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Activity 1

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

None

Materials

To Gather

Activity Narrative

The purpose of this activity is for students to find the area of a rectangle by tiling and multiplying the side lengths. Students use inch tiles to build rectangles with a given side length and find the area of those rectangles. They work together to compare and explain the strategies used to find the area of rectangles and make connections between strategies. Students observe how the area of rectangles with a given width varies as the length changes and make predictions about what areas are possible with the given widths (MP7).

MLR2 Collect and Display. Circulate, listen for and collect the language students use as they build rectangles. On a visible display, record words and phrases such as: “row,” “column,” “area,” “length,” “width,” “wide.” Invite students to borrow language from the display as needed, and update it throughout the lesson.
Advances: Conversing, Reading.

Launch

Display the rectangle in the student book.
“Look at the rectangle on your page and describe it to a partner.” (It has 6 units. There are 2 rows and 3 columns.)
Give each group 10 tiles.
“Build all the rectangles you can using all 10 tiles. Describe them to a partner.”
2 minutes: partner discussion
“Who has a rectangle that is 2 tiles wide, 5 tiles wide, 10 tiles wide?”
Draw each rectangle as students share their responses.

Activity

Give students more inch tiles.
“Now build five different rectangles that are each 2 tiles wide. Record the area of each rectangle in the table.”
“Repeat with rectangles that are each 3 tiles and 4 tiles wide.”
5–7 minutes: partner work time
Monitor for students who:
- Build one row or column and repeat the same number of tiles over again to build the area.
- Skip-count or multiply to determine the area of each rectangle.
- Combine skip-counting with another counting strategy.

Build 5 different rectangles with each of the given widths. Record the area of each rectangle in the table.

Diagram. Rectangle partitioned into 2 rows of 3 of the same size squares.

	area of rectangle
2 tiles wide
3 tiles wide
4 tiles wide

Discuss with a partner what you notice about the areas in each row of the table.
Predict the area of another rectangle that has each width. Explain your reasoning.
- 2 tiles:
- 3 tiles:
- 4 tiles:

Student Response

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Advancing Student Thinking

If students count tiles by 1 to determine the area of the rectangles they build, consider asking:

“How did you determine the area of the rectangles you built?”
“How could you count groups of tiles to determine the area?”

Activity Synthesis

Collect predictions for areas of rectangles with a width of 2. (18, 14, 20, 30)
“For rectangles that are 2 tiles wide, how can we tell if our area predictions are true without building each rectangle?” (Each area is an even number. It is what we say when counting by 2 or multiplying by 2.)
“How can we check our predictions for rectangles that are 3 or 4 tiles wide?” (The predictions are numbers we get when we multiply a number by 3 or 4.)

Activity 2

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

None

Materials

To Copy (from Blackline Masters)

Centimeter Grid Paper - Standard

To Gather

Activity Narrative

The purpose of this activity is for students to explore the idea of multiples through an area context. Students learn that a multiple of a number is the result of multiplying any whole number by another whole number. As students build and find the area of rectangles given one side length, they see that every area is a multiple of each of the side lengths of a rectangle.

Representation: Develop Language and Symbols. Synthesis: Maintain a visible display to record new vocabulary. Invite students to suggest details (words, pictures, or equations) that will help them remember the meaning of the terms. In this lesson, include the terms “multiple,” “even,” and “odd.” Throughout the unit, add the terms “factor,” “factor pair,” “composite,” and “prime.”
Supports accessibility for: Language, Memory

Launch

Groups of 2
Give each group inch tiles and access to grid paper.
“I am thinking of a rectangle that is 2 tiles wide. What could be the area of my rectangle?”
1 minute: partner discussion
Share and record responses.
“How do we know all of these are possible areas?” (We can multiply another number by 2 to get those numbers.)

Activity

“In this activity, we are going to think about what the area of a rectangle could be if we only know one side length. Work with your partner to answer these questions.”
5–7 minutes: partner work time
Monitor for students who notice that areas you can build are a result of multiplying 3 by another possible side length.

Elena builds rectangles with a width of 3 units and an area of 30 square units or less.
1. Build the rectangles Elena could make and draw the rectangles on grid paper. Label the area and the side lengths of each rectangle.
2. What is the area of each rectangle you built?
3. What do you notice about the areas?
Why is 28 square units not a possible area for a rectangle with a width of 3 units?
Elena decides that the area of the rectangle can be more than 30 square units. Find 2 other areas it could have. Explain or show your reasoning.
What is an area that is not possible for a rectangle with a width of 3 units? Explain or show your reasoning.

Student Response

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Advancing Student Thinking

Activity Synthesis

Display a set of student-generated areas that are less than 30 square units.
“What did you notice about the areas you found?”
Ask students to explain why the rectangle couldn’t have an area of 28 square units.
“For the last two questions, how did you know whether a rectangle with a width of 3 units could have that area?”
“We could have an area of 12 square units when the width of the rectangle is 3 units. That is because 12 is a multiple of 3.”
“A multiple of a number is the result of multiplying a number by a whole number.”
“Look back at your work and discuss with your partner: Which numbers are multiples of 3?” (3, 6, 9, 12, 15, 18, 21, 24, 27, and 30)
“Which numbers are not multiples of 3?” (29, 28, 26, 25, 23, 22, 20, 19, 17, 16, 14, 13, 11, 10, 8, 7, 5, 4, 2, 1)
2 minutes: partner discussion