Algebraic Thinking: Properties of Whole Numbers CCSS 3.OA.5

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Table of Contents

There are 5 different types of properties of whole numbers. At the end of the lesson, students will be able to apply properties of operations as strategies to multiply and divide.

See the fact file below for more information on the properties of whole numbers or alternatively, you can download our 23-page Algebraic Thinking: Properties of Whole Numbers CCSS 3.OA.5 worksheet pack to utilise within the classroom or home environment.

Key Facts & Information

LEARNING OBJECTIVE

At the end of the lesson, students will be able to apply properties of operations as strategies to multiply and divide.

A NOTE FOR THE TEACHER

When teaching properties of numbers, try the following in your lesson:
- Using an array to show different layouts for the same product is a good way to start.
- Emphasize that the properties below apply only to addition and multiplication and does not apply to subtraction and division.
- It helps to say the factors and product out loud so that the learner can repeat it.

THEORY

There are 5 different types of properties of whole numbers:
- Identity property is the product of any number and 1 is equal to that number.
- The Zero property is the product of any number and zero is equal to 0.
- Commutative property for addition and multiplication.
- Associative property for addition and multiplication.
- Distributive property of multiplication over addition.
The identity property says that any number multiplied by 1 is equal to that number.
We therefore say that the IDENTITY ELEMENT for MULTIPLICATION is 1
- Example: 5 x 1 = 5
The zero property says that any number multiplied by 0 is equal to 0. We therefore say that the IDENTITY ELEMENT for MULTIPLICATION is 0
- Example: 5 x 0 = 0
The commutative property says that the numbers can be added or multiplied in any order, and you will still get the same answer. This does not apply to subtraction and division.
Example:
- 3 x 4 = 12 or 4 x 3 = 12
The associative property says that the way in which factors are grouped in a multiplication problem does not change the product. This does not apply to subtraction and division.
Example:
- 2 x 5 x 4 = or
- 5 x 4 = 20 2 x 5 = 10
- 20 x 2 = 40 10 x 4 = 40
The distributive property of multiplication over addition can be used when you multiply a number by a sum.
Example :
- 3 x (2 + 3) = 15
- 3 x 2 = 6
- 3 x 3 = 9 6 + 9 = 15