Lesson 10
Multiplication and Division
Warmup: Which One Doesn’t Belong: Multiplication and Division (10 minutes)
Narrative
This warmup prompts students to compare four representations. The reasoning here prepares students to connect the previous multiplication work to the division work of this lesson. It gives students an opportunity to use precise terms such as “factors,” “product,” and “quotient” in making comparisons (MP6). During the synthesis, ask students to explain the meaning of any terminology they use.
Launch
 Groups of 2
 Display images and expression.
 “Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”
 1 minute: quiet think time
Activity
 “Discuss your thinking with your partner.”
 23 minutes: partner discussion
 Share and record responses.
Student Facing
Which one doesn’t belong?
Student Response
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Activity Synthesis
 “What equation can each diagram represent?” (The array represents \(4\times6=24\) because there are 4 rows of 6 dots, and there are 24 dots in the array. The area diagram could represent \(4\times7=28\) or \(28\div4=7\) since the sides are 4 and 7, and the area is 28. The tape diagram could represent \(24\div3={?}\) or \(3\times{?}=24\) because we know the total is 24 and there are 3 groups, but we don’t know how many are in each group.)
Activity 1: Card Sort: Find the Match (25 minutes)
Narrative
The purpose of this activity is for students to relate multiplication and division using a variety of representations. Students are given a card with a base ten diagram, tape diagram, area diagram, multiplication equation with a missing factor, or division equation. Students need to find the other student who has the card that matches their card. Each pair of cards includes a division equation. After students find the student with the matching card, they work together to create another diagram and a division situation that their cards could represent (MP2).
Here are images of the cards for reference:
Supports accessibility for: Organization, SocialEmotional Functioning
Required Materials
Materials to Gather
Materials to Copy
 Find the Match
Required Preparation
 The blackline master has 24 cards. Copy and cut enough cards so that each student can have one card.
Launch
 Groups of 2
 Give one card to each student.
 Display an example of each type of representation shown on the cards (division equation, multiplication equation with missing factor, area diagram, tape diagram, and base ten diagram).
 “We saw in the warmup that different diagrams and equations can represent the same situation such as 4 groups of 6 or 4 times 6.”
 “Think about what situation or quantities your card represents. Then, think about what another representation of the situation or quantities might look like.”
 1 minute: quiet think time
Activity
 “Find a student whose card represents the same situation or quantities as your card does. Be ready to explain why your cards belong together.”
 23 minutes: partner work time
 Invite 23 groups to share their matches and how they knew they matched.
 “Work with your partner to create a poster that includes your cards and a diagram and situation that match your division equation. We’ll use these for a gallery walk, so organize your work so others can understand it.”
 Give students glue or tape and tools for creating a visual display.
 1015 minutes: partner work time
Student Facing
Your teacher will give you a card that shows an equation or a diagram.
 Find a classmate whose card represents the same situation or quantities as your card does. Be prepared to explain why your cards belong together.

Work with your partner to create a poster that includes:
 your cards
 a different diagram that your division equation could represent
 a situation that your division equation could represent
Show your thinking and organize it so it can be followed by others.
Student Response
For access, consult one of our IM Certified Partners.
Activity Synthesis
 Display students' posters around the room.
Activity 2: Find the Match Gallery Walk (10 minutes)
Narrative
The purpose of this activity is to reinforce students' understanding of the relationship between multiplication and division by examining different representations of that relationship.
Advances: Representing, Conversing
Required Materials
Materials to Gather
Required Preparation
 Keep posters from the previous activity displayed.
Launch
 Groups of 2
Activity
 Arrange for half of the groups to stand at their poster and answer questions while the other half visit their posters.
 8–10 minutes: gallery walk
 Ask groups to switch roles after 4–5 minutes.
Student Facing
As you visit the posters with your partner, answer these questions:
 Describe a representation you saw that was different from the ones you showed in your poster.
 Choose a poster that is not yours. Describe one way that it shows the relationship between multiplication and division.
Student Response
For access, consult one of our IM Certified Partners.
Activity Synthesis
 See lesson synthesis.
Lesson Synthesis
Lesson Synthesis
“Today we created posters that showed ways to represent division.”
“How does an area diagram show us the relationship between multiplication and division?” (It shows that multiplying is like finding the area of a rectangle when the two side lengths are known, and dividing is like finding a side length when we know the area and the other side length.)
“How does a tape diagram or equalgroups diagram show multiplication and division?” (Both show multiplying as a way to find the total when we know the number of groups and how many in each group, and dividing as a way to find either the number of groups or the size of each group when the total is known.)
“What were some aspects of the posters you saw that helped make the math your classmates used clear for you?” (Clear labels on diagrams that helped me understand their thinking. Units on their answers. When other students wrote their explanations, it helped me understand their thinking.)
Cooldown: Relate Multiplication to Division (5 minutes)
CoolDown
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