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Teacher’s Edition
GRADE 2
TOPIC 1
PRE-PUBLICATION COPY
Quality assurance review not complete
Major Cluster 2.OA.B
TOPIC
1
Math Background: focus
F C R FOCUS
COHERENCE
MAJOR
CLUSTER
SUPPORTING
CLUSTER
RIGOR
ADDITIONAL
CLUSTER
Content Focus in
Topic 1 focuses on addition and subtraction within 20 using
strategies such as counting on, counting back, doubles,
near doubles, make 10.
LESSONS
TOPICS
2.G.A
1
2.MD.D
3
2.MD.B
12
•Addition Strategies In Lessons 1-1, 1-2, 1-3, 1-4, and
1-8, students apply addition strategies such as counting
on, using doubles (e.g., 6 + 6) and near doubles (e.g.,
6 + 7), making 10 (e.g., 8 + 5 = 8 + 2 + 3 = 10 +
3 = 13), and analyzing addition fact patterns. These
strategies can be represented using tools to build fluency
with addition facts (e.g., a number line can show
counting on). (2.OA.B.2)
2.OA.C
2.
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13
ADD AND SUBTRACT WITHIN 20
2
2.OA.B
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14
CLUSTERS
16
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2.MD.A
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FOCUS ON
COMMON CORE
CLUSTERS
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2.NBT.B
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How can you describe
a pattern for all the
sums of six?
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5
2.MD.C
6
2.OA.A
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It makes
a diagonal
pattern.
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6
7
8
9
10
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10
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10 11
2
2
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4
5
6
7
8
9
10 11 12
3
3
4
5
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7
8
9
10 11 12 13
4
4
5
6
7
8
9
10 11 12 13 14
5
5
6
7
8
9
10 11 12 13 14 15
6
6
7
8
9
10 11 12 13 14 15 16
7
7
8
9
10 11 12 13 14 15 16 17
8
8
9
10 11 12 13 14 15 16 17 18
9
9
10 11 12 13 14 15 16 17 18 19
10 10 11 12 13 14 15 16 17 18 19 20
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Fluently Add and Subtract Within 20
TOPIC 1 FOCUSES ON
MAJOR CLUSTER 2.OA.B
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Fluently add and subtract within 20 using mental strategies for all the sums of
two one-digit numbers.
1A Topic 1 Cluster Overview
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PearsonRealize.com
PD
Content Focus in
(continued)
REPRESENT AND SOLVE PROBLEMS
•Subtraction Strategies In Lessons 1-5, 1-6, 1-7, and 1-8,
students apply subtraction strategies such as counting on
and counting back, thinking about the inverse relationship
between addition and subtraction, and making 10. As with
the addition strategies, these subtraction strategies can be
represented using tools, which can be used to build fluency.
(2.OA.B.2)
You can count
on to subtract.
Count on to 10 to find the difference.
16
Pat has 9 cards. Frank has 2 more cards than Steve. Steve has 3 cards. How many more cards does Pat have than Frank?
2
4,
3
4
5
,
5
6
7
6
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7
8
,
9
8
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10 11 12 13 14 15
9
,
,
Cards Frank has:
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Start with the lesser number.
Students write equations to represent and solve “add to,”
“take from,” “put together,” “take apart,” and “compare”
type problems. (2.OA.A.1, 2.OA.B.2)
2.
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Find 10 - 4.
•Solve Addition and Subtraction Word Problems In Lesson 1-9, students add and subtract within 20 to solve
word problems.
10
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It takes 6 moves to count on from 4 to 10.
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move
So, 10 - 4 = 6.
Draw each
as you count.
○
Pat has
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When students count on to subtract, they use the inverse
relationship between addition and subtraction. Counting
on to subtract reinforces that subtraction is an unknownaddend problem. Counting back is generally more difficult for
students, but may seem more natural in certain contexts.
PD
○
○
more cards than Frank.
Professional Development Videos Topic Overview Videos
and Listen and Look For Lesson Videos present additional
important information about the content of this cluster.
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More cards Pat has than Frank:
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1B
TOPIC
1
Major Cluster 2.OA.B
Math Background: coherence
F C FOCUS
R
F C R COHERENCE
RIGOR
Content Coherence in
look back
Students learn best when ideas are connected in a coherent
curriculum. This coherence is achieved through various types
of connections including connections within clusters, across
clusters, across domains, and across grades.
How does Topic 1 connect to what students learned earlier?
grade 1
Big Ideas in Grades K–6
16
•Addition and Subtraction Situations In Topic 1,
students solved problems involving “add to,” “put together,”
“take from,” “take apart,” and “compare” situations.
(1.OA.A)
2.
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Big Ideas are the conceptual underpinnings of
enVisionmath2.0 and provide conceptual cohesion of
the content. Big Ideas connect Essential Understandings
throughout the program.
•Add and Subtract Within 10 By the end of Grade
1, students fluently added and subtracted within 10 using
strategies such as counting on and counting back, doubles,
near doubles, adding in any order, and thinking addition to
subtract. (1.OA.B, 1.OA.C)
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A part of a Big Idea that connects much of the work in this
cluster is that each operation is related to other operations.
10 + 3 = 13
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I added 6 to 7
to make 13.
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7 + 3 = 10
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7 + 6 = 13,
so 13 - 7 = 6.
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For a complete list of Big Ideas, see pages 110–111 in the
Teacher’s Edition Program Overview.
1C Topic 1 Cluster Overview
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One way is to start with 7
and add 3 to get to 10.
7
,e
Next, add 3 more to
make 13.
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Find 13 - 7. You can use
10 to help you subtract.
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For example, students see how addition and subtraction are
related when they count on to subtract, find missing addends to
subtract, or make 10 to subtract.
+
=
•Add and Subtract Within 20 In Topics 3 and 4, students
began adding and subtracting within 20, enlisting additional
strategies such as making 10. They also worked with fact
families. (1.OA.B, 1.OA.C)
You can use
different ways to solve
subtraction facts.
You can count on or back
to solve subtraction facts.
You can make a 10 to
subtract 12 - 8.
14
10 - 3 = ?
0
1
2
You can think addition to
subtract 14 - 6.
6
3
4
5
6
10 - 3 =
7
7
8
9 10
12 - 8 =
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4
6+
?
8
14 - 6 =
= 14
8
Content Coherence in
(continued)
topic 1
look ahead
How is content connected within Topic 1?
How does Topic 1 connect to what students will learn later?
•Connect Strategies Throughout Topic 1, the strategies
students use to fluently add and subtract within 20 are
interconnected. For example, the strategy of near doubles is
related to the strategy of doubles, counting back is related to
counting on, and making 10 to subtract is related to making
10 to add. In Lesson 1-8, students add and subtract within 20
by applying the strategies in Lessons 1-1 through 1-7.
(2.OA.B.2)
LATER IN GRADE 2
You can use the doubles fact to
help find a near doubles fact.
16
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7 + 8 is 1 more than 7 + 7.
7 + 8 = 15
and 7 + 9 = 16
These are near
doubles facts.
Doubles Fact: 7 + 7 = 14
•Add and Subtract Length In Topic 13, students will add
and subtract within 100 to solve problems involving lengths.
(2.MD.B.5)
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7 + 9 is 2 more than 7 + 7.
Doubles
5+5
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4+4
•Add and Subtract Data In Topic 14, students will solve
simple “put together,” “take apart,” and “compare” problems
using data in a graph. (2.MD.D.10)
After-School Activities
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•Connect Addition and Subtraction In Lesson 1-6,
students use the relationship between addition and subtraction
to help develop fluency with subtraction. They see that every
subtraction fact has a related addition fact. The connection
between addition and subtraction is underscored in the
counting on and counting back subtraction strategies
in Lesson 1-5 and the make 10 subtraction strategies in
Lesson 1-7. (2.OA.B.2)
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Do You Understand?
Read
Write
Draw
Play
012345678910
11
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Show Me! How can thinking
about 10 help you find
14 - 8?
Activities
3+3
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You can use
a doubles fact to
help you add.
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Find 7 + 8 and find 7 + 9.
•Add and Subtract Larger Numbers In Topics 3 through
7, students will develop fluency for addition and subtraction
within 100, and solve one- and two-step word problems.
Some of the strategies students will use with larger numbers
are based on the strategies in Topic 1. For example, in
Topic 5, students will count back to subtract within 100 on
an open number line. Students will also use addition to check
subtraction, reinforcing their understanding of the additionsubtraction relationship. In Topics 11 and 12, students will
add and subtract within 1,000. (2.OA.A.1, 2.NBT.B)
Number of Students
GRADE 3
•Fluently Add and Subtract Within 1,000 In Topic 9,
students will use strategies, properties, and algorithms to
develop fluency with adding and subtracting within 1,000.
(3.NBT.A.2)
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1D
TOPIC
1
Major Cluster 2.OA.B
Math Background: rigor
F C FOCUS
R
COHERENCE
F C R RIGOR
Content Rigor in
A rigorous curriculum emphasizes conceptual understanding, procedural skill
and fluency, and applications.
procedural skill and fluency
•Make Sense of Addition and Subtraction Strategies In Topic 1, students develop deeper understanding of addition
and subtraction strategies. These strategies are linked to
relevant visual models such as number lines and ten-frames.
For example, a ten-frame is used to show two different ways
students can make 10 to find 13 - 5. Students can “subtract
back” from 13 by decomposing 5 into 3 and 2, subtracting
the 3 to make 10, and then subtracting the 2. Or they can
“add up” from 5 by adding 5 to make 10 and then adding
another 3 to make 13. (2.OA.B.2)
Fluency with adding and subtracting within 20 is an expectation
in this cluster. (2.OA.B.2)
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•Use Strategies to Add and Subtract Within 20 Throughout Topic 1, students practice various strategies and
use the relationship between addition and subtraction to learn
the addition and subtraction facts. In Lesson 1-8, students
quickly and accurately recall basic facts by drawing on these
strategies. (2.OA.B.2)
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12
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3.
7
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•Apply the Commutative Property Students change the
order of the addends to facilitate fluency with addition facts.
It is important for students to understand the Commutative
Property as it will be applied throughout students’
mathematics education. (2.OA.B.2)
•Relate Addition and Subtraction The development of
various subtraction strategies helps to strengthen students’
understanding of the inverse relationship between addition
and subtraction. As illustrated in the ten-frame example
above, students see the relationship between 13 - 5 = 8 and
5 + 8 = 13. Students learn that every addition fact has a
related subtraction fact, and they see how both an addition
equation and the related subtraction equation can represent
the same word problem. (2.OA.1.A, 2.OA.B.2)
applications
•Addition and Subtraction Situations Students write
addition and subtraction equations to represent and solve
“add to,” “put together,” “take from,” “take apart,” and
“compare” problems. Algebraic thinking is promoted when
students realize that they can subtract to find the missing
number in an addition equation such as 5 +
= 13 and
can add to find the missing number in a subtraction equation
such as
- 6 = 8. In Lesson 1-9, students are introduced
to bar diagrams that represent comparison problems.
(2.OA.A.1, 2.OA.B.2)
17 books are on a table.
8 books are on a shelf.
How many fewer books
are on the shelf than on
the table?
You can use
a bar diagram
and an equation
to model the
problem.
1E Topic 1 Cluster Overview
11
- 5
6
You added 5 + 8 = 13. So, 13 - 5 = 8.
tio
You have 8 left. So, 13 - 5 = 8.
Add or subtract. Use any strategy.
nV
Another way
Add 5 + 5 to make a 10.
Add 3 more to make 13.
10 + 3 = 13
es
One way
Subtract 13 - 3 to make a 10.
Subtract 2 more to subtract 5 in all.
10 - 2 = 8
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Another Look! You can make a 10 to help you subtract. Find 13 - 5.
The shelf has fewer books.
You can write an addition or
subtraction equation for the problem.
books on table
17
17 - 8 =
8+
8
books on
shelf
9
9
?
fewer books
on shelf
17
= 17
8
So, there are 9 fewer
books on the shelf.
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9
Major Cluster 2.OA.B
PearsonRealize.com
Math Practices
MP
Connecting Math Practices and Content Standards in
Math practices and content standards are connected within all lessons including
the lessons that focus on math practices.
LESSON THAT FOCUSES on math practices
•MP.1 Make sense of problems and persevere in solving them.
•Lesson 1-10 This lesson focuses on MP.3. Students solve
addition and subtraction problems and use mathematical
arguments including pictures, words, and numbers to explain
their solutions. Explicit modeling by the teacher using pictures
and numbers, and talking out loud about reasoning help
students develop this mathematical practice.
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math practices within lessons
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Students persevere as they try to understand problems involving
addition and subtraction. Students must plan how to solve them,
determine if there is extraneous information, and consider
whether their solution makes sense. (e.g., p. 20, Item 16)
•MP.2 Reason abstractly and quantitatively.
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Students reason quantitatively when they determine whether
a change in the order of the addends in an addition fact will
change the sum of that addition fact. Students are asked to
explain their thinking. (e.g., p. 5, Solve and Share)
How can I use math
to explain my work?
Is my explanation
clear?
,e
•MP.3 Construct viable arguments and critique the reasoning
of others.
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Students solve addition and subtraction problems and make
arguments to justify solutions using words, pictures, and
numbers. (e.g., p. 59, Solve and Share)
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•MP.4 Model with mathematics.
•Math Practices and Problem Solving Handbookbefore
Topic 1; includes Math Practices Proficiency Rubrics.
•Math Practices Postersto display in your classroom
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Students model with math when they apply what they have
previously learned about addition and subtraction to solve
problems using expressions, equations, number lines, and
other pictures. (e.g., p. 50, Item 35)
Revisit the information about MP.3 in these other resources:
MP
Pr
•MP.5 Use appropriate tools strategically.
Math Practices Animations, one for each math practice,
available at PearsonRealize.com.
Students use tools such as counters and ten-frames to
represent addition and subtraction problems. (e.g., p. 44,
Items 16 and 17)
•MP.6 Attend to precision.
Students attend to precision when they show that they have
fully accounted for all possible solutions to a problem. (e.g.,
p. 58, Item 3)
•MP.7 Look for and make use of structure.
Students look for and use patterns associated with addition facts.
(e.g., p. 36, Show Me!)
•MP.8 Look for and express regularity in repeated reasoning.
Students use repeated reasoning when they generalize about
how to subtract by using a related addition fact. (e.g., p. 40,
Item 5)
FOR REVIEW ONLY - PAGES NOT FINAL
1F
TOPIC
1
major cluster 2.OA.B
PearsonRealize.com
differentiated instruction
I
O On-Level
Intervention
Ongoing Intervention
A Advanced
Learn Assessment
Strategic Intervention
Tools
Games
Intensive Intervention
During the core lesson,
monitor progress, reteach as
needed, and extend students’
thinking.
1
At the end of the lesson,
assess to identify students’
strengths and needs and then
provide appropriate support.
As needed, provide more
instruction that is on or below
grade level for students who are
struggling.
Guiding Questions
•In the Teacher’s Edition Guiding
questions are used to monitor
understanding during instruction.
Quick Check
In the Student’s Edition Assess the
lesson using 3 items checked in the
Teacher’s Edition.
Math Diagnosis and
Intervention System 2.0
•Diagnosis Use the diagnostic tests in the
system. Also, use the item analysis charts
given with program assessments at the
start of a grade or topic, or at the end
of a topic, group of topics, or the year.
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Assessment
Intervention Activity I
Teachers work with struggling students.
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Prevent Misconceptions
This feature in the Teacher’s Edition is
embedded in the guiding questions.
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Reteach to Build Understanding I
This is a page of guided reteaching.
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Error Intervention: If... then...
This feature in the Teacher’s Edition
is provided during Guided Practice.
It spotlights common errors and gives
suggestions for addressing them.
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•Intervention Lessons These two-page
lessons include guided instruction
followed by practice. The system
includes lessons below, on, and above
grade level.
•Teacher Support Teacher Notes
provide the support needed to conduct
a short lesson. The lesson focuses on
vocabulary, concept development, and
practice. The Teacher’s Guide contains
individual and class record forms and
correlations to Student’s Edition lessons.
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Technology Center I O A
Digital Math Tools Activities
reinforce the lesson content or
Tools
previously taught content using a
suite of digital math tools.
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Reteaching
Reteaching sets are at the end of the topic
in the Student’s Edition. They provide
additional examples, reminders, and
practice. Use these sets as needed before
students do the Independent Practice.
Higher Order Thinking
These problems require students to think
more deeply about the rich, conceptual
knowledge developed in the lesson.
Online Quick Check You can also
assess the lesson using 5 online,
machine-scored, multiple-choice
items.
2.
0
Online Guiding Questions Guiding questions are also in
the online Visual Learning
Animation Plus.
3
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m
Learn
2
Games
Online Games provide practice on
the lesson content or previously
taught content.
Homework and Practice I O A
Use the leveled assignment to provide
differentiated homework and practice.
Additional resources to support differentiated
instruction for on-level and advanced students
include:
On-Level and Advanced
Activity Centers O A
•Center Games are provided in on-level
and advanced versions.
•Math and Science Activity is related to
the topic science theme introduced at
the start of the topic.
Resources for Fluency Success
•A variety of print and digital resources
are provided to ensure success on
Common Core fluency standards.
See Steps to Fluency Success on
pages 1M–1P and 321E–321H.
•Problem-Solving Reading Mat is used
with a lesson-specific activity.
1G Topic 1 Cluster Overview
FOR REVIEW ONLY - PAGES NOT FINAL
major cluster 2.OA.B
PearsonRealize.com
the language of math
Glossary Games
English Language Learners
Math Vocabulary
Story
Story
Math and Reading
Build math vocabulary using the
vocabulary cards, vocabulary activities,
vocabulary review, and glossary plus the
online glossary and vocabulary game.
Connect reading and math using a
data-filled reading mat for the topic with
accompanying activity masters and guide.
Also use topic interactive math stories.
Visual Learning
The visual learning that is infused in
enVisionmath2.0 provides support for
English language learners. This support
includes a Visual Learning Animation Plus
and a Visual Learning Bridge for each
lesson.
My Word Cards
Vocabulary cards for a topic are provided
in the Student’s Edition. Students study the
word on the front of the card to complete
a sentence with the word on the back.
Problem-Solving Reading Mats
There is a large, beautiful mat for each
topic. At the start of the topic, help
students become familiar with the mat and
the vocabulary used by reading the mat
aloud as students follow along. Use the
Problem-Solving Reading Activity Guide
for suggestions about how to use the mat.
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Addition facts that have two
addends that are the same
are called
.
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English Language Learners Toolkit
This resource provides professional
development and resources for supporting
English language learners.
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Vocabulary Activities
The Teacher’s Edition provides vocabulary
activities at the start of topics. These
include activities for vocabulary in
My Word Cards and/or activities for
vocabulary in Review What You Know.
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doubles
English Language
Learners Instruction
Lessons provide instruction for English
language learners at Beginning,
Intermediate, and Advanced levels of
English proficiency.
16
Provide ELL support through visual
learning throughout the program, ELL
instruction in every lesson, and additional
ideas in an ELL Toolkit.
Vocabulary Review
A page of vocabulary review is provided
at the end of each topic. It reviews
vocabulary used in the topic.
Glossary
A glossary is provided at the back of the
Student’s Edition.
Problem-Solving Reading Activity
At the end of some lessons, a ProblemSolving Reading Activity provides a page
of math problems to solve by using the
data on the mat.
Interactive Math Stories
An interactive math story provides
an introduction to each topic. The
Story
story is available as an online story
book and an animated story at
Story
PearsonRealize.com as well as a
color-in, take-home story in the
Teacher’s Resource Masters.
Animated Glossary
An online, bilingual, animated
glossary uses motion and sound
Glossary
to build understanding of math
vocabulary.
Online Vocabulary Game
An online vocabulary game is
available in the Game Center.
Games
FOR REVIEW ONLY - PAGES NOT FINAL
1H
FLUENTLY ADD AND SUBTRACT WITHIN 20
Lesson 1-1
Lesson 1-2
Lesson 1-3
MAKE 10 TO ADD pp. 17–22
DOUBLES AND NEAR DOUBLES
pp. 11–16
ADDITION FACT STRATEGIES pp. 5–10
Content Standard 2.OA.B.2
Mathematical Practices MP.4, MP.6,
MP.7. MP.8
Content Standard 2.OA.B.2
Mathematical Practices MP.2, MP.4,
MP.7, MP.8
Objective Use doubles and near doubles
to add quickly and accurately.
Essential Understanding Counting on
is a strategy that can be used to find sums.
The order of the addends does not change
the sum. Essential Understanding Basic
addition facts that are near doubles can
be found using a related doubles fact.
Vocabulary Equation, Addends, Sum
Vocabulary Doubles, Near doubles
ELL Listening: Learn academic vocabulary.
ELL Speaking: Speak using content area
vocabulary in context.
Materials Connecting cubes (or Teaching
Tool 5)
Materials Connecting cubes (or Teaching
Tool 5)
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Lesson Resources
Digital
Essential Understanding Some
addition facts can be found by changing
to an equivalent fact with 10.
On-Level and Advanced
Activity Centers
•Math and Science Activity
Vocabulary None
ELL Speaking: Use abstract and contentbased vocabulary during speaking
assignments.
Materials Counters (or Teaching Tool 6),
Double Ten-Frame Mat (Teaching Tool 8)
On-Level and Advanced
Activity Centers
•Math and Science Activity
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On-Level and Advanced
Activity Centers
•Problem Solving Reading Mat
Objective Use the strategy of making ten
to add quickly and accurately.
2.
0
Objective Use counting on to add
numbers and add numbers in any order.
Content Standard 2.OA.B.2
Mathematical Practices MP.1, MP.2,
MP.3, MP.5, MP.7
16
1
Topic Planner
©
20
TOPIC
•Student’s Edition
•Daily Common Core Review
•Reteach to Build Understanding
•Center Games
•Math and Science Activity
•Problem-Solving Reading Mat
•Problem-Solving Reading Activity
Digital
•Listen and Look For PD Lesson Video
•Student’s Edition eText
•Today’s Challenge
•Solve & Share
•Visual Learning Animation Plus
•Animated Glossary
•Math Tools
•Quick Check
•Another Look Homework Video
•Math Games
Print
1I Topic 1
FOR REVIEW ONLY - PAGES NOT FINAL
PearsonRealize.com
Digital
Lesson 1-4
Lesson 1-5
ADDITION FACT PATTERNS pp. 23–28
Lesson 1-6
COUNT ON AND COUNT BACK TO
SUBTRACT pp. 29–34
Content Standard 2.OA.B.2
Mathematical Practices MP.1, MP.2,
MP.4, MP.5
Content Standard 2.OA.B.2
Mathematical Practices MP.2, MP.7,
MP.8
16
Content Standard 2.OA.B.2
Mathematical Practices MP.2, MP.5,
MP.6, MP.7, MP.8
THINK ADDITION TO SUBTRACT
pp. 35–40
Objective Count on and count back on a
number line to subtract.
Objective Think addition to subtract
quickly and accurately.
Essential Understanding Patterns in
a 0–10 addition facts table are useful
for adding numbers and for developing
mental math strategies and number sense.
Essential Understanding A number
line is a tool you can use to help you count
on or count back to subtract.
Vocabulary None
Vocabulary Difference
ELL Listening: Use visual support to
confirm understanding.
ELL Reading: Use visual support to
enhance/confirm understanding.
Materials Addition Tables (Teaching
Tool 11)
Materials Number Lines (Teaching Tool 12), Centimeter Cubes (or Teaching Tool 60).
Materials Counters (or Teaching Tool 6)
On-Level and Advanced
Activity Centers
•Center Games
On-Level and Advanced
Activity Centers
•Center Games
Essential Understanding Addition and
subtraction have an inverse relationship.
The inverse relationship between addition
and subtraction can be used to find
subtraction facts; every subtraction fact
has a related addition fact.
Vocabulary None
ELL Speaking: Speak using content area
vocabulary in context.
TOPIC Resources
Digital
tio
ic
a
bl
ep
u
Pr
On-Level and Advanced
Activity Centers
•Center Games
n
pa
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es
,e
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is
i
on
m
at
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2.
0
©
20
Objective Use number patterns on an
addition facts table to complete related
addition equations that show basic facts.
Start of Topic
•Interactive Math Story
•Math and Science Project
•Home-School Connection
•Review What You Know
•My Word Cards
End of Topic
•Fluency Practice Activity
•Vocabulary Review
•Reteaching
•Topic Assessment
•Topic Performance Assessment
Start of Topic
•Topic Overview PD Video
Digital
End of Topic
•Math Practices Animations
•Online Topic Assessment
•ExamView® Test Generator
Print
FOR REVIEW ONLY - PAGES NOT FINAL
1J
PearsonRealize.com
TOPIC
1
Topic Planner
FLUENTLY ADD AND SUBTRACT WITHIN 20
Lesson 1-7
Lesson 1-8
Lesson 1-9
PRACTICE ADDITION AND SUBTRACTION
FACTS pp. 47–52
MAKE 10 TO SUBTRACT
pp. 41–46
SOLVE ADDITION AND SUBTRACTION
WORD PROBLEMS pp. 53–58
Content Standard 2.OA.B.2
Mathematical Practices MP.2, MP.3,
MP.4, MP.8
Content Standards 2.OA.A.1,
2.OA.B.2
Mathematical Practices MP.1, MP.2,
MP.6
©
20
16
Content Standard 2.OA.B.2
Mathematical Practices MP.3, MP.4,
MP.5, MP.7, MP.8
Objective Use addition and subtraction
to solve word problems.
Objective Add and subtract quickly and
accurately using mental math strategies.
Essential Understanding Some
subtraction facts can be simplified by
making use of the numbers’ relationships
to 10.
Essential Understanding The addends
determine efficient strategies, such as
making 10 or using doubles facts, for
finding addition facts. “Think of a related
addition fact” is an efficient strategy for
finding a subtraction fact.
Vocabulary None
Vocabulary None
ELL Reading: Use visual support to
develop vocabulary.
ELL Speaking: Speak using content area
vocabulary in context.
ELL Listening: Demonstrate listening
comprehension by retelling.
Materials Counters (or Teaching Tool 6)
Materials Counters (or Teaching Tool 6)
Materials Counters (or Teaching Tool 6)
Essential Understanding Objects,
diagrams, and equations can help you
solve different types of word problems.
Vocabulary None
tio
n
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es
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is
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on
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at
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2.
0
Objective Make 10 to subtract quickly
and accurately.
On-Level and Advanced
Activity Centers
•Center Games
On-Level and Advanced
Activity Centers
•Problem Solving Reading Mat
Pr
ep
u
bl
ic
a
On-Level and Advanced
Activity Centers
•Center Games
Notes
1K Topic 1
FOR REVIEW ONLY - PAGES NOT FINAL
PearsonRealize.com
Digital
Lesson 1-10
MATH PRACTICES AND PROBLEM
SOLVING: CONSTRUCT ARGUMENTS
pp. 59–64
©
20
16
Mathematical Practices MP.3, MP.1,
MP.2, MP.4
Content Standards 2.OA.A.1,
2.OA.B.2
at
h
2.
0
Objective Use words, pictures, numbers,
and symbols to construct viable math
arguments.
is
i
on
m
Essential Understanding Good math
thinkers use math to explain why they are
right. They can talk about the math that
others do, too.
,e
nV
Vocabulary None
es
ELL Speaking: Express ideas.
n
pa
g
Materials Counters (or Teaching Tool 6),
Double Ten-Frame Mat (Teaching Tool 8)
Pr
ep
u
bl
ic
a
tio
On-Level and Advanced
Activity Centers
•Center Games
FOR REVIEW ONLY - PAGES NOT FINAL
1L
1
INTERACTIVE MATH STORY
PearsonRealize.com
ADDITION STRATEGIES
Story
Before the Story
DURING THE STORY
Picture Walk
Project the online PDF that
contains a full-color version of
this story. Read the title, author’s
name, and illustrator’s name to
the students. This story is about
a Math Machine. Let’s see what
this machine does. As you page
through the story, have students
name the objects pictured in the
machine. [Cubes, balls, flowers,
shoes] Point out the order of the
groups in the top picture and
the order of the groups in the
lower picture.
This book belongs to:
TOPIC
Tom
1
Story
2.
0
©
20
16
Written by Emily James
Illustrated by
Luciana Navarro-Powell
at
h
Story
Story
on
m
Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 2
Activate Prior Knowledge
The Math Machine switches the
order of two groups. Let’s try
10 balls go into the machine.
8 cubes go into the machine.
11doing
shoes
into the machine.
thisgoourselves.
On a large
index
card,
draw
2
orange
The machine turns them around, but
The machine turns them around, but
The machine turns them around, but
stars. On another index card,
the number of balls stays the same.
the number of cubes stays the same.
the number of shoes stays the same.
draw 4 green stars. Have
5
6
9 + 1 = 10
3
5
+
=
11
+
=
8
students count the stars on each
6 +and5 the= total
11 number of
1 + 9 = 10
5 + 3 = 8
card
stars. SwitchTopic
the
order
of
the
1
Topic 1
Topic 1
4
41
42
cards. Did the number of stars
on either of the cards change?
[No] Did the total number
READ
GESTURE
COLOR
of stars change? [No] Help
Read the story aloud for
Reread the big book.
Distribute Interactive
students count to confirm
enjoyment. On the first
On the first page, have
Math Story books to
their answers.
page, have students help
students point to the
students. Students should
you count the cubes in the
groups in the top picture,
color the groups in the
Repeat the activity with
top picture. How many
using a left finger to point
top picture on the page.
equations from a different fact
striped cubes do you see?
to the left group and a
Then they should color the
family.
[3] How many other cubes? right finger to point to the
lower picture to match.
Play the animated version of
[5] How did the machine
right. Then have students
Remember, each group is
Story the story.
shown in the top picture
change the cubes? [The
slide their fingers to the
and in the lower picture.
order changed; the striped
corresponding groups in
Use the same color each
cubes are on the right,
the lower picture. What
time you color the group.
not on the left.] Is the
happened to the groups?
[The groups are the same,
Does the number in the
total number of cubes the
group change when the
same either way? Explain.
but their order changed.]
position of the group
[Yes; each time the number
Repeat with the objects on
the remaining pages.
changes? [No]
is the same.] Repeat with
the remaining pages.
is
i
The mach
nV
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es
fold down
/147/PE01513_ENG_TRM/MATH/NA/TRM/2013/G2/XXXXXXXXXX/Layout/Interior_Files/Topic_0 ...
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1Q Topic 1
12 flower
FOR REVIEW ONLY - PAGES NOT FINAL
the numb
fold down
TOPIC
8
4
+
+
4
8
The Math Machine
This is a story in which students gain an understanding that the
order in which two numbers are added does not affect the sum.
After the Story
Extension
ThisUse
book
a belongs
shoeboxto:
as a classTOPIC
Math Machine. Let a volun­
Tom
1teerStory
= 12
= 12
Topic 1
at
h
on
m
the number of cubes stays the same.
is
i
the number of shoes stays the same.
5
6
+
6
5
43
/147/PE01513_ENG_TRM/MATH/NA/TRM/2013/G2/XXXXXXXXXX/Layout/Interior_Files/Topic_0 ...
+
=
11
Topic 1
3
5
+
+
5
3
4
MTH16_ANC02_CC2_T01_IMS.indd Page 2 16/09/14 6:11 PM S-015
=8
=
8
Topic 1
41
/147/PE01513_ENG_TRM/MATH/NA/TRM/2013/G2/XXXXXXXXXX/Layout/Interior_Files/Topic_0 ...
ep
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SPEAK
Invite students to retell
the story in their own
words. Assign each page
to a different student.
As students retell the
story, encourage them to
describe and count the
objects. What color are
your cubes? [Answers
will vary.] How did the
machine change the order?
[It turned the addends
around.] Did the total
number of cubes change?
[No]
Pr
WRITE
Guide students through
the first addition sentence
on the first page. Look
at the top picture. How
many cubes are in the first
group? [3] Write 3 on the
first line. How many cubes
are in the second group?
[5] Write 5 after the plus
sign. How many cubes in
all? [8] Help students use
data from the lower picture
to complete the second
addition sentence. Repeat
with the remaining pages.
= 11
fold down
+
4
8
pa
g
+
The machine turns them around, but
n
8
4
The machine turns them around, but
nV
the number of flowers stays the same.
8 cubes go into the machine.
,e
e same.
You may wish to have students
take home their Interactive Math
Story books and share what they
have learned about the order of
addends with a family member.
11 shoes go into the machine.
es
The machine turns them around, but
fold down
nd, but
Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 2
12 flowers go into the machine.
Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 2
2.
0
©
20
16
show two number cards,
say
Written by Emily James
Illustrated by
the addition sentence, and
put
Luciana Navarro-Powell
the cards in the machine. Let
a different volunteer take the
number cards out of the machine
in the opposite order and say
that addition sentence. Write
the two addition sentences on
the board.
FOR REVIEW ONLY - PAGES NOT FINAL
1R
TOPIC
1
TOPIC OPENER
FLUENTLY ADD AND SUBTRACT WITHIN 20
TOPIC ESSENTIAL QUESTION
What are strategies for finding addition and
subtraction facts?
Revisit the Topic Essential Question throughout the
topic, and see a note about answering the question
in the Teacher’s Edition for the Topic Assessment.
1
Different
papers have different
properties.
at
h
on
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is
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•Choose a type of paper to make flash cards of
,e
one
1
/132/PE01513_SE/ENVISION_MATH_ENGLISH/NA/SE/2013/G2/XXXXXXXXXX/Layout/Interior_Fi ...
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MTH16_SE02_CC2_T01_TO.indd Page 1 5/30/14 10:51 PM s-w-56
Home-School Connection
n
ic
a
bl
Sample Student Work for Math and Science Project
ep
u
•Glue samples of paper and tell what
you found.
es
Topic 1
tio
EXTENSION
Have students draw a picture to show a math story
problem about one of the addition or subtraction
facts from their flashcards.
Journal: Make a Book Show what you
find out in a book. In your book, also:
Directions Read the character speech bubbles to students. Find Out! Have students find out about wild animals. Say: Talk to friends and relatives
about animals in the wild. Ask which animals can be seen in groups. Make
a Poster Then
students makefacts.
a poster. Have them choose one wild
addition
andhave
subtraction
animal that they learned about. Ask them to draw a group with 6-10 of the animal they chose and write a number to tell how many animals.
Project-Based Learning Have students work
on the Math and Science Project over the course of
several days.
Pr
Games
16
Ask students to think about different uses of paper
in their daily lives. Have them describe how they
use paper.
Find Out Collect different types of
paper. Talk about the uses of paper.
Tell how strong each type of paper
is. Tell how the paper feels. Tell if
the paper
can soak
up water.
Math
and Science
Project:
Wild Animals
Home-School
Connection
Name
Topic
Fluently Add and Subtract
Within 20
1
Topic 1 Standards
2.OA.A.1, 2.OA.B.2
See the front of the Student’s Edition for complete standards.
Send this page home at the start
of Topic 1 to give families an
overview of the content in the
topic.
Dear Family,
Your child is learning about addition and subtraction within 20. In this topic, he or she
will learn several strategies for finding sums and differences. Some of the strategies
include counting on, counting back, making ten, using doubles and near doubles, and
using the relationship between addition and subtraction. The model below can be used to
represent related addition and subtraction equations. It shows addition when both parts
(counters) are given and the total is unknown. It shows subtraction when the total and
one of the parts are given and the other part is unknown.
13
This bar diagram shows these equations:
4 + 9 = 13
13 - 9 = 4
9 + 4 = 13
13 - 4 = 9
Writing Addition and Subtraction Equations
Materials 15 small objects, paper, pencil
Separate 12 objects, such as paper clips or buttons, into two groups. Have your child write
two addition equations and two subtraction equations to model the objects. Then allow your
child to separate the objects into two different groups. Write two addition equations and
two subtraction equations to model the objects. Have your child help you decide if they are
correct. Repeat the activity with 6 and 9 objects.
Observe Your Child
Focus on Mathematical Practice 5
Use appropriate tools strategically.
Help your child become proficient with Mathematical Practice 5. After you and your child
decide if the equations are correct, ask him or her to explain how the objects represent the
numbers in the equations.
Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 2
MTH16_ANC02_CC2_T01_HSC.indd Page 13 09/10/14 5:10 AM S-015
1 Topic 1
Tools Assessment Help
©
20
Math and Science Project: Material Math
4 paper ships are left on the pond.
Glossary
2.
0
Discuss with students the different observable
properties of paper, such as color, texture,
hardness, flexibility, and absorbancy.
7–3=4
Learn
Wow!
Let’s do this project
and learn more.
Science Theme The science theme for this project is
Properties of Materials. This theme will be revisited in
the Math and Science Activities in Lessons 1-2 and 1-3.
Mark puts 7 paper ships on a pond. Then
he takes 3 of the ships out of the pond. How
many paper ships are left on the pond?
Solve
Essential Question: What are strategies for finding addition
and subtraction facts?
Look at the different
types of paper!
MATH AND SCIENCE PROJECT STEM
Digital Resources
Fluently Add and Subtract
Within 20
TOPIC
/147/PE01513_ENG_TRM/MATH/NA/TRM/2013/G2/XXXXXXXXXX/Layout/Interior_Files/Topic_0 ...
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Item Analysis for Diagnosis
and Intervention
Name
Vocabulary
1. Circle the symbol for
equals.
2. Circle the symbol for
minus.
-
-
+
+
=
=
3. Circle the number that
is the whole.
4+2= 6
Items
Standards
MDIS
1–3
2.OA.B.2
B1
4
2.OA.A.1, 2.OA.B.2
B8
5
2.OA.A.1, 2.OA.B.2
B4
Addition Stories
5. Write an equation to solve
the problem.
two
+
2 =
8
6
+
2.
0
at
h
is
i
4
B17
on
m
Kate draws 4 big stars.
Then she draws 2 small
stars. How many stars
does Kate draw in all?
5 birds
2
© Pearson Education, Inc. 2
= 10
Topic 1
es
2
6. Write the numbers
that showawayto
make 10.
2.OA.B.2
nV
4. There are 7 birds on a
fence. 2 fly away.
How many birds are left?
Making 10
,e
Subtraction Stories
©
20
6
16
A-Z
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MTH16_SE02_CC2_T01_TO.indd Page 2 4/22/14 4:03 AM s-w-56
n
Topic 1 Vocabulary Words Activity
2+5=7
ep
u
addend
Study the words on the front of the card.
Complete the activity on the back.
sum
Pr
My Word Cards
bl
ic
a
tio
Use the Topic 1 activity on page 66 with the Topic 1 words below.
3+4=7
addends
sum
doubles
4+4=8
near doubles
4+5=9
✂
difference
Topic 1
My Word Cards
MTH16_SE02_CC2_T01_MWC.indd Page 3 4/22/14 4:33 AM s-w-56
The answer in a subtraction
equation is called the
14 - 6 = 8
difference
14
-6
8
three
3
/132/PE01513_SE/ENVISION_MATH_ENGLISH/NA/SE/2013/G2/XXXXXXXXXX/Layout/Interior_Fi ...
4
four
Use what you know to complete the sentences.
Extend learning by writing your own sentence using each word.
The answer in an addition
equation is called the
uses an equal sign ( = ) to
show that the value on the
left is the same as the value
on the right.
14 - 6 = 8
difference
✂
An equation
equation
3+4=7
4
+3
7
My Word Cards
Glossary
.
sum
Numbers that are added
are called
.
addends
.
Addition facts that have
two addends that are close
are called
Addition facts that have two
addends that are the same
are called
near doubles
doubles
© Pearson Education, Inc. 2
MTH16_SE02_CC2_T01_MWC.indd Page 4 4/22/14 4:33 AM s-w-56
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.
Topic 1
.
My Word Cards
/132/PE01513_SE/ENVISION_MATH_ENGLISH/NA/SE/2013/G2/XXXXXXXXXX/Layout/Interior_Fi ...
2–4
LESSON 1-1
ADDITION FACT STRATEGIES
DIGITAL RESOURCES PearsonRealize.com
Animated
Glossary
Solve
Think
Math Tools
Glossary
Tools
Another Look
Homework
Video
LESSON OVERVIEW
F C R FOCUS • COHERENCE • RIGOR
Help
Assessment
Math Games
Games
MATH ANYTIME
Daily Common Core Review
COHERENCE
1.G.A.1
1. Which number is the sum?
2. Which of these 3-D shapes
have at least one vertex?
Choose all that apply.
at
h
on
m
is
i
𝖠𝖠 10
𝖢𝖢 8
𝖡𝖡 9
𝖣𝖣 7
1.OA.A.1
1.OA.A.1
3. Draw a picture to solve
the problem. Then write
an addition equation.
4. Complete the bar diagram
to solve the problem. Then
write a subtraction equation.
,e
nV
Eve has 7 cards. Otis has
the same number of cards.
How many cards do Eve
and Otis have in all?
7
7
3
n
7 + 7 = 14
14 cards
tio
bl
ep
u
Pr
There are 7 cars parked at
the fair. Then 4 cars drive
away. How many cars are
still parked at the fair?
In 3 and 4, check
students’ drawings.
pa
g
This lesson emphasizes conceptual
understanding and fluency. As students
change the order of the addends, they deepen
their sense of number and operation. This
knowledge will be helpful later when students
add more than two 2-digit numbers. When
adding digits, students learn to find sums of
digits that are compatible.
Watch the Listen and Look For Lesson
PD Video.
1-1
1.OA.C.6
3+5=
es
RIGOR
Daily Common
Core Review
Name
2.
0
This lesson focuses on counting on to add
and adding numbers in any order. Students
have learned how to use counting on to find
sums in Grade 1. Using the Commutative
Property of Addition, students discover that
since 9 + 3 = 12 and 3 + 9 = 12, then
9 + 3 = 3 + 9. That understanding helps
students as they learn basic addition facts.
Students also discover that it is easier to
count on 3 from 9 than it is to count on 9
from 3. That realization makes addition
problems easier.
ic
a
Domain 2.OA Operations and Algebraic
Thinking
Cluster 2.OA.B Add and subtract within 20.
Content Standard 2.OA.B.2 Fluently add
and subtract within 20 using mental strategies.
By end of Grade 2, know from memory all
sums of two one-digit numbers.
Mathematical Practices MP.2, MP.4, MP.7,
MP.8
Objective Use counting on to add numbers
and add numbers in any order.
Essential Understanding Counting on
is a strategy that can be used to find sums.
The order of the addends does not change
the sum.
Vocabulary Equation, Addends, Sum
Materials Connecting cubes (or Teaching
Tool 5)
Learn
Quick Check
FOCUS
Visual Learning
Animation Plus
Solve and
Share
16
PD
eText
Today’s
Challenge
©
20
Listen and
Look For
Lesson Video
Student and
Teacher eTexts
D 1•1
MTH16_ANC02_CC2_T01_L01_DR.indd Page 11 10/10/14 3:01 AM S-015
Think
-
4
=
3
cars
Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 2
/147/PE01513_ENG_TRM/MATH/NA/TRM/2013/G2/XXXXXXXXXX/Layout/Interior_Files/Topic_0 ...
Today’s Challenge
Use Topic 1 problems any time
during this topic.
ENGLISH LANGUAGE LEARNERS
Listening Learn academic vocabulary.
Use before the Solve and Share on Student’s
Edition, p. 5.
Say the word equation and have students
repeat it. Remind students that, in grammar,
a sentence is made by joining certain types
of words together. Give some examples of
simple sentences. Write 3 + 6 = 9 on the
board and tell students this is one type of
math sentence called an equation. Parts of an
equation include numbers and symbols.
5A Topic 1
Ask a volunteer to describe how to make an
equation. Lead the volunteer to use the words
numbers and symbols.
Beginning Have students work in groups
to create equations using the frame:
____ + ____ = ____. Students should take
turns identifying the numbers and the symbols
in each equation.
Intermediate Have students work in pairs
to write the definition for addition equation
and give two examples. Ask one student in
each pair to read the definition aloud and
the other student to read the examples.
Advanced Each student should define
addition equation, give two examples, and
then read his or her definitions and examples
to a partner. After listening to the partner’s
definition, each student should revise his or
her own.
Summarize What are the parts of an
addition equation?
FOR REVIEW ONLY - PAGES NOT FINAL
STEP
1
DEVELOP: PROBLEM-BASED LEARNING
PearsonRealize.com
COHERENCE: Engage students by connecting prior knowledge to new ideas.
Students show 4 + 5 with cubes and they explain what happens to the total number of cubes if the
order of the addends is changed. This prepares them for the next part of the lesson where they learn
to count on and change the order of the addends in basic addition facts.
10–15 min
Whole
Class
BEFORE
Name
1. Pose the Solve-and-Share Problem
Provide each student with 20 connecting cubes
(10 of one color and 10 of another color).
MP.2 Reasoning In this problem, students use
cubes to determine whether a change in the order
of the addends in an addition fact will change the
sum of that addition fact.
Lesson 1-1
Addition Fact
Strategies
What will happen to the total number of cubes if you
change the order of the numbers being added? Explain.
I can …
count on to add and add in
any order.
Content Standard 2.OA.B.2
Mathematical Practices MP.2,
MP.4, MP.7, MP.8
16
at
h
2.
0
©
20
See margin for sample student work.
is
i
on
m
DURING
4+5=
,e
nV
+
Topic 1
Lesson 1
=
five
Digital Resources at PearsonRealize.com
5
es
3. Ask Guiding Questions As Needed
How can you use connecting cubes to help you
model and solve the problem? [Sample answer:
You can make a cube train that shows both of the
parts.] Can you write another addition fact with
4, 5, and 9? [Yes; 5 + 4 = 9]
pa
g
AFTER
MTH16_SE02_CC2_T01_L01_VLB.indd Page 5 4/18/14 11:37 PM s-w-56
Analyze Student Work
Yuki’s Work
Frederick’s Work
ep
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ic
a
tio
n
4. Share and Discuss Solutions
Start with students’ solutions. Have them share
Solve the strategies used to solve the problem. If
needed, project and analyze Yuki’s work to model
4 + 5 and to discuss the outcome of changing the
order of addends in addition facts.
/132/PE01513_SE/ENVISION_MATH_ENGLISH/NA/SE/2013/G2/XXXXXXXXXX/Layout/Interior_Fi ...
5. Transition to the Visual Learning Bridge
The addition facts 4 + 5 = 9 and 5 + 4 = 9 have
the same parts and whole.
Changing the order of the parts added does not
change the whole.
Pr
Whole
Class
Solve
Use cubes to show 4 + 5.
2. Build Understanding
What are you asked to do? [Use cubes to show
4 + 5. Then explain what happens to the total
number of cubes if the order of the numbers being
added is changed.] What tools do you have to
solve this problem? [Connecting cubes]
Small
Group
Solve
6. Extension for Early Finishers
Have students generate two more equations to
show they can add in any order. What addition
fact can you write if you change the order of the
numbers being added in 4 + 4 = 8? [It is the
same. 4 + 4 = 8]
4+5=
+
=
Yuki correctly models 4 + 5 with cubes.
Yuki also shows 5 + 4 with cubes, and
she writes a related addition equation.
Yuki explains that the order of the
addends does not affect the total number
of cubes by saying the total number of
cubes is 9 in both trains.
4+5=
+
=
Frederick models the parts and the
whole and understands the problem, but
he does not write the related addition
equations. Frederick explains the effect
on the sum by saying changing the order
of the numbers does not change the total
number of cubes.
FOR REVIEW ONLY - PAGES NOT FINAL
5
STEP
2
DEVELOP: VISUAL LEARNING
PearsonRealize.com
The Visual Learning Bridge connects students’ thinking in Solve &
Share to important math ideas in the lesson. Use the Visual Learning
Bridge to make these ideas explicit. Also available as a Visual
Learning Animation Plus at PearsonRealize.com
MP.8 Generalize How
are these two addition
equations alike? [They both
use the same numbers, 3,
6, and 9. They both have
the same sum, 9.] How are
they different? [The order of
the addends is different.]
How is 6 + 3 the same as or
equal to 9? [When you add
6 + 3, its value is 9; and 9
is equal to 9.] Does 3 + 6
also have the same value as
9? [Yes.]
Learn
Glossary
How do you know that
3 + 6 = 6 + 3? [3 + 6 = 9 and
6 + 3 = 9, so 3 + 6 = 6 + 3]
Make sure students understand
that they can write the facts
horizontally or vertically, as
shown.
Glossary
7
8
9
Or count on to find 3 + 6.
3
4
5 6
7 8
6
6+3=9
3
=
2.
0
9
So, 6 + 3 = 3 + 6.
The sum is
the same.
3
9
3+6=9
+
6
=
9
You can write the
facts this way, too.
6
+3
9
is
i
Counting on
from the greater
number is easier!
+
You can add numbers in
any order, and the sum is
the same.
at
h
6
You can change the order
of the addends.
An equation uses an equal
sign ( = ) to show that the
value on the left is the same
as the value on the right.
,e
nV
addend addend sum
3
+6
9
Visual Learning Bridge
You can count on to
find 6 + 3.
on
m
Learn
©
20
16
Is counting on 3 cubes from
6 easier or harder than
just counting all the cubes?
[Easier] Why is it easier to
count on from the greater
number, 6, than to count on
from the lesser number, 3?
[If you count from the greater
number, you don not have to
count on as many.]
Visual Learning
Count on to find the sum. Then change
the order of the addends.
Show Me! Does
5 + 2 = 2 + 5?
How do you know?
pa
g
es
Do You Understand?
1.
3+1=
4
□
7
ic
a
1
+
3
=
□
□
□
3
+
4
7
4
Pr
ep
u
bl
4
+3
tio
n
Yes; Sample answer:
5 + 2 = 7 and
2 + 5 = 7, so the sum
is the same. You can
add in any order. So,
2 + 5 = 5 + 2.
2.
6
six
Do You Understand? Show Me! MP.2 Reasoning Have
MTH16_SE02_CC2_T01_L01_VLB.indd Page 6 5/30/14 11:01 PM s-w-56
students use reasoning to explain how they know the sum of each
side of the equation is equal to 7. It might help to also have students
use connecting cubes to model 5 + 2 = 2 + 5.
Coherence In this lesson, students discover that the order of the
addends does not change the sum, concluding that one can add
numbers in any order and still get the same sum. Students will
apply this knowledge throughout the year (e.g., when they add
compatible numbers first, when adding more than two numbers).
Topic 1
© Pearson Education, Inc. 2
Lesson 1
Error Intervention: Item 2
If students have difficulty trying to reverse the order of the
addends in the equations,
then have them model each addend with connecting cubes.
/132/PE01513_SE/ENVISION_MATH_ENGLISH/NA/SE/2013/G2/XXXXXXXXXX/Layout/Interior_Fi ...
1
Reteaching Assign Reteaching Set A, p. 67.
sk the following Essential Question: If you add two
A
numbers in a different order will you get the same sum?
Explain. [Sample answer: Yes, if you add the two
numbers in a different order, you get the same sum both ways. For
example, 2 + 3 = 5 and 3 + 2 = 5.]
6 Topic 1
FOR REVIEW ONLY - PAGES NOT FINAL
PearsonRealize.com
QUICK CHECK
Check mark indicates items for prescribing differentiation on the next page.
Items 11 and 15 are each worth 1 point. Item 14 is worth up to 3 points.
Items 3–11 MP.7 Use Structure Have students
check their work by drawing crossed arrows to
connect the addends in each pair of addition
equations. Did you connect the same addends in
each pair of addition equations? [Yes] Are the sums
in each pair the same? [Yes]
Tools Assessment
20–30 min
Name
Tools
Assessment
Count on to find the sum. Then change the order of the addends.
Use cubes if needed.
8 + 4 = 12
□
□
□ □
9.
4 +
8 = 12
10.
2
7
+
+ 2
9
7
+ 2
+
8
11.
2
9 = 12
7 + 3 = 10
3 +
□
□
□ □
6
on
m
9
8.
7 = 11
©
20
4 +
9 + 3 = 12
3 +
7 + 4 = 11
7.
2.
0
6.
5.
8 = 13
5 +
8 = 10
2 +
at
h
Item 12 In the equation 6 + ____ = 4 + 6, what are
the addends on the right side? [4 and 6] What do
you know about an equation? [Sample answer: The
value on the left side of the equals sign is the same as
the value on the right.] What is the value on the left?
[10] What do you add to 6 to get 10? [4]
8 + 5 = 13
4.
16
8 + 2 = 10
3.
7 = 10
□
□
□ □
6
5
6
+ 6
8
11
5
+
11
12. Algebra Write the missing numbers.
is
i
4 =4+6
2 +8
9+3=3+
9
4 +8=4+8
4 +7=7+4
,e
8+2=
5 =5+6
6+
nV
6+
Lesson 1
seven
es
Topic 1
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g
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7
Solve the problems below.
13.
bl
ic
a
tio
n
Item 13 MP.4 Model with Math Explain to
students that drawing pictures of bean and corn
plants can also model an addition equation. You may
want to draw an example of a pod of beans and an
ear of corn on the board for students.
Pr
ep
u
Item 15 This is a put together, total unknown
problem. Remind students that they can count on from
either addend in an addition problem. Do any of the
choices show counting on from 5? [No] Do any of
the choices show counting on from 7? If so, which
choices? [Yes. Choices A and D.] How many do you
need to count on from 7 to find the total? [5]
8 +
6 = 14
6 +
8 = 14
Check students’ drawings.
14. Higher Order Thinking Find the objects
in Box 1 and Box 2 that are the same.
Write an equation to show how many of
each object there are. Then change the
order of the addends.
Box 1
8
Your picture
and your equation will
show the problem.
MP.4 Model Joy has 8 bean plants and
6 corn plants in her garden. How many plants
does she have in all? Draw a picture.
Then write facts for this story with the
addends in a different order.
Box 2
Assessment Kate has 7 fish.
Nick has 5 fish. How many fish do
Kate and Nick have in all?
Which shows how to count on to solve
the problem?
𝖠𝖠
𝖡𝖡
𝖢𝖢
𝖣𝖣
6 +
2 =
8 =
2 +
6
4 +
5 =
9 =
5 +
4
3 +
5 =
8 =
5 +
eight
15.
7, 8, 9, 10, 11, 12
1, 2, 3, 4, 5
7-5
7, 8, 9, 10, 11
3
© Pearson Education, Inc. 2
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Topic 1
Lesson 1
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7–8
STEP
3
ASSESS AND DIFFERENTIATE
2
Use the QUICK CHECK on the previous page to prescribe differentiated instruction.
I
Intervention
O On-Level
A Advanced
0–3 points on the Quick Check
4 points on the Quick Check
5 points on the Quick Check
Intervention Activity I
Reteach I
Reteach to Build
Understanding
Name
Windmill Facts
Materials
10 blue and 10 red connecting cubes
(or Teaching Tool 5), paper and pencil
(Colored pencils are optional.)
•Have students write the new equation
for the blade. [2 + 7 = 9]
1-1
Vocabulary
1. The equation below has addends. You can count on to
find the sum.
•Students can continue the activity by
making other two-color blades and
recording fact pairs.
3+5=?
You can change the order of the addends. 3 + 5 and
5
•On a piece of paper, have partners
draw the tower part of a windmill.
+
3
have the same sum.
16
It’s easier to count on from the greater addend. 5 + 3 = ?
Count on 3 from 5.
5,
6, 7, 8
©
20
•Guide students to make the windmill
blade by connecting 7 red cubes to
2 blue cubes and placing the blade at
the top of the tower with the red cubes
on the left.
2.
0
at
h
on
m
3+8=
8
+
11
3
=
11
6
+
13
7 = 13
3. Draw a picture. Show how you know that 4 + 2 and 2 + 4
have the same sum. Check students’ work.
R 1•1
MTH16_ANC02_CC2_T01_L01_BU.indd Page 47 26/09/14 7:40 PM S-015
pa
g
es
,e
nV
7+6=
On the Back!
is
i
•Tell students that the wind blows the
blade to make it turn. Now the blue
cubes are on the left. Let partners rotate
the blade with their fingers.
ep
u
bl
ic
a
tio
n
On-Level and Advanced Activity Centers O A
Pr
See the Problem-Solving Reading Activity
Guide for other suggestions on how to use
this mat.
9A Topic 1
8.
2. Count on to find each sum. Then change the order of
the addends.
•Have students write the equation for the
blade. [7 + 2 = 9]
Problem-Solving Reading Mat
Have students read the Problem-Solving
Reading Mat for Topic 1 and then complete
Problem-Solving Reading Activity 1-1.
So, 3 + 5 =
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PearsonRealize.com
TIMING
The time allocated to Step 3 will depend on the teacher’s instructional
decisions and differentiation routines.
Leveled Assignment
I Items 1–4, 7 O Items 1–2, 5–7, Technology Center I O A
Math Tools and Math Games
A link to a specific math tools activity
or math game to use with this lesson is
provided at PearsonRealize.com.
Name
A
Help
Tools
Tools
Homework
& Practice 1-1
Games
You can count on to find a sum. Counting on from a
greater number is easier.
Addition Fact
Strategies
I can add numbers
in any order and get
the same sum.
5+2=
7
7
2
3 4 5 6
2
2.
0
6
©
20
16
HOME ACTIVITY Have your
+
5
=
child use small clothing
items, such as socks or
mittens, to model counting
on to find 5 + 4. Then ask
your child to explain why
5 + 4 and 4 + 5 have the
same sum.
7
7
at
h
5
Games
Items 3–7
Another Look!
Games
Count on to find the sum. Then change the order of the addends.
1.
2.
7
+
+ 4
nV
,e
3 =
□
9
7
3.
7 + 6 = 13
5
9
6 +
7 = 13
pa
g
es
4 +
□
□
□
4
5
is
i
3+4=
on
m
Tools
Help
15–30 min
Lesson 1
nine
Digital Resources at PearsonRealize.com
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9
/132/PE01513_SE/ENVISION_MATH_ENGLISH/NA/SE/2013/G2/XXXXXXXXXX/Layout/Interior_Fi ...
Write two addition facts for each story. Then solve.
4.
Pr
ep
u
bl
ic
a
tio
n
Topic 1
MP.2 Reasoning Danny collects toy
train cars. He has 9 red train cars and
5 black train cars. How many train cars
does he have in all?
5.
MP.2 Reasoning Ana draws
3 red circles and 8 blue circles.
How many circles does Ana draw?
9 +
5 = 14
3 +
8 = 11
5 +
9 = 14
8 +
3 = 11
5 train cars
11 circles
6. Higher Order Thinking Draw a picture
to solve. Then write two addition facts for
the story.
7.
Assessment Which shape belongs
in the second equation?
15 cows live at a farm.
Some of the cows are
brown and some are
white. How many of
Sample
each color could be
answers given.
at the farm?
Check students’
8 +
7 = 15
7 +
8 = 15
8 brown cows
10
+
+
=
?
=
drawings.
𝖠𝖠𝖠
𝖠𝖠𝖠
𝖠𝖠𝖠
𝖠𝖠
7 white cows
ten
MTH16_SE02_CC2_T01_L01.indd Page 10 5/26/14 11:20 PM s-w-56
© Pearson Education, Inc. 2
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Topic 1
Lesson 1
9–10
/132/PE01513_SE/ENVISION_MATH_ENGLISH/NA/SE/2013/G2/XXXXXXXXXX/Layout/Interior_Fi ...
LESSON 1-2
Doubles and Near Doubles
DIGITAL RESOURCES PearsonRealize.com
Animated
Glossary
Solve
Think
Math Tools
Glossary
Tools
Another Look
Homework
Video
LESSON OVERVIEW
F C R FOCUS • COHERENCE • RIGOR
Help
Assessment
Math Games
Games
MATH ANYTIME
Daily Common Core Review
COHERENCE
1-2
1.OA.C.6
at
h
Which equations show how
many apples in all?
Choose all that apply.
𝖠𝖠 6
on
m
𝖡𝖡 7
𝖢𝖢 9
7 + 5 = 12
𝖣𝖣 10
5 + 7 = 12
7 + 4 = 11
is
i
4 + 7 = 11
1.OA.A.1
3. Draw a picture to show the addition story.
Then write an addition equation to solve.
,e
Pam sees 5 birds. Then she sees 5 more birds.
How many birds does Pam see in all?
Check students’ drawings.
es
5
+
5 = 10
10 birds
pa
g
1.OA.A.1
4. Draw a picture to show the subtraction story.
Then write a subtraction equation to solve.
Hector has 9 shells. Bill has 3 fewer shells than Hector.
How many shells does Bill have?
n
Check students’ drawings.
tio
bl
ep
u
2. Fred has 7 apples.
Mindy has 4 apples.
5+2=
This lesson emphasizes conceptual
understanding and fluency. The focus
is on doubles and near doubles. Encourage
students develop the habit of looking for and
thinking about doubles and near doubles
when adding and subtracting.
Watch the Listen and Look For Lesson
PD Video.
9
-
3
=
6
6
D 1•2
MTH16_ANC02_CC2_T01_L02_DR.indd Page 11 10/10/14 3:02 AM S-015
Think
Pr
2.OA.A.1
1. Which number is the sum?
nV
RIGOR
Daily Common
Core Review
Name
2.
0
Students build on their knowledge of doubles
when they develop their understanding of
near doubles. Confirm that students have
gained mastery of basic doubles facts before
moving on to near doubles. Using the addition
chart with doubles facts highlighted can help
students see the relationship between doubles
facts and near doubles.
ic
a
Domain 2.OA Operations and Algebraic
Thinking
Cluster 2.OA.B Add and subtract within 20.
Content Standard 2.OA.B.2 Fluently add
and subtract within 20 using mental strategies.
By end of Grade 2, know from memory all
sums of two one-digit numbers.
Mathematical Practices MP.4, MP.6, MP.7,
MP.8
Objective Use doubles and near doubles to
add quickly and accurately.
Essential Understanding Basic addition
facts that are near doubles can be found using
a related doubles fact.
Vocabulary Doubles, Near doubles
Materials Connecting cubes (or Teaching
Tool 5)
Learn
Quick Check
FOCUS
Visual Learning
Animation Plus
Solve and
Share
16
PD
eText
Today’s
Challenge
©
20
Listen and
Look For
Lesson Video
Student and
Teacher eTexts
shells
Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 2
/147/PE01513_ENG_TRM/MATH/NA/TRM/2013/G2/XXXXXXXXXX/Layout/Interior_Files/Topic_0 ...
Today’s Challenge
Use Topic 1 problems any time
during this topic.
ENGLISH LANGUAGE LEARNERS
Speaking Speak using content area
vocabulary in context.
the Math column on the board and remind
students this is a doubles fact.
Use before the Visual Learning Bridge on
Student Edition, p. 12.
Beginning Have students work in small
groups. Students should take turns saying
doubles facts while the rest of the group adds
them to the Math column of their tables.
Write the word Doubles on the board. Draw
a two-column table. Label one column Me
and the other Math. Have students copy the
table. Ask students to name parts of their
bodies that are doubles, such as ears, eyes,
and so on. Write the words under Me in
the table on the board. Have students copy
the words in their tables. Write 2 + 2 = 4 in
11A Topic 1
Intermediate Have students work in pairs
to create flashcards with doubles addition
problems. Partners should alternate reading
the problem aloud and solving the problem,
helping each other when needed.
Advanced Have a volunteer write a
doubles addition problem on the board, but
do not solve it. Have a different volunteer
describe how to solve the problem, and then
solve it. Repeat several times with different
volunteers.
Summarize Students should be able to
recall doubles facts before introducing near
doubles.
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STEP
1
DEVELOP: PROBLEM-BASED LEARNING
PearsonRealize.com
COHERENCE: Engage learners by connecting prior knowledge to new ideas.
Students explain how a doubles fact might help them solve a near doubles fact. This prepares
them for the next part of the lesson where they learn about doubles, near doubles, and how they
are related.
Whole
Class
BEFORE
Name
1.Pose the Solve-and-Share Problem
Have students work in pairs. Provide each pair
with 10 connecting cubes (5 of one color and 5
of another color) to model the problem.
MP.4 Model with Math In this problem,
students use connecting cubes to model 2 + 2
and 2 + 3. This modeling helps students see
how a doubles fact can help them solve a near
doubles fact.
Solve
I can …
use doubles and near doubles
to add quickly and accurately.
©
20
16
Content Standard 2.OA.B.2
Mathematical Practices MP.4,
MP.6, MP.7, MP.8
2.
0
at
h
on
m
DURING
2+3=
See margin for sample student work.
,e
nV
is
i
2+2=4
Lesson 2
eleven
Digital Resources at PearsonRealize.com
tio
n
AFTER
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Analyze Student Work
Brian’s Work
Ana’s Work
Pr
ep
u
bl
ic
a
4. Share and Discuss Solutions
Start with students’ solutions. Have them share
Solve the strategies used to solve the problem. If
needed, project and analyze Brian’s work to
discuss how using the doubles fact, 2 + 2 = 4,
helps you find the near doubles fact, 2 + 3 = 5.
11
es
Topic 1
pa
g
3. Ask Guiding Questions As Needed
What is different about the numbers in 2 + 2 and
the numbers in 2 + 3? [In 2 + 2, the two numbers
being added are the same; in 2 + 3, the two
numbers being added are 1 apart.] How many
more cubes will you need to model 2 + 3? [One
more cube]
Whole
Class
Lesson 1-2
Doubles and
Near Doubles
You know that 2 + 2 = 4.
Tell how knowing that fact can help you find 2 + 3.
2.Build Understanding
What are you asked to find out? [How 2 + 2 = 4
can be used to help solve 2 + 3] What tools
do you have to solve the problem? [Connecting
cubes]
Small
Group
Solve
10–15 min
5. Transition to the Visual Learning Bridge
Later in this lesson, you will learn about special
facts called doubles and near doubles.
Basic addition facts that are near doubles can be
found using a related doubles fact.
6. Extension for Early Finishers
How could knowing 7 + 7 = 14 help you solve
7+9=
? [Sample answers: Double 7 and
add 2 more; Take 1 from the 9 and add it to the
7 to make double 8.]
2+2=4
2+3=
Brian uses connecting cubes and explains
that since the numbers added in 2 + 3 are
one apart from those in 2 + 2, then the
sums should be one apart.
2+2=4
2+3=
Ana correctly models and solves
2 + 2 = 4 and 2 + 3 = 5 but can’t explain
how the doubles fact helps solve the near
doubles fact.
FOR REVIEW ONLY - PAGES NOT FINAL
11
STEP
2
DEVELOP: VISUAL LEARNING
PearsonRealize.com
The Visual Learning Bridge connects students’ thinking in Solve &
Share to important math ideas in the lesson. Use the Visual Learning
Bridge to make these ideas explicit. Also available as a Visual
Learning Animation Plus at PearsonRealize.com
MP.8 Generalize How
do you know when an
addition fact is a doubles
fact? [The numbers that
are added are the same.]
Visual Learning
Learn
Glossary
MP.7 Use Structure One set of cube towers shows
7 + 8 and the other shows 7 + 9. These towers are
almost the same as the towers that show 7 + 7 . What
is different? [The towers that show 7 + 8 have one more
cube than the towers that show 7 + 7. The towers that
show 7 + 9 have two more cubes than the towers that
show 7 + 7.] You know the doubles fact 7 + 7 equals
14. How can you use it to find 7 + 8 and 7 + 9?
[7 + 7 = 14, so 7 + 8 is 1 more than 14, which is 15;
and 7 + 9 is 2 more than 14, which is 16.]
Glossary
7 + 8 is 1 more than 7 + 7.
Doubles Fact: 7 + 7 = 14
on
m
7 + 8 = 15
and 7 + 9 = 16
These are near
doubles facts.
7 + 9 is 2 more than 7 + 7.
Doubles
5+5
is
i
3+3
,e
nV
4+4
Complete the doubles facts.
Use the doubles facts to solve the near doubles.
1. 2 + 2 =
2.
2+3=
3
+3
+4
6
7
4.
MTH16_SE02_CC2_T01_L02_VLB.indd Page 12 16/06/14 11:24 AM sw-055
ncourage students to give a clear and correct explanation.
E
Suggest they use math terms, such as the ones shown in the Visual
Learning Bridge to communicate precisely.
sk the following Essential Question: How can you use a
A
doubles fact to find a near doubles fact? Explain.
[Sample answer: If you know the doubles fact, you can
add 1 or 2 to that sum to find a near doubles fact. For example, if
you know 6 + 6 = 12, you can add 1 to 12 to find 6 + 7 = 13,
and you can add 2 to 12 to find 6 + 8 = 14.]
5
5
+5
+7
10
12
□ □
□ □
twelve
5
9 =4+5
3
3.
Do You Understand? Show Me! MP.6 Be Precise
12 Topic 1
4
8 =4+4
Pr
ep
u
bl
ic
a
tio
n
Sample answer:
7 + 9 is 2 more than
7 + 7. So, since
7 + 7 = 14, I know
7 + 9 = 16.
pa
g
Show Me! How could you
use the doubles fact 7 + 7 to
find 7 + 9?
es
Do You Understand?
12
Visual Learning Bridge
You can use
a doubles fact to
help you add.
You can use the doubles fact to
help find a near doubles fact.
2.
0
Find 7 + 8 and find 7 + 9.
at
h
Learn
©
20
16
Is 7 + 7 a doubles fact? [Yes; The
numbers being added are the
same.] What do you notice about
the cubes? [There are 7 cubes in
each row (or tower) and 14 cubes
in all.] We’ll use this doubles fact
to look at some near doubles facts.
Topic 1
© Pearson Education, Inc. 2
Lesson 2
Error Intervention: Item 2
If the student has difficulty connecting the doubles fact 4 + 4 to
the near doubles fact 4 + 5,
then allow students to build a doubles tower with connecting
cubes and line them up to see the double plus 1.
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1
Reteaching Assign Reteaching Set B, p. 67.
FOR REVIEW ONLY - PAGES NOT FINAL
PearsonRealize.com
QUICK CHECK
Check mark indicates exercises for prescribing differentiation on the next page.
Exercises 7 and 18 are each worth 1 point. Exercise 17 is worth up to 3 points.
Name
Tools
Assessment
thirteen
13
Complete the doubles facts. Use the doubles facts to solve
the near doubles.
5. 6 + 6 = 12
6 + 7 = 13
6. 5 + 5 = 10
7. 8 + 8 = 16
8 + 10 = 18
8.
2
+2
+3
□
□
5
3
3
+3
+5
12.
+4
□
□
6
on
m
8
4
8
+5
5
+5
+7
□
8
8
+8
+9
16
14.
12
□
17
7
7
+7
+9
□
□
10
4 =1+3
□
9
5
13.
11.
□
©
20
□
4
4
10.
5 + 6 = 11
2 =1+1
16
2
9.
2.
0
Item 15 Discuss with students possible answers for
the first problem. 9 plus what number equals 18?
[9] Then discuss how the doubles fact could help
find different near doubles facts. What near doubles
fact could you find using 9 + 9 = 18? [Sample
answers: 9 + 10 = 19, 10 + 9 = 19, 8 + 9 = 17, or
9 + 8 = 17] How does the doubles fact help? [You
can start with the doubles fact, then add 1 (or 2) or
take away 1 (or 2), to find a near doubles fact.]
at
h
Items 5–14 MP.4 Model with Math If needed,
allow students to use connecting cubes to model the
doubles fact to help them complete the near doubles
fact.
Tools Assessment
20–30 min
14
□
16
15. Algebra Complete the doubles and near doubles facts.
□
= 18
is
i
9
□ □
9
+ 10 = 19
,e
nV
9+
Lesson 2
es
Topic 1
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Solve the problems below.
16.
bl
ic
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tio
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Item 16 MP.4 Model with Math In this
problem, students must find the total number of houses
John drew. If John drew the same number of houses
twice, what equation would you write? [4 + 4 = 8].
In this problem, what is different about the number of
houses he drew? [John drew 4 houses, then he drew
one more than 4 houses, or 5 houses.]
ep
u
Draw a picture and write an equation.
Pr
Item 17 Encourage students to write the near
doubles fact and have them refer to it as they draw.
How is a drawing of a near doubles fact different
from a drawing of a doubles fact? [In a drawing of a
near doubles fact, one part has one or two more or
one or two fewer pictures. In a pictures of a doubles
fact, the two parts each have the same number of
pictures.] What are some types of stories that you
can tell using near doubles facts? [Responses might
include addition stories about joining groups or about
parts and a whole.]
MP.4 Model John drew 4 houses.
Then he drew 5 more houses.
How many houses did John draw in all?
4 +
5 =
Check students’ drawings.
9 houses
17. Higher Order Thinking Choose
a doubles fact. Use that doubles
fact to draw a picture
that shows a near
doubles story.
18.
Which equation shows how many
puppies in all?
𝖠𝖠
𝖡𝖡
𝖢𝖢
𝖣𝖣
Check students’ drawings.
14
fourteen
Assessment Kate’s dog had
6 puppies. Jim’s dog had 1 more
puppy than Kate’s dog.
6+1=7
6 + 6 = 12
6 + 7 = 13
7 + 7 = 14
© Pearson Education, Inc. 2
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Topic 1
Lesson 2
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13–14
ASSESS AND DIFFERENTIATE
STEP
3
Use the QUICK CHECK on the previous page to prescribe differentiated instruction.
2
I
Intervention
O On-Level
A Advanced
0–3 points on the Quick Check
4 points on the Quick Check
5 points on the Quick Check
Intervention Activity I
Reteach I
Reteach to Build
Understanding
Name
Clap-Clap-Stomp Near Doubles
1-2
Vocabulary
1. You can use a doubles fact to solve a near doubles fact.
•Have students join you in repeating the
pattern and then add one foot stomp
to create a near double. Draw and
shade one more circle on the board
to represent the stomp. Ask how many
claps and stomps there were altogether.
•Explain that the clap and echo pattern
created a doubles fact. Have students
identify the fact.
6 + 8 is
2. Use a doubles fact to solve the near doubles fact.
16
9 + 10 = ?
•Ask students to state the near doubles
fact that was demonstrated. Repeat,
using other numbers.
•Now, write a doubles fact on the board
and ask students to clap or stomp out
the sum.
9+9=
18
1 more than 9 + 9.
9 + 10 = 19
9 + 10 is
3. Complete each doubles fact. Solve each near doubles fact.
8+8=
16
8+9=
17
5+5=
10
Check students’ work.
R 1•2
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es
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1-2
ic
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Adding with Paper
Did You Know? Paper is thin, flat, and smooth.
Cut the construction paper into 18 thin strips.
2
Use the strips of paper to model two
addition equations.
Make at least one doubles fact.
3
Write the addition equations you modeled.
8
6
+
+
3 = 11
6 = 12
Sample answers given.
4
Use the strips to model a near doubles fact.
Then write the near doubles fact you modeled.
5
Extension Use a different number of strips.
Show all the addition equations you can make
with that number of strips. Show your work below.
6
+
7 = 13
Sample Student Work
Pr
1
ep
u
Get some construction paper and scissors.
bl
Paper can be folded, cut, ripped, and burned.
Sometimes paper has color. Most paper is made
from wood.
Math and Science Activity STEM
This activity revisits the science theme Properties of Materials, introduced on
page 1 in the Student’s Edition.
tio
Math and Science
Activity
Sample answer given.
Check students’ answers.
Math and Science Activity
MTH16_ANC02_CC2_T01_L02_SC.indd Page 9 26/09/14 8:18 PM S-015
15A Topic 1
1•2
12
4. Draw 2 cube trains to show a doubles fact.
Draw 1 or 2 more cubes to show a near doubles fact.
Write the doubles fact and the near doubles fact.
On-Level and Advanced Activity Centers O A
Name
5+7=
On the Back!
,e
nV
is
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on
m
at
h
•Write the doubles fact on the board
and ask students to state the sum.
12
2 more than 6 + 6.
So, 6 + 8 = 14 .
6+6=
©
20
•Ask students how many times they
clapped. Draw circles on the board
to represent each clap. Then ask how
many claps there were in all.
6+8=?
2.
0
•Clap 4 times. Ask students to listen
carefully so they can clap the same
number of times.
Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 2
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FOR REVIEW ONLY - PAGES NOT FINAL
PearsonRealize.com
TIMING
The time allocated to Step 3 will depend on the teacher’s instructional
decisions and differentiation routines.
Leveled Assignment
I Items 1–5, 7, 9 O Items 2–7, 9 Technology Center I O A
Math Tools and Math Games
A link to a specific math tools activity
or math game to use with this lesson is
provided at PearsonRealize.com.
Name
Another Look!
You can use a doubles
fact to solve a near doubles fact.
Tools
Tools
Homework
& Practice 1-2
Games
Doubles and
Near Doubles
To solve a near
doubles fact, you can
add 1 or 2 more to the
doubles fact.
HOME ACTIVITY Have your
12
13
6+7=
Near Doubles Fact
at
h
2.
0
Doubles Fact
child use common objects,
such as pennies or buttons,
to show doubles and near
doubles. Then ask your
child to write equations to
show the facts.
©
20
6+6=
Games
Items 3–9
16
Games
A
Help
on
m
Write and solve the doubles facts and the near doubles facts.
1.
4 =
8
4 +
2.
5 =
9
,e
nV
4 +
is
i
Tools
Help
15–30 min
3. 7 + 7 = 14
5 +
es
pa
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tio
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bl
7
= 12
8 + 10 = 18
Lesson 2
fifteen
Digital Resources at PearsonRealize.com
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15
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In 5 and 6, write an equation to solve the problem. Use doubles facts to help you.
5. Algebra A number plus 6
equals 12.
What is the number?
6
6 = 12
The number is 6 .
Pr
ep
u
5 +
4. 8 + 8 = 16
7 + 9 = 16
Topic 1
5 = 10
+
6. Algebra 6 plus a number
equals 13.
What is the number?
6 +
7 = 13
The number is 7 .
8. Higher Order Thinking Draw a picture to
show the story.
Then write an equation for the story.
Jane has 5 books.
Fred has 2 more books than Jane.
How many books do Fred and
Jane have in all?
9.
7.
A-Z Vocabulary Which is a
near doubles fact?
Circle the fact.
4+4=8
4+5=9
2+7=9
0+5=5
Assessment Terry’s dollhouse has
7 windows on the first floor and 8 windows
on the second floor.
Which shows how Terry found the number
of windows in all?
𝖠𝖠
𝖡𝖡
𝖢𝖢
𝖣𝖣
Check students’ drawings.
6 + 6 and 1 more is 13.
7 + 7 and 1 more is 15.
8 + 8 and 1 more is 17.
9 + 9 and 1 more is 19.
5 + 7 = 12
12 books
16
sixteen
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© Pearson Education, Inc. 2
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Topic 1
Lesson 2
15–16
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LESSON 1-3
MAKE A 10 to Add
DIGITAL RESOURCES PearsonRealize.com
Animated
Glossary
Solve
Think
Math Tools
Glossary
Tools
Another Look
Homework
Video
LESSON OVERVIEW
F C R FOCUS • COHERENCE • RIGOR
Help
Assessment
Math Games
Games
MATH ANYTIME
Daily Common Core Review
COHERENCE
1-3
2.OA.B.2
at
h
11 12 1
10
2
9
3
8
4
7 6 5
𝖠𝖠 11
𝖡𝖡 10
𝖢𝖢 9
𝖠𝖠 12:15
𝖢𝖢
3:15
𝖣𝖣 8
𝖡𝖡 12:00
𝖣𝖣
3:00
1.OA.A.1
is
i
3. Which addition facts match the story?
nV
Brad eats 4 crackers. Then he eats 5 more crackers.
Brad eats 9 crackers in all.
es
,e
𝖠𝖠
𝖡𝖡
𝖢𝖢
𝖣𝖣
4+5=9
5+4=9
4+5=9
5 + 5 = 10
4+5=9
9 + 4 = 13
4 + 6 = 10
6 + 4 = 10
pa
g
1.OA.D.8
4. Draw the missing part. Write a subtraction
equation with the missing part.
8
n
Check students’ drawings.
8
tio
bl
ep
u
2. Which time is shown on the
clock?
4+4=
This lesson emphasizes conceptual
understanding and fluency. By making a
10 to add, students deepen their understanding
of addition and they begin to develop flexibility
in their ability to add mentally. Make sure
students understand that making a ten is
a strategy that can help them add quickly.
Eventually, with practice, most students will be
able to do the “make a 10” strategy in their
heads, without the aid of tools.
Watch the Listen and Look For Lesson
PD Video.
-
6
=
2
D 1•3
MTH16_ANC02_CC2_T01_L03_DR.indd Page 11 10/10/14 3:03 AM S-015
Think
Pr
1.MD.B.3
1. Which number is the sum?
on
m
RIGOR
Daily Common
Core Review
Name
2.
0
In order to be successful with this lesson,
students must have a firm grasp of the sums
of 10. Students first worked on sums to 10 in
Grade K (K.OA.A.4). In Grade 1, students
also used the make 10 strategy (1.OA.C.6).
ic
a
Domain 2.OA Operations and Algebraic
Thinking
Cluster 2.OA.B Add and subtract within 20.
Content Standard 2.OA.B.2 Fluently add
and subtract within 20 using mental strategies.
By end of Grade 2, know from memory all
sums of two one-digit numbers.
Mathematical Practices MP.1, MP.2, MP.3,
MP.5, MP.7
Objective Use the strategy of making a ten
to add quickly and accurately.
Essential Understanding Some addition
facts can be found by changing to an
equivalent fact with 10.
Materials Counters (or Teaching Tool 6)
Double Ten-Frame Mat (Teaching Tool 8)
Learn
Quick Check
FOCUS
Visual Learning
Animation Plus
Solve and
Share
16
PD
eText
Today’s
Challenge
©
20
Listen and
Look For
Lesson Video
Student and
Teacher eTexts
Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 2
/147/PE01513_ENG_TRM/MATH/NA/TRM/2013/G2/XXXXXXXXXX/Layout/Interior_Files/Topic_0 ...
Today’s Challenge
Use Topic 1 problems any time
during this topic.
ENGLISH LANGUAGE LEARNERS
Speaking Use abstract and content-based
vocabulary during speaking assignments.
Use before the Solve and Share on Student’s
Edition, p.17.
Write the sentence frame ____ and ____
make 10 on the board and have students
copy it. Complete the sentence frame using
the numbers 2 and 8. Read the sentence
aloud slowly and have students repeat it after
you. Repeat the exercise several times, using
different pairs of numbers that make 10.
17A Topic 1
Beginning Have students work in groups of
three. Each student should copy the sentence
frame three times. Students should work
together to find three pairs of numbers that
make 10 and use the numbers to complete
the sentence frames. Each student should
read one of the sentences aloud and then try
to say the sentence without reading it.
Advanced Each student should use the
sentence frame to write three examples of
number pairs that make 10. Ask volunteers to
give one example for the class.
Summarize Students should be comfortable
making 10 before introducing the lesson.
Intermediate Have students work in pairs.
Students should take turns completing the
sentence frames and saying the completed
sentence to their partner, until each partner
has said three examples.
FOR REVIEW ONLY - PAGES NOT FINAL
STEP
1
DEVELOP: PROBLEM-BASED LEARNING
PearsonRealize.com
COHERENCE: Engage learners by connecting prior knowledge to new ideas.
Students explain how they can use two ten-frames to solve 9 + 3. This prepares students for the
next part of the lesson where they learn how to make 10 to add, using ten-frames as a tool.
Solve
10–15 min
Whole
Class
BEFORE
Name
1. Pose the Solve-and-Share Problem
Have students work in pairs. Distribute
12 counters to each pair (9 of one color, 3 of
another color).
MP.5 Use Appropriate Tools Strategically
In this problem, students use ten-frames and
counters to model addition.
Solve
Make a 10 to Add
How can thinking about 10 help you find 9 + 3?
Use the ten-frames and counters to show how.
Content Standard 2.OA.B.2
Mathematical Practices MP.1,
MP.2, MP.3, MP.5, MP.7
16
©
20
2.
0
at
h
DURING
on
m
3. Ask Guiding Questions As Needed
How can you show 9? [By placing 9 counters
on the first ten-frame] How can you show 3? [By
placing 3 counters on the second ten-frame]
Topic 1
□
Lesson 3
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Analyze Student Work
Deonna’s Work
Megan’s Work
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5. Transition to the Visual Learning Bridge
You can make a 10 to help you solve
addition facts.
You can use ten-frames to help you add numbers.
seventeen
Digital Resources at PearsonRealize.com
pa
g
4. Share and Discuss Solutions
Start with students’ solutions. If needed,
Solve project and analyze Deonna’s work to
demonstrate ways to think about 10 when solving
the problem.
9
+3
es
AFTER
,e
nV
is
i
See margin
for sample
student work.
6.Extension for Early Finishers
Can you make 10 to find 9 + 0? Explain. [No,
9 + 0 = 9. There is no 1 in the second addend to
make 10.]
Pr
Whole
Class
I can …
make a 10 to help me add
quickly and accurately.
2.Build Understanding
What are you asked to find? [How two ten-frames
can be used to show 9 plus 3] What tools do you
have to help you solve the problem? [Counters,
ten-frames]
Small
Group
Lesson 1-3
9
+ 3
9
+ 3
□
□
Deonna starts with 9 red counters and
then makes a 10 by moving 1 yellow
counter from the second frame to the
first. She then counts on 2 more to find
9 + 3 = 12.
Megan counts all of the red and yellow
counters to solve the addition, but she
does not make a 10 to find the sum.
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17
STEP
2
DEVELOP: VISUAL LEARNING
PearsonRealize.com
The Visual Learning Bridge connects students’ thinking in Solve &
Share to important math ideas in the lesson. Use the Visual Learning
Bridge to make these ideas explicit. Also available as a Visual
Learning Animation Plus at PearsonRealize.com
MP.7 Use Structure
What addition
sentence do you see
modeled here? [8 + 5]
Why might you want
to make a10 to add?
[Accept all reasonable
answers.]
Look at the ten-frames.
Why do you think
2 counters are moved?
[Two counters are needed
to fill the top frame to
make a 10.] When those
counters are moved, how
many are left in the bottom
frame? [3]
Visual Learning
Learn
Glossary
How does knowing the sum of 10 + 3 help you find the sum of 8 + 5?
[The sums are the same. So, if I know the sum of 10 + 3, I also know the
sum of 8 + 5.] How do you know that the sums are the same? [Because
the total number of counters did not change.]
Prevent
Misconceptions
Students may have difficulty keeping track of the value of the second
addend. If so, provide opportunities for students to work with counters
and ten-frames as they use this strategy.
Glossary
Move 2 counters
to make a 10.
10
8
+ 3 so, + 5
13
13
Add with 10.
at
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8
+5
?
1.
7
+4
□
?
ic
a
tio
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Sample answer: I
move 2 counters from
5 to 8 to make a 10.
Then it’s easy to add
10 + 3.
pa
g
Show Me! Why do you move
2 counters to add 8 + 5?
Make a 10 to add.
Use counters and ten-frames.
es
Do You Understand?
+
bl
eighteen
Do You Understand? Show Me! MP.2 Reasoning
MTH16_SE02_CC2_T01_L03_VLB.indd Page 18 16/06/14 11:51 AM sw-055
tudents should be able to explain and demonstrate that adding
S
2 counters to the set of 8 will make 10 and that the sum of 10 and
3 is equal to the sum of 8 and 5.
sk the following essential question: Why is making a 10
A
a good strategy to help you add quickly and accurately?
[Sample answer: You can change an addition fact into
a fact with 10 without changing the sum. Facts with 10 are easy
to add.]
18 Topic 1
7
10
ep
u
Pr
18
Visual Learning Bridge
You can make a 10 to help
you add.
2.
0
Learn
©
20
16
1
□1
11
□
so,
+
□
□
4
11
Topic 1
© Pearson Education, Inc. 2
Lesson 3
Error Intervention: Item 1
If students’ sums are consistently greater than they should be,
then have them move counters to make a 10 and say the new
number sentence. Check that students understand the total number
of counters has not changed, just their positions. So the sum of 10
and 1 is equal to the sum of 7 and 4.
/132/PE01513_SE/ENVISION_MATH_ENGLISH/NA/SE/2013/G2/XXXXXXXXXX/Layout/Interior_Fi ...
1
Reteaching Assign Reteaching Set C, p. 68.
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PearsonRealize.com
QUICK CHECK
Check mark indicates items for prescribing differentiation on the next page.
Items 10 and 18 are each worth 1 point. Item 17 is worth up to 3 points.
Item 4 To make 10, is it easier to start with the
lesser number, 6, or the greater number, 7? Why?
[Sample answer: It is easier to start with the greater
number, 7, because there are fewer counters to add
and 7 + 3 is a counting-on fact that we know.]
Tools Assessment
20–30 min
Name
Tools
Make a 10 to add. Use counters and ten-frames.
8
2.
3.
+ 4
□
Item 11 MP.7 Use Structure What does the
equal sign tell you? [That 8 + 5 and □ + 3 are equal;
that they have the same value.] What will you do
first? [Add to find the value of 8 + 5.]
3
6
4.
7
6.
+ 7
+ 8
+ 5
12
13
13
12
8. 3 + 8 = 11
□
□
□
9. 4 + 9 = 13
10. 7 + 9 = 16
©
20
16
7. 5 + 9 = 14
Check students’
work.
+ 9
□
12
5
5.
Assessment
12. 6 + 9 = 10 +
□
5
13. 8 + 9 = 10 +
□
7
on
m
+3
at
h
□
11. 8 + 5 = 10
2.
0
Algebra Which number is missing?
14. Higher Order Thinking Can you make a 10 to help you add 7 + 4 + 5? Explain.
is
i
Sample answer: Yes; I can add 4 + 5 = 9.
nV
Then I can make a 10 to find the sum.
,e
7 + 9 = 10 + 6 = 16.
Lesson 3
nineteen
es
Topic 1
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19
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Item 15 How many points did they score in all?
[16] Can you write an addition equation to show the
problem? [Yes; 9 + ____ = 16] What is the missing
number? How do you know? [7; Sample answer:
9 + 7 is an addition fact that I recall. I counted on
from 9 to 16 to check, and I got 7.]
15. Tan’s team scored 16 points in a game.
During the first half, they scored 9 points.
How many points did the team score in the
second half of the game?
Pr
Item 16 MP.1 Make Sense and Persevere What do you need to find? [How many coats were
donated in all] Will you add or subtract? [Add.]
Which numbers will you add? [8 + 8]
Make a 10 to solve the problems below.
16.
MP.1 Make Sense The school has
a clothing drive for charity. Ana’s class
donates 8 coats. Nico’s class donates
5 hats. Adam’s class donates 8 coats.
How many coats were donated in all?
7 points
16 coats
17. Higher Order Thinking Draw a picture
to show how you can make a 10 to help
you add 3 + 5 + 9.
18.
Assessment Mary wrote an
equation. Which number makes her
equation true?
8 + 9 = 10 +
Check students’ drawings.
20
twenty
𝖠𝖠
𝖡𝖡
𝖢𝖢
𝖣𝖣
5
6
7
8
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Think about
making a 10.
Find the missing
addend!
Topic 1
Lesson 3
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19–20
ASSESS AND DIFFERENTIATE
STEP
3
Use the QUICK CHECK on the previous page to prescribe differentiated instruction.
2
I
Intervention
O On-Level
A Advanced
0–3 points on the Quick Check
4 points on the Quick Check
5 points on the Quick Check
Intervention Activity I
Reteach I
Reteach to Build
Understanding
Name
Stacking and Making 10
Materials
Connecting cubes (or Teaching Tool 5)
1-3
Vocabulary
1. You can make a 10 to find the sum
of 7 + 5.
The first ten-frame shows the addend
•Guide students to write the new
addition problem modeled by the cubes
and to complete the number equation
8+5=
. [10 + 3 = 13; 13]
•Give 8 cubes to one student
and 5 cubes to the other. Write
8+5=
on the board.
5.
3 counters to make a 10.
Add with 10. You know 10 + 2 = 12 .
So, 7 + 5 = 12 .
addend
Move
16
•Have students work in pairs.
7.
The second ten-frame shows the
©
20
•Repeat with 7 + 8 and 9 + 6.
•Ask students to explain how they can
make a train of 10 cubes. [Take 2
cubes from the group of 5 and add
them to the group of 8.]
2. Make a 10. Draw counters on the second
set of ten-frames to show your thinking.
at
h
2.
0
Find 8 + 6. Check students’ work.
Move
2
You know 10 + 4 =
on
m
.
6
.
counters to make a 10.
14 .
On the Back!
14 .
Check students’ drawings.
Sample answer: 7 + 8 = 15
3. Draw two ten-frames. Draw 7 counters in the first frame.
Draw counters for your age in the second frame. Find the sum.
is
i
10 + 3 =
8
The second ten-frame shows the addend
So, 8 + 6 =
R 1•3
nV
8+5=
The first ten-frame shows the addend
/147/PE01513_ENG_TRM/MATH/NA/TRM/2013/G2/XXXXXXXXXX/Layout/Interior_Files/Topic_0 ...
pa
g
es
,e
MTH16_ANC02_CC2_T01_L03_BU.indd Page 47 26/09/14 8:27 PM S-015
Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 2
n
On-Level and Advanced Activity Centers O A
1-3
bl
Sample Student Work
Pr
Get some construction paper and scissors.
ep
u
Did You Know? A mobile is a sculpture that moves.
One of the largest mobiles hangs at the National
Gallery of Art in Washington, D.C. It is made of
aluminum. The metal is light. This lets the mobile
swing and move easily.
ic
a
Make an Addition Mobile
Math and Science Activity STEM
This activity revisits the science theme Properties of Materials, introduced on
page 1 of the Student’s Edition.
tio
Math and Science
Activity
Name
1
2
Joe’s class started making this mobile. Finish the
mobile. Cut out 9 shapes, such as circles, squares,
or triangles. You may cut different shapes of different
sizes. Or you can make shapes that are all the same.
Place 3 or more of your shapes in the bottom row.
Write the number of shapes in the top row:
Sample answers given.
8
Write the number of shapes in the bottom row:
3
shapes
Make a 10 to find the number of shapes in all.
10 +
So,
4
shapes
5
3 = 13
8 + 5 = 13.
Sample answers given.
Extension Repeat steps 2 and 3 for a different
number of shapes. Check students’ answers.
Math and Science Activity
MTH16_ANC02_CC2_T01_L03_SC.indd Page 2 26/09/14 9:46 PM S-015
21A Topic 1
1•3
10 +
So,
=
+
=
.
Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 2
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PearsonRealize.com
TIMING
The time allocated to Step 3 will depend on the teacher’s instructional
decisions and differentiation routines.
Tools
Games
Leveled Assignment
I Items 1–7, 9–10 O Items 2–10 A Items 2–10
Technology Center I O A
Math Tools and Math Games
A link to a specific math tools activity
or math game to use with this lesson is
provided at PearsonRealize.com.
Name
Help
Another Look!
Games
Tools
Games
You can make a 10 to help you add.
This shows 8 + 4.
Make a 10 to Add
Show 10 + 2.
Move 2 counters to make a 10.
HOME ACTIVITY Have your
16
child use buttons to make
a group of 9 and a group
of 5. Ask your child to show
you how to make a group
of 10 buttons to help find
the sum.
8+4
is the same as
12
©
20
The sums
are the same!
10 + 2.
10 + 2 =
12
at
h
8+4=
Homework
& Practice 1-3
2.
0
Tools
Help
15–30 min
on
m
Make a 10 to help you add.
Move 1 counter to make a 10.
2. Find 7 + 5.
,e
nV
is
i
1. Find 9 + 7.
es
9+7
Move
is the same as
pa
g
9 + 7 = 16
10 +
7 + 5 is the same as 10 + 2 .
6 = 16
Lesson 3
7 + 5 = 12
10 +
2 = 12
twenty-one
Digital Resources at PearsonRealize.com
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21
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Add. Then draw lines to match addition problems with the same sum.
Pr
ep
u
bl
ic
a
tio
n
Topic 1
6 .
10 +
3 counters to make a 10.
3. 9 + 6 = 15
10 + 2 = 12
4. 7 + 5 = 12
10 + 3 = 13
5. 9 + 5 = 14
10 + 4 = 14
6. 5 + 8 = 13
10 + 5 = 15
7.
MP.3 Explain Blanca wants to
add 5 + 8. Describe how she can
make a 10 to solve.
5 + 8 = 13
Sample answer: Move 2 from
5 to 8 to make a 10. Then add
8. Higher Order Thinking
Explain how
Jay has 14 blocks in all.
you solved the
problem!
He has 6 yellow blocks.
The rest of the blocks are green.
How many green blocks does Jay have?
Make a 10 to solve.
Jay has 8 green blocks.
Sample answer: Add 4 to 6 to make
3 + 10 = 13.
a 10. Since 14 is 4 more than 10, the
number of green blocks is 4 + 4 = 8.
9.
22
Assessment Beth has 8 fish and
7 snails. How can Beth make a 10 to
find how many fish and snails she has
in all?
10 + 9
10 + 8
10 + 7
10 + 5
𝖠𝖠𝖠
𝖠𝖠𝖠
𝖠𝖠𝖠
𝖠𝖠
twenty-two
MTH16_SE02_CC2_T01_L03.indd Page 22 5/29/14 4:32 AM s-w-56
10.
Assessment Use the ten-frames.
Show how to find 7 + 6 by making a 10.
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Topic 1
Lesson 3
21–22
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