Demonstrate the commutative property of multiplication by arranging the same number of “chocolate chips” on two different batches of “cookies”.

Curriculum Topics: The Commutative Property of Multiplication, Patterns & Relationships

### Standards

Idea Sheets are cross-referenced to subjects listed in the Common Core, Next Generation Science Standards, and California Content Standards.

Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 3||Mathematical Practices|||3.OA.5. Apply properties of operations as strategies to multiply and divide.2 Examples: If 6 ? 4 = 24 is known, then 4 ? 6 = 24 is also known. (Commutative property of multiplication.) 3 ? 5 ? 2 can be found by 3 ? 5 = 15, then 15 ? 2 = 30, or by 5 ? 2 = 10, then 3 ? 10 = 30. (Associative property of multiplication.) Knowing that 8 ? 5 = 40 and 8 ? 2 = 16, one can find 8 ? 7 as 8 ? (5 + 2) = (8 ? 5) + (8 ? 2) = 40 + 16 = 56. (Distributive property.)||Common Core Mathematics||Grade 3||Operations And Algebraic Thinking||Understand Properties Of Multiplication And The Relationship Between Multiplication And Division|||Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 4||Mathematical Practices|||4.OA.1. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 ? 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.||Common Core Mathematics||Grade 4||Operations And Algebraic Thinking||Use The Four Operations With Whole Numbers To Solve Problems|||4.OA.2. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.1||Common Core Mathematics||Grade 4||Operations And Algebraic Thinking||Use The Four Operations With Whole Numbers To Solve Problems

1.5 Recognize and use the commutative and associative properties of multiplication (e.g., if 5 x 7 = 35, then what is 7 x 5?, if 5 x 7 x 3 = 105, then what is 7 x 3 x 5?).||CA Mathematics||Grade 3||02. Algebra and Functions||1.0 Students select appropriate symbols, operations and properties to represent, describe, simplify, and solve simple number relationships.|||1.1 Use letters, boxes, or other symbols to stand for any number in simple expressions or equations (e.g., demonstrate an understanding and the use of the concept of a variable).||CA Mathematics||Grade 4||02. Algebra and Functions||1.0 Students use and interpret variables, mathematical symbols, and properties to write and simplify expressions and sentences.

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