# Lesson 13

Solve Problems With Equal Groups

## Warm-up: Estimation Exploration: Multiply Teens (10 minutes)

### Narrative

The purpose of an Estimation Exploration is to practice the skill of estimating a reasonable answer based on experience and known information.

### Launch

- Groups of 2
- Display the expression.
- “What is an estimate that’s too high? Too low? About right?”
- 1 minute: quiet think time

### Activity

- “Discuss your thinking with your partner.”
- 1 minute: partner discussion
- Record responses.

### Student Facing

\(4 \times 18\)

Record an estimate that is:

too low | about right | too high |
---|---|---|

\(\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}\) | \(\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}\) | \(\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}\) |

### Student Response

### Activity Synthesis

- Consider asking:
- “Is anyone’s estimate less than ___? Is anyone’s estimate greater than ___?”
- “Based on this discussion does anyone want to revise their estimate?”

## Activity 1: Problems with Teen Numbers (20 minutes)

### Narrative

The purpose of this activity is for students to work with problems that involve multiplication within 100 where one factor is a teen number. This is the first time students have worked with problems with numbers in this range, so they should be encouraged to use the tools provided to them during the lesson if they choose (MP5). Students should also be encouraged to use strategies and representations from the previous section. As students are paired to create posters for the next activity, try to include a variety of approaches for students to see during the gallery walk in the next activity such as:

- Counting by the teen number.
- Counting by the single digit number.
- Use the distributive property to decompose the teen number to multiply in parts.
- Use the distributive property and place value understanding to decompose the teen number into tens and ones to multiply in parts.

### Required Materials

Materials to Gather

Materials to Copy

- Centimeter Grid Paper - Standard

### Launch

- Groups of 2
- “Turn and talk to your partner about how the first problem is the same and different than problems you’ve seen before.” (It involves equal groups. It's about a farmers market. It’s asking for the total number of something. It uses the word dozen instead of saying the number.)
- 1–2 minutes: partner discussion
- If needed clarify that a dozen is 12 and refer students to the illustration of a dozen eggs.
- Give students access to connecting cubes or counters, grid paper, and base-ten blocks.

### Activity

- “Solve these problems and show your thinking using objects, a drawing, or a diagram.”
- 6–8 minutes: independent work time
- As students work, consider asking:
- “What strategies have you used before that you could try here?”
- “How can you represent your thinking about the problem?”
- “Where can you see _____ in your work?”

- Monitor for students who solve the second problem in the same way to pair to create a poster together. Try to include a variety of approaches.
- “Now you are going to create a poster to show your thinking on the second problem with a partner who solved the problem in the same way you did.”
- Give each group tools for creating a visual display.
- 6–8 minutes: partner work time

### Student Facing

Solve each problem. Show your thinking using objects, a drawing, or a diagram.

- A seller at a farmers market has 7 dozen eggs when they close for the day. How many eggs does the seller have?
- At the farmers market there’s a space for performers to play music with some chairs for people to sit and listen. There are 5 rows of chairs and each row has 15 chairs. How many chairs are there?
- A booth at a farmers market has a table top that has lengths of 4 feet and 16 feet. What is the area of the table top?

### Student Response

### Advancing Student Thinking

- “What is the problem about?”
- “How could you use base-ten blocks or grid paper to help you solve the problem?”

### Activity Synthesis

- Display posters around the room.

## Activity 2: Gallery Walk: Problems with Teen Numbers (15 minutes)

### Narrative

The purpose of this activity is for students to consider what is the same and what is different about the ways that students solved problems involving multiplication of a teen number. Students may notice representations that were used, as well as different strategies that were used to find the total in the problem. The important thing is that students see a variety of ways to represent and solve the problem.

*MLR7 Compare and Connect.*Synthesis: After the Gallery Walk, lead a discussion comparing, contrasting, and connecting the different representations. “How did the number of chairs show up in each method? Why did the different approaches lead to the same outcome?” To amplify student language, and illustrate connections, follow along and point to the relevant parts of the displays as students speak.

*Advances: Representing, Conversing*

*Engagement: Develop Effort and Persistence.*Invite students to generate a list of shared expectations for group work. Record responses on a display and keep visible during the activity.

*Supports accessibility for: Social-Emotional Functioning*

### Launch

- Groups of 2
- “Before you begin the gallery walk, what are some things you could look for as you look at other students’ work?” (Ways they showed their thinking. How they found the solution to the problem.)
- Share responses.

### Activity

- “Visit the posters. Discuss with your partner what is the same and what is different about the thinking on each poster.”
- 8–10 minutes: gallery walk

### Student Facing

### Student Response

### Activity Synthesis

- Give students a chance to ask questions they have about any posters.
- “What is the same about the thinking shown on the posters?”
- “What is different about the thinking shown on the posters?”

## Lesson Synthesis

### Lesson Synthesis

“Today we solved some problems that involved multiplying teen numbers. What were some strategies or representations you saw today that you’d like to try in the future?” (One of the posters that I saw used groups of 5 to find the total. One of the groups broke the teen number into tens and ones. One group used a grid to represent the problem. One of the groups used base-ten blocks to represent the problem.)

“How did your work multiplying smaller numbers help you multiply teen numbers?” (I broke the teen numbers apart like I did with smaller numbers that are challenging to multiply.)

## Cool-down: Bags of Oranges (5 minutes)

### Cool-Down

Teachers with a valid work email address can click here to register or sign in for free access to Cool-Downs.