Q: Joe works for 7 days earning $20 a day, and Bill works for $7 a day for 20 days. Who ends up with more money?

7 × 20 = 140 and 20 × 7 = 140. They end up with the same amount of money.

Q: There are 3 grade 3 classes, each with 20 students. If each grade 3 student gets 5 cookies, can you write a mathematical expression to represent how many cookies there are in total?

3 × 20 × 5. Ask if anyone found any other way to represent the expression.

Q: Put parentheses around the factors that you will multiply first to make it easier to solve: 9 × 8 × 5. Which property allows you to do that?

9 × (8 × 5); the associative property.

Question 1

What is a factor? Can you give an example?

Accepted Answer

A factor is a number that another number can be divided by. A factor is a number that divides another number. A factor is a number that, when multiplied by another number, makes a certain product.

Question 2

What is a product? Can you think of an example?

Accepted Answer

When you multiply numbers together, the result is called the product. 20 is the product of 4 and 5.

Question 3

What are some factors of 24?

Accepted Answer

The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.

Question 4

Joe works for 7 days earning $20 a day, and Bill works for $7 a day for 20 days. Who ends up with more money?

Accepted Answer

7 &times; 20 = 140 and 20 &times; 7 = 140. They end up with the same amount of money.

Question 5

There are 3 grade 3 classes, each with 20 students. If each grade 3 student gets 5 cookies, can you write a mathematical expression to represent how many cookies there are in total?

Accepted Answer

3 &times; 20 &times; 5. Ask if anyone found any other way to represent the expression.

Question 6

State the commutative property in your own words.

Accepted Answer

When we multiply, the order in which we multiply does not change the product.

Question 7

What is the name of the property that says that multiplying two factors is the same as splitting one of the factors into two parts, multiplying both parts by the other factor, and adding the products together?

Accepted Answer

The distributive property.

Question 8

State the associative property in your own words.

Accepted Answer

When we multiply, we can group the factors in any order and the product will be the same.

Question 9

We can use the distributive property to write 5 &times; 23 as (5 &times; 4) + (5 &times; 19). Does this make it easier to find the product? Can you think of a better way to split 23?

Accepted Answer

No, this expression is not easier. A better way is to split 23 into 20 and 3: (5 &times; 20) + (5 &times; 3).

Question 10

Put parentheses around the factors that you will multiply first to make it easier to solve: 9 &times; 8 &times; 5. Which property allows you to do that?

Accepted Answer

9 &times; (8 &times; 5); the associative property.

Multiplication Properties (Commutative, Associative & Distributive)

Discussion Questions

Vocabulary

Reading Material

Practice Word Problems

Practice Number Problems

Lesson Plan

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Assessment