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Algebra in the Early Grades

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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

Commutative law of multiplication

Distributive law

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)

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)

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

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 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

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?