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Activity 1

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

None

Materials

None

Activity Narrative

The purpose of this activity is for students to solve a real-world problem involving area. The activity includes a rectangle in which the side lengths are labeled. When students solve problems with multiple solutions and have to choose and justify a solution, they make sense of problems and persevere in solving them (MP1). In their small groups and in the class discussion, students have an opportunity to explain and defend their choices (MP3).

MLR8 Discussion Supports. Synthesis: Create a display of the diagram. As students share their strategies, annotate the display to illustrate connections. For example, as students share the numbers of columns and rows, draw them on the diagram, and write “3 rows and 6 columns.”
Advances: Speaking, Representing

Launch

Groups of 3 or 4
“A community garden is a garden space that is shared by members of the community. Each member gets their own space to create their part of the community garden.”
“This is a problem about painting a wall in a community garden. What materials do you need when you paint?” (paint, brushes, paint rollers, drop cloth, painter’s tape)
1 minute: quiet think time
Share responses.

Activity

“Work with your group to solve the problem.”
5 minutes: small-group work time
Monitor for different solutions mentioned in the sample responses.

Noah is painting a wall in a community garden. The wall is shaped like a rectangle. A diagram of the wall is shown here.

<p>Rectangle. Horizontal side, 6 meters. Vertical side, 3 meters.</p>

Paint is sold in 3 different sizes:

A small container will cover 3 square meters.
A medium container will cover 10 square meters.
A large container will cover 40 square meters.

What should Noah buy? Explain your reasoning.

Picture of small, medium, and large paint containers.

Student Response

to access Student Response.

Advancing Student Thinking

If students don’t find a solution to the problem, consider asking:

“Tell me what you’ve done so far to solve the problem.”
“How could you represent the problem?”

Activity Synthesis

“How did you find the area of the wall that Noah is painting?” (I counted by 3 six times since I pictured 3 squares in each column and 6 columns. I multiplied 3 by 6 and got 18.)
Discuss several different responses and their accompanying reasoning.
Consider asking:
- “How do you know that would be enough to cover the whole wall?”
- “Would there be paint left over? Enough to paint how many square yards?”

Activity 2

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

MLR6 Three Reads

Materials

To Copy (from Blackline Masters)

Centimeter Grid Paper - Standard

To Gather

Inch tiles Tools for creating a display

Activity Narrative

The purpose of this activity is for students to solve an area problem that involves unknown side lengths. The problem has multiple solutions, with the area of the garden between 20 square feet and 30 square feet. The Launch serves to familiarize students with the ideas involved in designing a garden before they solve the problem.

When students share with other groups and describe what others did that was different, they are making and understanding mathematical arguments (MP3).

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

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 3 or 4
Display the image.

MLR6 Three Reads

Display only the problem stem, without revealing the question(s).
“We are going to read this problem 3 times.”
1st Read: “Elena is planning to build a raised garden bed for the community garden. The garden bed will be rectangular. One side must be 3 feet long. To fit all her plants, Elena needs the bed to cover at least 20 square feet. She has enough soil for a garden bed that covers 30 square feet.”
“What is this situation about?”
1 minute: small-group discussion
Listen for and clarify any questions about the context.
2nd Read: “Elena is planning to build a raised garden bed for the community garden. The garden bed will be rectangular. One side must be 3 feet long. To fit all her plants, Elena needs the bed to cover at least 20 square feet. She has enough soil for a garden bed that covers 30 square feet.”
“Name the quantities. What can we count or measure in this situation?”
30 seconds: quiet think time
1–2 minutes: group discussion
Share and record all quantities.
Reveal the question(s).
3rd Read: Read the entire problem, including the question aloud.
“What are some strategies we can use to solve this problem?”
30 seconds: quiet think time
1–2 minutes: group discussion
Give each group tools for creating a display and access to square tiles and grid paper.

Activity

“Work with your group to solve the problem. Create a poster to show how you solved the problem.”
10 minutes: group work time
Monitor for students who:
- Recognize that one side length of the garden is unknown.
- Write an expression or an equation that represents the unknown side length as an unknown factor.
- Think of multiple gardens that could be built.

Elena is planning to build a raised garden bed for the community garden. The garden bed will be rectangular. One side must be 3 feet long. To fit all her plants, Elena needs the bed to cover at least 20 square feet. She has enough soil for a garden bed that covers 30 square feet.

What are some possible sizes for the garden bed?

Create a poster to show your thinking. Organize your poster so it can be followed by others.
As you look at the posters with your group:
1. Describe how another group solved the problem, using a different way than your group did.
2. Write 3 things you saw that helped you understand how other groups solved the problem.

Activity Synthesis

Display students' posters around the room.
“Now, half of the class is going to stand with their posters while the other half visits those posters. If you’re standing with your poster, explain how you solved the problem. As you visit other posters, ask any questions you have about the solution to the problem.”
Ask half of the groups to stand with their posters and share their ideas or answer questions as the other half visits them.
5 minutes: Gallery Walk
Remind students to switch places after 2 minutes, if they haven’t already, so they see a few posters.
Switch group roles and repeat.

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Settings

Language

Audience

Assessment Access

Lesson 10

Solve Area Problems

Warm-up

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Student Response

Advancing Student Thinking

Activity Synthesis

Activity 1

Standards Alignment

Building On

Addressing

3.MD.C.7.b

Building Toward

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Student Response

Advancing Student Thinking

Activity Synthesis

Activity 2

Standards Alignment

Building On

Addressing

3.MD.C.7.b

Building Toward

Instructional Routines

Materials

To Copy (from Blackline Masters)

To Gather

Activity Narrative

Launch

Activity

Activity Synthesis

Lesson Synthesis

Standards Alignment

Building On

3.OA.B.5

Addressing

3.OA.C.7

Building Toward

Student Response

Advancing Student Thinking

3.OA.D.9