## Multiplying Multiples of 10

Introducing the Concept

Introduce students to this topic by showing them how they can use doubling, the multiplication properties, and basic multiplication facts to multiply by 10 and multiples of 10.

**Materials:** none

**Preparation:** none

**Prerequisite Skills and Background:** Students should know the basic multiplication facts.

**Ask:***When 0 is a factor in a multiplication sentence, what is the product?*(0)

Have students suggest examples of multiplication sentences in which 0 is a factor.Write

**5 x 0 = 0**on the board.**Ask:***Will the product change if 5 is doubled?*

Give students time to formulate their answers. You may want to take a vote to see how many students believe that the product will change. Students should conclude that the product will remain unchanged.Write

**2 x 5 x 0 = 2 x 0**under the first sentence.**Ask:***Why doesn't the product change?*(Because doubling 0 is still 0; 2 x 0 = 0.)**Ask:***How can we use the Associative Property to make this sentence easier to multiply?*

(Place parentheses around 2 and 5 in the sentence. (2 x 5) x 0 = 2 x 0.)Write parentheses around 2 and 5:

**(2 x 5) x 0 = 2 x 0.****Ask:***Let's find 2 x 5 and 2 x 0. What new sentence do we get?*(10 x 0 = 0)Write

**10 x 0 = 0**on the board.**Ask:***Notice that our first sentence now has a factor of 10. What happens to the product when I double 10?*(Students should now realize that doubling 0 is still 0.)Write

**20 x 0 = 0**on the board. Continue doubling the factor. Guide students to realize that doubling the factor to 40, then 80, will not change the product of 0.Write

**5 x 3 =**on the board.*n***Ask:***Now look at the sentence 5 x 3 =**n.**What is the product of 5 and 3?*(15) Replace*n*with 15.**Ask:***What will happen when you double 5?*(Students should recognize that the product will also double.)Write

**2 x 5 x 3 = 2 x 15**below**5 x 3 = 15.****Ask:***Do you see factors of 10 in this equation?*(yes)*How can we use the Associative Property to help us?*(Guide students to associate 2 and 5 by placing parentheses around the first two factors.)*What is double 15?*(30)After placing the parentheses in the sentence, write the sentence

**10 x 3 = 30**below it.**Ask:***Let's double 10. What will happen?*(Have students share their predictions.)Write

**(2 x 10) x 3 = 2 x 30**on the board. Then write**20 x 3 = 60**below it.**Ask:***How do the sentences compare? Why?*(Students should recognize that both sentences have the same meaning.)**Ask:***We now have a factor of 20. What will happen if we double 20?*(After students answer, write**40 x 3 = 120**on the board.)Circle the following 3 sentences on the board:

**10 x 3 = 30, 20 x 3 = 60, 40 x 3 = 120.****Ask:***What patterns do you see in these sentences?*

Students should recognize the basic facts of 1 x 3 = 3, 2 x 3 = 6, and 4 x 3 = 12. They should also recognize that each product has a zero in the ones place because one factor in each sentence is a multiple of 10.