# Lesson 13

Situations Involving Equal-size Groups

## Warm-up: Estimation Exploration: Lots of Paletas (10 minutes)

### Narrative

This Estimation Exploration prompts students to practice making a reasonable estimate based on experience and known information. In this case, it is not practical to count the paletas, but students could reason about groups of paletas by color, or estimate the complete rows and columns of paletas and extend their estimate to the whole set. Some students might also make an estimate based on their familiarity with how paletas are usually arranged in cases.

### Launch

• Groups of 2
• Display the image.
• “These are ice pops called paletas. They originated in Mexico and are typically made with many different fruits.”
• Ask students to estimate without counting.
• “What is an estimate that’s too high?” “Too low?” “About right?”
• 1 minute: quiet think time

### Activity

• 1 minute: partner discussion
• Record responses.

### Student Facing

How many paletas are in the case?

Record an estimate that is:

too low about right too high
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### Activity Synthesis

• “Is anyone’s estimate less than 30? Greater than 80?”
• “How did you know that 30 (or another number) would be too low and 80 (or another number) too high?”
• “Based on this discussion does anyone want to revise their estimate?”

## Activity 1: Paletas for a Class Party (15 minutes)

### Narrative

In this activity, students recall what they know about division from grade 3. The context allows students to connect lived experiences to the math of the activity. By inviting students to consider treats that they enjoy in their homes or neighborhoods, they share experiences and foster connections that build community.

The first question gives students an opportunity to co-craft mathematical questions based on a situation before answering a question based on a division equation. Students divide a two-digit number by a one-digit divisor, as they did in grade 3, in a way that makes sense to them. The activity synthesis highlights different representations students made and relates them to the situation. The term dividend is re-introduced in this lesson to describe a number being divided into equal groups.

Action and Expression: Develop Expression and Communication. Give students access to concrete manipulatives (connecting cubes, counters, or square tiles) and grid paper. Invite students to use these to act out or draw $$84 \div 7$$.
Supports accessibility for: Conceptual Processing, Attention

### Launch

• Groups of 2
• “What are some of your favorite treats or snacks from home?”
• 30 seconds: quiet think time
• 1 minute: partner discussion

MLR 5: Co-craft Questions

• Display the opening paragraph and the first question.
• 2 minutes: independent work time
• 2–3 minutes: partner discussion
• Invite several students to share one question with the class. Record responses.
• “How are these questions alike?” (The questions involve multiplying or dividing.) “How are they different?” (The questions can be answered using different operations.)
• “Let’s look at the next question in the activity.”

### Activity

• 3–4 minutes: quiet work time

### Student Facing

Diego’s aunt is buying paletas, which are ice pops, for a class party. At the local market, paletas come in different flavors. She buys the same number of paletas of each flavor.

2. Here is an equation:

$$84 \div 7 = {?}$$

In the situation about the class party, what questions could the equation represent?

3. Find the answer to one of the questions you wrote. Show your reasoning.

### Student Response

If students are unsure how to write a division question for $$84 \div 7$$, consider asking:

• “If you were to act out the meaning of this expression, what would you do?”
• “If you were to explain its meaning, what would you say?”
• “In what type of situations would these types of actions take place?”

### Activity Synthesis

• Display two questions that students wrote for the equation $$84 \div 7 = {?}$$ .
• “What does the 84 represent in both problems?” (The amount being divided into equal groups.)
• “In mathematics, the number being divided is known as the dividend.”
• Invite students to share their strategies for the last question. Highlight strategies that show equal-size groups and reasoning that relates multiplication and division.

## Activity 2: More Snacks for a Class Party (20 minutes)

### Narrative

In this activity, students continue to use any strategy to solve division problems in context and to recall the two interpretations of division. One problem involves finding how many in each group and the second involves finding the number of groups. Students work with two- and three-digit dividends and encounter division that results in a number with a remainder. They consider what the leftover means in the given context.

During the synthesis, highlight that both multiplication and division can be used to reason about the solutions, and elicit equations can be written to represent students' reasoning about equal-size groups. Introduce remainders as “leftovers” or quantities that remain after dividing a number into equal groups.

### Launch

• Groups of 2
• Display images of snacks in the activity.
• “Take a look at the images. What do you notice? What do you wonder?”
• Share responses.
• Gulab jamuns are sweet treats that are popular in India, Pakistan, and their neighboring countries in South Asia.
• Breadsticks that are covered with chocolate, strawberry cream, or other flavors are popular snacks in Japan, Taiwan, and other East Asian countries.
• “The problems in this activity involve treats that students enjoy from different places around the world.”

### Activity

• 6–8 minutes: independent work time
• 2–3 minutes: partner discussion
• Monitor for students who reason in terms of partial products or partial quotients and record their thinking as equations.
• Monitor for the different ways students describe and decide what to do with the 2 leftover breadsticks.

### Student Facing

1. Priya’s mom made 85 gulab jamuns for the class to share. Priya gave 5 to each student in the class.

How many students are in Priya’s class? Explain or show your reasoning.

2. Han’s uncle sent in 110 chocolate-covered breadsticks for a snack. The students in Han's class are seated at 6 tables. Han plans to give the same number of breadsticks to each table.

How many breadsticks does each table get? Explain or show your reasoning.

### Activity Synthesis

• Invite students to share their response for the first problem.
• If no students wrote equations to show their thinking, ask: “What equations can represent how you found the solution to the first problem?“
• Record both multiplication and division equations for all to see. For example:
• $$5 \times 10 = 50$$ and $$5 \times 7 = 35$$, so $$5 \times 17 = 85$$.
• $$50 \div 5 = 10$$ and $$35 \div 5 = 7$$, so $$85 \div 5 = 17$$.
• Invite other students to discuss the second problem.
• “When we divide, sometimes we have leftovers that are not enough to make a new group or not enough to put an additional item to each group. We call the leftovers remainders.”
• “What was the remainder when 110 breadsticks were divided by 6?” (2 breadsticks were leftover)
• “How are the questions in the two situations—gulab jamuns and breadsticks—alike?” (They involved division into equal groups.)
• “How are they different?” (The first looks for the number of groups. The second looks for the size of a group. The second involves some leftovers.)

## Lesson Synthesis

### Lesson Synthesis

“Today we solved problems involving division of whole numbers. We thought about the kinds of division problems we were solving—whether we were trying to find the number of groups or the amount in each group.”

Display:

Eight students are sharing 96 breadsticks equally.
How many breadsticks would each student get?

“How is this situation related to division?” (It's about putting 96 breadsticks into equal-size groups.)

“What are we finding out when we divide 96 by 8?” (How many breadsticks each student would get.)

“What are some ways to find the answer?” (Multiply 8 by a number until we get 96. Divide smaller numbers by 8, until 96 are divided by 8.)

“What equations could we write to represent the problem and the solution, or how we find the solution?” ($$8 \times 12 = 96$$ or $$96 \div 8 = 12$$, or a series of equations such as $$8 \times 10 = 80$$ and $$8 \times 2 = 16$$, or $$80 \div 8 = 10$$ and $$16 \div 8 = 2$$.)