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Activity 1

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

MLR7 Compare and Connect

Materials

To Copy (from Blackline Masters)

Centimeter Grid Paper - Standard

To Gather

Glue or tape Inch tiles Scissors Tools for creating a display

Activity Narrative

The purpose of this activity is for students to find all the possible pairs of whole-number side lengths given the area of a rectangle. Each group is assigned 2 areas. Groups find all the possible rectangles for each given area. They draw and cut out possible rectangles with that area. In the next activity, they will display the rectangles in a Gallery Walk. To find all possible rectangles with a given area, students may use tiles. They may also start to observe patterns such as if there are an even number of rows then the number of tiles in the rectangle is an even number (MP7).

Areas to assign (in square units):

Group A: 11, 27

Group B: 25, 5

Group C: 16, 8

Group D: 9, 18

Group E: 24, 12

Group F: 14, 28

Group G: 15, 30

Group H: 19, 20

This activity uses MLR7 Compare and Connect. Advances: representing, conversing.

Engagement: Provide Access by Recruiting Interest. Students may benefit from 2–3 minutes of independent work time to make sense of and begin the task before joining a group.
Supports accessibility for: Conceptual Processing, Visual-Spatial Processing

Launch

8 groups
Give each group access to inch tiles, grid paper, poster paper, scissors, and glue.

Activity

MLR7 Compare and Connect

“You are going to be given 2 numbers. Each number represents the area of a rectangle. With your group, draw all the possible rectangles with that area and create a poster for each area. Inch tiles are available if you find them helpful.”
“Your poster should show the rectangles with each of your assigned areas. Include details such as area and side lengths to help others understand your thinking.”
Assign each group 2 area values.
15 minutes: small-group work time

Your teacher will assign 2 numbers to your group. Each number represents the area of a rectangle.

On grid paper:
- Draw all the possible rectangles that have the given area.
- Label the area and side lengths of each rectangle.
- Use only whole numbers for side lengths.
- Use each pair of side lengths only once.
  
  (For example, if you draw a rectangle with 4 units across and 6 units down, you don’t need to also draw a rectangle with 6 units across and 4 units down because they have the same pair of side lengths.)
When you think you've drawn all the possible rectangles for both areas, cut out your rectangles and put them on a poster. Make 1 poster for each area you were assigned.
Display your poster for all to see.

Activity Synthesis

“Before we walk around and look at all the posters, take a minute to reflect on the numbers you worked with. What did you notice and wonder as you worked on this activity?”
1–2 minutes: quiet think time

Activity 2

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

MLR7 Compare and Connect

Materials

None

Activity Narrative

In this activity, students examine the rectangles drawn by their classmates and learn the term factor pairs. Students recognize the side lengths of each rectangle as a factor pair of its area.

This activity uses MLR7 Compare and Connect. Advances: representing, conversing

Launch

Groups of 2

Activity

5–7 minutes: gallery walk
Monitor for different explanations students offer for how they know whether all possible rectangles with a given area have been found.

As you visit each poster, discuss with your partner:

What do you notice? Use the following sentence frames when you share:
1. “I notice that some of the posters . . . .”
2. “I notice the posters for areas _____ and _____ are alike because . . . .”
How do you know that all possible rectangles were found for the given area?

Student Response

to access Student Response.

Advancing Student Thinking

Activity Synthesis

MLR7 Compare and Connect

“What is the same and what is different about the rectangles on the posters?”
30 seconds: quiet think time
1 minute: partner discussion
“How do you know that all possible rectangles have been found for the given area?” (We couldn't find any other numbers that multiply together to make the area.)
Display the rectangles for 21: 1 by 21 and 3 by 7.
“Are there any more rectangles we can draw? Why or why not?” (No, there are no more whole-number factors of 21. Or, no, because to get 21 we can multiply only 1 and 21, 3 and 7, 7 and 3, and 21 and 1.)
“We call 1 and 21 a factor pair of 21 because each of them is a factor of 21 and multiplying them gives you a product of 21. Another factor pair of 21 is 3 and 7.”
“Work with your partner to write down the factor pairs for the areas you were assigned.”
2 minutes: partner work time

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Audience

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Lesson 2

Factor Pairs

Warm-up

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Student Response

Advancing Student Thinking

Activity Synthesis

Activity 1

Standards Alignment

Building On

Addressing

4.OA.B.4

Building Toward

Instructional Routines

Materials

To Copy (from Blackline Masters)

To Gather

Activity Narrative

Launch

Activity

Activity Synthesis

Activity 2

Standards Alignment

Building On

Addressing

4.OA.B.4

Building Toward

Instructional Routines

Materials

Activity Narrative

Launch

Activity

Student Response

Advancing Student Thinking

Activity Synthesis

Lesson Synthesis

Standards Alignment

Building On

3.OA.C.7

Addressing

Building Toward

Student Response

Advancing Student Thinking