# Lesson 12

Represent and Solve Multiplication Problems

## Warm-up: How Many Do You See: Lots of Dots (10 minutes)

### Narrative

The purpose of this warm-up is for students to subitize or use grouping strategies to describe the images they see. When students decompose the images into groups of 10 to count efficiently, they are looking for and making use of structure (MP7). For these images, students may need them displayed for a longer amount of time in order to see the structure.

### Launch

• Groups of 2
• “How many do you see? How do you see them?”
• Flash image.
• 30 seconds: quiet think time

### Activity

• Display image.
• “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Record responses. Use multiplication expressions when students share explanations involving equal groups.
• Repeat for each image.

### Student Facing

How many do you see? How do you see them?

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• “What pattern was helpful in finding the total number of dots?”
• “Who can restate the way _____ saw the dots in different words?”
• “Did anyone see the dots the same way but would explain it differently?”
• “Does anyone want to add an observation to the way ______ saw the dots?”

## Activity 1: Tyler’s Boxes (15 minutes)

### Narrative

The purpose of this activity is for students to use the Co-craft Questions math language routine to make sense of a multiplication situation before solving. Students are first asked to generate questions they could ask about part of a problem. Then, students are given the full problem and asked to solve it. The activity concludes with students reflecting on the representations they used. In this activity, students will need to see the full problem to solve. Before the lesson, record the problem and have it hidden until the appropriate time in the lesson or write it for all to see at that point during the activity.

This activity uses MLR5 Co-craft Questions. Advances: writing, reading, representing

### Launch

• Groups of 2

MLR5 Co-Craft Questions

• Display only the problem stem, “Tyler has 3 boxes.” without revealing the question.
• “Write a list of mathematical questions that could be asked about this situation.” (What’s in the boxes? How many things are in the boxes? How many things does he have altogether?)
• 2 minutes: independent work time
• 2–3 minutes: partner discussion
• Invite several students to share one question with the class. Record responses.
• “What do these questions have in common? How are they different?”
• Reveal the task (students open books), and invite additional connections.

### Activity

• “Think about how you’ll solve the problem.”
• 30 seconds: quiet think time
• 2–3 minutes: partner work time

### Student Facing

Tyler has 3 boxes. He has 5 baseballs in each box. How many baseballs does he have altogether? Show your thinking using diagrams, symbols, or other representations.

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• Display student work with different representations of the problem one at a time (drawings of equal groups, tape diagrams, and expressions). If no student writes an expression, write one for students to analyze.
• “How does each representation help us see what’s happening in the problem?”

## Activity 2: Solve Equal Groups Problems (20 minutes)

### Narrative

The purpose of this activity is for students to use what they’ve learned about multiplication to solve and represent situations that involve equal groups. Students now have experience with multiple representations and have the opportunity to choose which representation is most helpful to represent multiplication situations.

The launch of the activity is an opportunity for students to share their experiences and ask questions about the objects to ensure each student has access to the context. If it is helpful, display images of the items for students to reference.

MLR8 Discussion Supports. Synthesis: As students describe their representations of the problems, use gestures to emphasize the number of groups and how many are in each group. For example, trace with your finger around each group, and point to each object in each group to show how many there are.
Representation: Access for Perception. Provide access to connecting cubes. Ask students to identify correspondences between the concrete and visual representation used.
Supports accessibility for: Conceptual Processing

### Launch

• Groups of 2
• Write the list of objects (“teams, earrings, pencils, pieces of glass, carrots”) on a display for all students to see.
• “Take a minute to read this list. When you are done, discuss the objects you know or have questions about.”
• 3 minutes: partner discussion
• Share a few responses.
• “Now we’re going to represent and solve more problems with equal groups. Take a couple of minutes to begin working on the problems before you work in partners.”
• 2–3 minutes: independent work time

### Activity

• “Work with your partner to solve each problem.”
• 5–7 minutes: partner work
• Identify students who use different representations like drawings of equal groups or tape diagrams as they solve the problems.

### Student Facing

Solve each problem. Show your thinking using diagrams, symbols, or other representations.

1. There are 4 soccer fields. Two teams are on each field. How many teams are there altogether?
2. There are 7 windows. Each window has 2 pieces of glass. How many pieces of glass are there in the windows?
3. Jada has 5 bags. Each bag has 10 earrings. How many earrings does Jada have?
4. Kiran has 4 boxes. Each box has 5 pencils in it. How many pencils does Kiran have?
5. Andre has 3 bags of carrots. Each bag has 10 carrots. How many carrots does Andre have?

### Student Response

For access, consult one of our IM Certified Partners.

### Advancing Student Thinking

If students add or subtract instead of multiply to solve the problems, consider asking:

• “Tell me about how you solved this problem.”
• “How does the problem involve equal groups?”

### Activity Synthesis

• For each problem, display different representations, one at a time.
• “How does this representation help us see what’s happening in the problem?” (You can see there are 4 groups for the fields and 2 dots in each group for the teams. The diagram is split into 5 parts for the 5 bags, and each section has a 10 in it for the number of earrings.)
• “How could each representation help us solve the problem?” (Counting the dots. Counting by 10.)
• If needed, “What expression could we write to represent this situation?”

## Lesson Synthesis

### Lesson Synthesis

Display samples of student work with different representations (drawings of equal groups, tape diagrams, and equations).

“Which representation did you find most helpful today and why?” (Drawings of equal groups because I could see what was happening in the problem. Diagrams because it helped me understand the problem, but I didn’t have to draw all the dots.)

## Cool-down: Ducks in a Pond (5 minutes)

### Cool-Down

For access, consult one of our IM Certified Partners.