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.)

Quarter 1
===Quarter 2===

Quarter 3
===Quarter 4===

Apply properties of operations as strategies to add and subtract.

If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known.

(Commutative property of addition)

Apply properties of operations as strategies to add and subtract.
Commutative property of addition continued
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.)
Apply properties of operations as strategies to add and subtract.

If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known.

(Commutative property of addition).

Apply properties of operations as strategies to add and subtract.

Commutative property of addition continued

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.)
Apply properties of operations as strategies to add and subtract.

Commutative property of addition continued

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.)
Apply properties of operations as strategies to add and subtract.

Commutative property of addition continued.

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.)

Increasing Rigor

  • How would you describe the commutative property to someone from another planet?
  • Show me 2 different examples that proves the commutative property.
  • Why does the total stay the same, even though you are adding in a different order? (example 6+5=11 and 5+6=11) Use drawings and/or models to help explain.
  • Would you get the same sum if you had two blue buttons and three red buttons as you would if you had three blue buttons and two red buttons? Can you write the addition sentences that show that?
  • Laura had 5 fish. Her mother gave her 1 more. Laura’s brother Frank had 1 fish. Their mother gave Frank 5 more. Laura cried, “That’s not fair! He has more fish than I do!” Frank doesn’t agree. Who is correct? How you know?
  • I own a pet store. There are 9 dogs, 1 cat and 3 fish in the store. How many pets are in the store? What number sentence could you write to match this story problem? Where is 10 in this number sentence? What new number sentence could we write to match what we did?
  • Laura solved the following problem: 7 + 2 + 3 = 12 How do you decide which numbers to add together first? What “friendly” number combinations do you see? Will we get the same number if we solve it different ways?

About the Math

It is a focus for students to discover and apply the commutative and associative properties as strategies for solving addition problems. Students do not need to learn the names for these properties. It is important for students to share, discuss, and compare their strategies as a class. First graders should be working with sums and differences less than or equal to 20 using the numbers 0 to 20.

Ask students to show addition problems using unifix cubes or linker cubes. Say: "Show me 5 + 4 using two different colors". Students could show 5 red cubes and 4 blue cubes. Ask them to look at the bar and then turn it over so there are 4 blue cubes and 5 red cubes. Ask: So is 5 + 4 the same as 4 + 5? How do you know?
Provide investigations that require students to identify and then apply a pattern or structure in mathematics. For example, pose a string of addition and subtraction problems involving the same three numbers chosen from the numbers 0 to 20, like 4 + 13 = 17 and 13 + 4 = 17. Students analyze number patterns and create conjectures or guesses. Have students choose other three number combinations and explore to see if the patterns work for all numbers 0 to 20. Students then share and discuss their reasoning. Be sure to highlight students’ uses of the commutative and associative properties and the relationship between addition and subtraction. Essential vocabulary for this standard includes: addition, add, subtraction, subtract, commutative, and associative property (online dictionary, HCPSS Vocabulary Cards).

The Illustrative Mathematics tasks below demonstrate expectation for this standard

Rich Tasks for Multiple Means of Engagement, Expression, and Representation (UDL)

Rich Problems:
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Give students some unifix cubes. Tell them the sum is 12. Ask them to show what two numbers were added together to get 12 using . Use your unifix cubes or linker cubes to show the two numbers that are represented by two different colors. Share all the ways to make 12.

Instructional Resources:
One focus in this cluster is for students to discover and apply the commutative and associative properties as strategies for solving addition problems. Students do not need to learn the names for these properties. It is important for students to share, discuss and compare their strategies as a class. The second focus is using the relationship between addition and subtraction as a strategy to solve unknown-addend problems. Students naturally connect counting on to solving subtraction problems. For the problem “15 – 7 = ?” they think about the number they have to add to 7 to get to 15. First graders should be working with sums and differences less than or equal to 20 using the numbers 0 to 20.

Expand the student work to three or more addends to provide the opportunities to change the order and/or groupings to make tens. This will allow the connections between place-value models and the properties of operations for addition to be seen. Understanding the commutative and associative properties builds flexibility for computation and estimation, a key element of number sense.

Provide multiple opportunities for students to study the relationship between addition and subtraction in a variety of ways, including games, modeling and real-world situations. Students need to understand that addition and subtraction are related, and that subtraction can be used to solve problems where the addend is unknown.

Journal Prompt:
  • Roll two dice and draw them. Write the number sentence and the turn around fact. Repeat.
  • Build a two color train using less than 10 unifix cubes. Place cubes of the same color together. Draw your train and write a matching number sentence. Flip the train and write the turn around fact. Repeat with other trains.
  • Molly was excited. She said "Look what I found out, 2+4=6 and 4+2=6." "Molly said, "I can show you why that works." Describe what Molly did.
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Print Resources

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Brain Compatible Activities for Mathematics 2-3
(33-35)
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Super Source Snap Cubes K-2
(70-73)
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Nimble with Numbers 2-3
(98-99)



Web Resources:

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Games and Centers
Lessons
Student Resources
Video Segments
Printables
Turn Around Trains
Turn Around Dominoes
Domino Fact Families
Expresso 3 Numbers
Lessons
Introduction to Fact Families
Commutative Property
Finding Addition Patterns
One Two Switcheroo
More and More Buttons
12 apples and bananas
4 Square Fact or Fiction
10 and some more
Turnaround Trains (Michelle Glenn, CLES)


Connecting Children's Literature:

Click on the books for additional activities.

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Math Fablesby Greg Tang
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Math Fables Too
by Greg Tang


Questions/Comments:

Contact John SanGiovanni at jsangiovanni@hcpss.org.


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Howard County Public Schools Office of Elementary Mathematics Curricular Projects has licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.