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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

Algebra in the Early Grades

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

slide2
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

associative law of addition
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)

associative law of multiplication
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)

commutative law of addition
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

commutative law of multiplication
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

the distributive law
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

slide8
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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