# Lesson 12

Story Problems and Diagrams

## Warm-up: Notice and Wonder: Mancala (10 minutes)

### Narrative

The purpose of this warm-up is for students to make sense of a problem before solving it by familiarizing themselves with a context. While students may notice and wonder many things about the image, what students notice about the number and position of the seeds and students’ experiences and questions about the game are the important discussion points.

During the synthesis, invite students who share experience with the mancala family of games to share what they call the game, what materials they use when they play, and how they play. If time, or if no students share experiences with the game materials, share the facts provided in the synthesis. Consider researching the rules of one the mancala games mentioned in the synthesis or one of the variants mentioned by students to play with the class.

### Launch

• Groups of 2
• Display the image.
• “What do you notice? What do you wonder?”
• 1 minute: quiet think time

### Activity

• “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Share and record responses.

### Student Facing

What do you notice? What do you wonder?

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• “The picture shows a type of a game called mancala. It is one of the world’s oldest games.”
• “Mancala was created in Africa. The game has over 800 different names and can be played in many different ways. Most games are played with a board that has different pits or holes in it. Each player uses a certain amount of seeds that they place on their side of the board. Players might use real seeds or they may use shells, rocks, or beads.”
• “Each player takes turns placing their seeds on the board. In most games, you try to ‘capture’ more seeds than the other player.”
• “In Ghana and the Caribbean, one popular mancala game is called Oware. The board has 12 pits, 6 for each player, and the game uses 32 seeds.”
• “In Sudan, one popular mancala game is called Bao. The board for Bao has 28 pits, 14 pits for each player, and the game uses 64 seeds.”
• “The largest mancala game is called En Gehé and is played in Tanzania. The board can have up to 50 pits and the players use 400 seeds!”
• “Mancala is played all over the world. This board shows a game played in India called Pallanguzhi. The board has 14 pits and uses 70 seeds.”
• “What math questions could we ask about this image?” (How many seeds are there in all? How many seeds are in the holes? How many more seeds are on the top than on the bottom?)

## Activity 1: Interpret the Diagram (15 minutes)

### Narrative

The purpose of this activity is for students to make sense of tape diagrams, and how they can be used to show part-part-whole relationships. Students have previously used tape diagrams to show comparisons. In this activity, they connect tape diagrams to Compare problems and Put Together/Take Apart problems (MP2).

Students begin the activity by looking at the first problem displayed, rather than in their books. At the end of the launch, students open their books and work to find the diagram that matches the story problem. They do not solve the problems in this activity. The activity and synthesis are focused on developing student strategies for making sense of problems before solving them (MP1).

This activity uses MLR6 Three Reads. Advances: reading, listening, representing

### Required Materials

Materials to Gather

### Launch

• Groups of 2
• Give students access to base-ten blocks.
• “Clare and Han are playing a game like mancala with seeds.”

### Activity

MLR6 Three Reads

• Display only the problem stem for the first problem, without revealing the question.
• “We are going to read this problem 3 times.”
• 1st Read: “Clare captured 54 seeds. Han captured 16 fewer seeds. ”
• “What is this story about?”
• 1 minute: partner discussion.
• Listen for and clarify any questions about the context.
• 2nd Read: “Clare captured 54 seeds. Han captured 16 fewer seeds.”
• “What are all the things we can count in this story?” (Clare’s seeds. Han’s seeds. The difference between their seeds.)
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share and record all quantities.
• Reveal the question.
• 3rd Read: Read the entire problem, including the question aloud.
• Ask students to open their books.
• "Which of the diagrams shows a way we could represent this problem?" (See Student Responses for the first problem).
• 30 seconds: quiet think time
• 1–2 minutes: partner discussion
• Share responses.
• “Read each story with your partner. Then choose a diagram that matches on your own.”
• “When you have both selected a match, compare your choices and explain why the diagram matches the story or why other diagrams do not match the story.”
• 5 minutes: partner work time

### Student Facing

Circle the diagrams that match each story. Then explain your match to your partner.

1. Clare captured 54 seeds. Han captured 16 fewer seeds than Clare. How many seeds did Han capture?

2. Clare has 54 seeds on her side of the board. Han has 16 seeds on his side. How many seeds are on the board in all?

3. Clare has 54 seeds. 16 seeds are in her hand. The rest of her seeds are on the game board. How many of her seeds are on the game board?

4. There are 54 seeds on the game board. Some seeds are on Han’s side. 16 seeds are on Clare’s side. How many seeds are on Han’s side of the board?

Choose the 2 diagrams that match.

### Student Response

For access, consult one of our IM Certified Partners.

### Advancing Student Thinking

Students may say Diagram A matches the second story problem because the diagram shows the amount of seeds both students have in the story. Consider asking:
• “What does the question mark in each diagram represent?”
• “Which diagram best matches Han and Clare’s seeds and the question the story asks?”

### Activity Synthesis

• Invite students to share correct diagrams for the last three problems.
• Display each correct choice. Consider asking:
• “How does the diagram match the story problem?”
• “How does the diagram show what is known and what is unknown?”
• “How do you see addition or subtraction?”

## Activity 2: Card Sort: Story Problems and Diagrams (20 minutes)

### Narrative

The purpose of this activity is for students to connect different types of story problems to tape diagrams and solve the problems. Students identify representations that match a story problem and justify their decisions by describing how the diagrams represent the relationships between the quantities or the actions in the story problem (MP4). When students analyze and connect the quantities and structures in the story problems and tape diagrams, they think abstractly and quantitatively (MP2) and make use of structure (MP7). Students will use the story problems from this card sort again in a future lesson.

Engagement: Develop Effort and Persistence. Check in and provide each group with feedback that encourages collaboration and community. For example, make sure students are discussing amongst themselves and highlight groups that are following the protocol, so that students know what is being expected of them.
Supports accessibility for: Social-Emotional Functioning, Organization

### Required Materials

Materials to Gather

Materials to Copy

• Card Sort Story Problem and Diagram Cards

### Required Preparation

• Create a set of cards from the blackline master for each group of 2.
• The sets of cards will be used again in the next lesson.

### Launch

• Groups of 2
• Give each group one set of cards from the blackline master.
• Give students access to base-ten blocks.
• “You are going to take turns reading a story problem. After one person reads, work together to find the diagram that matches. When you think you have found a match, explain to your group 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.
• “When your group finishes, choose 2 story problems from Cards A, B, C, or D and solve them.”

### Activity

• 8 minutes: small-group work time
• Monitor for students who explain how each diagram matches the quantities in the context of the story problem.
• 4 minutes: independent work time
• Monitor for students who solve Card B or C using methods based on place value for sharing in the synthesis.

### Student Facing

1. Match each story problem with a diagram. Explain why the cards match.
2. Choose 2 story problems and solve them. Show your thinking.

### Student Response

For access, consult one of our IM Certified Partners.

### Advancing Student Thinking

Students may mismatch stories and diagrams. Consider asking:
• “What do you know? What does the story problem ask you to find?”
• “How does the diagram show the numbers that you know? How does the diagram show what you need to find?”

### Activity Synthesis

• Invite students to share and explain their matches for cards A, B, and C.
• Consider asking:
• “How do you know the diagram matches the story problem?”
• “What did you do to solve the problem?”
• If time, select previously identified student(s) to share their method for solving Cards B or C.

## Lesson Synthesis

### Lesson Synthesis

“Today we read many different kinds of story problems and matched them with diagrams.”

Display Card L and Card N from the card sort.

“How are these diagrams the same? How are they different?”

“Think of a story that could match Card N.”

## Cool-down: Find the Match (5 minutes)

### Cool-Down

For access, consult one of our IM Certified Partners.