# Lesson 15

Diagrams with All Kinds of Compare Problems

## Warm-up: Number Talk: 10 and Some More (10 minutes)

### Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for making 10 when adding. These understandings help students develop fluency with operations within 20.

When students look for ways to rearrange and decompose numbers to make 10, they notice and make use of structure of expressions and whole numbers (MP7).

### Launch

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

### Activity

- Record answers and strategies.
- Keep expressions and work displayed.
- Repeat for each expression.

### Student Facing

Find the value of each sum mentally.

- \(4 + 8 + 2\)
- \(4 + 5 + 3 + 2\)
- \(9 + 3 + 1\)
- \(9 + 5\)

### Student Response

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### Activity Synthesis

- “How did making a ten help when finding the sums?”

## Activity 1: Shell Collections (15 minutes)

### Narrative

The purpose of this activity is for students to interpret a Compare problem with the smaller value unknown and connect the problem to a tape diagram. The launch of the activity is an opportunity for students to share their experiences and ask questions about a beach to ensure each student has access into the context. If it is helpful, display a few images from beaches from different areas around the world. The story problem is introduced without numbers in order to allow students to consider the relationship between quantities. Students consider who has more or less, which supports their interpretation of the tape diagram. If needed to help students connect the tape diagram to the subtraction equation, show students that if you look at Diego’s rectangle and cover up the portion below that part that shows 20, it will be the same as Lin’s rectangle.

At the beginning of this activity, make sure students do not have their workbook open yet.

*Action and Expression: Develop Expression and Communication.*Give students access to connecting cubes to build the comparison with a concrete manipulative. The numbers from the problem are shown exactly, with the difference very apparent as well. This supports the pictorial images of the tape diagrams.

*Supports accessibility for: Conceptual Processing, Organization*

### Launch

- Groups of 2
- “I am going to tell you a quick story about two students who visited a beach. But before I do, tell your partner something you know or questions you have about a beach.”
- Share responses.
- “Now, our story: Diego has some shells. Lin has fewer shells.”
- "Talk to your partner about how many shells Diego could have and how many shells Lin could have."
- Share responses. Highlight that Diego has more and ask how they know he should have more.
- 1 minute: partner discussion
- Record responses.

### Activity

- “Diego has 55 shells and Lin has 20 fewer shells than Diego.”
- Display the partially-labeled diagram.
- “This diagram shows some parts of the story problem you just read, but it is missing some labels.”
- “Label the diagram so that it shows how many shells Diego has and how many Lin has. Then write an equation to show how you could find the unknown part. Use a question mark to show the unknown.”
- 2 minutes: independent work time
- 3 minutes: partner discussion
- Monitor for students who explain how each part of the diagram and equation connects to the story problem.

### Student Facing

Diego has 55 shells. Lin has 20 fewer shells than Diego.

- Use the story problem to complete the diagram.
- Write an equation to show how you could find the unknown number of shells. Use a question mark to represent the unknown.

### Student Response

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### Activity Synthesis

- Invite previously identified student(s) to explain how they labeled the tape diagram.
- Consider asking:
- “Which part represents Diego’s shells? How do you know?”
- “Which part represents Lin’s shells? How do you know?”
- “Which part shows the difference between the amount of shells each student has?”
- “Could someone explain how _____ decided to label the diagram in their own words?”

- Invite previously identified student(s) to share the equation they used to represent the story problem.
- “How did you use the diagram to write your equation?” (The diagram helped me see I could start with 55 and take away 20 to find Lin’s shells. The diagram helped me see that Lin’s shells and 20 more would be the same as 55.)
- Consider having student(s) describe what the numbers and symbols in the equation represent, as they did for the diagram.

## Activity 2: Card Sort: At the Beach (20 minutes)

### Narrative

The purpose of this activity is for students to connect Compare problems, tape diagrams, and equations with unknowns in all positions. Support students with interpreting “more” or “fewer” in the context of the story problem by encouraging them to explain which quantity should be the bigger quantity and which should be the smaller quantity. Ask them to describe what they look for in a diagram or equation to make sure it matches a story problem. When students analyze and connect the quantities and structures in the story problems, diagrams, and equations, they think abstractly and quantitatively (MP2) and make use of structure (MP7).

If students are not yet reading independently, consider reading one story problem at a time and giving students time to independently find their matches. It is recommended to read the story problems in order beginning with story problem A if facilitated in this way.

*MLR8 Discussion Supports.*To support students as they take turns finding a match and explaining their reasoning, display the following sentence frames for all to see: “I noticed ___ , so I matched . . .” Encourage students to challenge each other when they disagree.

*Advances: Speaking, Conversing*

### Required Materials

Materials to Copy

- Card Sort: At the Beach

### Required Preparation

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

### Launch

- Groups of 2
- Give each group a set of cards from the blackline master.
- “Lin and Diego want to compare other things they collected and did at the beach.”
- “Find one diagram and one equation that match a story problem. There may be more than one equation that matches each story problem.”
- “Take turns reading a story problem. After one partner reads, work together to find other cards that match. When you think you have found a match, explain to your partner why the cards match.”
- “If it helps, you may label the diagrams to explain your matches.”
- As needed, demonstrate the activity with a student volunteer.

### Activity

- 8 minutes: partner work time
- Monitor for students who explain how each diagram and equation matches the quantities in the context of the story problem.
- “Compare your matches with the matches of another group. If you have different matches, work together to explain which cards belong or why a card could belong to different groups.”
- 4 minutes: small-group work time

### Student Facing

- Read a card with a story problem.
- Find cards that match the story problem.
- Explain why the cards match.

### Student Response

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### Advancing Student Thinking

If students match story problems with equations or diagrams that do not accurately show the quantities or their relationships, consider asking:

- "How did you choose which equation or diagram matches the story?"
- "Can you explain how the story problem matches this diagram or equation?"

### Activity Synthesis

- Invite 2–3 student groups to share their matches. Consider selecting groups to share their matches for story problems A, B, and C.
- Consider asking:
- “How do you know the diagram matches the story problem?”
- “How does your equation match the story problem?”
- “Is there another equation that could match your story problem? How do you know?”

## Lesson Synthesis

### Lesson Synthesis

“Today, we worked more with diagrams to represent Compare story problems. Diagrams can help show if we need to find the bigger number, the smaller number, or the difference.”

Display: Card H, J, and L from Activity 2.

“Which diagram shows that you are looking for the bigger number? How do you know?” (L because the bigger bar has a question mark.)

“Which diagram shows that you are looking for the smaller number? How do you know?” (Diagram J, because the smaller bar has a question mark.)

## Cool-down: At the Beach (5 minutes)

### Cool-Down

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