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.

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.)

Enduring Understanding

Mathematical operations are used in solving problems in which a new value is produced from one or more values.
Algebraic thinking involves choosing, combining, and appying effective strategies for answering

Essential Questions

In what ways can operations affect numbers?
How can different strategies be helpful when solving a problem?

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.

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

Rich Problems:

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.

## 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.)

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

(Commutative property of addition)

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

(Commutative property of addition).

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.)

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.)

Mathematical operations are used in solving problems in which a new value is produced from one or more values.Enduring UnderstandingAlgebraic thinking involves choosing, combining, and appying effective strategies for answering

In what ways can operations affect numbers?Essential QuestionsHow can different strategies be helpful when solving a problem?

addition, add, subtraction, subtract, commutative, associative propertyVocabulary (online dictionary, HCPSS Vocabulary Cards)

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.About the MathAsk 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.

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

Rich Problems: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:Print ResourcesBrain Compatible Activities for Mathematics 2-3

(33-35)

Super Source Snap Cubes K-2

(70-73)

Nimble with Numbers 2-3

(98-99)

Web Resources:Games and CentersLessonsStudent ResourcesVideo SegmentsTurn Around Trains

Turn Around Dominoes

Domino Fact Families

Introduction to Fact Families

Commutative Property

Let's Learn Those Facts

One Two Switcheroo

Lesson Seeds

Teaching Commutative Property

Grouping to Make Seven

Connecting Children's Literature:Click on the books for additional activities.Math Fablesby Greg TangMath Fables Tooby Greg Tang

## Questions/Comments:

Contact John SanGiovanni at jsangiovanni@hcpss.org.Use and Sharing of HCPSS Website and Resources: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.