Multiples of Tens and Hundreds

Est. Class Sessions: 1–2

Developing the Lesson

Use Base-Ten Pieces to Multiply. Direct students' attention to Question 1 on the Multiples of Tens and Hundreds page in the Student Guide. Reference the patterns for tens on the multiplication table and the notes on 10s from the Patterns for Remembering the Facts class chart when discussing the question.

Read the short vignette that follows. It introduces the use of base-ten pieces to help students see patterns when multiplying numbers by multiples of ten or one hundred.

Ask:

What is a multiple? (Possible response: When you skip count, you say the multiples of a number.)
Give some examples of multiples of 10. (Answers will vary. Possible responses: 20, 80, 360, etc. Any number times 10 is a multiple of 10.)
Give some examples of multiples of 100. (Answers will vary. Possible responses: 400, 900, 1600, etc. Any number times 100 is a multiple of 100.)
What do you notice about multiples of 10 and multiples of 100? (They all end in zeros.)

Assign Questions 2–6. Students will use base-ten shorthand to help them see patterns while solving problems and then describe the patterns. For Question 6, students use the patterns to make predictions about larger numbers and check their predictions with a calculator.

When students have finished, discuss Question 5.

Ask:

What patterns did you find when you multiplied by a multiple of ten? (Possible response: When you multiply a number by a ten, you just multiply the first digits and then add a zero onto the end of the product.)
Can you give an example? (Possible response: To multiply 3 × 50, multiply 3 × 5 to get 15 and then write a zero after the 15, 150.)
Why do you add a zero at the end of the product? (Possible response: You have to add a zero because you are not just multiplying 3 times 5 ones. You are multiplying 3 times 5 tens.)
What patterns did you find when you multiplied by a multiple of one hundred? (Possible response: When you multiply a number by a hundred, you multiply the first digits and then add two zeros onto the end of the product.)
Can you give an example? (Possible response: To multiply 3 × 500, multiply 3 times 5 to get 15 and then write two zeros after the 15, 1500.)

This pattern is correct and students may use it to solve problems. However, it is important to discuss why the pattern works. See the Sample Dialog in which the students are discussing 3 × 50 and 3 × 500. To remind students that they are multiplying by tens and hundreds, ask them to justify their answers for Question 4 with a display set of base-ten pieces.

Ask:

Use base-ten pieces to show and tell how you solved 4 × 3, 4 × 30, and 4 × 300. (Possible response: 4 groups of 3 bits is 12. 4 groups of 3 skinnies is 12 skinnies or 12 tens. 10, 20, 30, and so on. 12 × 10 = 120. 4 groups of 3 flats is 12 flats or 12 hundreds. 100, 200, 300, and so on. 12 × 100 = 1200.)

Students discussing 3 × 50 and 3 × 500:

Teacher: Why do you think your pattern works? Think about what you did with the base-ten pieces.

Luis: When I used the skinnies, I laid down 5 skinnies 3 times and then I had 15 skinnies. Then, I skip counted by fives until I got to 150.

Nila: What does that have to do with tens?

Teacher: That's a good question. What do you think, Luis?

Luis: Well, 15 skinnies is 15 tens, that's like 15 times 10 and that's 150. It follows the pattern on the multiplication chart for 10s.

Teacher: Does it work the same way for multiplying by 100, 200, 300, and so on?

Ana: It's the same, but you use flats. Lay down 5 flats 3 times and you have 15 flats. 15 flats is 15 hundreds.

Teacher: Write that as a number sentence. [Ana writes 3 × 500 = 1500.] Read your number sentence for me.

Ana: Three times 500 equals fifteen hundred.

Teacher: That's one way to read it. What if you showed 15 flats in the fewest pieces rule? What pieces would you have?

Ana: I would trade 10 flats for one pack. That's 1000. I would still have 5 flats. So I would have one thousand five hundred.

Teacher: So fifteen hundred is the same as one thousand five hundred.

Multiply with Function Machines. Direct students' attention to the Multiply with Function Machines pages in the Student Activity Book. Assign Questions 1–5. Encourage students to use base-ten pieces or base-ten shorthand as needed to solve or check the problems.

When students are finished, discuss the problem 8 × 50 in Question 2. Some students may have difficulty when the fact within the problem itself generates a zero. 5 × 200 in Question 3, and 5 × 400 in Question 5 involve similar problems.

Ask:

Explain how you solved 8 × 50. (Possible response: I multiplied 8 × 5 and got 40. Then I added another 0 at the end of 40 because I was multiplying 5 tens, not just 5 ones.)
Can someone find another way to check that problem? (Possible response: I thought of money and doubling. 2 × 50¢ = 100¢, 4 × 50¢ = 200¢, and 8 × 50¢ = 400¢. 8 × 50 = 400.)
Did anyone make a mistake on this problem? Can you explain why? (Possible response: Yes. At first I wrote 8 × 50 = 40. I thought since 50 was a ten that there should be one 0 on the answer, but that didn't make sense.)
Why does the product of 8 × 50 yield two zeros? (There is one zero from 8 × 5 = 40, and another zero because I multiplied 5 tens. 8 × 5 tens is 400.)
In the table for Question 3, how did you find the input when the output was 600? (Possible response: I thought, “How many 200s would I need to get to 600?” 200 + 200 + 200 = 600, so 3 × 200 = 600. The input is 3.)