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Algebra in the Early Grades

Algebra in the Early Grades. Session 8: What does understanding the laws of arithmetic mean in the elementary grades? Part 1. The laws of arithmetic (AKA: Algebraic Properties): Associative law of addition Associative law of multiplication Commutative law of addition

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Algebra in the Early Grades

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  1. Algebra in the Early Grades Session 8: What does understanding the laws of arithmetic mean in the elementary grades? Part 1

  2. The laws of arithmetic (AKA: Algebraic Properties): Associative law of addition Associative law of multiplication Commutative law of addition Commutative law of multiplication Distributive law

  3. Associative law of addition If you are given three or more numbers to add, such as a + b + c, adding the sum of a + b to c is the same as adding a to the sum of b + c. (a + b) + c = a + ( b + c)

  4. Associative law of multiplication If you are given three or more numbers to multiply, such as a x b x c, multiplying the product of a x b to c is the same as multiplying a to the product of b + c. (a x b) x c = a x ( b x c)

  5. Commutative law of addition If you are given two numbers to add, such as a + b, the sum of a + b is the same as the sum of b + a. a + b = b + a

  6. Commutative law of multiplication If you are given two numbers to multiply, such as a x b, the product of a x b is the same as the product of b x a. a x b = b x a

  7. The distributive law The product of a number and a sum such as a(b + c) is the same as the product of the number and the parts of the sum. a(b + c) = ab + ac

  8. Looking at the student thinking in this reading, where are the students in relation to understanding the laws of arithmetic? What are they on the verge of learning?

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