## Lesson: Multiplying Multiples of 10 Developing the Concept

In this lesson, students further their understanding of multiplication by using basic multiplication facts and word names for factors that are multiples of 10. The focus is on pattern development and multiplication properties.

Materials: base-ten blocks, colored chalk

Preparation: none

Prerequisite Skills and Background: Students should know the basic multiplication facts, how to use base-ten blocks, word names for multiples of 10, and how to multiply by 10 and 100. Students should also recall the Property of One for Multiplication.

• Say: Today we will practice multiplying by multiples of 10. How can I find the product of 3 tens and 8 ones? (Multiply the two numbers.)

Write “3 tens x 8 ones = n” on the board.

• Ask: What is 3 times 8? (24)
• Ask: What is the product of tens and ones? (tens) How do you know? (Any number times 1 is that number.) What property states this? (the Property of One for Multiplication)
• Ask: What is the final product? (24 tens)
• Say: So we used the basic fact of 3 times 8 to make 24. Then we found the product of tens and ones, which is tens. How can we write the product? (24 tens or 240)

Write 240 in place of n on the board.

• Say: Let's see if there is a change when I find the product of 8 tens and 3 ones. Write 8 tens x 3 ones = n on the board.
• Ask: What is the product of 8 and 3? (24) What is the product of tens and ones? (tens) What is the final product? (24 tens)

Replace n with 240 on the board.

• Ask: How are these two multiplication sentences alike? (Both have the same product, the same digits 3 and 8, and both have “tens” and “ones.”)
• Ask: How can we write the factors without words? (Rewrite 8 tens as 80, 3 ones as 3, 3 tens as 30, and 8 ones as 8.)

Write 30 x 8 = 240 and 3 x 80 = 240 on the board.

• Ask: Why do you think the products each have one zero? (Students should realize that there is one zero in the factors for each sentence.)

Using colored chalk, draw an arrow from each zero in the factor to the zero in the product.

• Ask: What do you notice? (There is one zero in the factors and one zero in the product.)
• Ask: What other basic facts have products equal to 24? (4 and 6, 6 and 4)

Write 4 x 6 = 24 on the board. Then write 4 x 6 = 240 and 4 x 6 = 240.

• Ask: In each sentence, what can I do to one factor so that the product is 240? (Write a zero to the right of 4 in the first sentence and a zero to the right of 6 in the second sentence.) Using colored chalk write a zero in each blank.

Engage students in a discussion that helps them understand that each factor is now 10 times greater than the original factor.

Now the board shows 40 x 6 = 240 and 4 x 60 = 240. Draw an arrow from each zero in the factors to the corresponding zero in the products.

• Ask: What do you notice? (There is one zero in the factors and one zero in the product.) How many times greater than 24 is 240? (10 times)

Write 60 x 70 = n on the board.

• Ask: What basic multiplication fact can you use? (6 x 7 = 42)
• Ask: What is the product of tens and tens? (hundreds)
• Ask: What is the final product? (42 hundreds)
• Ask: How can we write the product? (4,200)

Replace n with 4,200. Using colored chalk, draw arrows from the zeros in the factors to the zeros in the product.

• Ask: What do you notice? (There are 2 zeros in the factors and 2 zeros in the product.)
• Provide a few more examples that have multiples of 10 as factors. Guide students to realize that counting the number of zeros in the factors will determine the number of zeros in the product after the basic fact has been written.

Wrap-Up and Assessment Hints
This concept is essential to ensure accurate mental math. Have students work in pairs to quiz each other with similar examples. One student can write the multiplication expression, having either one or both factors as multiples of 10, on one side of an index card. The other student can write its product on the other side of the card. Exchange cards between pairs of students for checking.