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
“Discuss your thinking with your partner.”
1 minute: partner discussion
Share and record responses.
What do you notice? What do you wonder?
Student Response
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Advancing Student Thinking
Activity Synthesis
“What is the value the diagram represents?” (120)
“How could noticing groups of tens 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 and .
Activity 1
Standards Alignment
Building On
Addressing
3.NBT.A.3
Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., , ) using strategies based on place value and properties of operations.
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 () and then find its value using strategies that make sense to them. For example, students may count by 20 four times or think of \$20 in terms of two \$10 bills and find (or ). 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, ensure that each member of the group has a chance to share their solution and thinking. Supports accessibility for: Social-Emotional Functioning
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 Activity 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.
Six friends played a board game that uses play money. The paper bills come in \$5, \$10, \$20, \$50, and \$100.
Every player starts with \$100. Which of the following could be the bills that a player started with?
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
During the game, Noah had to pay Lin \$150. He gave her that amount using the same type of bill.
Which bill and how many of it could Noah have used to make \$150? Name all the possibilities.
Write an expression for each way that Noah could have paid Lin.
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 had 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
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
Standards Alignment
Building On
Addressing
3.NBT.A.3
Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., , ) using strategies based on place value and properties of operations.
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 or base-ten diagrams to support their thinking. Students analyze two strategies for multiplying. Both strategies are based on place value, but the second strategy also uses the associative property to think about as or .
Launch
Groups of 2
“Take some time to look at Jada and Kiran’s strategies for multiplying .”
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.
Give students access to grid paper and base-ten blocks.
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 into ?” ( is 8 groups of 3 tens, so that’s 24 tens. You can see and 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 Activity Synthesis.
Activity Synthesis
Select 2–3 students who used a strategy based on the associative property (for example, thinking of as 28 tens) to share their responses.
Consider asking:
“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
“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 greater than we had found before?” (Using tens helped us count or multiply a lot faster. If we know , we can think of that many tens to find . 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.)
Standards Alignment
Building On
Addressing
3.NBT.A.3
Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., , ) using strategies based on place value and properties of operations.
