# Lesson 12

Multiply Multiples of Ten

## Warm-up: Notice and Wonder: Tens (10 minutes)

### Narrative

The purpose of this warm-up is to elicit the idea that 3 groups of 40 can also be seen as 12 groups of 10, which will be useful when students multiply one-digit whole numbers by multiples of 10 in a later activity. While students may notice and wonder many things, seeing that the total can be decomposed into rows of 30 and further decomposed into units of 10 are the important discussion points.

### Launch

• Groups of 2
• Display the image.
• “What do you notice? What do you wonder?”
• 1 minute: quiet think time

### Activity

• 1 minute: partner discussion
• Share and record responses.

### Student Facing

What do you notice? What do you wonder?

### Activity Synthesis

• “What is the value the diagram represents?” (120)
• “How could noticing groups of ten help us find the total number of squares?” (There are 3 groups of 4 tens, which is 12 tens. There are 4 groups of 30, which is 12 tens. We could count by tens to find the total. We know 12 tens would be 120.)
• Record equations that reflect student thinking such as $$3 \times 4 \times 10 = 12 \times 10$$ and $$4 \times 30 = 12 \times 10$$.

## Activity 1: A Whole Lot of Dollars (15 minutes)

The purpose of this activity is for students to work with products of whole numbers and multiples of 10 in a concrete and familiar context before reasoning more abstractly about them. Given some numbers of dollar bills (for instance, four \$20 bills), students write expressions to represent the amount ($$4 \times 20$$) and then find its value using strategies that make sense to them. For example, they may count by 20 four times, think of \$20 in terms of two \$10 bills and find $$4 \times 2 \times 10$$ (or $$8 \times 10$$). Consider giving students access to play money, if available, to help them visualize the quantities and support their reasoning. The reasoning here prompts students to use strategies based on place value and properties of operations (especially the associative property). It prepares students to work more flexibly with products involving factors and multiples of 10 in which the product is greater than 100. MLR8 Discussion Supports. Prior to solving the problems, invite students to make sense of the situations and take turns sharing their understanding with their partner. Listen for and clarify any questions about the context. Advances: Reading, Representing Engagement: Develop Effort and Persistence. Check in and provide each group with feedback that encourages collaboration and community. For example, ensuring each member of the group has a chance to share their solution and thinking. Supports accessibility for: Social-Emotional Functioning ### Required Materials Materials to Gather Materials to Copy • Centimeter Grid Paper - Standard ### Launch • Groups of 2 • “We’re going to solve a problem about a game that involves play money. What do you know about games that involve play money?” • 1 minute: quiet think time • Share responses. • Give students access to base-ten blocks, grid paper, and play money, if available. ### Activity • “Work with your partner to complete the problems.” • 7-10 minutes: partner work time • In the last problem monitor for students who use the following strategies to highlight in the synthesis: • Count by multiples of 10 to find a total, such as 50, 100, 150, 200, 250, 300. • Use place value to find a total, such as knowing that 14 tens is 10 tens or 100, and 4 more tens or 40, which makes 140. ### Student Facing Six friends are playing a board game that uses play money. The paper bills come in \$5, \$10, \$20, \$50, and \$100.

1. Every player received \$100 to start. Which of the following could be the bills that a player received? Write an expression to represent the play bills and the amount in dollars. bills expression dollar amount one \$100 bill
four \$20 bills ten \$10 bills
ten \$5 bills five \$20 bills
twenty \$10 bills twenty \$5 bills
two \$50 bills 2. At one point in the game, Noah had to pay Lin \$150. He gave her that amount using the same type of bill.

1. Which bill and how many of it could Noah have used to make \$150? Name all the possibilities. 2. Write an expression for each way that Noah could have paid Lin. 3. The table shows what the players had at the end of the game. The person with the most money wins. Who won the game? Write an expression to represent the bills each person has and the amount in dollars. player bills expression dollar amount Andre nine \$10 bills and ten \$5 bills Clare fourteen \$10 bills
Jada ten \$10 bills and three \$50 bills
Lin eight \$20 bills Noah six \$50 bills
Tyler twenty-one \$10 bills ### Student Response Teachers with a valid work email address can click here to register or sign in for free access to Student Response. ### Advancing Student Thinking If students don’t find the product of one-digit whole numbers and multiples of 10 in the last problem, consider asking: • “What have you tried so far to find the product?” • “How could you represent the product with base-ten blocks?” ### Activity Synthesis • Invite students to share different combinations of the same bill that could be used to make \$150. Record and display expressions for each combination.
• Select previously identified students to share their strategies for how they found one of the totals in the last problem.

## Activity 2: Two Strategies (20 minutes)

### Narrative

The purpose of this activity is for students to continue to reason about products of a whole number and a multiple of 10, this time using base-ten blocks to support their thinking. They analyze two strategies for multiplying. Both strategies are based on place value, but the second strategy also uses the associative property to think about $$8 \times 30$$ as $$8 \times 3 \times 10$$ or $$24 \times 10$$.

### Required Materials

Materials to Gather

Materials to Copy

• Centimeter Grid Paper - Standard

### Launch

• Groups of 2
• “Take some time to look at Jada and Kiran’s strategies for multiplying $$8 \times 30$$.”
• 30 seconds: quiet think time
• “Talk to your partner about how we can see Jada and Kiran’s strategies in the diagram.” (We can see Jada’s skip counting by 30 in the rows. The 8 in Kiran’s strategy is the 8 rows and the 3 is the 3 tens in each row, so there are 24 tens.)
• 2–3 minutes: partner discussion
• Share responses.

### Activity

• “Work with your partner on the first problem.”
• 2–3 minutes: partner discussion
• Invite students to share how the strategies are alike and how they’re different.
• “How was Kiran able to turn $$8 \times 30$$ into $$24 \times 10$$?” (Eight times 30 is like 8 groups of 3 tens, so that’s like 24 tens. You can see $$8 \times 30$$ and $$24 \times 10$$ in the same diagram, so they are the same amount.)
• “Now, work with your partner to find the value of other products.”
• 5–7 minutes: partner work time
• Monitor for students who use the associative property as a strategy to highlight during the synthesis.

### Student Facing

1. Two students used base-ten blocks to find the value of $$8 \times 30$$.

• Jada counted: 30, 60, 90, 120, 150, 180, 210, 240, and said the answer is 240.
• Kiran said he knew $$8 \times 3$$ is 24, then found $$24 \times 10$$ to get 240.

How are Jada and Kiran’s strategies alike? How are they different?

2. Find the value of each expression. Explain or show your reasoning.

1. $$5 \times 60$$

2. $$8 \times 50$$

3. $$4 \times 30$$

4. $$7 \times 40$$

5. $$9 \times 20$$

### Activity Synthesis

• Select 2–3 students who used a strategy based on the associative property (for example, thinking of $$7 \times 40$$ as 28 tens) to share their responses.
• “Where do we see the original expression in _____’s work?”
• “How did _____ change the original expression to make it easier to find the total?”
• “How does _____’s strategy for multiplying work?”

## Lesson Synthesis

### Lesson Synthesis

“Today we multiplied one-digit whole numbers by multiples of 10.”

“How did thinking about tens help us find the value of products that were larger than we had found before?” (Using tens helped us count or multiply a lot faster. If we know $$5 \times 6$$, we can think of that many tens to find $$5 \times 60$$. We can use what we already know to find other products.)

“What were some strategies that were helpful as you multiplied one-digit whole numbers by multiples of 10?” (Decomposing one of the factors and finding smaller products. Using place value to multiply by 10 since we know 10 tens is 100.)