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Domain: Operations and Algebraic Thinking Cluster: Understand and apply properties of operations and the relationship between addition and subtraction. 1.OA.B.3 Apply properties of operations as strategies to add and subtract.* 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 = 10+2 = 12. (Associative property of addition.) *Students need not use formal terms for these properties. Notes to Teacher: Adding more than two numbers (1.OA.A.2) is the ideal context for developing students’ understanding of number properties—specifically the commutative and associative properties. As students work with three addends teachers should encourage them to explore different ways to combine the numbers to make them easier to add. Ask students to try changing the order of the addends to see if there is a particular order that works best. Ask them to check the solutions each time to verify that the sum doesn’t change (commutative property). Ask students to group the numbers in different ways to see if there is a particular grouping that works best. Ask them to check the solutions each time to verify that the sum doesn’t change (associative property). Provide students with numerous opportunities to share their thinking with each other. Facilitate conversations about various strategies that children used to solve these problems. Through these discussions, guide students to discover that order and grouping do not affect the sum. Task Explanation/Comments Sample Student Work There are 4 boys and 5 girls on Laticia’s Example of Commutative Property of soccer team. There are 5 boys and 4 girls on Addition her brother’s team. Laticia says that she knows that there is the same number of players on both teams because she knows that 4+5 and 5+4 are the same amount. Do you agree with Laticia? Explain. You may use objects or drawings to help you solve this problem. On Monday, 3 girls and 2 boys sat at the round table. 4 boys sat at the square table. Use objects or drawings to represent this situation. On Tuesday, only the 3 girls sat at the round table. Two boys sat with the other 4 boys at the square table. Use objects or drawings to represent this situation. Regina says that there were more children seated at the tables on Monday than on Tuesday. Do you agree? Explain. Example of Associative Property of Addition