter 2
1_MNYCETS221970_C02RML04.indd 38
Essential Question
How do you solve subtraction problems by
making a model?
Possible answer: I find the information I
need from the problem. Then I decide if the
information is a part or a whole. I draw the
whole at the bottom and show the parts
in the two bars above the whole. I use the
model to find the number to subtract.
Math Journal
Choose a model from a problem you
solved. Write a new subtraction problem
to match.
© Houghton Mifflin Harcourt Publishing Company
CC.1.OA.1 Use addition and subtraction within 20 to solve word
problems involving situations of adding to, taking from, putting
together, taking apart, and comparing, with unknowns in all
positions, e.g., by using objects, drawings, and equations with
a symbol for the unknown number to represent the problem.
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Lesson 2.5
Use Pictures and Subtraction
to Compare
• How can drawing a picture help you
solve the problem?
• How will you use the numbers in the
problem?
• How did you find your answer?
• How can you tell if your answer makes
sense?
Instructional Time: 1 day
Common Core Standard
CC.1.OA.8 Determine the unknown whole number in an addition
or subtraction equation relating three whole numbers.
Practice
3 PRACTICE
Lesson Objective
Compare pictorial groups to understand
subtraction.
Share and Show
How can you use pictures to compare and
subtract?
Use the checked exercise as a diagnostic
assessment. If students answer the
exercise incorrectly, see RtI (Response to
Intervention).
Materials
On Your Own
Essential Question
• MathBoard
• HMH Mega Math
• Math Journal
• iTools: Counters
• 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
20 min.
© Houghton Mifflin Harcourt Publishing Company
Approximately 10 min.
Listen and Draw • 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 pictures to
show comparisons and subtraction. As
students work through Listen and Draw,
gauge their level of understanding to
make better decisions about how to
progress through instruction.
Build on students’ understanding of
modeling subtraction to develop sound
mathematical practices by asking these
questions.
Approximately 10 min.
Students can begin independent practice
once they understand the concept of
comparing two numbers. Select exercises
based on students’ depth of understanding.
The exercises below require higher order
thinking skills and critical reasoning, making them especially rich.
Exercises 2, 4, 5, or 6–7
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How can you use pictures to compare and
subtract?
Possible answer: I can match pictures in the
two groups one to one. The extras show
the difference.
Math Journal
Draw pictures to compare to find 8 2 2.
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Lesson 2.6
Hands On • Subtract to Compare
Build on students’ understanding of
comparisons to develop sound
mathematical practices by asking these
questions.
• What is the problem asking?
• What is a good way to model the
problem?
• What does it mean when a problem asks
“how many more?”
Instructional Time: 1 day
Common Core Standard
CC.1.OA.1 Use addition and subtraction within 20 to solve word
problems involving situations of adding to, taking from, putting
together, taking apart, and comparing, with unknowns in all
positions, e.g., by using objects, drawings, and equations with
a symbol for the unknown number to represent the problem.
Lesson Objective
Practice
3 PRACTICE
Share and Show
Model and compare groups to show the
meaning of subtraction.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
Essential Question
How can you use models to compare and
subtract?
On Your Own
Materials
• Animated Math
Models
• two-color counters • HMH Mega Math
• Math Journal
• iTools: Counters
Engage Approximately 5 min.
1 ENGAGE
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Listen and Draw • 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 comparisons and subtraction. As
students work through Listen and Draw,
gauge their level of understanding to
make better decisions about how to
progress through instruction.
40
Approximately 10 min.
Students can begin independent practice
once they understandthe concept of
subtracting to compare. Select exercises
based on students’ depth of understanding.
The exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 3, 4, or 5
• MathBoard
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 models to compare and
subtract?
Possible answer: I can use a bar model to
compare the numbers. Then I can subtract
to find the difference.
Math Journal
Write a subtract to compare problem and
draw a bar model to solve it.
© Houghton Mifflin Harcourt Publishing Company
Also CC.1.OA.8
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Lesson 2.7
Subtract All or Zero
Instructional Time: 1 day
Common Core Standard
CC.1.OA.8 Determine the unknown whole number in an addition
or subtraction equation relating three whole numbers.
Lesson Objective
Identify how many are left when subtracting
all or 0.
Essential Question
What happens when you subtract 0 from a
number?
Materials
• MathBoard
• Animated Math
Models
• two-color counters • iTools: Counters
• 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
© Houghton Mifflin Harcourt Publishing Company
20 min.
Listen and Draw • 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
pictures to subtract all or 0. As students
work through Listen and Draw, gauge
their level of understanding to make
better decisions about how to progress
through instruction.
Build on students’ understanding of
the number zero to develop sound
mathematical practices by asking these
questions.
• What does it mean to take away zero?
• What does it mean to take away all?
• How can you model both questions?
• How can you tell if your answer makes
sense?
Practice
3 PRACTICE
Share and Show
Approximately 10 min.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
On Your Own
Approximately 10 min.
Students can begin independent practice
once they understand how to subtract 0.
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, 17–18, or 19–21
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
What happens when you subtract 0 from
a number?
Possible answer: You take nothing away,
so the answer is the number you started
with.
Math Journal
Use pictures and numbers to show 2 – 0.
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Lesson 2.8
Hands On: Algebra • Take Apart
Numbers
Build on students’ understanding of
“taking apart” to develop sound
mathematical practices by asking these
questions.
• How many answers is the problem
asking for?
• How would you start to solve the
problem?
• Is there another way to model the
problem?
Instructional Time: 1 day
Common Core Standard
CC.1.OA.1 Use addition and subtraction within 20 to solve word
problems involving situations of adding to, taking from, putting
together, taking apart, and comparing, with unknowns in all
positions, e.g., by using objects, drawings, and equations with
a symbol for the unknown number to represent the problem.
Model and record all of the ways to take apart
numbers within 10.
Practice
3 PRACTICE
Share and Show
Essential Question
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
How can you show all the ways to take apart
a number?
Materials
• MathBoard
• connecting cubes
• Math Journal
On Your Own
• Animated Math
Models
• HMH Mega Math
• iTools: Counters
Teach and
Approximately
2 TEACH
andTalk
TALK
Summarize Approximately 5 min.
4 SUMMARIZE
20 min.
Listen and Draw • 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 different ways to take apart.
As students work through Listen and
Draw, 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 can use models to show various
ways to take apart a given number. 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, 16, 21, or 22
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 show all the ways to take
apart a number?
Possible answer: I can start with 0 and
keep subtracting 1 more until I subtract all.
Math Journal
Use pictures and numbers to show all the
ways to take apart 8.
© Houghton Mifflin Harcourt Publishing Company
Lesson Objective
Chapter 2
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Lesson 2.9
Subtraction from 10 or Less
Instructional Time: 1 day
Common Core Standard
CC.1.OA.6 Add and subtract within 20, demonstrating fluency for
addition and subtraction within 10. Use strategies such as counting
on; making ten; decomposing a number leading to a ten; using the
relationship between addition and subtraction; and creating equivalent but easier or known sums.
Essential Question
Why are some subtraction facts easy to
subtract?
On Your Own
Materials
• HMH Mega 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
20 min.
Listen and Draw • 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 pictures to
show subtraction within 10. As students
work through Listen and Draw, gauge
their level of understanding to make
better decisions about how to progress
through instruction.
Build on students’ understanding of
subtraction problems 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, see RtI (Response to
Intervention).
Build fluency for subtraction within 10.
© Houghton Mifflin Harcourt Publishing Company
Practice
3 PRACTICE
Share and Show
Lesson Objective
• MathBoard
• Math Journal
• How can you tell that the problems are
the same?
• What other ways can you model the
problems?
• What is the first thing you will do?
Approximately 10 min.
Students can begin independent practice
once they understand these subtraction
facts. 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, 23, or 24–25
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
Why are some subtraction facts easy to
subtract?
Possible answers: When I subtract all, the
answer is 0; When I subtract 0, the answer
is the number I start with; I just know the
answers to some facts.
Math Journal
Find 10 – 3. Write the subtraction fact two
ways.
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Lesson 3.1
Algebra • Add in Any Order
Build on students’ understanding of
addition sentences to develop sound
mathematical practices by asking these
questions.
• What does “you can add in any order”
mean?
• Do you think that will always work?
• What else could help you solve the
problem?
Instructional Time: 1 day
Common Core Standard
CC.1.OA.3 Apply properties of operations as strategies to add and
subtract.
Lesson Objective
Understand and apply the Commutative
Property of Addition for sums within 20.
What happens if you change the order of the
addends when you add?
Practice
3 PRACTICE
Share and Show
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
Materials
• MathBoard
• blue and red
crayons
• Math Journal
• Animated Math
Models
• HMH Mega Math
On Your Own
Engage Approximately 5 min.
1 ENGAGE
Teach and
Approximately
2 TEACH
andTalk
TALK
Summarize Approximately 5 min.
4 SUMMARIZE
20 min.
Listen and Draw • 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 adding in any order. As students
work through Listen and Draw, gauge
their level of understanding to make
better decisions about how to progress
through instruction.
46
Approximately 10 min.
Students can begin independent practice
once they understand the Commutative
Property of Addition. 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, 14, 16, or 17–19.
• iTools: Counters
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 happens if you change the order
of the addends when you add?
Possible answer: Only the order of the
addends change. The sum is the same.
Math Journal
Use pictures or words to explain how you
would use the sum of 13 to show how to
add in any order.
© Houghton Mifflin Harcourt Publishing Company
Essential Question
Chapter 3
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Lesson 3.2
Count On
Build on students’ understanding of
“adding to” to develop sound
mathematical practices by asking these
questions.
• How does it help to “count on”?
• What can you use to model counting
on?
• How can you tell if your answer makes
sense?
Instructional Time: 1 day
Common Core Standard
CC.1.OA.5 Relate counting to addition and subtraction.
Also CC.1.OA.6, CC.1.OA.8
Lesson Objective
Use count on 1, 2, or 3 as a strategy to find
sums within 20.
Practice
3 PRACTICE
Essential Question
How do you count on 1, 2, or 3?
Share and Show
Materials
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
• MathBoard
• (optional)
connecting cubes
or two-color
counters
• Math Journal
• Animated Math
Models
• HMH Mega Math
Approximately 10 min.
Students can begin independent
practice once they understand the concept
of counting on. 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, 20, 31, or 32–33
• 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.
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
Teach and
Approximately
2 TEACH
andTalk
TALK
How do you count on 1, 2, or 3?
Possible answer: I start with the greater
number and add 1, 2, or 3.
20 min.
© Houghton Mifflin Harcourt Publishing Company
On Your Own
Approximately 10 min.
Listen • 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 pictures to
understand counting on from a given
number. As students work through
Listen, gauge their level of understanding
to make better decisions about how to
progress through instruction.
Math Journal
Use pictures or words to explain how you
can find 9 1 3 by counting on.
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Lesson 3.3
Hands On • Add Doubles
Build on students’ understanding of
addition facts to develop sound
mathematical practices by asking these
questions.
• What does the word “doubles” mean?
• What are some ways to add doubles?
• What shortcut might you use to solve
doubles?
Instructional Time: 1 day
Common Core Standard
CC.1.OA.6 Add and subtract within 20, demonstrating fluency for
addition and subtraction within 10. Use strategies such as counting
on; making ten; decomposing a number leading to a ten; using the
relationship between addition and subtraction; and creating equivalent but easier or known sums.
Also CC.1.OA.8
Practice
3 PRACTICE
Share and Show
Use doubles as a strategy to solve addition
facts with sums within 20.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
Essential Question
What are doubles facts?
Materials
• MathBoard
• connecting cubes
• Math Journal
On Your Own
• Animated Math
Models
• HMH Mega Math
• iTools: Number
Charts
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Listen and Draw • 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 adding doubles. As students
work through Listen and Draw, gauge
their level of understanding to make
better decisions about how to progress
through instruction.
48
Approximately 10 min.
Students can begin independent practice
once they understand the facts of adding
doubles. 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, 13, or 14–15
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.
Approximately 10 min.
Essential Question
What are doubles facts?
Possible answer: Doubles facts have two
addends that are the same.
Math Journal
Use pictures or words to explain how you
could find the sum of 7 1 7.
© Houghton Mifflin Harcourt Publishing Company
Lesson Objective
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Lesson 3.4
Hands On • Use Doubles to Add
Build on students’ understanding of
doubles to develop sound mathematical
practices by asking these questions.
• What could be another good model for
this problem?
• Have you solved a problem that is
something like this problem?
• What will you do first?
Instructional Time: 1 day
Common Core Standard
CC.1.OA.6 Add and subtract within 20, demonstrating fluency for
addition and subtraction within 10. Use strategies such as counting
on; making ten; decomposing a number leading to a ten; using the
relationship between addition and subtraction; and creating
equivalent but easier or known sums.
Also CC.1.OA.8
Practice
3 PRACTICE
Lesson Objective
Share and Show
Use doubles to create equivalent but easier
sums.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
Essential Question
How can you use doubles to help you add?
Materials
• MathBoard
• blue and red
connecting cubes
• crayons
• Math Journal
• Animated Math
Models
• HMH Mega 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.
Listen and Draw • 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 pictures to
show how doubles can be used to add.
As students work through Listen and
Draw, gauge their level of understanding
to make better decisions about how to
progress through instruction.
Approximately 10 min.
On Your Own
Approximately 10 min.
Students can begin independent practice
once they understand how doubles can
make adding easier. Select exercises based
on students’ depth of understanding.
The exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 3, 7, 11, or 13
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How can you use doubles to help you add?
Possible answer: I can break apart one
addend to equal the other addend plus 1.
I group the two numbers that are the same
to show doubles. First, I add the doubles
fact and then I count on 1 to find the sum.
Math Journal
Draw and label a picture to show how
knowing 7 1 7 helps you find 7 1 8.
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Lesson 3.5
Hands On • Doubles Plus 1 and
Doubles Minus 1
Build on students’ understanding of
doubles facts to develop sound
mathematical practices by asking these
questions.
• How can using doubles help you add
and subtract?
• What did you do first to solve the
problem?
• What is another way to solve it?
• How else can you model the problem?
Instructional Time: 1 day
Common Core Standard
CC.1.OA.6 Add and subtract within 20, demonstrating fluency
for addition and subtraction within 10. Use strategies such as
counting on; making ten; decomposing a number leading to a ten;
using the relationship between addition and subtraction; and creating
equivalent but easier or known sums.
Also CC.1.OA.8
Practice
3 PRACTICE
Use doubles plus 1 and doubles minus 1 as
strategies to find sums within 20.
Share and Show
Approximately 10 min.
How can you use what you know about
doubles to find other sums?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
Materials
On Your Own
Essential Question
• MathBoard
• red and blue
connecting cubes
• Math Journal
• Animated Math
Models
• HMH Mega Math
Students can begin independent practice
once they understand these strategies of
doubles plus and minus 1. 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, 12, 14, or 15
• 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.
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Listen and Draw • 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 pictures to show
how they can use doubles facts to find
other sums. As students work through
Listen and Draw, gauge their level of
understanding to make better decisions
about how to progress through
instruction.
50
Approximately 10 min.
Essential Question
How can you use what you know about
doubles to find other sums?
Possible answer: If one addend is 1 more or
1 less than a doubles fact, then I can add or
subtract 1 from the sum of the doubles fact.
Math Journal
Use pictures or words to explain how you
would use doubles plus one to solve 4 1 5.
© Houghton Mifflin Harcourt Publishing Company
Lesson Objective
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Lesson 3.6
Practice the Strategies
Instructional Time: 1 day
Common Core Standard
CC.1.OA.6 Add and subtract within 20, demonstrating fluency
for addition and subtraction within 10. Use strategies such as
counting on; making ten; decomposing a number leading to a ten;
using the relationship between addition and subtraction; and creating
equivalent but easier or known sums.
Also CC.1.OA.8
Lesson Objective
Use the strategies count on, doubles, doubles
plus 1, and doubles minus 1 to practice
addition facts within 20.
Essential Question
What strategies can you use to solve addition
fact problems?
Materials
• MathBoard
• red, blue, and
yellow crayons
Practice
3 PRACTICE
Share and Show
• Animated Math
Models
• iTools: Number
Lines
On Your Own
• iTools: Number
Charts
• Math Journal
• 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.
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Listen and Draw • 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 words and
Approximately 10 min.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
• (optional)
connecting cubes
or two-color
counters
Engage Approximately 5 min.
1 ENGAGE
© Houghton Mifflin Harcourt Publishing Company
pictures to show different addition
strategies. As students work through
Listen and Draw, gauge their level of
understanding to make better decisions
about how to progress through
instruction.
Build on students’ understanding of
addition strategies to develop sound
mathematical practices by asking these
questions.
• Which way works best for you to solve
the problem?
• Why is there more than one way to
solve it?
• How can you tell if your answer makes
sense?
Approximately 10 min.
Students can begin independent practice
once they understand these strategies used
to solve addition facts. 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, 15, 17, 19, 20, or 21
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
What strategies can you use to solve
addition fact problems?
Possible answer: I can use doubles; doubles
plus one; doubles minus one; add in any
order; or count on 1, 2, or 3.
Math Journal
Use pictures or words to explain a strategy
you would use to find 8 + 9.
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Lesson 3.7
Hands On • Add 10 and More
make better decisions about how to
progress through instruction.
Build on students’ understanding of
counting on to develop sound
mathematical practices by asking these
questions.
• What short cut can help you add 10 and
another number?
• What is the meaning of “ten frame”?
• What other model could help solve the
problem?
• Will a ten frame always help you add
with ten?
Instructional Time: 1 day
Common Core Standard
CC.1.OA.6 Add and subtract within 20, demonstrating fluency for
addition and subtraction within 10. Use strategies such as counting
on; making ten; decomposing a number leading to a ten; using the
relationship between addition and subtraction; and creating
equivalent but easier or known sums.
Also CC.1.OA.8
Lesson Objective
Use a ten frame to add 10 and an addend less
than 10.
How can you use a ten frame to add 10 and
some more?
Practice
3 PRACTICE
Share and Show
Materials
• MathBoard
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
• red and yellow
crayons
• Math Journal
• Workmat 7
(ten frame)
• Workmat 8
• HMH Mega Math
(ten frames)
(see eTeacher
Resources)
• two-color counters • iTools: Counters
On Your Own
2
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
TEACH
andTalk
TALK
20 min.
Listen and Draw • 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 ten frame
to show adding 10 and some more. As
students work through Listen and Draw,
gauge their level of understanding to
52
Approximately 10 min.
Students can begin independent practice
once they understand how to model adding
10 and some more. 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, 15, 16, or 17
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 ten frame to add 10
and some more?
Possible answer: I can show 10 inside the
ten frame and the other number outside
the ten frame. Then I can count on from 10
to find the sum.
Math Journal
Use pictures or words to explain how you
can solve 10 1 6.
© Houghton Mifflin Harcourt Publishing Company
Essential Question
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Lesson 3.8
Hands On • Make a 10 to Add
As students work through Listen and
Draw, gauge their level of understanding
to make better decisions about how to
progress through instruction.
Build on students’ understanding of
make a ten to develop sound
mathematical practices by asking these
questions.
• What is the problem asking?
• How did the ten frame help you add
the two numbers?
• How do you know it can work?
Instructional Time: 1 day
Common Core Standard
CC.1.OA.6 Add and subtract within 20, demonstrating fluency for
addition and subtraction within 10. Use strategies such as counting
on; making ten; decomposing a number leading to a ten; using the
relationship between addition and subtraction; and creating
equivalent but easier or known sums.
Also CC.1.OA.8
Lesson Objective
Use make a ten as a strategy to find sums
within 20.
Practice
3 PRACTICE
Essential Question
Share and Show
How do you use the make a ten strategy to
add?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
Materials
• MathBoard
• Workmat 7
(ten frame)
• Math Journal
• Animated Math
Models
On Your Own
• Workmat 8
• HMH Mega Math
(ten frames)
(see eTeacher
Resources)
• two-color counters • iTools: Counters
• red and yellow crayons
Engage Approximately 5 min.
1 ENGAGE
Approximately 10 min.
Students can begin independent practice
once they understand make a ten as an
addition strategy. 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, or 8–11
Summarize Approximately 5 min.
4 SUMMARIZE
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.
Essential Question
How do you use the make a ten strategy
to add?
Possible answer: I can take numbers apart
and put them back together in ways that
make 10. Then it is easier to add 10 and
the other number.
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Listen and Draw • 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 ten frame
to show the strategy “make a ten to add.”
Math Journal
Use pictures or words to explain how you
would use the make a ten strategy to
solve 5 1 7.
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Lesson 3.9
Use Make a 10 to Add
better decisions about how to progress
through instruction.
Build on students’ understanding of
finding sums within 20 to develop sound
mathematical practices by asking these
questions.
• Which addend is usually in the ten
frame?
• What numbers do you need to solve the
problem?
• What is the first thing you need to do?
Instructional Time: 1 day
Common Core Standard
CC.1.OA.6 Add and subtract within 20, demonstrating fluency for
addition and subtraction within 10. Use strategies such as counting
on; making ten; decomposing a number leading to a ten; using the
relationship between addition and subtraction; and creating
equivalent but easier or known sums.
Also CC.1.OA.8
Lesson Objective
Practice
3 PRACTICE
Essential Question
Share and Show
How can you make a ten to help you add?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
Materials
• MathBoard
• red and yellow
crayons
• Math Journal
On Your Own
• 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.
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Listen and Draw • 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 pictures to
show how to make a ten. As students
work through Listen and Draw, gauge
their level of understanding to make
54
Approximately 10 min.
Students can begin independent practice
once they understand how to make a ten
to help solve addition sentences. Select
exercises based on students’ depth of
understanding. The exercises below
require higher order thinking skills and
critical reasoning, making them especially
rich.
Exercises 3, 4, 5, or 6–7
• (optional)
two-color counters • HMH Mega Math
• (optional)
Workmat 7
(see eTeacher
Resources)
• iTools: Counters
Engage Approximately 5 min.
1 ENGAGE
Approximately 10 min.
Essential Question
How can you make a ten to help you add?
Possible answer: I can break apart one
addend. I use one part to make a ten with
the other addend. Then I add 10 to the
part left over.
Math Journal
Draw to explain how you would make a
ten to find 5 1 8.
© Houghton Mifflin Harcourt Publishing Company
Use numbers to show how to use the make a
ten strategy to add.
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Lesson 3.10
Hands On: Algebra • Add 3
Numbers
decisions about how to progress through
instruction.
Build on students’ understanding of
addition strategies for two addends to
develop sound mathematical practices by
asking these questions.
• What does the word “addend” mean?
• Which way would you choose to solve
the addition problem?
• How else could you model the problem?
Instructional Time: 1 day
Common Core Standard
CC.1.OA.3 Apply properties of operations as strategies to add and
subtract.
Also CC.1.OA.6
Lesson Objective
Practice
3 PRACTICE
Use the Associative Property of Addition to
add three addends.
Essential Question
Share and Show
How can you add three addends?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
Materials
• MathBoard
• connecting cubes
in 3 colors
• Math Journal
• Animated Math
Models
• crayons
• (optional)
Workmat 7
(ten frame) (see
eTeacher
Resources)
• HMH Mega Math
• iTools: Counters
Engage Approximately 5 min.
1 ENGAGE
© Houghton Mifflin Harcourt Publishing Company
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.
Listen and Draw • 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
add three addends. As students work
through Listen and Draw, gauge their
level of understanding to make better
On Your Own
Approximately 10 min.
Approximately 10 min.
Students can begin independent practice
once they understand the Associative
Property of Addition. 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, 5, 6, or 7
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How can you add three addends?
Possible answer: I can add any two of the
addends first, and then add that sum to
the third addend.
Math Journal
Use pictures or words to explain how you
can find the sum for 3 1 5 1 2.
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Lesson 3.11
Algebra • Add 3 Numbers
Build on students’ understanding of
the Associative Property of Addition to
develop sound mathematical practices by
asking these questions.
• How do you know how to start?
• Have you solved a problem like this one?
• Will the way you solved it always work?
• What else could you use to help you
solve the problem?
Instructional Time: 1 day
Common Core Standard
CC.1.OA.3 Apply properties of operations as strategies to add and
subtract.
Also CC.1.OA.6
Lesson Objective
Practice
3 PRACTICE
Essential Question
Share and Show
How can you group numbers to add
three addends?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
Materials
• MathBoard
• crayons
• (optional)
connecting cubes
• Math Journal
• Animated Math
Models
• HMH Mega Math
On Your Own
Engage Approximately 5 min.
1 ENGAGE
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Listen and Draw • 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 pictures and
writing to add three addends. As students
work through Listen and Draw, gauge
their level of understanding to make
better decisions about how to progress
through instruction.
56
Approximately 10 min.
Students can begin independent practice
once they understand that three addends
can be grouped in various ways to find
their sum. 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, 15, 17–18, or 19–21
• iTools: Counters
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 group numbers to add three
addends?
Possible answer: I can use strategies to
choose which two numbers to add first.
Then I add the third addend.
Math Journal
Use pictures or words to explain how you
would find 6 1 4 1 4.
© Houghton Mifflin Harcourt Publishing Company
Understand and apply the Associative Property
or Commutative Property of Addition to add
three addends.
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Lesson 3.12
Problem Solving • Use Addition
Strategies
Instructional Time: 1 day
Common Core Standard
CC.1.OA.2 Solve word problems that call for addition of three
whole numbers whose sum is less than or equal to 20, e.g., by using
objects, drawings, and equations with a symbol for the unknown
number to represent the problem.
Also CC.1.OA.6
Lesson Objective
Practice
3 PRACTICE
Solve adding to and putting together
situations using the strategy draw a picture.
Share and Show
Essential Question
How do you solve addition word problems by
drawing a picture?
Materials
•
•
•
•
MathBoard
• Math Journal
two-color counters • HMH Mega Math
connecting cubes • iTools: Counters
Workmat 7 (ten frame) (see eTeacher
Resources)
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.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
On Your Own
Approximately 10 min.
Students can begin independent practice
once they understand how to solve
addition situations involving three addends.
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, 7, or 8
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
© Houghton Mifflin Harcourt Publishing Company
Build on students’ understanding of
addition strategies for adding three
addends to develop sound mathematical
practices by asking these questions.
• How will you use the numbers to solve
the problem?
• What else do you need to know?
• What is another way to model the
problem?
• How will you know that your answer
makes sense?
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
drawings to show addition strategies. 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 solve addition word problems
by drawing a picture?
Possible answer: I draw circles to show
each addend. Then I count the circles to
find the sum.
Math Journal
Draw a picture to show how you would
solve this problem. Jeb has 4 large rocks.
He has 4 medium rocks. He has 7 small
rocks. How many rocks does Jeb have?
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Lesson 4.1
Count Back
• How can counting back help you
subtract?
• What else can help you solve the
problem?
• Why does subtraction start with the
greater number?
Instructional Time: 1 day
Common Core Standard
CC.1.OA.5 Relate counting to addition and subtraction.
Also CC.1.OA.6, CC.1.OA.8
Use count back 1, 2, or 3 as a strategy to
subtract.
Practice
3 PRACTICE
Share and Show
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
Essential Question
How can you count back 1, 2, or 3?
Materials
On Your Own
• MathBoard
• Animated Math
Models
• two-color counters • HMH Mega Math
• Math Journal
• iTools: Number
Lines
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Listen and Draw • 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 counters
to count back from a given number. As
students work through Listen and Draw,
gauge their level of understanding to
make better decisions about how to
progress through instruction.
Build on students’ understanding of
counting forward to develop sound
mathematical practices by asking these
questions.
60
Approximately 10 min.
Students can begin independent practice
once they understand how to count back
to find differences. 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, 35, 37 or 38–39
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 count back 1, 2, or 3?
Possible answer: I can start at the greater
number in the subtraction problem and
count back 1, 2, or 3.
Math Journal
Use pictures or words to explain how you
can solve 7 2 3 by counting back.
© Houghton Mifflin Harcourt Publishing Company
Lesson Objective
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Lesson 4.2
Hands On • Think Addition to
Subtract
Instructional Time: 1 day
Common Core Standard
CC.1.OA.4 Understand subtraction as an unknown-addend problem.
Also CC.1.OA.8
Lesson Objective
Practice
3 PRACTICE
Recall addition facts to subtract numbers
within 20.
Share and Show
Essential Question
Materials
• Animated Math
Models
• green and orange • HMH Mega Math
connecting cubes
• Math Journal
• 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.
Listen and Draw • 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 drawings to relate addition to
subtraction. As students work through
Listen and Draw, 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, see RtI (Response to
Intervention).
How can you use an addition fact to find the
answer to a subtraction fact?
• MathBoard
Build on students’ understanding of
addition facts to develop sound
mathematical practices by asking these
questions.
• How can addition help you
subtract numbers?
• How else can you model this problem?
• How does adding help you know your
subtraction is correct?
On Your Own
Approximately 10 min.
Students can begin independent practice
once they understand how addition can
help them solve subtraction facts. 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, 8–9 or 10–12
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How can you use an addition fact to find
the answer to a subtraction fact?
Possible answer: When I know an addition
fact, I know that one of the addends is the
answer to the subtraction fact.
Math Journal
Use pictures or words to explain how you
can use 2 1 __ 5 7 to solve 7 2 2 5 __.
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Lesson 4.3
Use Think Addition to Subtract
Build on students’ understanding of “think
addition to subtract” to develop sound
mathematical practices by asking these
questions.
• What is the problem asking?
• How will you use the information
in the problem?
• What other ways can you use to model
the problem?
Instructional Time: 1 day
Common Core Standard
CC.1.OA.4 Understand subtraction as an unknown-addend problem.
Also CC.1.OA.8
Lesson Objective
Essential Question
Practice
3 PRACTICE
Share and Show
How can you use addition to help you find the
answer to a subtraction fact?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
Materials
• MathBoard
• green and blue
connecting cubes
• Math Journal
• Animated Math
Models
• HMH Mega Math
On Your Own
Engage Approximately 5 min.
1 ENGAGE
Teach and
Approximately
2 TEACH
andTalk
TALK
Summarize Approximately 5 min.
4 SUMMARIZE
20 min.
Listen and Draw • 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
drawings to show how addition can be
used to help solve subtraction sentences.
As students work through Listen and
Draw, gauge their level of understanding
to make better decisions about how to
progress through instruction.
62
Approximately 10 min.
Students can begin independent practice
once they understand how addition facts
and subtraction facts are related. 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, 8, 17
• iTools: Counters
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 addition to help you find
the answer to a subtraction fact?
Possible answer: I can think of an addition
fact that uses the same numbers as the
subtraction fact.
Math Journal
Use pictures or words to explain how you
can use addition to solve 14 2 9.
© Houghton Mifflin Harcourt Publishing Company
Use addition as a strategy to subtract numbers
within 20.
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Lesson 4.4
Hands On • Use 10 to Subtract
Build on students’ understanding of
subtraction strategies to develop sound
mathematical practices by asking these
questions.
• Have you solved this kind of
problem before?
• What will you do first to solve the
problem?
• What can you do if you don’t know
how to solve a problem?
Instructional Time: 1 day
Common Core Standard
CC.1.OA.6 Add and subtract within 20, demonstrating fluency for
addition and subtraction within 10. Use strategies such as counting
on; making ten; decomposing a number leading to a ten; using the
relationship between addition and subtraction; and creating
equivalent but easier or known sums.
Also CC.1.OA.8
Lesson Objective
Practice
3 PRACTICE
Use make a 10 as a strategy to subtract.
Essential Question
Share and Show
How can you make a ten to help you subtract?
Use the checked exercise as a diagnostic
assessment. If students answer the
exercise incorrectly, see RtI (Response to
Intervention).
Materials
• MathBoard
• Math Journal
• Ten Frames (see
• iTools: Counters
eTeacher
Resources)
• two-color counters
On Your Own
Approximately 10 min.
Students can begin independent
practice once they understand make a 10
as a subtraction strategy. Select exercises
based on students’ depth of understanding.
The exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 3, 5, 6 or 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.
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
Essential Question
20 min.
© Houghton Mifflin Harcourt Publishing Company
Approximately 10 min.
Listen and Draw • 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 ten frames to model ten
and some ones in order to help them solve
a subtraction problem. As students work
through Listen and Draw, gauge their level
of understanding to make better decisions
about how to progress through
instruction.
How can you make a ten to help you
subtract?
Possible answer: After I make a ten, I can
see how many more I need to make the
total number. Then I can count how many
counters I added.
Math Journal
Draw ten frames and counters to show
how to solve 18 2 9 5 __.
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Lesson 4.5
Break Apart to Subtract
Build on students’ understanding of
making a ten to develop sound
mathematical practices by asking these
questions.
• What are you being asked to solve?
• How many steps are there?
• How else can you solve the problem?
• How can you tell if your answer
makes sense?
Instructional Time: 1 day
Common Core Standard
CC.1.OA.6 Add and subtract within 20, demonstrating fluency for
addition and subtraction within 10. Use strategies such as counting
on; making ten; decomposing a number leading to a ten; using the
relationship between addition and subtraction; and creating
equivalent but easier or known sums.
Also CC.1.OA.8
Subtract by breaking apart to make a ten.
Practice
3 PRACTICE
Share and Show
Essential Question
Use the checked exercise as a diagnostic
assessment. If students answer the
exercise incorrectly, see RtI (Response to
Intervention).
How do you break apart a number to
subtract?
Materials
• MathBoard
• Ten Frames
(see eTeacher
Resources)
• two-color
counters
On Your Own
• Math Journal
• iTools: Counters
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Listen and Draw • 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 ten frames
to show taking apart. As students work
through Listen and Draw, gauge their
level of understanding to make better
decisions about how to progress through
instruction.
64
Approximately 10 min.
Students can begin independent
practice once they understand how
breaking a number apart can help them
subtract. Select exercises based on students’
depth of understanding. The exercises
below require higher order thinking skills
and critical reasoning, making them
especially rich.
Exercises 2, 3 or 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.
Approximately 10 min.
Essential Question
How do you break apart a number to
subtract?
Possible answer: I start with the total and
take away counters to make a 10. Then I
figure out how many more counters I need
to take away from 10.
Math Journal
Draw ten frames and counters to show
how you would break apart a number to
find 14 2 6.
© Houghton Mifflin Harcourt Publishing Company
Lesson Objective
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Lesson 4.6
Problem Solving • Use
Subtraction Strategies
Build on students’ understanding of
various subtraction strategies to develop
sound mathematical practices by asking
these questions.
• What is the problem asking?
• When did you use this strategy before?
• What information do you need to solve
the problem?
• How else could you solve it?
Instructional Time: 1 day
Common Core Standard
CC.1.OA.1 Use addition and subtraction within 20 to solve word
problems involving situations of adding to, taking from, putting
together, taking apart, and comparing, with unknowns in all
positions, e.g., by using objects, drawings, and equations with a
symbol for the unknown number to represent the problem.
Lesson Objective
Solve subtraction problem situations using the
strategy act it out.
Share and Show
Approximately 10 min.
How can acting out a problem help you solve
the problem?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
Materials
On Your Own
Essential Question
• MathBoard
• Math Journal
• two-color counters • HMH Mega Math
• Ten Frames (see
• iTools: Counters
eTeacher
Resources)
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 model and act
out subtraction scenarios to help them
solve. 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.
Students can begin independent practice
once they understand how subtraction
strategies can help them solve subtraction
problems. 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, 7, 8
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How can acting out a problem help you
solve the problem?
Possible answer: When I use objects to act
out a problem, I can show what happens in
the problem to get the answer.
Math Journal
Use pictures or words to explain how you
would act out the following problem. Joe
has 9 toy cars. Dan has 6 toy cars. How
many fewer toy cars does Dan have than
Joe?
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Lesson 5.1
Problem Solving • Add or
Subtract
Build on students’ understanding of
addition and subtraction rules to develop
sound mathematical practices by asking
these questions.
• If the number of turtles left on the
beach was more than 9, would the
number that swim away change?
• How do you know the number of
turtles that swim away is less than 16?
• What is another way you can model
the problem?
Instructional Time: 1 day
Common Core Standard
CC.1.OA.1 Use addition and subtraction within 20 to solve word
problems involving situations of adding to, taking from, putting
together, taking apart, and comparing, with unknowns in all
positions, e.g., by using objects, drawings, and equations with a
symbol for the unknown number to represent the problem.
Lesson Objective
Practice
3 PRACTICE
Essential Question
Share and Show
How can making a model help you solve a
problem?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
Materials
• MathBoard
• red and yellow
connecting cubes
• Math Journal
• iTools: Counters
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 models
to show addition and subtraction
situations. As students work through
Unlock the Problem, gauge their level of
understanding to make better decisions
about how to progress through
instruction.
68
Approximately 10 min.
Students can begin independent practice
once they understand how to set up
addition and subtraction problems.
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, 7, 8
Engage Approximately 5 min.
1 ENGAGE
Teach and
Approximately
2 TEACH
andTalk
TALK
Approximately 10 min.
Essential Question
How can making a model help you solve a
problem?
Possible answer: Making a model helps me
see what is happening in the problem.
Math Journal
Write an addition story problem. Have a
classmate solve your problem.
© Houghton Mifflin Harcourt Publishing Company
Solve addition and subtraction problem situations using the strategy make a model.
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Lesson 5.2
Hands On • Record Related Facts
Build on students’ understanding of how
addition relates to subtraction to develop
sound mathematical practices by asking
these questions.
• How will your model for the first
problem be different than your
model for the second problem?
• For which problem should you use
different colors of cubes?
• Which parts of your first number
sentence match the words in the
first problem?
Instructional Time: 1 day
Common Core Standard
CC.1.OA.6 Add and subtract within 20, demonstrating fluency for
addition and subtraction within 10. Use strategies such as counting
on; making ten; decomposing a number leading to a ten; using the
relationship between addition and subtraction; and creating
equivalent but easier or known sums.
Also CC.1.OA.8
Lesson Objective
Record related facts within 20.
Practice
3 PRACTICE
Essential Question
How do related facts help you find missing
numbers?
Share and Show
Materials
• MathBoard
• red and blue
connecting cubes
• red and blue
crayons
• Math Journal
• Animated Math
Models
• HMH Mega 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.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
On Your Own
Approximately 10 min.
Students can begin independent practice
once they understand the concept of
related facts. 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 or 8
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
Essential Question
20 min.
© Houghton Mifflin Harcourt Publishing Company
Approximately 10 min.
Listen and Draw • 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 pictures to show related
facts. As students work through Listen and
Draw, gauge their level of understanding
to make better decisions about how to
progress through instruction.
How do related facts help you find missing
numbers?
Possible answer: Related facts show
relationships with numbers. I can add two
numbers in any order and get the same
sum. I can subtract either number from
the sum and get the other number.
Math Journal
Write four related facts. Use pictures to
show how the number sentences are
related.
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Lesson 5.3
Identify Related Facts
Build on students’ understanding of related addition facts to develop sound mathematical practices by asking these questions.
• What is another subtraction sentence
you can write using your model?
• How many subtraction sentences can
you write that are related to 4 1 9 5 13?
• What do you remember about the
numbers used in related facts?
Instructional Time: 1 day
Common Core Standard
CC.1.OA.6 Add and subtract within 20, demonstrating fluency for
addition and subtraction within 10. Use strategies such as counting
on; making ten; decomposing a number leading to a ten; using the
relationship between addition and subtraction; and creating
equivalent but easier or known sums.
Also CC.1.OA.8
Identify related addition and subtraction facts
within 20.
Practice
3 PRACTICE
Share and Show
Approximately 10 min.
How do you know if addition and subtraction
facts are related?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
Materials
On Your Own
Essential Question
• MathBoard
• red and blue
connecting cubes
• red, blue, and
green crayons
• Math Journal
• Animated Math
Models
• HMH Mega 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.
Students can begin independent practice
once they can understand and identify
related facts. 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 or 11-14
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Listen and Draw • 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 and draw related addition and subtraction facts. As students
work through Listen and Draw, gauge
their level of understanding to make
better decisions about how to progress
through instruction.
70
Approximately 10 min.
Essential Question
How do you know if addition and
subtraction facts are related?
Possible answer: They are related if
addition and subtraction facts have the
same parts and whole.
Math Journal
Use numbers and pictures to show related
facts with the numbers 7, 9, and 16.
© Houghton Mifflin Harcourt Publishing Company
Lesson Objective
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Lesson 5.4
Use Addition to Check
Subtraction
Build on students’ understanding of “think
addition to subtract” to develop sound
mathematical practices by asking these
questions.
• How can you model the first problem?
• What do you notice about the numbers
in both number sentences you wrote?
• How is your model for the first problem
alike and different than your model for
the second problem?
Instructional Time: 1 day
Common Core Standard
CC.1.OA.6 Add and subtract within 20, demonstrating fluency for
addition and subtraction within 10. Use strategies such as counting
on; making ten; decomposing a number leading to a ten; using the
relationship between addition and subtraction; and creating
equivalent but easier or known sums.
Also CC.1.OA.8
Practice
3 PRACTICE
Lesson Objective
Apply the inverse relationship of addition and
subtraction.
Essential Question
How can you use addition to check
subtraction?
• HMH Mega 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.
Listen and Draw • 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 pictures and
numbers to show related addition and
subtraction sentences. As students work
through Listen and Draw, 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, see RtI (Response to
Intervention).
On Your Own
Materials
• MathBoard
• Math Journal
• Animated Math
Models
Share and Show
Approximately 10 min.
Students can begin independent practice
once they understand the concept of
inverse relationships. 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, 11
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How can you use addition to check
subtraction?
Possible answer: I add the difference to the
number I subtracted and I get the number
I started with.
Math Journal
Find 12 2 9. Then write or draw how you
can add to check your answer.
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Lesson 5.5
Hands On: Algebra • Missing
Numbers
Build on students’ understanding of
addition and subtraction facts to develop
sound mathematical practices by asking
these questions.
• What did you do first to show the story?
• Is there another way you could show
this story?
• If Calvin had 9 toy cars that were red
instead of 10, how would you show
the number of blue cars?
Instructional Time: 1 day
Common Core Standard
CC.1.OA.8 Determine the unknown whole number in an addition or
subtraction equation relating three whole numbers.
Also CC.1.OA.6
Lesson Objective
Practice
3 PRACTICE
Essential Question
Share and Show
How can you use a related fact to find a
missing number?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
Materials
• MathBoard
• red and blue
connecting cubes
• red and blue
crayons
• Math Journal
• Animated Math
Models
• HMH Mega Math
• iTools: Counters
On Your Own
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Listen and Draw • 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
drawings to find unknown numbers. As
students work through Listen and Draw,
gauge their level of understanding to
make better decisions about how to
progress through instruction.
72
Approximately 10 min.
Students can begin independent practice
once they understand the strategies they
can use to find unknown numbers. 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, 11, 13 or 14-16
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 related fact to find a
missing number?
Possible answer: If a related fact is easier
to solve, then use it to find the missing
number.
Math Journal
Use words, pictures, or numbers to show
how to find the missing numbers for
8 1 __ 5 17 and 17 2 8 5 __.
© Houghton Mifflin Harcourt Publishing Company
Use related facts to determine unknown
numbers.
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Lesson 5.6
Algebra • Use Related Facts
Instructional Time: 1 day
Common Core Standard
CC.1.OA.8 Determine the unknown whole number in an addition or
subtraction equation relating three whole numbers.
Also CC.1.OA.6
Lesson Objective
Use a related fact to subtract.
Essential Question
Practice
3 PRACTICE
How can you use a related fact to find a
missing number?
Share and Show
Materials
•
•
•
•
MathBoard
crayons
Math Journal
Animated Math
Models
• HMH Mega 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.
Listen and Draw • 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 pictures to
show how to find a missing number. As
students work through Listen and Draw,
gauge their level of understanding to
make better decisions about how to
progress through instruction.
Build on students’ understanding of
related facts to develop sound
mathematical practices by asking these
questions.
• If you subtract your answer from 10,
what number will you get?
• If you found 8 and 10 on a number line,
how would you find the answer to the
problem?
• What subtraction fact is related to the
answer?
Approximately 10 min.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
On Your Own
Approximately 10 min.
Students can begin independent practice
once they understand that related facts
can be used as strategies to subtract.
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, 8, 9-10 or 11-15
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How can you use a related fact to find a
missing number?
Children’s answers should show an
understanding that addition and
subtraction are inverse operations.
Math Journal
Draw pictures to show how to solve
14 2 7 5 __ and 7 1 __ 5 14.
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Lesson 5.7
Choose an Operation
Build on students’ understanding of
addition and subtraction operations to
develop sound mathematical practices by
asking these questions.
• How can you show this problem using
objects?
• How can you use addition to check your
answer?
• What number sentence can you write to
help solve this problem?
Instructional Time: 1 day
Common Core Standard
CC.1.OA.1 Use addition and subtraction within 20 to solve word
problems involving situations of adding to, taking from, putting
together, taking apart, and comparing, with unknowns in all
positions, e.g., by using objects, drawings, and equations with a
symbol for the unknown number to represent the problem.
Also CC.1.OA.6
Choose an operation and strategy to solve an
addition or subtraction word problem.
Practice
3 PRACTICE
Share and Show
Essential Question
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
How do you choose when to add and when to
subtract to solve a problem?
Materials
• MathBoard
• two-color
counters
• red and yellow
crayons
On Your Own
• Math Journal
• HMH Mega Math
• iTools: Counters
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Listen and Draw • 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 pictures to
solve a word problem. As students work
through Listen and Draw, gauge their
level of understanding to make better
decisions about how to progress through
instruction.
74
Approximately 10 min.
Students can begin independent practice
once they understand when to use addition
and subtraction to solve problems. 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 or 8-10
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 choose when to add and
when to subtract to solve a problem?
Possible answer: I think about what I know
and what I need to find out. Then I decide
which strategy would work best.
Math Journal
Use words, numbers, or pictures to explain
how a classmate solved a problem.
© Houghton Mifflin Harcourt Publishing Company
Lesson Objective
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Lesson 5.8
Hands On: Algebra • Ways to
Make Numbers to 20
Build on students’ understanding of
addition facts and strategies to develop
sound mathematical practices by asking
these questions.
• Can you use the related fact for your
first model to make a second model?
• Can you use the same number of red
and blue cubes to make 10?
• How can you show your answers are
correct?
Instructional Time: 1 day
Common Core Standard
CC.1.OA.6 Add and subtract within 20, demonstrating fluency for
addition and subtraction within 10. Use strategies such as counting
on; making ten; decomposing a number leading to a ten; using the
relationship between addition and subtraction; and creating
equivalent but easier or known sums.
Lesson Objective
Represent equivalent forms of numbers using
sums and differences within 20.
Essential Question
Materials
• Math Journal
• Animated Math
Models
• HMH Mega 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.
Listen and Draw • 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 different ways to make a
given number. As students work through
Listen and Draw, 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, see RtI (Response to
Intervention).
How can you add and subtract in different
ways to make the same number?
• MathBoard
• red, blue,
and yellow
connecting cubes
• red and blue
crayons
Practice
3 PRACTICE
On Your Own
Approximately 10 min.
Students can begin independent practice
once they understand the various ways
to make and take apart a given number.
Select exercises based on students’ depth
of understanding. The exercises below
require higher order thinking skills and
critical reasoning, making them especially
rich.
Exercises 3, 5, 7-8 or 9-11
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How can you add and subtract in different
ways to make the same number?
Possible answer: I can put different
numbers together or take different
numbers apart and still end up with the
same number.
Math Journal
Use numbers and pictures to show two
ways to make the number 12.
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Lesson 5.9
Algebra • Equal and Not Equal
As students work through Listen and
Draw, gauge their level of understanding
to make better decisions about how to
progress through instruction.
Build on students’ understanding of
equivalent sums to develop sound
mathematical practices by asking these
questions.
• What did you do first to answer the
problem?
• What strategy could you use to make it
easier to find the sum or difference on
each card?
• How can you use models to help you
with the problem?
Instructional Time: 1 day
Note: The instructional time for this lesson can
also be 2 days. On Day 1, emphasize how and
why different equations can have the same
sum or difference. Explain the concepts of true
and false in terms of equations. Use the extra
time on Day 2 to guide students to understand
how to change a false number sentence to a
true one. Then do Extend the Math, and apply
questioning in Go Deeper to equations that
are false.
Common Core Standard
Also CC.1.OA.6
Practice
3 PRACTICE
Lesson Objective
Share and Show
Determine if an equation is true or false.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
Essential Question
How can you decide if a number sentence is
true or false?
On Your Own
Materials
• MathBoard
• crayons
• Math Journal
Engage Approximately 5 min.
1 ENGAGE
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Listen and Draw • 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 visual
representations to recognize equal sums.
76
Approximately 10 min.
Students can begin independent practice
once they understand how to distinguish
true and false number sentences. 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, 11, 13-14 or 15-16
• HMH Mega Math
• iTools: Counters
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 decide if a number sentence
is true or false?
Possible answer: I can add or subtract to
solve each side of the equal sign. Then I
can compare the numbers to see if they
have the same value.
Math Journal
Write 5 1
5 6 1 8. Write a number
to make the sentence true. Draw a quick
picture to explain.
© Houghton Mifflin Harcourt Publishing Company
CC.1.OA.7 Understand the meaning of the equal sign, and
determine if equations involving addition and subtraction are true
or false.
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Lesson 5.10
Basic Facts to 20
Build on students’ understanding of
addition and subtraction facts to develop
sound mathematical practices by asking
these questions.
• How can you use a number line to
help you solve the problem?
• What are some other strategies you
can use to solve the problem?
• How can you use subtraction to
check your answer?
Instructional Time: 1 day
Common Core Standard
CC.1.OA.6 Add and subtract within 20, demonstrating fluency for
addition and subtraction within 10. Use strategies such as counting
on; making ten; decomposing a number leading to a ten; using the
relationship between addition and subtraction; and creating
equivalent but easier or known sums.
Lesson Objective
Add and subtract facts within 20 and
demonstrate fluency for addition and
subtraction within 10.
Practice
3 PRACTICE
Share and Show
Essential Question
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
How can addition and subtraction strategies
help you find sums and differences?
Materials
• MathBoard
• two-color
counters
• Math Journal
• Animated Math
Models
• HMH Mega 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.
On Your Own
Approximately 10 min.
Students can begin independent practice
once they understand these addition and
subtraction strategies. Select exercises
based on students’ depth of understanding.
The exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 35, 42, 43 or 44-46
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
Essential Question
20 min.
© Houghton Mifflin Harcourt Publishing Company
Approximately 10 min.
Listen and Draw • 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 pictures to
show and solve addition facts. As students
work through Listen and Draw, gauge
their level of understanding to make
better decisions about how to progress
through instruction.
How can addition and subtraction
strategies help you find sums and
differences?
Possible answer: I can use drawings,
models, related facts, and basic facts
to add and subtract.
Math Journal
Choose two numbers from 5 to 9. Use your
numbers to write an addition sentence.
Draw a picture to show your work.
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Lesson 6.1
Count by Ones to 120
• How did you decide what number to
place in the first box?
• What do you notice about the number
that comes right after a number?
• What do you notice about a number
that is in the box right below another
number?
• What other patterns can you find?
Instructional Time: 1 day
Common Core Standard
CC.1.NBT.1 Count to 120, starting at any number less than 120.
In this range, read and write numerals and represent a number of
objects with a written numeral.
Lesson Objective
Practice
3 PRACTICE
Essential Question
Share and Show
How can knowing a counting pattern help you
count to 120?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
Materials
• MathBoard
• Counting Chart
(see eTeacher
Resources)
• Math Journal
• Animated Math
Models
• iTools: Number
Chart
On Your Own
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Listen and Draw • 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 hundred
chart to find missing numbers in a
sequence. As students work through
Listen and Draw, gauge their level of
understanding to make better decisions
about how to progress through
instruction.
Build on students’ understanding of
counting patterns to develop sound
mathematical practices by asking these
questions.
80
Approximately 10 min.
Students can begin independent practice
once they understand using Counting
Charts as a strategy. 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, 11, 14-15 or 16-17
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 knowing a counting pattern help
you count to 120?
Possible answer: I know the counting pattern when I count from 1 to 20. I use the
same pattern when I count from 100 to
120, but I say one hundred before each
number.
Math Journal
Choose a number between 90 and 110.
Write the number. Then count forward to
write the next 5 numbers.
© Houghton Mifflin Harcourt Publishing Company
Count by ones to extend a counting sequence
up to 120.
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Lesson 6.2
Count by Tens to 120
Build on students’ understanding of
counting sequences to develop sound
mathematical practices by asking these
questions.
• What do you remember about hundred
charts?
• If you placed a counter on each square
of the hundred chart, how many
counters would be in each row?
• What would the pattern be like if you
started on a different number and
counted forward by tens?
Instructional Time: 1 day
Common Core Standard
CC.1.NBT.1 Count to 120, starting at any number less than 120.
In this range, read and write numerals and represent a number of
objects with a written numeral.
Lesson Objective
Count by tens from any number to extend a
counting sequence up to 120.
Essential Question
How do numbers change as you count by tens
to 120?
Share and Show
Materials
• MathBoard
• Counting Chart
(see eTeacher
Resources)
• Math Journal
• Animated Math
Models
• 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
20 min.
© Houghton Mifflin Harcourt Publishing Company
Practice
3 PRACTICE
Listen and Draw • 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 hundred
chart to show how to count by tens. As
students work through Listen and Draw,
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, see RtI (Response to
Intervention).
On Your Own
Approximately 10 min.
Students can begin independent practice
once they understand counting by tens
from a given number. 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, 5, 10-11 or 12-15
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How do numbers change as you count by
tens to 120?
Possible answer: You add ten to each
number as you count.
Math Journal
Use numbers to explain the pattern you
see when you count forward by tens.
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Lesson 6.3
Understand Ten and Ones
• What information do you need to
answer the problem?
• Can you write an addition sentence to
show your work?
• How would your model be different if
Tim gave 2 pennies away instead of
getting 2 pennies?
Instructional Time: 1 day
Common Core Standard
CC.1.NBT.2b Understand that the two digits of a two-digit number
represent amounts of tens and ones. Understand the following as
special cases: The numbers from 11 to 19 are composed of a ten and
one, two, three, four, five, six, seven, eight, or nine ones.
Use models and write to represent equivalent
forms of ten and ones.
Practice
3 PRACTICE
Share and Show
Approximately 10 min.
How can you use different ways to write a
number as ten and ones?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
Materials
On Your Own
Essential Question
•
•
•
•
MathBoard
connecting cubes
Math Journal
Animated Math
Models
• HMH Mega Math
• iTools: Counters
Students can begin independent practice
once they understand the relationship
between ones and tens. Select exercises
based on students’ depth of understanding.
The exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 3, 4, 5 or 6-7
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.
Listen and Draw • 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
pictures to show a ten and some ones.
As students work through Listen and
Draw, gauge their level of understanding
to make better decisions about how to
progress through instruction.
Build on students’ understanding of tens
and ones to develop sound mathematical
practices by asking these questions.
82
Approximately 10 min.
Essential Question
How can you use different ways to write a
number as ten and ones?
Possible answer: I can write 1 ten and some
ones. I can write the number as 10 plus a
number.
Math Journal
Show twelve in four different ways. Use
words, pictures, and numbers.
© Houghton Mifflin Harcourt Publishing Company
Lesson Objective
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Lesson 6.4
Hands On • Make Ten and Ones
Instructional Time: 1 day
Common Core Standard
CC.1.NBT.2b Understand that the two digits of a two-digit number
represent amounts of tens and ones. Understand the following as
special cases: The numbers from 11 to 19 are composed of a ten and
one, two, three, four, five, six, seven, eight, or nine ones.
Lesson Objective
Use objects, pictures, and numbers to
represent a ten and some ones.
Practice
3 PRACTICE
Essential Question
How can you show a number as ten and ones?
Share and Show
Materials
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
•
•
•
•
MathBoard
connecting cubes
Math Journal
Animated Math
Models
• HMH Mega 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
20 min.
© Houghton Mifflin Harcourt Publishing Company
Build on students’ understanding of the
relationship between ones and tens to
develop sound mathematical practices by
asking these questions.
• Which way of showing a group of ten is
easier to count?
• Can you think of another way to show a
group of ten?
• Which way might you use if you needed
to show 3 or more groups of ten?
Listen and Draw • 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 1 ten in multiple ways. As students
work through Listen and Draw, 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 the concept
of grouping tens and ones. 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, 9 or 10-12
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How can you show a number as ten and
ones?
Possible answer: I can group 10 cubes
to show 1 ten. I show the leftover cubes
as ones.
Math Journal
Choose a number from 11 to 19. Write the
number and number word. Use words and
pictures to show how many tens and ones.
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Lesson 6.5
Hands On • Tens
Build on students’ understanding of
grouping tens and ones to develop sound
mathematical practices by asking these
questions.
• How can you check to see if your first
model shows 14?
• Is 1 ten and 0 ones the same or different
than 1 ten?
• Can you write an addition sentence that
shows 1 ten and 0 ones?
Instructional Time: 1 day
Common Core Standards
CC.1.NBT.2a Understand that the two digits of a two-digit number
represent amounts of tens and ones. Understand the following as
special cases: 10 can be thought of as a bundle of ten ones—called
a “ten.”
CC.1.NBT.2c Understand that the two digits of a two-digit number
represent amounts of tens and ones. Understand the following as
special cases: The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to
one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).
Practice
3 PRACTICE
Use objects, pictures, and numbers to
represent tens.
Share and Show
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
Essential Question
How can you model and name groups of ten?
Materials
• MathBoard
• connecting cubes
• Workmat 7 (see
eTeacher
Resources)
On Your Own
• Math Journal
• Animated Math
Models
• HMH Mega Math
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Listen and Draw • 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
drawings to show a ten and some ones.
As students work through Listen and
Draw, gauge their level of understanding
to make better decisions about how to
progress through instruction.
84
Approximately 10 min.
Students can begin independent practice
once they understand how to represent
groups of tens. Select exercises based on
students’ depth of understanding.
The exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 3, 4, 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 model and name groups of
ten?
Possible answer: I can make cube trains
of 10 connecting cubes or draw a line to
show each ten. I can use numbers or
number words to name groups of ten.
Math Journal
Draw a quick picture and write a number
to show thirty.
© Houghton Mifflin Harcourt Publishing Company
Lesson Objective
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Lesson 6.6
Hands On • Tens and Ones to 50
Instructional Time: 1 day
Note: The instructional time for this lesson can
also be 2 days. On Day 1, after Engage, use
secret code cards to model the number 15 and
connect the concept of 15 to base-ten blocks
that model 15. Have students use secret code
cards in Unlock the Problem and Model and
Draw. Use the extra time on Day 2 to have
students work independently on items 5–9 in
On Your Own. Have students share their
answers and connect writing numbers to
models using the secret code cards. Spend
more time to complete Go Deeper.
Common Core Standard
CC.1.NBT.2 Understand that the two digits of a two-digit number
represent amounts of tens and ones.
Practice
3 PRACTICE
Lesson Objective
Share and Show
Group objects to show numbers to 50 as tens
and ones.
How can you group cubes to show a number
as tens and ones?
On Your Own
Materials
MathBoard
connecting cubes
base-ten blocks
Math Journal
• HMH Mega Math
• iTools: Base-Ten
Blocks
© Houghton Mifflin Harcourt Publishing Company
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.
Listen and Draw • Activity to Build
Conceptual Understanding
Remember, this is the core instruction
for this lesson, in which conceptual
development is key. The goal of this
Approximately 10 min.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
Essential Question
•
•
•
•
activity is for students to use base–ten
blocks to identify the tens and ones
digits. As students work through
Listen and Draw, gauge their level of
understanding to make better decisions
about how to progress through
instruction.
Build on students’ understanding of
modeling with base–ten blocks to develop
sound mathematical practices by asking
these questions.
• After you make 1 ten, how many ones
are left over?
• Are 13 ones more or less than 10 ones?
• How could you use ten frames to show
this problem?
Approximately 10 min.
Students can begin independent practice
once they understand how to model
the tens and ones in a given number.
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, 8, 9 or 10–13
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How can you group cubes to show a
number as tens and ones?
Possible answer: Make as many groups of
ten as you can and the leftovers are ones.
Math Journal
Write a number from 20 to 50 that has
both tens and ones. Use pictures and
words to show the tens and ones.
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Lesson 6.7
Hands On • Tens and Ones to 100
Build on students’ understanding of
modeling with base–ten blocks to develop
sound mathematical practices by asking
these questions.
• What did you do first to solve the
problem?
• What do you notice about the first digit
in each number, and the number of tens
in your quick picture?
• What do you notice about the second
digit in each number, and the number
of ones in your quick picture?
Instructional Time: 1 day
Common Core Standard
CC.1.NBT.2 Understand that the two digits of a two-digit number
represent amounts of tens and ones.
Lesson Objective
Group objects to show numbers to 100 as tens
and ones.
Essential Question
Materials
•
•
•
•
MathBoard
base-ten blocks
connecting cubes
Math Journal
Practice
3 PRACTICE
Share and Show
• Animated Math
Models
• HMH Mega Math
• iTools: Base-Ten
Blocks
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
On Your Own
Engage Approximately 5 min.
1 ENGAGE
Teach and
Approximately
2 TEACH
andTalk
TALK
Listen and Draw • 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 base–ten
blocks to identify the tens and ones
digits. As students work through
Listen and Draw, gauge their level of
understanding to make better decisions
about how to progress through
instruction.
86
Approximately 10 min.
Students can begin independent practice
once they understand how to model the
tens and ones in a given number. 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, 10, 11 or 12-14
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.
Approximately 10 min.
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How can you show numbers to 100 as tens
and ones?
Possible answer: I can use base-ten blocks
to show tens and ones. If I know the tens
and ones I can write the number.
Math Journal
Use words and pictures to show 59 and 95.
© Houghton Mifflin Harcourt Publishing Company
How can you show numbers to 100 as tens
and ones?
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Lesson 6.8
Problem Solving • Show Numbers
in Different Ways
Instructional Time: 1 day
Common Core Standards
CC.1.NBT.2a Understand that the two digits of a two-digit number
represent amounts of tens and ones. Understand the following as
special cases: 10 can be thought of as a bundle of ten ones—called
a “ten.”
CC.1.NBT.3 Compare two two-digit numbers based on meanings of
the tens and ones digits, recording the results of comparisons with
the symbols ., 5, and ,.
Lesson Objective
Practice
3 PRACTICE
Solve problems using the strategy make a
model.
Essential Question
Share and Show
How can making a model help you show a
number in different ways?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
Materials
•
•
•
•
MathBoard
base-ten blocks
Math Journal
Animated Math
Models
• HMH Mega Math
• iTools: Base-Ten
Blocks
• 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
understanding to make better decisions
about how to progress through
instruction.
Build on students’ understanding of
two-digit numbers to develop sound
mathematical practices by asking these
questions.
• Can Gary take 3 sheets of ten stickers?
• Is there a way for Gary and Jill to each
have the same number of sheets and
single stickers?
• How can you check that your quick
pictures both show 23?
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
show that the tens and ones in a
number can be expressed in multiple
ways. As students work through Unlock
the Problem, gauge their level of
On Your Own
Approximately 10 min.
Approximately 10 min.
Students can begin independent
practice once they understand how to
show two-digit numbers in multiple ways.
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 making a model help you show a
number in different ways?
Possible answer: I can show numbers with
base-ten blocks. I can trade one ten for ten
ones to show numbers different ways.
Math Journal
Draw to show 55 three different ways.
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Lesson 6.9
Hands On • Model, Read, and
Write Numbers from 100 to 110
develop sound mathematical practices by
asking these questions.
• What do you remember about hundred
charts?
• What shortcut do you use to find a
number that has 1 more one than
a number?
• What shortcut do you use to find a
number that has 1 more ten than
a number?
• Can you tell what row a number is in
when you know how many tens are in
the number?
Instructional Time: 1 day
Common Core Standard
CC.1.NBT.1 Count to 120, starting at any number less than 120.
In this range, read and write numerals and represent a number of
objects with a written numeral.
Lesson Objective
Read and write numerals to represent a
number of 100 to 110 objects.
How can you model, read, and write numbers
from 100 to 110?
Practice
3 PRACTICE
Share and Show
Materials
•
•
•
•
MathBoard
crayons
base-ten blocks
Counting Chart
(see eTeacher
Resources)
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
• Math Journal
• iTools: Number
Chart
• iTools: Base-Ten
Blocks
On Your Own
Teach and
Approximately
2 TEACH
andTalk
TALK
Summarize Approximately 5 min.
4 SUMMARIZE
20 min.
Listen and Draw • 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 two-digit numbers
based on descriptions of their tens and
ones. As students work through Listen and
Draw, gauge their level of understanding
to make better decisions about how to
progress through instruction.
Build on students’ understanding of the
components of two-digit numbers to
88
Approximately 10 min.
Students can begin independent practice
once they understand how to write
numbers up to 110. 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, 11, 14 or 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 model, read, and write
numbers from 100 to 110?
Possible answer: First, I use 10 tens blocks
to model 100. Then I count out the correct
number of ones blocks. When I know the
tens and ones, I can name and write the
number.
Math Journal
Choose a number from 101 to 110. Write
it. Draw a picture to show it as 10 tens
and more.
© Houghton Mifflin Harcourt Publishing Company
Essential Question
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Lesson 6.10
Hands On • Model, Read, and
Write Numbers from 110 to 120
Build on students’ understanding of
numbers through 110 to develop sound
mathematical practices by asking these
questions.
• What strategy did you use to help you
answer the problem?
• What was the first step you took?
• Could you use the same strategy if there
were 11 rows of 10?
Instructional Time: 1 day
Common Core Standard
CC.1.NBT.1 Count to 120, starting at any number less than 120.
In this range, read and write numerals and represent a number of
objects with a written numeral.
Lesson Objective
Practice
3 PRACTICE
Read and write numerals to represent a
number of 110 to 120 objects.
Share and Show
Essential Question
How can you model, read, and write numbers
from 110 to 120?
Materials
• MathBoard
• base-ten blocks
• Counting Chart
(see eTeacher
Resources)
• Math Journal
• iTools: Number
Chart
• 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.
Listen and Draw • 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 visual representations to
identify three-digit numbers. As students
work through Listen and Draw, 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, see RtI (Response to
Intervention).
On Your Own
Approximately 10 min.
Students can begin independent practice
once they understand how to model and
write three-digit numbers. 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, 10, 11-13 or 14-16
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How can you model, read, and write
numbers from 110 to 120?
Possible answer: I can use tens and ones
blocks to model the number. Then I can
count by tens and then ones to know how
to read and write the number.
Math Journal
Choose a number from 111 to 120. Write
the number. Draw a picture to show it as
tens and ones.
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Lesson 7.1
Hands On: Algebra • Greater Than
• How does lining up the tens in your
2 quick pictures help you solve the
problem more quickly?
• What is another way you can model the
problem?
• How could you know which number is
greater if both numbers have the same
number of tens?
Instructional Time: 1 day
Common Core Standard
CC.1.NBT.3 Compare two two-digit numbers based on meanings of
the tens and ones digits, recording the results of comparisons with
the symbols ., 5, and ,.
Lesson Objective
Practice
3 PRACTICE
Essential Question
Share and Show
How can you compare two numbers to find
which is greater?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
Materials
•
•
•
•
MathBoard
connecting cubes
base-ten blocks
Math Journal
• Animated Math
Models
• iTools: Base-Ten
Blocks
On Your Own
Teach and
Approximately
2 TEACH
andTalk
TALK
Summarize Approximately 5 min.
4 SUMMARIZE
20 min.
Listen and Draw • 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 which of two numbers is greater.
As students work through Listen and
Draw, gauge their level of understanding
to make better decisions about how to
progress through instruction.
Build on students’ understanding of the
values of tens and ones to develop sound
mathematical practices by asking these
questions.
92
Approximately 10 min.
Students can begin independent practice
once they understand strategies to compare
two numbers. 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, 8 or 10
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 two numbers to
find which is greater?
Possible answer: First, I compare the tens.
The number with more tens is the greater
number. If the tens are the same, then I
compare the ones.
Math Journal
Write a number that is greater than 29.
Draw quick pictures to explain.
© Houghton Mifflin Harcourt Publishing Company
Model and compare two-digit numbers to
determine which is greater.
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Lesson 7.2
Hands On: Algebra • Less Than
Instructional Time: 1 day
Common Core Standard
CC.1.NBT.3 Compare two two-digit numbers based on meanings of
the tens and ones digits, recording the results of comparisons with
the symbols ., 5, and ,.
Practice
3 PRACTICE
Lesson Objective
Model and compare two-digit numbers to
determine which is less.
Share and Show
Approximately 10 min.
How can you compare two numbers to find
which is less?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
Materials
On Your Own
Essential Question
•
•
•
•
•
MathBoard
base-ten blocks
connecting cubes
Math Journal
Animated Math
Models
• HMH Mega Math
• iTools: Base-Ten
Blocks
Engage Approximately 5 min.
1 ENGAGE
Students can begin independent practice
once they understand how to make “less
than” comparisons by looking at tens and
ones. 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, 5, 8 or 10-13
Essential Question
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Listen and Draw • 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
drawings to show which of two numbers is
less. As students work through Listen and
Draw, gauge their level of understanding
to make better decisions about how to
progress through instruction.
Build on students’ understanding of
greater than and more to develop sound
mathematical practices by asking these
questions.
1_MNYCETS221970_C07RML02.indd 93
Approximately 10 min.
Summarize Approximately 5 min.
4 SUMMARIZE
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
• What information do you need to solve
the problem?
• What is another way you can model the
problem?
• Can you use the same model to show
which number is more?
How can you compare two numbers to
find which is less?
Possible answer: I compare the tens first.
The number with fewer tens is less. If the
tens are the same, I compare the ones in
the same way.
Math Journal
Write a number that is less than 41. Draw
quick pictures to explain.
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Lesson 7.3
Hands On: Algebra • Use Symbols
to Compare
Build on students’ understanding of less
than, greater than, fewer, and more to
develop sound mathematical practices by
asking these questions.
• What do you remember about drawing
pictures to find which is more or less?
• What number sentence could you write
to find a number that is 1 less than 36?
• What strategy did you use to model a
number greater than 36?
Instructional Time: 1 day
Common Core Standard
CC.1.NBT.3 Compare two two-digit numbers based on meanings of
the tens and ones digits, recording the results of comparisons with
the symbols >, =, and <.
Also CC.1.OA.7
Lesson Objective
Practice
3 PRACTICE
Share and Show
Essential Question
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
How can you use symbols to show how
numbers compare?
Materials
•
•
•
•
•
MathBoard
base-ten blocks
connecting cubes
Math Journal
Animated Math
Models
On Your Own
• 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.
Approximately 10 min.
Students can begin independent practice
once they understand how to complete
comparison number sentences. 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, 13, 16-21
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Listen and Draw • 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 pictures
and symbols to represent numerical
comparisons. As students work through
Listen and Draw, gauge their level of
understanding to make better decisions
about how to progress through
instruction.
94
Approximately 10 min.
Essential Question
How can you use symbols to show how
numbers compare?
Possible answer: I can write ., ,, or 5
between two numbers to show that the
first number is greater than, is less than,
or is equal to the second number.
Math Journal
Choose some numbers to compare to 55.
Use ,, ., and 5.
© Houghton Mifflin Harcourt Publishing Company
Use symbols for is less than “,”, is greater
than “.”, and is equal to “5” to compare
numbers.
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Lesson 7.4
Problem Solving • Compare
Numbers
Instructional Time: 1 day
Note: The instructional time for this lesson can
also be 2 days. On Day 1, introduce problems
featuring number cards to help students
understand how to compare numbers. After
completing the problems in Unlock the
Problem and Try Another Problem, have
students work with a partner to come up with
their own word problem. Have students make
a model for their word problem using number
cards. Use the extra time on Day 2 to focus on
the Extend the Math Activity and emphasize
act it out as a strategy.
Common Core Standard
CC.1.NBT.3 Compare two two-digit numbers based on meanings of
the tens and ones digits, recording the results of comparisons with
the symbols >, =, and <.
Lesson Objective
Essential Question
Materials
• HMH Mega Math
• iTools: Counters
© Houghton Mifflin Harcourt Publishing Company
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.
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 graphic
organizers and learned strategies to
Share and Show
On Your Own
How can making a model help you compare
numbers?
Engage Approximately 5 min.
1 ENGAGE
Practice
3 PRACTICE
Approximately 10 min.
Use the checked exercise as a diagnostic
assessment. If students answer the
exercise incorrectly, see RtI (Response to
Intervention).
Solve problems using the strategy make a
model.
• MathBoard
• Math Journal
compare 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
comparison strategies to develop sound
mathematical practices by asking these
questions.
• What did you do first to solve the
problem?
• Are the cards left greater than 49 or less
than 49? How do you know?
• Are the cards left greater than 53 or less
than 53? How do you know?
Approximately 10 min.
Students can begin independent practice
once they understand how to construct
models to compare numbers. 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, 8
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How can making a model help you
compare numbers?
Possible answer: I can make a model to
show the numbers in the problem. Then
I can tell which numbers are greater and
which numbers are less.
Math Journal
Write your own problem. Choose a secret
number. Write clues about the number
using the words is greater than and is
less than.
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Lesson 7.5
Hands On • 10 Less, 10 More
• What strategy did you use to solve the
problem?
• Which child’s markers did you show
first? Why?
• What is another way to model this
problem?
Instructional Time: 1 day
Common Core Standard
CC.1.NBT.5 Given a two-digit number, mentally find 10 more or
10 less than the number, without having to count; explain the
reasoning used.
Identify numbers that are 10 less or 10 more
than a given number.
Practice
3 PRACTICE
Share and Show
Essential Question
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
How can you identify numbers that are 10 less
or 10 more than a number?
Materials
• MathBoard
• base-ten blocks
• Math Journal
On Your Own
• iTools: Base-Ten
Blocks
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Listen and Draw • 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
pictures to compare numbers that are ten
more or ten less than one another. As
students work through Listen and Draw,
gauge their level of understanding to
make better decisions about how to
progress through instruction.
Build on students’ understanding of one
more and one less to develop sound
mathematical practices by asking these
questions.
96
Approximately 10 min.
Students can begin independent practice
once they can use mental math to find
10 more and 10 less. 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, 16 or 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 identify numbers that are
10 less or 10 more than a number?
Possible answer: I can think about the
number as tens and ones. For 10 less, I
count back 1 from the number of tens and
keep the ones the same. For 10 more, I
count on 1 from the number of tens and
keep the ones the same.
Math Journal
Choose a number from 10 to 90. Draw and
write to show the numbers that are 10 less
and 10 more than your number.
© Houghton Mifflin Harcourt Publishing Company
Lesson Objective
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Lesson 8.1
Add and Subtract within 20
Instructional Time: 1 day
Common Core Standard
CC.1.OA.6 Add and subtract within 20, demonstrating fluency
for addition and subtraction within 10. Use strategies such as
counting on; making ten; decomposing a number leading to a ten;
using the relationship between addition and subtraction; and creating
equivalent but easier or known sums.
Lesson Objective
Practice
3 PRACTICE
Share and Show
Add and subtract within 20.
Approximately 10 min.
What strategies can you use to add and
subtract?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
Materials
On Your Own
Essential Question
•
•
•
•
MathBoard
• Math Journal
connecting cubes • HMH Mega Math
two-color counters • iTools: Counters
Workmat 8 (see eTeacher Resources)
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
• What do you remember about addition
facts?
• Is there another strategy you could use
to solve the problem?
• How could you use subtraction to check
your answer?
Listen and Draw • 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
drawings to show an addition fact. As
students work through Listen and Draw,
gauge their level of understanding to
make better decisions about how to
progress through instruction.
Build on students’ understanding of
addition and subtraction strategies to
develop sound mathematical practices by
asking these questions.
Approximately 10 min.
Students can begin independent practice
once they understand how to model and
write related facts. 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, 23, 43 or 44-46
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
What strategies can you use to add and
subtract?
Possible answers: I can use related facts;
I can think about doubles; I can draw
pictures or use models such as counters
or connecting cubes.
Math Journal
Write an addition and subtraction fact.
Then write a strategy you could use to
solve the fact.
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Lesson 8.2
Hands On • Add Tens
Build on students’ understanding of
addition facts and strategies to develop
sound mathematical practices by asking
these questions.
• What is another way you can model this
problem?
• What do you remember about the
number of tens in a 2-digit number?
• What addition sentence can be written
to show your answer?
Instructional Time: 1 day
Common Core Standard
CC.1.NBT.4 Add within 100, including adding a two-digit number
and a one-digit number, and adding a two-digit number and a
multiple of 10, 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. Understand that
in adding two-digit numbers, one adds tens and tens, ones and ones;
and sometimes it is necessary to compose a ten.
Draw a model to add tens.
Practice
3 PRACTICE
Essential Question
Share and Show
How can you add tens?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
Materials
• MathBoard
• base-ten blocks
• Math Journal
• Animated Math
Models
• connecting cubes • HMH Mega Math
• Workmats 4 and 8 • iTools: Base-Ten
(see eTeacher
Blocks
Resources)
On Your Own
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Listen and Draw • 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
quick pictures to add 2 tens. As students
work through Listen and Draw, gauge
their level of understanding to make
better decisions about how to progress
through instruction.
100
Approximately 10 min.
Students can begin independent practice
once they understand how to use quick
pictures to find the sum of 2 tens. 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, 9 or 10
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 add tens?
Possible answer: I show tens for both
addends. The total number of tens that I
have is the sum.
Math Journal
Choose an addition problem from the
spider web. Draw a quick picture and write
the number sentence.
© Houghton Mifflin Harcourt Publishing Company
Lesson Objective
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Lesson 8.3
Hands On • Subtract Tens
Build on students’ understanding of
subtraction facts and strategies to develop
sound mathematical practices by asking
these questions.
• How can you solve a simpler problem to
help you solve this problem?
• If there were 10 big shells instead of 20,
how would your picture change?
• What subtraction sentence could you
write to show your answer?
Instructional Time: 1 day
Common Core Standard
CC.1.NBT.6 Subtract multiples of 10 in the range 10–90 from
multiples of 10 in the range 10–90 (positive or zero differences),
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
Draw a model to subtract tens.
Practice
3 PRACTICE
Essential Question
How can you subtract tens?
Share and Show
Materials
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
• MathBoard
• base-ten blocks
• Math Journal
• Animated Math
Models
• connecting cubes • HMH Mega Math
• Workmats 3 and 8 • iTools: Base-Ten
(see eTeacher
Blocks
Resources)
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.
Listen and Draw • 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 quick pictures
to show how you can subtract tens. As
students work through Listen and Draw,
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 how to show the
subtracting tens. 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, 9
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How can you subtract tens?
Possible answer: I show tens for the
starting number, and then I cross out some
tens. The tens that are not crossed out are
the difference.
Math Journal
Draw a picture to show how to solve
50 – 40.
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Lesson 8.4
Use a Hundred Chart to Add
Build on students’ understanding of how
a hundred chart is structured and used to
develop sound mathematical practices by
asking these questions.
• What do you remember about patterns
on hundred charts?
• When do you move across a row, and
when do you move down a column?
• How could you use a model to check
your answer?
Instructional Time: 1 day
Common Core Standard
CC.1.NBT.4 Add within 100, including adding a two-digit number
and a one-digit number, and adding a two-digit number and a
multiple of 10, 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. Understand that
in adding two-digit numbers, one adds tens and tens, ones and ones;
and sometimes it is necessary to compose a ten.
Use a hundred chart to find sums.
Practice
3 PRACTICE
Share and Show
Essential Question
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
How can you use a hundred chart to count
on by ones or tens?
Materials
• MathBoard
• Hundred Chart
(see eTeacher
Resources)
On Your Own
• Math Journal
• iTools: Number
Charts
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Listen and Draw • 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 hundred chart to add
ones and tens to a given number.
As students work through Listen and
Draw, gauge their level of understanding
to make better decisions about how to
progress through instruction.
102
Approximately 10 min.
Students can begin independent practice
once they understand how to use a
hundred chart to add. 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, 11, 13 or 14-15
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.
Approximately 10 min.
Essential Question
How can you use a hundred chart to count
on by ones or tens?
Possible answer: I start at the number and
then move one space to the right for each
one I add. I start at the number and then
move down one row for each ten I add.
Math Journal
Write a number sentence to add 6 ones to
21. Write a number sentence to add 6 tens
to 21.
© Houghton Mifflin Harcourt Publishing Company
Lesson Objective
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Lesson 8.5
Hands On • Use Models to Add
Instructional Time: 1 day
Common Core Standard
CC.1.NBT.4 Add within 100, including adding a two-digit number
and a one-digit number, and adding a two-digit number and a
multiple of 10, 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. Understand that
in adding two-digit numbers, one adds tens and tens, ones and ones;
and sometimes it is necessary to compose a ten.
Practice
3 PRACTICE
Lesson Objective
Use concrete models to add ones or tens to
a two-digit number.
Share and Show
Approximately 10 min.
How can models help you add ones or tens to
a two-digit number?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
Materials
On Your Own
Essential Question
• MathBoard
• base-ten blocks
• Animated Math
Models
• iTools: Base-Ten
Blocks
• 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 how
base ten blocks can show ones and tens to
develop sound mathematical practices by
asking these questions.
• Can you combine all the ones to make
another ten? Explain.
• Is there another strategy you could use
to solve the problem?
• How could you use subtraction to check
your answer?
Listen and Draw • 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 base ten
blocks and drawings to show addition of
ones and tens. As students work through
Listen and Draw, gauge their level of
understanding to make better decisions
about how to progress through
instruction.
Approximately 10 min.
Students can begin independent practice
once they understand how to model
adding ones and tens. 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, 12, 15-16 or 17-19
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How can models help you add ones or
tens to a two-digit number?
Possible answer: Modeling the addends
with base-ten blocks helps me see that I
add tens to tens and ones to ones.
Math Journal
Write a story problem about 40 apples
and 17 pears.
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Lesson 8.6
Hands On • Make Ten to Add
Build on students’ understanding of the
meaning of “a ten” and “a one” to
develop sound mathematical practices by
asking these questions.
• Does the number of tens change?
• Does the number of ones change?
• How can a simpler problem help you
check your answer?
Instructional Time: 1 day
Common Core Standard
Practice
3 PRACTICE
Lesson Objective
Share and Show
Make a ten to add a two-digit number and
a one-digit number.
Use the checked exercise as a diagnostic
assessment. If students answer the
exercise incorrectly, see RtI (Response to
Intervention).
Essential Question
How can making a ten help you add a
two-digit number and a one-digit number?
On Your Own
• base-ten blocks
• Math Journal
• Animated Math
Models
• 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.
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Listen and Draw • 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
quick pictures to find the sum of two
numbers. As students work through
Listen and Draw, gauge their level of
understanding to make better decisions
about how to progress through
instruction.
104
Approximately 10 min.
Students can begin independent practice
once they understand making a ten to
make adding easier. Select exercises based
on students’ depth of understanding. The
exercises below require higher order
thinking skills and critical reasoning,
making them especially rich.
Exercises 2, 3, 5-6 or 7-9
Materials
• MathBoard
Approximately 10 min.
Essential Question
How can making a ten help you add a
two-digit number and a one-digit number?
Possible answer: When I draw all the
tens and ones, I can write that number
as the sum.
Math Journal
Use words or pictures to explain how to
solve 44 1 7.
© Houghton Mifflin Harcourt Publishing Company
CC.1.NBT.4 Add within 100, including adding a two-digit number
and a one-digit number, and adding a two-digit number and a
multiple of 10, 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. Understand that
in adding two-digit numbers, one adds tens and tens, ones and ones;
and sometimes it is necessary to compose a ten.
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Lesson 8.7
Hands On • Use Place Value
to Add
Instructional Time: 1 day
Common Core Standard
CC.1.NBT.4 Add within 100, including adding a two-digit
number and a one-digit number, and adding a two-digit number
and a multiple of 10, 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. Understand that
in adding two-digit numbers, one adds tens and tens, ones and ones;
and sometimes it is necessary to compose a ten.
Lesson Objective
Use tens and ones to add two-digit numbers.
Essential Question
How can you model tens and ones to help you
add two-digit numbers?
Materials
• MathBoard
• base-ten blocks
• Animated Math
Models
• iTools: Base-Ten
Blocks
• 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.
Practice
3 PRACTICE
Share and Show
Approximately 10 min.
Use the checked exercise as a diagnostic
assessment. If students answer the
exercise incorrectly, see RtI (Response to
Intervention).
On Your Own
Approximately 10 min.
Students can begin independent
practice once they understand adding tens
to tens and ones to ones to find sums.
Select exercises based on students’ depth
of understanding. The exercises below
require higher order thinking skills and
critical reasoning, making them especially
rich.
Exercises 2, 3, 5-6 or 7-8
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
Essential Question
20 min.
© Houghton Mifflin Harcourt Publishing Company
gauge their level of understanding to
make better decisions about how to
progress through instruction.
Build on students’ understanding of how
two-digit numbers have tens and ones to
develop sound mathematical practices by
asking these questions.
• What do you remember about adding
tens?
• Would the sum change if there were 35
shiny pennies and 20 dull pennies?
• What is another way to show this
problem?
Listen and Draw • 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 digits in two-digit numbers. As
students work through Listen and Draw,
How can you model tens and ones to help
you add two-digit numbers?
Possible answer: I add the tens to the tens.
I add the ones to the ones. Then I add
those numbers to find the sum.
Math Journal
Write and solve a story problem to add 12
and 18.
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Lesson 8.8
Problem Solving • Addition
Word Problems
about how to progress through
instruction.
Build on students’ understanding of
adding two-digit numbers to develop
sound mathematical practices by asking
these questions.
• How many ones do you have after
showing both numbers?
• How many ones do you need to make
a ten?
• How does making another ten help you
solve the problem more easily?
Instructional Time: 1 day
Common Core Standard
CC.1.NBT.4 Add within 100, including adding a two-digit number
and a one-digit number, and adding a two-digit number and a
multiple of 10, 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. Understand that
in adding two-digit numbers, one adds tens and tens, ones and ones;
and sometimes it is necessary to compose a ten.
Solve and explain two-digit addition word
problems using the strategy draw a picture.
Practice
3 PRACTICE
Share and Show
Essential Question
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
How can drawing a picture help you explain
how to solve an addition problem?
Materials
On Your Own
• MathBoard
• base-ten blocks
• connecting cubes
• Math Journal
• HMH Mega Math
• iTools: Base-Ten
Blocks
• Hundred Chart (see eTeacher Resources)
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 model adding
a one-digit number to a two-digit
number. As students work through
Unlock the Problem, gauge their level of
understanding to make better decisions
106
Approximately 10 min.
Students can begin independent practice
once they understand how to use addition strategies to add 2 two-digit numbers.
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, 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 drawing a picture help you
explain how to solve an addition problem?
Possible answer: It can help me see each
part of the problem so I can find the sum.
Math Journal
Draw a picture to show how to find
12 1 37.
© Houghton Mifflin Harcourt Publishing Company
Lesson Objective
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Lesson 8.9
Practice Addition and Subtraction
Instructional Time: 1 day
Note: The instructional time for this lesson can
also be 2 days. On Day 1 have students solve the
problem in the Listen and Draw section using
a strategy they choose. Then, have students
solve the problem using a different strategy.
Have students compare the two strategies and
discuss how to use the strategies in the Model
and Draw section. On Day 2, use the extra time
to have students complete the problems in the
Share and Show section using a strategy they
choose. Then have students complete problems
19, 24, and 31 in the On Your Own section.
Explore the Go Deeper section and have
students discuss which strategy might work best
for each of the problems in the On Your Own
and Share and Show sections.
Common Core Standard
CC.1.NBT.4 Add within 100, including adding a two-digit number
and a one-digit number, and adding a two-digit number and a
multiple of 10, 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. Understand that
in adding two-digit numbers, one adds tens and tens, ones and ones;
and sometimes it is necessary to compose a ten.
Lesson Objective
Essential Question
What different ways can you use to add and
subtract?
Materials
© Houghton Mifflin Harcourt Publishing Company
Listen and Draw • 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
drawings to show various addition and
subtraction strategies. As students work
through Listen and Draw, gauge their level
of understanding to make better decisions
about how to progress through
instruction.
Build on students’ understanding of
addition and subtraction facts and
strategies to develop sound mathematical
practices by asking these questions.
• What do you remember about making
a ten?
• What is the sum you are trying to find?
• Why can you make another ten from
the ones in your model?
Share and Show
Add and subtract within 100, including
continued practice with facts within 20.
• connecting cubes
• Hundred Chart
(see eTeacher
Resources)
20 min.
Practice
3 PRACTICE
Also CC.1.NBT.6, CC.1.OA.6
• MathBoard
• base-ten blocks
Teach and
Approximately
2 TEACH
andTalk
TALK
• Math Journal
• Animated Math
Models
• 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.
Approximately 10 min.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, see RtI (Response to
Intervention).
On Your Own
Approximately 10 min.
Students can begin independent practice
once they understand when to use
specific addition and subtraction strategies
to solve problems. 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, 38, 40 or 43-45
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
What different ways can you use to add
and subtract?
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Lesson 9.1
Hands On • Order Length
• About how many keys long is the straw?
• Can an object be both longer than the
straw and shorter than the key? Explain.
• Do you think it’s helpful to use objects
to measure other objects?
Instructional Time: 1 day
Common Core Standard
CC.1.MD.1 Order three objects by length; compare the lengths of
two objects indirectly by using a third object.
Practice
3 PRACTICE
Order objects by length.
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 do you order objects by length?
Materials
• MathBoard
• classroom objects
• an assortment
of yarn and
crayons of
different lengths
On Your Own
• Math Journal
• HMH Mega Math
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Listen and Draw • 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 the lengths of the objects. As
students work through Listen and Draw,
gauge their level of understanding to make
better decisions about how to progress
through instruction.
Build on students’ understanding of shorter
and longer to develop sound mathematical
practices by asking these questions.
110
Approximately 10 min.
Students can begin independent
practice once they understand how to
order lengths. 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, 11, 12, 13, or 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.
Approximately 10 min.
Essential Question
How do you order objects by length?
Possible answer: I can line up objects at
one end to quickly see which objects are
the shortest and longest.
Math Journal
Draw three different lines in order from
shortest to longest. Label the shortest line
and the longest line.
© Houghton Mifflin Harcourt Publishing Company
Lesson Objective
Chapter 9
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Lesson 9.2
Indirect Measurement
Instructional Time: 1 day
Common Core Standard
CC.1.MD.1 Order three objects by length; compare the lengths of
two objects indirectly by using a third object.
Lesson Objective
Use the Transitivity Principle to measure
indirectly.
Essential Question
Practice
3 PRACTICE
How can you compare lengths of three
objects to put them in order?
Share and Show
Materials
• MathBoard
• crayons
• Math Journal
• Animated Math
Models
• HMH Mega Math
Approximately 10 min.
Use the checked exercise as a diagnostic
assessment. If students answer the
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 how to describe
lengths as shorter or longer. Select
exercises based on students’ depth of
understanding. The exercises below
require higher order thinking skills and
critical reasoning, making them especially
rich.
Exercises 2, 3, or 4
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
ordering lengths to develop sound
mathematical practices by asking these
questions.
• Do you know exactly how long any of
the strings are?
• Do you have enough information to
put the strings in order from longest to
shortest?
• When could indirect measurement be
useful? Explain.
Listen and Draw • 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 what they
know about comparing lengths to
measure indirectly. As students work
through Listen and Draw, 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 compare lengths of three
objects to put them in order?
Possible answer: I can compare two lengths
at a time until I figure out the longest and
the shortest.
Math Journal
Use different colors to draw 3 lines that
are different lengths. Then write
3 sentences comparing their lengths.
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Lesson 9.3
Hands On • Use Nonstandard
Units to Measure Length
Build on students’ understanding of
measurement to develop sound
mathematical practices by asking these
questions.
• Do you know the exact length of
Jimmy’s boat?
• Would you always use color tiles to
measure things? Explain.
• What is another way you could measure
Jimmy’s boat?
Instructional Time: 1 day
Common Core Standard
CC.1.MD.2 Express the length of an object as a whole number of
length units, by laying multiple copies of a shorter object (the length
unit) end to end; understand that the length measurement of an
object is the number of same-size length units that span it with no
gaps or overlaps.
Measure length using nonstandard units.
Practice
3 PRACTICE
Essential Question
Share and Show
How do you measure length using
nonstandard units?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response to
Intervention).
Materials
• MathBoard
• color tiles
• classroom objects
• Math Journal
• Animated Math
Models
• HMH Mega Math
On Your Own
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Listen and Draw • 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 draw pictures to
model measuring with non-standard units.
As students work through Listen and
Draw, gauge their level of understanding
to make better decisions about how to
progress through instruction.
112
Approximately 10 min.
Students can begin independent practice
once they understand how to use color
tiles to measure. 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, 9, 10, or 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 do you measure length using
nonstandard units?
Possible answer: I place a color tile under
an object, starting at the same place as the
object. Then I set color tiles in a row next
to the first one until I get to the end of the
object. I count the tiles to find about how
long the object is.
Math Journal
Use words or pictures to explain how to
measure an index card using color tiles.
© Houghton Mifflin Harcourt Publishing Company
Lesson Objective
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Lesson 9.4
Hands On • Make a Nonstandard
Measuring Tool
Instructional Time: 1 day
Note: The instructional time for this lesson
can also be 2 days. On Day 1 give students
paper clips and have them try to solve Share
and Show problems by measuring objects and
recording their measurements. Use the extra
time on Day 2 to explore Go Deeper and have
students estimate the length of each object
and then check their measurements. Then
complete the Extend the Math activity by
having pairs compare their measurements.
Common Core Standard
CC.1.MD.2 Express the length of an object as a whole number of
length units, by laying multiple copies of a shorter object (the length
unit) end to end; understand that the length measurement of an
object is the number of same-size length units that span it with no
gaps or overlaps.
Practice
3 PRACTICE
Lesson Objective
Make a nonstandard measuring tool to
measure length.
Share and Show
Approximately 10 min.
How do you use a nonstandard measuring
tool to measure length?
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
• different color
paper clips of the
same size
• tape
• sturdy paper
• classroom objects
© Houghton Mifflin Harcourt Publishing Company
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 how to
measure correctly using nonstandard
tools. As students work through Listen and
Draw, gauge their level of understanding
to make better decisions about how to
progress through instruction.
Build on students’ understanding of
measurement in addition to develop sound
mathematical practices by asking these
questions.
• How could Alli make her measurement
more correct?
• Could you also use the pencil to measure
other things? Explain.
• What is another object you could use to
measure the length of the pencil?
• 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.
Listen and Draw • Activity to Build
Conceptual Understanding
1_MNYCETS221970_C09RML04.indd 113
Approximately 10 min.
Students can begin independent practice
once they understand how to use
nonstandard tools to measure. 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, or 10
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How do you use a nonstandard measuring
tool to measure length?
Possible answer: I line up the measuring
tool with one edge of the object and count
the units to the other end of the object.
Math Journal
Use words or pictures to explain how
to measure a table using a paper clip
measuring tool.
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Lesson 9.5
Problem Solving • Measure and
Compare
Build on students’ understanding of
comparing measurements to develop
sound mathematical practices by asking
these questions.
• Could you also use the measurements
to order the ribbons from longest to
shortest?
• If you put the red ribbon and green
ribbon together, would it be longer or
shorter than the blue ribbon? How do
you know?
• What is another way to act out the
measurement of the ribbons? Do you
get the same answer?
Instructional Time: 1 day
Common Core Standard
CC.1.MD.2 Express the length of an object as a whole number of
length units, by laying multiple copies of a shorter object (the length
unit) end to end; understand that the length measurement of an
object is the number of same-size length units that span it with no
gaps or overlaps.
Lesson Objective
Solve measurement problems using the
strategy act it out.
How can acting it out help you solve
measurement problems?
Practice
3 PRACTICE
Share and Show •
Materials
• MathBoard
• paper clip
measuring tool
• classroom objects
• red, green, blue,
yellow, and
orange ribbon
Use the checked exercise as a diagnostic
assessment. If students answer the
exercise incorrectly, use RtI (Response to
Intervention).
Have students work on exercise 5 based on
their depth of understanding. The exercise
requires higher order thinking skills and
critical reasoning, making it especially rich.
• scissors
• Math Journal
• HMH Mega Math
Engage Approximately 5 min.
1 ENGAGE
Summarize Approximately 5 min.
4 SUMMARIZE
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.
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 measure objects and
compare their measurements. As students
work through Unlock the Problem, gauge
their level of understanding to make better
decisions about how to progress through
instruction.
114
Guided Practice
Essential Question
How can acting it out help you solve
measurement problems?
Possible answer: Acting it out can help me
find the lengths of objects before I draw
them.
Math Journal
Measure and draw to show a blue crayon
and a green crayon that is about 1 paper
clip longer than the blue crayon.
© Houghton Mifflin Harcourt Publishing Company
Essential Question
Chapter 9
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Lesson 9.6
Time to the Hour
Instructional Time: 1 day
Common Core Standard
CC.1.MD.3 Tell and write time in hours and half-hours using analog
and digital clocks.
Lesson Objective
Write times to the hour shown on analog
clocks.
Practice
3 PRACTICE
Essential Question
Share and Show
How do you tell time to the hour on a clock
that has only an hour hand?
Materials
• MathBoard
• green yarn
• adhesive notes
• glue
• Animated Math
Models
• HMH Mega Math
• iTools:
Measurement
• 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.
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 how to tell time
to the hour. 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, 10, 14, 16, and 17
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
© Houghton Mifflin Harcourt Publishing Company
• How are the number line and the clock
face on your page similar? How are they
different?
• How did you know what numbers to
write in the boxes?
• How would you describe the direction
you follow when you count in order
along a clock face?
Listen and Draw • 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 in order
to complete the clock. As students work
through Listen and Draw, gauge their level
of understanding to make better decisions
about how to progress through
instruction.
Build on students’ understanding of
counting to develop sound mathematical
practices by asking these questions.
How do you tell time to the hour on a
clock that has only an hour hand?
Possible answer: The number that the
hour hand points to names the time to
the hour.
Math Journal
Look at Exercise 17. Write a similar word
problem about when Manny gets home
from school. Then show how to solve the
problem.
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Lesson 9.7
Time to the Half Hour
• What can you tell about the time by
looking at the hour hand?
• Where does the hour hand point for
times that end in “:00”?
• How long would it take the hour hand
to move from the 4 to the 6? How do
you know?
Instructional Time: 1 day
Common Core Standard
CC.1.MD.3 Tell and write time in hours and half-hours using analog
and digital clocks.
Write times to the half hour shown on analog
clocks.
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 do you tell time to the half hour on a
clock that has only an hour hand?
Materials
• MathBoard
• Math Journal
• Animated Math
Models
On Your Own
• HMH Mega Math
• iTools:
Measurement
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Listen and Draw • 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 hour
hand to tell time. As students work
through Listen and Draw, gauge their
level of understanding to make better
decisions about how to progress through
instruction.
Build on students’ understanding of telling
time to the hour to develop sound
mathematical practices by asking these
questions.
116
Approximately 10 min.
Students can begin independent practice
once they understand how to tell time to
the half hour. 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, 10, 11, or 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.
Approximately 10 min.
Essential Question
How do you tell time to the half hour on
a clock that has only an hour hand?
Possible answer: The hour hand will be
halfway between two numbers. I can name
the time as half past the lesser number.
Math Journal
Draw clocks to show where the hour
hand points for 5:00 and half past 5:00.
© Houghton Mifflin Harcourt Publishing Company
Lesson Objective
Chapter 9
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Lesson 9.8
Tell Time to the Hour and
Half Hour
Build on students’ understanding of telling
time to the hour and half hour to develop
sound mathematical practices by asking
these questions.
• How would you describe the direction
the minute hand points when the time
ends in “:00”?
• When does the minute hand point
straight down?
• How far around the clock does the
minute hand move every half hour?
• Which do you think moves faster, the
hour hand or the minute hand? How
do you know?
Instructional Time: 1 day
Common Core Standard
CC.1.MD.3 Tell and write time in hours and half-hours using
analog and digital clocks.
Lesson Objective
Tell times to the hour and half hour using
analog and digital clocks.
Essential Question
How are the minute hand and hour hand
different for time to the hour and time to
the half hour?
Practice
3 PRACTICE
Materials
• MathBoard
• Analog Clock
Model (see
eTeacher
Resources)
• demonstration
analog clock
• Animated Math
Models
• HMH Mega Math
• iTools:
Measurement
Approximately 10 min.
Students can begin independent practice
once they understand how to tell time to
the hour and half hour. 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, 10, 11, 12, or 14
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
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
Listen and Draw • 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 what they
already know about telling time to tell
time to the hour and half hour. As
students work through Listen and Draw,
gauge their level of understanding to
make better decisions about how to
progress through instruction.
1_MNYCETS221970_C09RML08.indd 117
Share and Show
How are the minute hand and hour hand
different for time to the hour and time to
the half hour?
Possible answer: For time to the hour, the
minute hand points to 12 and the hour
hand points to the hour. For time to the
half hour, the minute hand points to 6 and
the hour hand points halfway between
two numbers.
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Lesson 9.9
Practice Time to the Hour and
Half Hour
• Could you tell just by looking at the
minute hand which answers could not
be correct? How?
• Could you tell just by looking at the
hour hand which answer could be
correct? How?
• How do you know the middle clock
could not be the correct answer to the
second problem?
Instructional Time: 1 day
Common Core Standard
CC.1.MD.3 Tell and write time in hours and half-hours using analog
and digital clocks.
Lesson Objective
Practice
3 PRACTICE
Essential Question
Share and Show
How do you know whether to draw and
write time to the hour or half hour?
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
On Your Own
Teach and
Approximately
2 TEACH
andTalk
TALK
Summarize Approximately 5 min.
4 SUMMARIZE
20 min.
Listen • 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 correctly read
the time on a clock. As students work
through Listen, gauge their level of
understanding to make better decisions
about how to progress through
instruction.
Build on students’ understanding of
telling time to develop sound
mathematical practices by asking these
questions.
118
Approximately 10 min.
Students can begin independent practice
once they understand how to tell and show
time on a clock. 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, 12, 13, 14, or 16
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 know whether to draw and
write time to the hour or half hour?
Possible answer: I can look at the hour
hand to see if it shows time to the hour or
time to the half hour. Then I know how to
draw and write the time.
Math Journal
Draw a clock to show a time to the hour.
Draw another clock to show a time to the
half hour. Write each time.
© Houghton Mifflin Harcourt Publishing Company
Use the hour hand to draw and write times
on analog and digital clocks.
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Lesson 10.1
Read Picture Graphs
Instructional Time: 1 day
Common Core Standard
CC.1.MD.4 Organize, represent, and interpret data with up to three
categories; ask and answer questions about the total number of data
points, how many in each category, and how many more or less are
in one category than in another.
Lesson Objective
Analyze and compare data shown in a picture
graph where each symbol represents one.
Practice
3 PRACTICE
Share and Show
Approximately 10 min.
What do the pictures in a picture graph show?
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
• blue and green
connecting cubes
• Math Journal
• Animated Math
Models
• HMH Mega 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.
Approximately 10 min.
Students can begin independent practice
once they understand how to read picture
graphs. 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, 10, 11, or 14
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
What do the pictures in a picture graph
show?
Possible answer: The pictures show the
number of each item.
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
© Houghton Mifflin Harcourt Publishing Company
• How do your pictures help you solve the
problem?
• Can you draw the pictures a different
way to get the same result?
• How could you write the problem as a
subtraction sentence? Explain.
Listen and Draw • 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 cubes to make
a picture graph. As students work through
Listen and Draw, gauge their level of
understanding to make better decisions
about how to progress through instruction.
Build on students’ understanding of
counting cubes to develop sound
mathematical practices by asking these
questions.
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Lesson 10.2
Hands On • Make Picture Graphs
Build on students’ understanding of
picture graphs to develop sound
mathematical practices by asking these
questions.
• How does your drawing help you solve
the problem?
• If Asaf got 3 more bats, which group
would have more?
• Could you use this kind of graph to
compare more than 2 groups? Explain.
Instructional Time: 1 day
Common Core Standard
CC.1.MD.4 Organize, represent, and interpret data with up to three
categories; ask and answer questions about the total number of data
points, how many in each category, and how many more or less are
in one category than in another.
Lesson Objective
Essential Question
Practice
3 PRACTICE
Share and Show
How do you make a picture graph to answer a
question?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response to
Intervention).
Materials
• MathBoard
• two-color
counters
• Math Journal
• Animated Math
Models
• HMH Mega Math
• iTools: Counters
On Your Own
Engage Approximately 5 min.
1 ENGAGE
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Listen and Draw • 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 record data in a picture graph.
As students work through Listen and
Draw, 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 how to make a
picture graph. 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, 7, 8, 10, or 11
• 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 do you make a picture graph to
answer a question?
Possible answer: I can draw a simple
picture in a row of the graph to show each
person’s answer to a question. Then I
compare the rows.
Math Journal
Write a question that can be answered by
making a picture graph.
© Houghton Mifflin Harcourt Publishing Company
Make a picture graph where each symbol
represents one and interpret the information.
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Lesson 10.3
Read Bar Graphs
Instructional Time: 1 day
Common Core Standard
CC.1.MD.4 Organize, represent, and interpret data with up to three
categories; ask and answer questions about the total number of data
points, how many in each category, and how many more or less are
in one category than in another.
Lesson Objective
Analyze and compare data shown in a bar
graph.
Practice
3 PRACTICE
Essential Question
Share and Show
How can you read a bar graph to find the
number that a bar shows?
• Math Journal
On Your Own
Approximately 10 min.
Students can begin independent practice
once they understand how to read data in
a bar graph. 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, 9, 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
Summarize Approximately 5 min.
4 SUMMARIZE
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).
Materials
• MathBoard
• two-color
counters
• Can you use the information shown in
the graph to answer more than one
question? Explain.
• Can you use the information in the
graph to tell how many boys had laces
and how many girls had no laces?
Explain.
• Can the information in this graph be
arranged another way? Would it change
the information?
Listen • 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
reading data in a graph. As students work
through Listen, gauge their level of
understanding to make better decisions
about how to progress through
instruction.
Build on students’ understanding of
reading graphs to develop sound
mathematical practices by asking these
questions.
Essential Question
How can you read a bar graph to find the
number that a bar shows?
Possible answer: I match the end of a bar
to the number below.
Math Journal
Use numbers and pictures to compare two
items in a bar graph.
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Lesson 10.4
Hands On • Make Bar Graphs
• Can you use the bar graph to show
which food sold the least? How can
you tell?
• If Dan sells 10 tacos, could you show
that information on this graph? Why or
why not?
• Can you use the graph to tell how many
items Dan sold in all? Explain.
Instructional Time: 1 day
Common Core Standard
CC.1.MD.4 Organize, represent, and interpret data with up to three
categories; ask and answer questions about the total number of data
points, how many in each category, and how many more or less are
in one category than in another.
Make a bar graph and interpret the
information.
Practice
3 PRACTICE
Share and Show
Essential Question
Use the checked exercise as a diagnostic
assessment. If students answer the
exercise incorrectly, use RtI (Response to
Intervention).
How does a bar graph help you compare
information?
Materials
• MathBoard
• connecting cubes
• crayons
On Your Own
• Math Journal
• iTools: Graphs
Teach and
Approximately
2 TEACH
andTalk
TALK
Summarize Approximately 5 min.
4 SUMMARIZE
20 min.
Listen and Draw • 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 what they
know about graphs to make a bar graph.
As students work through Listen and
Draw, gauge their level of understanding
to make better decisions about how to
progress through instruction.
Build on students’ understanding of bar
graphs to develop sound mathematical
practices by asking these questions.
124
Approximately 10 min.
Students can begin independent practice
once they understand how to make a bar
graph. Select exercises based on students’
depth of understanding. The exercises
below require higher order thinking skills
and critical reasoning, making them
especially rich.
Exercises 2, 3, 4, or 5
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 does a bar graph help you compare
information?
Possible answer: You can see the answer
without counting since the longer row
has more.
Math Journal
Use words and pictures to show how to
make a bar graph about favorite
storybooks.
© Houghton Mifflin Harcourt Publishing Company
Lesson Objective
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Lesson 10.5
Read Tally Charts
Instructional Time: 1 day
Common Core Standard
CC.1.MD.4 Organize, represent, and interpret data with up to three
categories; ask and answer questions about the total number of data
points, how many in each category, and how many more or less are
in one category than in another.
Lesson Objective
Analyze and compare data shown in a tally
chart.
Essential Question
How do you count the tallies on a tally chart?
Materials
• MathBoard
• two-color
counters
• red and yellow
crayons
• large and small
paper clips
(optional)
• 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.
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 how to read a tally
chart. 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, 13, or 14
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
counting and charts to develop sound
mathematical practices by asking these
questions.
• If you sort the crayons in different
ways, does the total number of crayons
change?
• Do you think a tally chart is a good way
to compare the sorted crayons? Explain.
• How does a tally chart help you count
numbers more quickly?
Listen and Draw • 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 objects
and make a tally chart. As students work
through Listen and Draw, gauge their level
of understanding to make better decisions
about how to progress through
instruction.
How do you count the tallies on a tally
chart?
Possible answer: Each tally mark stands for
one thing that is counted. A group of 5 is
shown with a slash over a group of 4.
Math Journal
Use words, numbers, or pictures to show
how to group and count tally marks for
the number 8.
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Lesson 10.6
Hands On • Make Tally Charts
• Which game do the children in Ava’s
class like least? How do you know?
• Can you use the tally chart to find the
total number of children in Ava’s class?
• Can you use the tally chart to tell how
many children like computer games?
Explain.
Instructional Time: 1 day
Common Core Standard
CC.1.MD.4 Organize, represent, and interpret data with up to three
categories; ask and answer questions about the total number of data
points, how many in each category, and how many more or less are
in one category than in another.
Make a tally chart and interpret the
information.
Practice
3 PRACTICE
Share and Show
Approximately 10 min.
Why is a tally chart a good way to show
information that you have collected?
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
Students can begin independent practice
once they understand how to make tally
charts. 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, 7, 8, 10, or 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.
Teach and
Approximately
2 TEACH
andTalk
TALK
Summarize Approximately 5 min.
4 SUMMARIZE
20 min.
Listen • 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 complete a tally
chart. As students work through Listen,
gauge their level of understanding to
make better decisions about how to
progress through instruction.
Build on students’ understanding of tally
charts to develop sound mathematical
practices by asking these questions.
126
Approximately 10 min.
Essential Question
Why is a tally chart a good way to show
information that you have collected?
Possible answer: I can make a tally mark in
the chart for each thing to show the group
where it belongs.
Math Journal
Write a question that can be answered by
making a tally chart.
© Houghton Mifflin Harcourt Publishing Company
Lesson Objective
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Lesson 10.7
Problem Solving • Represent Data
Instructional Time: 1 day
Common Core Standard
CC.1.MD.4 Organize, represent, and interpret data with up to three
categories; ask and answer questions about the total number of data
points, how many in each category, and how many more or less are
in one category than in another.
Practice
3 PRACTICE
Lesson Objective
Solve problem situations using the strategy
make a graph.
Share and Show
Approximately 10 min.
How can showing information in a graph help
you solve problems?
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
• HMH Mega Math
• 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.
Approximately 10 min.
Students can begin independent practice
once they understand how to use graphs
and charts to show data. 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, 5, 6, 7, or 8
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
Essential Question
20 min.
© Houghton Mifflin Harcourt Publishing Company
• Which animal does Brad see the most?
How can you tell?
• Why do the deer have the shortest bar
on the graph?
• Can you represent the data in this
problem using a different chart or
graph?
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 bar graph
to solve a problem. 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 how
to read and show data to develop sound
mathematical practices by asking these
questions.
How can showing information in a graph
help you solve problems?
Possible answer: You can see all the
information you need in an organized
way. It helps you compare information
easily.
Math Journal
Write the names of 3 types of animals.
Count the letters in each name. Make a
bar graph showing the letters for each
animal.
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Lesson 11.1
Hands On • Three-Dimensional
Shapes
Build on students’ understanding of
three-dimensional shapes to develop
sound mathematical practices by asking
these questions.
• Is there another way to sort the shapes?
Explain.
• Why is it helpful to sort shapes in
different ways?
• Can a shape have both a flat surface
to stack and a curved surface to roll?
Explain.
Instructional Time: 1 day
Common Core Standard
CC.1.G.1 Distinguish between defining attributes (e.g., triangles are
closed and three-sided) versus non-defining attributes (e.g., color,
orientation, overall size); build and draw shapes to possess defining
attributes.
Lesson Objective
Essential Question
Practice
3 PRACTICE
Share and Show
How can you identify and describe
three-dimensional shapes?
Use the checked exercise as a diagnostic
assessment. If students answer the
exercise incorrectly, use RtI (Response to
Intervention).
Materials
• MathBoard
• models of three-dimensional shapes
• Three-Dimensional Shapes (see eTeacher
Resources)
• Math Journal
• Animated Math Models
• HMH Mega Math
• iTools: Geometry
On Your Own
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Listen and Draw • 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 and sort
three-dimensional shapes. 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 the
attributes of three-dimensional shapes.
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 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.
Approximately 10 min.
Essential Question
How can you identify and describe
three-dimensional shapes?
Possible answer: I can describe a shape as
having flat or curved surfaces, or both.
I can identify the shape if I know
how many flat surfaces it has and if it
has a curved surface.
© Houghton Mifflin Harcourt Publishing Company
Identify and describe three-dimensional
shapes according to defining attributes.
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Lesson 11.2
Hands On • Combine
Three-Dimensional Shapes
Instructional Time: 1 day
Common Core Standard
CC.1.G.2 Compose two-dimensional shapes (rectangles, squares,
trapezoids, triangles, half-circles, and quarter-circles) or
three-dimensional shapes (cubes, right rectangular prisms, right
circular cones, and right circular cylinders) to create a composite
shape, and compose new shapes from the composite shape.
Lesson Objective
Compose a new shape by combining
three-dimensional shapes.
Essential Question
How can you combine three-dimensional
shapes to make new shapes?
Materials
•
•
•
•
MathBoard
models of three-dimensional shapes
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
© Houghton Mifflin Harcourt Publishing Company
20 min.
Listen and Draw • 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 combine
three-dimensional shapes to make
new shapes. As students work through
Listen and Draw, gauge their level of
understanding to make better decisions
about how to progress through
instruction.
Build on students’ understanding of
combining shapes to develop sound
mathematical practices by asking these
questions.
• Does the rectangular prism change if
you stack the cubes in different ways?
• Could you stack a cylinder on a cube, or
a cube on a cylinder? Explain.
• Can you think of a shape that cannot be
stacked?
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 •
Independent Practice
Students can begin independent practice
once they understand how to combine
shapes. 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 or 9–11
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How can you combine three-dimensional
shapes to make new shapes?
Possible answer: I can match two flat
surfaces to combine shapes.
Math Journal
Combine two shapes to make a new shape.
Describe how you put the shapes together.
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Lesson 11.3
Hands On • Make New
Three-Dimensional Shapes
Build on students’ understanding of
making three-dimensional shapes to develop sound mathematical practices
by asking these questions.
• Can this new shape be stacked?
• How many surfaces and vertices does
this new shape have?
• Is there another way to put the boxes
together to copy the shape? Explain.
Instructional Time: 1 day
Common Core Standard
CC.1.G.2 Compose two-dimensional shapes (rectangles, squares,
trapezoids, triangles, half-circles, and quarter-circles) or
three-dimensional shapes (cubes, right rectangular prisms, right
circular cones, and right circular cylinders) to create a composite
shape, and compose new shapes from the composite shape.
Use composite three-dimensional shapes to
build new shapes.
Practice
3 PRACTICE
Share and Show
Approximately 10 min.
How can you use a combined shape to build
new shapes?
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
Students can begin independent practice
once they understand how to make new
three-dimensional shapes. 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
• MathBoard
• models of three-dimensional shapes
• Three-Dimensional Shapes (see eTeacher
Resources)
• 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.
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Listen and Draw • 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
describe new three-dimensional shapes.
As students work through Listen and
Draw, gauge their level of understanding
to make better decisions about how to
progress through instruction.
132
Approximately 10 min.
Essential Question
How can you use a combined shape to
build new shapes?
Possible answers: I can stack shapes with
flat surfaces. I can combine shapes side
by side.
Math Journal
Use a cube and a cylinder to build a new
shape. Repeat. Draw to show how you can
combine these two new shapes to make a
larger shape.
© Houghton Mifflin Harcourt Publishing Company
Lesson Objective
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Lesson 11.4
Problem Solving • Take Apart
Three-Dimensional Shapes
Instructional Time: 1 day
Common Core Standard
CC.1.G.2 Compose two-dimensional shapes (rectangles, squares,
trapezoids, triangles, half-circles, and quarter-circles) or
three-dimensional shapes (cubes, right rectangular prisms, right
circular cones, and right circular cylinders) to create a composite
shape, and compose new shapes from the composite shape.
Lesson Objective
Practice
3 PRACTICE
Identify three-dimensional shapes used to
build a composite shape using the strategy
act it out.
Share and Show
Approximately 10 min.
How can acting it out help you take apart
combined shapes?
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
•
•
•
•
Approximately 10 min.
Students can begin independent practice
once they understand how to take apart
shapes. 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, 10
MathBoard
models of three-dimensional shapes
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.
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
© Houghton Mifflin Harcourt Publishing Company
Build on students’ understanding of
taking apart shapes to develop sound
mathematical practices by asking these
questions.
• What shapes did Mike NOT use in his
bridge?
• What shapes could Mike use to make his
bridge taller?
• Is it possible to build a bridge using
all 4 of Mike’s shapes? Explain.
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 decompose
shapes. As students work through
Unlock the Problem, gauge their level
of understanding to make better decisions
about how to progress through
instruction.
How can acting it out help you take apart
combined shapes?
Possible answer: If I can use blocks to copy
the combined shape, it helps me see the
shapes that are used.
Math Journal
Draw a picture of a house made from
shapes. Write the shape names you used.
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Lesson 11.5
Hands On • Two-Dimensional
Shapes on Three-Dimensional
Shapes
about how to progress through
instruction.
Build on students’ understanding of
putting together to develop sound
mathematical practices by asking these
questions.
• How is a cylinder different from a cone?
• Can you trace around a curved surface?
Explain.
• What shape has a flat surface that is a
square?
Instructional Time: 1 day
Common Core Standard
CC.1.G.1 Distinguish between defining attributes (e.g., triangles are
closed and three-sided) versus non-defining attributes (e.g., color,
orientation, overall size); build and draw shapes to possess defining
attributes.
Identify two-dimensional shapes on
three-dimensional shapes.
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).
What two-dimensional shapes do you see on
the flat surfaces of three-dimensional shapes?
Materials
•
•
•
•
•
•
On Your Own
MathBoard
models of three-dimensional shapes
Math Journal
Animated Math Models
HMH Mega Math
iTools: Geometry
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Listen and Draw • 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 twodimensional shapes on three-dimensional
shapes. As students work through Listen
and Draw, gauge their level of
understanding to make better decisions
134
Approximately 10 min.
Students can begin independent practice
once they understand how to identify
two-dimensional shapes on three-dimensional shapes. 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, 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
What two-dimensional shapes do you see
on the flat surfaces of three-dimensional
shapes?
Possible answer: I see squares on a
cube, squares and other rectangles on a
rectangular prism, and circles on a cone
and cylinder.
Math Journal
Use pictures or words to explain how you
would describe the shapes of flat surfaces
you may see on a tissue box.
© Houghton Mifflin Harcourt Publishing Company
Lesson Objective
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Lesson 12.1
Sort Two-Dimensional Shapes
Instructional Time: 1 day
Common Core Standard
CC.1.G.1 Distinguish between defining attributes (e.g., triangles are
closed and three-sided) versus non-defining attributes (e.g., color,
orientation, overall size); build and draw shapes to possess defining
attributes.
Lesson Objective
Practice
3 PRACTICE
Use defining attributes to sort shapes.
Share and Show
Essential Question
How can you use attributes to sort
two-dimensional shapes?
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response to
Intervention).
Materials
On Your Own
• MathBoard
• HMH Mega Math
• Math Journal
• iTools: Geometry
• 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.
Approximately 10 min.
Approximately 10 min.
Students can begin independent practice
once they understand how to use
attributes of shapes to sort them. 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, 10, 12, or 13
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
Essential Question
20 min.
© Houghton Mifflin Harcourt Publishing Company
• Are there any other ways to sort the
shapes into triangles and rectangles?
• Could you sort circles into one of these
two groups? Explain.
• Could you sort hexagons into one of
these two groups? Explain.
Listen and Draw • 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 similarities
and differences among two-dimensional
shapes. As students work through
Listen and Draw, gauge their level of
understanding to make better decisions
about how to progress through
instruction.
Build on students’ understanding of
two-dimensional shapes to develop sound
mathematical practices by asking these
questions.
How can you use attributes to sort
two-dimensional shapes?
Possible answer: I can sort by the number
of sides or vertices, by straight or curved
sides, or by closed or open shapes.
Math Journal
Explain how you would name a sorting
rule for 1 square, 1 rectangle, and
1 triangle.
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Lesson 12.2
Hands On • Describe
Two-Dimensional Shapes
As students work through Listen and
Draw, gauge their level of understanding
to make better decisions about how to
progress through instruction.
Build on students’ understanding of
attributes of two-dimensional shapes to
develop sound mathematical practices by
asking these questions.
• Can a square or rectangle ever have
curved sides? Explain.
• Can a circle ever have straight sides?
Explain.
• Can a triangle ever have curved sides?
Explain.
Instructional Time: 1 day
Common Core Standard
CC.1.G.1 Distinguish between defining attributes (e.g., triangles are
closed and three-sided) versus non-defining attributes (e.g., color,
orientation, overall size); build and draw shapes to possess defining
attributes.
Lesson Objective
Describe attributes of two-dimensional shapes.
Essential Question
Materials
Practice
3 PRACTICE
Share and Show
• MathBoard
• models of two-dimensional shapes or
Two-Dimensional Shapes (see eTeacher
Resources) and glue
• pattern blocks
• red and blue crayons
• Math Journal
• Animated Math Models
• HMH Mega Math
• iTools: Geometry
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response to
Intervention).
On Your Own
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Listen and Draw • 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 attributes to
describe two-dimensional shapes.
138
Approximately 10 min.
Students can begin independent practice
once they understand how to describe
two-dimensional shapes. 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, 13, or 16
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 attributes can you use to describe
two-dimensional shapes?
Possible answer: I can describe shapes by
the number of sides and vertices, by being
open or closed, and by having curved or
straight sides.
© Houghton Mifflin Harcourt Publishing Company
What attributes can you use to describe
two-dimensional shapes?
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Lesson 12.3
Hands On • Combine
Two-Dimensional Shapes
Instructional Time: 1 day
Common Core Standard
CC.1.G.2 Compose two-dimensional shapes (rectangles, squares,
trapezoids, triangles, half-circles, and quarter-circles) or
three-dimensional shapes (cubes, right rectangular prisms, right
circular cones, and right circular cylinders) to create a composite
shape, and compose new shapes from the composite shape.
Lesson Objective
Use objects to compose new two-dimensional
shapes.
Essential Question
Practice
3 PRACTICE
Share and Show
Approximately 10 min.
How can you put two-dimensional shapes
together to make new two-dimensional
shapes?
Use the checked exercise as a diagnostic
assessment. If students answer the
exercise incorrectly, use RtI (Response to
Intervention).
Materials
On Your Own
• MathBoard
• pattern blocks
• 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.
Approximately 10 min.
Students can begin independent
practice once they understand how to
compose shapes. 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, or 7
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
© Houghton Mifflin Harcourt Publishing Company
Build on students’ understanding of
two-dimensional shapes to develop sound
mathematical practices by asking these
questions.
• Can you use the two triangles to make a
shape with more than 4 sides? Explain.
• Can you use the two triangles to make a
shape with fewer than 3 sides? Explain.
• What shape would you make if you used
3 triangles?
Listen and Draw • 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 draw twodimensional shapes made up of other
two-dimensional shapes. As students work
through Listen and Draw, gauge their level
of understanding to make better decisions
about how to progress through
instruction.
How can you put two-dimensional shapes
together to make new two-dimensional
shapes?
Possible answer: I can put shapes together
by matching some sides and vertices to
make a new shape.
Math Journal
Draw the shapes you could put together to
make a rectangle.
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Lesson 12.4
Combine More Shapes
Build on students’ understanding of
composing shapes to develop sound
mathematical practices by asking these
questions.
• Could you switch the places of the
triangle and the square to fill the
outline on the left?
• Is there any other way to fill the outline
on the right?
• Could you use all the shapes from the
outline on the right to fill the outline on
the left? Explain.
Instructional Time: 1 day
Common Core Standard
CC.1.G.2 Compose two-dimensional shapes (rectangles, squares,
trapezoids, triangles, half-circles, and quarter-circles) or
three-dimensional shapes (cubes, right rectangular prisms, right
circular cones, and right circular cylinders) to create a composite
shape, and compose new shapes from the composite shape.
Lesson Objective
Compose a new shape by combining
two-dimensional shapes.
How can you combine two-dimensional shapes
to make new shapes?
Practice
3 PRACTICE
Share and Show
Materials
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response to
Intervention).
•
•
•
•
MathBoard
models of two-dimensional shapes
Two-Dimensional Shapes
Two-Dimensional Shapes (to combine)
(see eTeacher Resources)
• Math Journal
• Animated Math Models
• HMH Mega Math
On Your Own
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Listen and Draw • 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 what they know about
shapes to make new shapes. As students
work through Listen and Draw, gauge
their level of understanding to make
better decisions about how to progress
through instruction.
140
Approximately 10 min.
Students can begin independent practice
once they understand how to combine
shapes to make new shapes. 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, 9, or 10
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 combine two-dimensional
shapes to make new shapes?
Possible answer: You can turn them in
different ways so that a side of each shape
is connected to the side of another shape.
Math Journal
Draw two shapes. Then draw what they
would look like if you put them together
to make a new shape.
© Houghton Mifflin Harcourt Publishing Company
Essential Question
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Lesson 12.5
Problem Solving • Make New
Two-Dimensional Shapes
Instructional Time: 1 day
Common Core Standard
CC.1.G.2 Compose two-dimensional shapes (rectangles, squares,
trapezoids, triangles, half-circles, and quarter-circles) or
three-dimensional shapes (cubes, right rectangular prisms, right
circular cones, and right circular cylinders) to create a composite
shape, and compose new shapes from the composite shape.
Lesson Objective
Make new shapes from composite
two-dimensional shapes using the strategy
act it out.
Practice
3 PRACTICE
Essential Question
How can acting it out help you make new
shapes from combined shapes?
Share and Show
Materials
• MathBoard
• Math Journal
• Two-Dimensional • Animated Math
Shapes (to combine) Models
(see eTeacher
Resources)
• tape
• HMH Mega Math
Engage Approximately 5 min.
1 ENGAGE
© Houghton Mifflin Harcourt Publishing Company
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.
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 reasoning
to make new shapes. 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
composing two-dimensional shapes to
develop sound mathematical practices
by asking these questions.
• Can you still make a circle if you put the
shapes in a different order? Explain.
• If you used more or less than 4 small
shapes, could you still make the circle?
• Would you be able to make a circle with
a different shape? Explain.
Approximately 10 min.
Use the checked exercise as a diagnostic
assessment. If students answer the
exercise incorrectly, use RtI (Response to
Intervention).
Have students work on exercise 4 based on
their depth of understanding. The exercise
requires higher order thinking skills and
critical reasoning, making it especially rich.
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How can acting it out help you make new
shapes from combined shapes?
Possible answer: I can use shapes to make
a new shape. Then I can copy the new
shape and put those two together to make
a different new shape.
Math Journal
Use pictures to show how you can make a
new shape using a combined shape made
from two trapezoids.
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Lesson 12.6
Hands On • Find Shapes in
Shapes
• Can you rearrange the pattern blocks to
make the same shape a different way?
Explain.
• Could you make the same shape with
2 hexagons and 1 triangle?
• How many more hexagons and triangles
would you need to make a second shape
that matches the first?
Instructional Time: 1 day
Common Core Standard
Lesson Objective
Practice
3 PRACTICE
Share and Show
Decompose combined shapes into shapes.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response to
Intervention).
Essential Question
How can you find shapes in other shapes?
Materials
• MathBoard
• pattern blocks
• Math Journal
On Your Own
• Animated Math
Models
• HMH Mega Math
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Listen and Draw • 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 pattern
blocks to make shapes. As students work
through Listen and Draw, gauge their level
of understanding to make better decisions
about how to progress through
instruction.
Build on students’ understanding of
composing shapes to develop sound
mathematical practices by asking these
questions.
142
Approximately 10 min.
Students can begin independent practice
once they understand how to find
two-dimensional shapes within other
two-dimensional shapes. 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, 9, 10, or 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 shapes in other shapes?
Possible answer: I can put different pattern
blocks together to make the shape.
Math Journal
Use pictures or words to explain what
shapes can be put together to make a
hexagon shape.
© Houghton Mifflin Harcourt Publishing Company
CC.1.G.2 Compose two-dimensional shapes (rectangles,
squares, trapezoids, triangles, half-circles, and quarter-circles) or
three-dimensional shapes (cubes, right rectangular prisms, right
circular cones, and right circular cylinders) to create a composite
shape, and compose new shapes from the composite shape.
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Lesson 12.7
Take Apart Two-Dimensional
Shapes
Build on students’ understanding of
decomposing shapes to develop sound
mathematical practices by asking these
questions.
• Are the triangles and the rectangles
the same size and shape in each of the
drawings?
• Are these drawings the only shapes
you can make with 2 triangles and
1 rectangle?
• Could you make the same drawings with
2 rectangles and 1 triangle?
Instructional Time: 1 day
Common Core Standard
CC.1.G.2 Compose two-dimensional shapes (rectangles,
squares, trapezoids, triangles, half-circles, and quarter-circles) or
three-dimensional shapes (cubes, right rectangular prisms, right
circular cones, and right circular cylinders) to create a composite
shape, and compose new shapes from the composite shape.
Lesson Objective
Decompose two-dimensional shapes into
parts.
Practice
3 PRACTICE
Essential Question
Share and Show
How can you take apart two-dimensional
shapes?
Materials
• MathBoard
• Animated Math
Models
• orange and purple • HMH Mega Math
crayons
• 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
© Houghton Mifflin Harcourt Publishing Company
20 min.
Listen and Draw • 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 what they
know about shapes to take apart
two-dimensional figures. As students
work through Listen and Draw, 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 how to take apart
shapes. 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, 9, 10, or 11
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
How can you take apart two-dimensional
shapes?
Possible answer: I can draw lines to show
parts of the shape.
Math Journal
Draw a shape. Then draw one or two lines
to show parts of the shape.
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Lesson 12.8
Equal or Unequal Parts
• What are you being asked to do in the
problem?
• What do you think will happen if you
draw the lines in a different direction?
• How can you draw another line to show
4 triangles?
Instructional Time: 1 day
Common Core Standard
Practice
3 PRACTICE
Lesson Objective
Share and Show
Identify equal and unequal parts (or shares) in
two-dimensional shapes.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response to
Intervention).
Essential Question
How can you identify equal and unequal parts
in two-dimensional shapes?
On Your Own
• MathBoard
• HMH Mega Math
• Math Journal
• iTools: Fractions
• Animated Math Models
Engage Approximately 5 min.
1 ENGAGE
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Listen and Draw • 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 divide a shape
into equal and unequal parts. As students
work through Listen and Draw, gauge
their level of understanding to make
better decisions about how to progress
through instruction.
Build on students’ understanding of parts
to develop sound mathematical practices
by asking these questions.
144
Approximately 10 min.
Students can begin independent
practice once they understand how to
divide shapes into equal and unequal
parts. 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, 12, 13, 14, or 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 you identify equal and unequal
parts in two-dimensional shapes?
Possible answer: If the parts of the shape
are the same size, then they are equal. If
the parts are different sizes, then they
are unequal.
© Houghton Mifflin Harcourt Publishing Company
CC.1.G.3 Partition circles and rectangles into two and four
equal shares, describe the shares using words halves, fourths, and
quarters, and use the phrases half of, fourth of, and quarter of.
Describe the whole as two of, or four of the shares. Understand for
these examples that decomposing into more equal shares creates
smaller shares.
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Lesson 12.9
Halves
Instructional Time: 1 day
Common Core Standard
CC.1.G.3 Partition circles and rectangles into two and four equal
shares, describe the shares using the words halves, fourths, and
quarters, and use the phrases half of, fourth of, and quarter of.
Describe the whole as two of, or four of the shares. Understand for
these examples that decomposing into more equal shares creates
smaller shares.
Practice
3 PRACTICE
Lesson Objective
Share and Show
Partition circles and rectangles into two equal
shares.
Use the checked exercises as a diagnostic
assessment. If students answer either
exercise incorrectly, use RtI (Response to
Intervention).
Essential Question
How can a shape be separated into two equal
shares?
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.
On Your Own
Approximately 10 min.
Approximately 10 min.
Students can begin independent practice
once they understand how to divide
two-dimensional shapes into halves.
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 or 15, 16, 17
Summarize Approximately 5 min.
4 SUMMARIZE
Essential Question
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
© Houghton Mifflin Harcourt Publishing Company
• How do the pictures help you solve the
problem?
• How can you tell if your answer makes
sense?
• In your own words, describe how you
cut the two sandwiches in the problem.
Listen and Draw • 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 divide the shape
into two equal parts. As students work
through Listen and Draw, gauge their level
of understanding to make better decisions
about how to progress through
instruction.
Build on students’ understanding of
dividing shapes into halves to develop
sound mathematical practices by asking
these questions.
How can a shape be separated into two
equal shares?
Possible answer: I can draw a line on the
shape to make two parts that are the
same size.
Math Journal
Draw a circle and separate it into halves.
Color each half a different color.
Chapter 12 145
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New York City Implementation Guide NYC133
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Lesson 12.10
Fourths
Build on students’ understanding of equal
parts to develop sound mathematical
practices by asking these questions.
• Is your drawing the only way to divide
the pizza?
• Can you draw the lines in a different
way to make four equal shares?
• Can you use the same number of lines to
make unequal shares? Explain.
Instructional Time: 1 day
Common Core Standard
CC.1.G.3 Partition circles and rectangles into two and four equal
shares, describe the shares using the words halves, fourths, and
quarters, and use the phrases half of, fourth of, and quarter of.
Describe the whole as two of, or four of the shares. Understand for
these examples that decomposing into more equal shares creates
smaller shares.
Partition circles and rectangles into four equal
shares.
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 a shape be separated into four equal
shares?
Materials
•
•
•
•
•
On Your Own
MathBoard
Math Journal
Animated Math Models
HMH Mega Math
iTools: Fractions
Summarize Approximately 5 min.
4 SUMMARIZE
Teach and
Approximately
2 TEACH
andTalk
TALK
20 min.
Listen and Draw • 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 divide the shape
into four equal parts. As students work
through Listen and Draw, 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 how to divide a
shape into fourths. 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, 14, 16 or 17, 18, 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 a shape be separated into four
equal shares?
Possible answer: I can draw lines on the
shape to make 4 parts that are all the
same size.
© Houghton Mifflin Harcourt Publishing Company
Lesson Objective
Chapter 12
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NYC134
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New York City Implementation Guide
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