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This Warm-up 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 discussion, ask students to explain the meaning of any terms they use.
Which 3 go together?
Find the Match Cards
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, a tape diagram, an area diagram, a multiplication equation with an unknown factor, or a 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).
Your teacher will give you a card that shows an equation or a diagram.
Work with your partner to create a poster that includes:
Show your thinking and organize your work so it can be followed by others.
The purpose of this activity is to reinforce students' understanding of the relationship between multiplication and division by examining different representations of that relationship.
As you visit the posters with your partner, discuss the following questions. Be prepared to explain your reasoning.
“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 2 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 equal-groups 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 both show 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 helped me understand their thinking. Units on their answers. When other students wrote their explanations, it helped me understand their thinking.)