# Lesson 5

Write Division Expressions

## Warm-up: Number Talk: What’s the Same? (10 minutes)

### Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for subtracting within 1,000, particularly with expressions with a constant difference. These understandings help to develop fluency for subtracting within 1,000. Consider drawing number lines as students share their strategies to emphasize that the difference of the two numbers in each expression is not changing.

### Launch

• Display one expression.
• “Give me a signal when you have an answer and can explain how you got it.”
• 1 minute: quiet think time

### Activity

• Keep expressions and work displayed.
• Repeat with each expression.

### Student Facing

Find the value of each expression mentally.

• $$225 - 100$$
• $$227 - 102$$
• $$230 - 105$$
• $$220 - 95$$

### Activity Synthesis

• ”What do you notice about these expressions?” (They all have the same value.)
• “Why do they all have the same value?” (Since the same number is added or subtracted to both numbers from the original expression, the difference does not change.)
• “Who can restate _____’s reasoning in a different way?”
• “Did anyone have the same strategy but would explain it differently?”
• “Did anyone approach the problem in a different way?”
• “Does anyone want to add on to _____’s strategy?”

## Activity 1: Card Sort: All about Bugs (15 minutes)

### Narrative

The purpose of this activity is for students to determine whether a situation is about an unknown number of groups or an unknown number of objects in each group. After sorting the situations, students write a division expression to represent each situation. The fact that the structure of the expressions is the same for representing an unknown number of groups or an unknown number of objects in each group further emphasizes that division expressions can be interpreted two ways. As students discuss and justify their decisions, they share a mathematical claim and the thinking behind it (MP3).

As students explain their reasoning around the unknown in the situation, encourage students to describe how they would start to solve the problem to make it clear what is unknown in the situation.

MLR8 Discussion Supports. Synthesis. Display a sentence frame to support whole-class discussion: “We noticed _____ so we . . . .”
Engagement: Develop Effort and Persistence. Chunk this task into more manageable parts. Give students a subset of the cards to start with and introduce the remaining cards once students have completed their initial set of matches.
Supports accessibility for: Organization, Attention

### Required Materials

Materials to Copy

• Card Sort: All About Bugs

### Required Preparation

• Create a set of cards from the blackline master for each group of 2.

### Launch

• Groups of 2
• Display the image.
• “We are going to work with some situations involving insects. Insects are a type of bug. These are all insects.”
• “What are some parts of the insects we could count?” (legs, eyes, wings, antennae, body segments)
• If needed, clarify what antennae are.
• Distribute one set of pre-cut cards to each group of students.

### Activity

• “In this activity, you will sort some cards into categories of your choosing. When you sort the situations, you should work with your partner to come up with categories.”
• 5 minutes: partner work time
• Select groups to share their categories and how they sorted their cards.
• Choose as many different types of categories as time allows, but ensure that one set of categories distinguishes between “how many groups?” and “how many in each group?” problems.
• If no students sorted the cards by type of division situation, give them a minute to do so, and then discuss how they know which type of division each situation represents.
• “Now work with your partner to sort your cards by ‘how many groups?’ and ‘how many in each group?’ problems.”
• “Once you have sorted your cards, write a division expression to represent each situation.”
• 5 minutes: partner work time

### Student Facing

1. Your teacher will give you a set of cards that show situations. Sort the cards into 2 categories of your choosing. Be prepared to explain the meaning of your categories.

A. Mole crickets have special legs for digging. Ten special legs belong to 5 mole crickets. How many special legs does each mole cricket have?

B. A beetle has a pair of antennae for sensing heat, touch, smell, and more. If there are 8 antennae, how many beetles are there?

$$\phantom{00}$$

C. Fourteen antennae belong to a group of bees. If each bee has 2 antennae, how many bees are there?

D. There are 12 wings. If each dragonfly has 4 wings, how many dragonflies are there?

$$\phantom{00}$$

E. Thirty legs belong to 5 ants. If all the ants have the same number of legs, how many legs does each ant have?

F. There are 50 spots on 5 butterflies. If each butterfly has the same number of spots, how many spots does each butterfly have?

2. Write a division expression to represent each situation. Be ready to explain your reasoning.

### Activity Synthesis

• Invite students to share the expression for each situation.
• “What does each number represent in the expression?”
• “Where do you see the number of groups in the expression?”
• “Where do you see the number of objects in each group in the expression?”

## Activity 2: Solve a Buggy Problem (20 minutes)

### Narrative

In this activity, students consolidate their understanding of the types of division situations and their representations to solve division problems.

During the synthesis, arrange and display students‘ posters by type, as sorted in the previous activity.

This activity uses MLR7 Compare and Connect. Advances: representing, conversing

### Launch

• Groups of 2
• Assign each group one of the problems from the previous activity to solve.
• Give each group tools for creating a visual display.

### Activity

MLR7 Compare and Connect
• “Create a visual display that shows your thinking about the problem you were assigned. You may want to include details such as notes, diagrams, drawings, etc. to help others understand your thinking.”
• 5 minutes: partner work time
• 8–10 minutes: gallery walk

### Student Facing

Create a visual display that shows your thinking and your solution to the problem.

### Activity Synthesis

• “What is the same about the two types of division problems?” (They both involve putting things into equal groups.)
• “What is different about them?” (Sometimes we know how many things are in each group and we need to find how many groups we can make. Sometimes we know how many groups there are, but we need to find how many things are in each group.)

## Lesson Synthesis

### Lesson Synthesis

“Over the last few lessons we have been learning about division. We represented and solved two kinds of division problems. Let’s summarize what we know about division together.”

“What are some of the big ideas we have learned about division?” (Division is about equal groups. We can find how many groups or how many there are in each group. We can represent division with drawings. We can write division expressions to represent division situations.)

Organize the class ideas on a chart with two columns, with representations of “how many groups?” in one column and those of “how many in each group?” in the other (as in the student lesson summary).

## Student Section Summary

### Student Facing

In this section, we learned that division is finding the number of groups or finding the size of each group when we put objects into groups of equal size. We represented division situations with drawings and expressions, and solved division problems.

“How many groups?”

“How many in each group?”

Han has 12 colored pencils. He wants to put 2 colored pencils in each box until he’s out of colored pencils. How many boxes does Han need?

Elena has 12 colored pencils. She has 2 boxes and wants to put the same number of colored pencils in each box. How many pencils will be in each box?

$$12 \div 2$$

$$12 \div 2$$