1st
Unit of Study 5: Addition and Subtraction Strategies
Projected Time Allotment: 14 days
Global Concept Guides: Counting On/Counting Back, Doubles, Addition and Subtraction With Ten, Think
Addition to Subtract, and Add Three Numbers
Prior Learning: K.OA.1, K.OA.2, K.OA.3, K.OA.4, K.OA.5
Progressions Document Link
Show What You Know Task: Modified Unit 5 Show What You Know
Common Core State Standards for Mathematical Content :
Represent and solve problems involving addition and subtraction.
1.OA.1 Use addition and subtraction within (10) 20 to solve word problems involving
situations of adding to, taking from, putting together, taking apart, and comparing,
with unknowns in all positions, e.g., by using objects, drawings, and equations
1.OA.2 Solve word problems that call for addition of three whole numbers whose
sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a
symbol for the unknown number to represent the problem.
Understand and apply properties of operations and the relationship between
addition and subtraction.
1.OA.3 Apply properties of operations as strategies to add and subtract.3 Examples:
If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of
addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2
+ 6 + 4 = 2 + 10 = 12. (Associative property of addition.)
1.OA.4 Understand subtraction as an unknown-addend problem. For example,
subtract 10 – 8 by finding the number that makes 10 when added to 8.
Add and subtract within 20.
1.OA.5 Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).
1.OA.6 Add and subtract within (10) 20, demonstrating fluency for addition and
subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8
+ 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 –
1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g.,
knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or
known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 =
13).
Comments:
Strikethroughs indicate that
only fluency to 10 with
addition and subtraction will
be the focus of the standard
in 1.OA.6 and will be building
blocks for fluency with
numbers to 20 in future units.
Notes on Assessment:
Unit 5 is a modified
assessment using questions
from chapter 3 and 4.
See Common Performance
Task link below
Unpacking the Standards for this Unit:
One of the Critical Areas for Grade 1 is developing an understanding of strategies for addition and subtraction within 20.
Students should use a variety of models, including discrete objects and length-based models (e.g., cubes connected to
form lengths), to model add to, take-from, put-together, take-apart, and compare situations to develop meaning of
addition and subtraction. It is important to move beyond the strategy of counting on, which is considered a less
important skill than others within this unit. Many times teachers believe that counting on is all a child needs, but it is not
significantly better than counting all and can become a hindrance when working with larger numbers. Students
understand connections between counting and addition and subtraction (e.g., adding two is the same as counting on
two). Provide multiple and varied experiences that will help students develop a strong sense of numbers based on
comprehension – not rules and procedures.
Common Performance Task with Rubric for this Unit:
Students explain the reasonableness of using specific strategies to solve problems, show and explain thinking
when using three addends, and show how to think addition when subtracting. Click here for Performance Task
Page
Future learning:
By studying patterns and relationships in addition facts and relating addition and subtraction, students build a
foundation for fluency. When students repeatedly use strategies that make sense to them, they internalize
facts and develop fluency for addition and subtraction within 10.
1
and Rubric.
Global Concept 1 of 5 for this Unit of Study: Counting On/Counting Back
Use counting on or back by 1 or 2 as a strategy to add and subtract.
Sample Essential Questions:
Day 1: How can you count on to add?
Day 2: How can you count back to subtract?
Related Unit 5 Assessment: Go Math Ch. 3 and 4 #
1st
Projected Time
Allotment: 2 days
Instructional Resources
Manipulatives:
• Two Colored Counters- Can be used with Go Math Lessons 3.2 and 4.1
• Dominoes - Do it With Dominoes activity
• Links- Links Away activity
• Number line- A linear model for counting on and counting back. Click here for a model of subtraction
on a number line.
• Hundred Chart- Another representation for counting on and counting back
Lesson Ideas:
• Go Math Lesson 3.2 - TE p.101, Listen and Draw, students will use a number line instead of SE. Share
and Show p.102, Go Deeper TE p. 103, Problem Solving p.104
• Go Math Lesson 4.1- Read problem solving questions aloud and have students complete tasks in their
journals or with manipulatives prior to opening the book.
• Voyages: Tug of War Game
• Do it With Dominoes activity – Lesson 1 Counting On to Add
• Links Away activity – Lesson 1 Counting on and Counting Back
• Plus One/ Plus Two PowerPoint
• Walkable Number Line- Create a number line on your floor using painters tape.
Interactive Online Resources:
• iTools- Number Lines – Adding Activity
• Counters - Adding Activity
For more information about integrating the content within this GCG, click here for the PowerPoint
Sample HOT Questions: Use these to facilitate student discussion. (SMP 1,3)
• Why do you start with the greater addend?
• How do you know where to start counting back when using a number line?
• Explain how counting on and counting back are similar. How are they different?
2
Because as teachers we…
• Provide problem solving scenarios that allow
students to choose their own strategies for solving
(SMP 7)
• Emphasize use of correct vocabulary: Counting on,
counting back, addition, subtraction (SMP 6)
• Provide opportunities for students to select their
own tools for solving problems (SMP 5)
Page
Our students are able to…
• Use the addition and subtraction strategies of
adding on and counting back to solve problems
more efficiently (SMP 7)
• Explain why beginning with the greater number
is a more efficient addition strategy (SMP 3)
• Select appropriate tools to solve addition and
subtraction problems efficiently (SMP 5)
For more info on SMP’s click here.
Global Concept 2 of 5 for this Unit of Study: Doubles
Recognize doubling as a strategy and apply doubles to double plus one and
1
double minus one situations.
Sample Essential Questions:
Day 1: What are doubles facts?
Day 2: How you can use doubles facts to help you add? Explain your thinking
Day 3: How can you use your knowledge of doubles facts to solve other problems?
Related Unit 5 Assessment: Go Math Ch. 3 and 4 #
st
Projected Time
Allotment:
3 days
Instructional Resources
Manipulatives:
• Snap Cubes – Doubles Facts Towers
• Two Colored Counter- Doubles Plus One Task
• Cuisenaire Rods – Cuisenaire Doubles
Lesson Ideas:
• Go Math Lesson 3.3- Listen and Draw p. 105 Problem Solving p.108
• Go Math Lesson 3.4- Listen and Draw p. 109 “Model and Draw” Activity in student journals or using
manipulatives prior to students opening the book p. 110
• Go Math Lesson 3.5- Listen and Draw activity p. 113 “Model and Draw” whole group with
manipulatives without the book
• Illuminations Lesson: Seeing Double
• Plus Doubles PowerPoint
• Voyages Grade 1: Double Up
Interactive Online Resources:
• Animated Math Model- Skill 14: Add Double, Skill 15: Doubles Plus One, Skill 16: Doubles and Doubles
Plus One
For more information about integrating the content within this GCG, click here for the PowerPoint
Sample HOT Questions: Use these to facilitate student discussion. (SMP 1,3)
• What is a doubles fact? Explain your thinking.
• How can a doubles fact can you use to solve 8+7? (From Math Talk in Action: Go Math TE p.113)
• Create a problem that uses the doubles plus one strategy.
• Create a problem that uses the doubles minus one strategy.
3
For more info on SMP’s click here.
Because as teachers we…
• Provide opportunities for students to explore
doubles facts prior to defining (SMP 1)
• Emphasize use of correct vocabulary: addend,
sum, doubles, doubles plus one, doubles minus
one (SMP 6)
Page
Our students are able to…
• Identify and use doubles facts to solve
problems more efficiently (SMP 7)
• Explain when/why they could use a doubles
plus one or doubles minus one fact to solve a
problem (SMP 4)
st
1
Global Concept 3 of 5 for this Unit of Study: Addition and Subtraction With Ten
Decompose numbers to make a ten as a strategy to add and subtract.
Projected Time
Allotment:
4 days
Sample Essential Questions:
Day 1: How can making a ten help you add?
Day 2: How can you decompose a number to help you add?
Day 3: How can making a ten help you subtract?
Day 4: How can you decompose a number to help you add or subtract?
Related Unit 5 Assessment: Go Math Ch. 3 and 4 #
Instructional Resources
For more info on SMP’s click here.
Because as teachers we…
• Provide ample opportunities for students to work
with ten frames to develop an understanding of
making a ten to add and subtract (SMP 5)
• Provide real world problems to give students
context even when one is not provided in the book
(SMP 1)
• Emphasize use of correct vocabulary: decompose,
compose, make a 10 (SMP 6)
Page
Our students are able to…
• Recognize opportunities to use the strategies
making a ten to add and making a ten to subtract
(SMP 7)
• Model the strategies of making a ten to add and
making a ten to subtract appropriately (SMP 5)
4
Manipulatives:
• Ten Frames- students need ample opportunities to work with ten frames to develop an understanding
of making a ten to add and subtract
• Two-Colored Counters/ Snap Cubes- can be used in conjunction with the ten frames
Lesson Ideas:
• Focus on word problems- these give the student a context for understanding the problems
• Go Math Lesson 3.8 Listen and Draw p.125 #4-6 p. 127 Problem Solving p.128
• Go Math Lesson 4.4 Listen and Draw p. 165 Problem Solving p. 168
• Go Math Lesson 4.5 Listen and Draw p. 169 Problem Solving p. 172
• Dana Center Early Mathematics Resource: Lesson 13 Composing 10 to Find a Sum
• Dana Center Early Mathematics Resource: Lesson 14/15 Practicing Addition Sums to 20
• Dana Center Early Mathematics Resource: Lesson 18 Building Up Through 10 to Add and Subtract
• Dana Center Early Mathematics Resource: Lesson 19 Backing Down Through 10 to Subtract
Interactive Online Resources:
• Animated Math Models- Skill 17: Make a ten to Add
For more information about integrating the content within this GCG, click here for the PowerPoint
Sample HOT Questions: Use these to facilitate student discussion. (SMP 1, 3)
• Rebecca used the counting on strategy to solve 7+8. Jessica used the make a ten strategy to solve 7+8.
Who used the more efficient strategy? Explain your thinking.
• When would you use the make a ten strategy? Why?
• Liz used the make a ten strategy to create the problem 10 + 5. What could have been the original
problem?
Global Concept 4 of 5 for this Unit of Study: Think Addition to Subtract
Projected Time
Allotment:
Identify the relationship between addition and subtraction and how addition can
1
2 days
be used to solve subtraction.
Sample Essential Questions:
Day 1: How can you rewrite a subtraction problem as an addition problem?
Day 2: How can you use addition to help find the answer to a subtraction problem?
Related Unit 5 Assessment: Go Math Ch. 3 and 4 #
st
Instructional Resources
Manipulatives:
• Snap Cubes/Two-Colored Counters– Can be used to model problem solving scenarios with and without
the tens frame
• Tens Frame- Can be used to model problem solving scenarios in order to visualize the relationship
between addition and subtraction
Lesson Ideas:
• Go Math Lesson 4.2- Listen and Draw: facilitate discussion using Math Talk p. 157 #8-9 p.159 Problem
Solving- Be looking for students that solve using addition and those that solve using subtraction so
both representations can be shared with the group p. 160
• Go Math Lesson 4.3- Listen and Draw p. 161 #17 p. 163
• Dana Center Early Mathematics Resource: Lesson 16 Relating Addition to Subtraction
• Dana Center Early Mathematics Resource: Lesson 17 Subtraction as “Think Addition”
Interactive Online Resources:
• Animated Math Model- Skill 20: Think Addition to Subtract , Skill 21: Relate Addition to Subtract
For more information about integrating the content within this GCG, click here for the PowerPoint
Sample HOT Questions: Use these to facilitate student discussion. (SMP 1, 3)
• How did you use the addition model to solve the subtraction problem?
• What subtraction sentence could be used to solve 2+6=8?
• How could a doubles fact help you to solve the following problem: Sue had 8 seashells, but she gave 4
away. How many seashells does she have now?
• How can 6+7 help you solve 13-6? How do you know?
5
For more info on SMP’s click here.
Because as teachers we…
• Provide students with problem solving
opportunities that go beyond basic recall and allow
them to think critically about the relationship of
addition and subtraction (SMP 2)
• Encourage students to explain their thinking
through discussion, journaling, and using
manipulatives (SMP 1, 3)
• Emphasize use of correct vocabulary: inverse
operation, opposite (SMP 6)
Page
Our students are able to…
• Think flexibly about problem solving situations in
order to solve subtraction problems by relating
them to addition (SMP 1, 2)
• Clearly express their understanding of the
relationship between addition and subtraction
using verbal and written representations (SMP 3)
• Use their understanding of other strategies to
help them solve subtractions problems by
thinking addition (SMP 7)
st
1
Global Concept 5 of 5 for this Unit of Study: Add Three Numbers
Solve problems with three addends using appropriate strategies.
Projected Time
Allotment:
2 days
Sample Essential Questions:
Day 1: How can you solve an addition problem with three addends?
Day 2: How can you group numbers to add three addends?
Related Unit 5 Assessment: Go Math Ch. 3 and 4 #
Instructional Resources
Manipulatives:
• Snap Cubes/Counters- can be used to model problem solving scenarios
• Tens frames- can be used to model problem solving scenarios
Lesson Ideas:
• Go Math Lesson 3.9- Listen and Draw p.129
• Go Math Lesson 3.10- Listen and Draw p.133
• Go Math Lesson 3.11- Listen and Draw p.137 Problem Solving p.140
• Go Math Lesson 3.12- Try Another Problem p.143 Any of the problems on- Make sure to have students
explain how/why they grouped the addends in order to meet day 2’s objective p. 143 and 144
Interactive Online Resources:
• Animated Math Model- Skill 18: Add 3 Numbers
For more information about integrating the content within this GCG, click here for the PowerPoint
Sample HOT Questions: Use these to facilitate student discussion. (SMP 1, 3)
• How did you choose which pair of addends to add first?
• Carlos and Lisa solved the problem 8+3+2=. Carlos added 8+2 first. Lisa said you must add 8+3 first. Do
you agree with Lisa’s thinking? Why or why not?
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6
Our students are able to…
Because as teachers we…
• Students are using tools to model their
• Helping students make connections between
thinking when adding up to three whole
strategies by selecting and sequencing students
numbers (SMP 4)
chosen to share (such as those that make a ten)
(SMP 3,7)
• Students are using their knowledge of making
*For more information on selecting and
a ten and doubles strategies to help them
sequencing students check out the Hot Talk Cool
with addition of three whole numbers (SMP
Moves Training offered through the district.
8)
• Providing tools that help students model their
thinking (SMP 5)
• Facilitating discussion as to how to apply observed
patterns and previously learned strategies to new
For more info on SMP’s click here.
problems (SMP 7)