Lesson 11
Arrays and Rectangles
Warmup: Which One Doesn’t Belong: All Kinds of Arrays (10 minutes)
Narrative
Launch
 Groups of 2
 Display the image.
 “Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”
 1 minute: quiet think time
Activity
 “Discuss your thinking with your partner.”
 2–3 minutes: partner discussion
 Record responses.
Student Facing
Which one doesn’t belong?
Student Response
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Activity Synthesis
 “What do B, C, and D have in common?” (They all show arrays with 3 in each row.)
 “D has 4 rows and 3 columns. This rectangle is partitioned into equalsize squares.”
Activity 1: Use Tiles to Make Arrays (15 minutes)
Narrative
The purpose of this activity is to make connections between arranging objects to make an array and making a rectangle from equalsize squares. They use the language of arrays to describe the rectangles they create (MP6) and learn that a rectangle composed of equalsize squares is an example of an array.
Supports accessibility for: Memory, Language
Required Materials
Materials to Gather
Launch
 Groups of 2
 Give students inch tiles and colored pencils.
 Arrange 6 tiles into an array with 2 rows and 3 columns. Pause, then push them together to make a rectangle.
 “What do you notice? What do you wonder?” (There are 6 squares. The squares make a rectangle. You made an array first, then you pushed them together and made a rectangle. Is the rectangle an array of squares? Why did you push them together? Could you make other rectangles?)
Activity
 “You and your partner can choose 12, 15, 16, 18, or 20 tiles. Arrange all the tiles in an array. Then push them together to make a rectangle.”
 “Shade in the same arrangement of squares on the grid paper to represent the rectangle you’ve made.”
 “Answer the questions about your rectangle. If you have time, choose a different number of tiles and make another rectangle.”
 10 minutes: partner work time
 Monitor for a variety of different rectangles to display during the synthesis.
Student Facing
 12
 15
 16
 18
 20
Arrange all the tiles in an array. Then push them together to make a rectangle.
 Shade in the same arrangement of squares on the grid paper.
 How many rows of squares does your rectangle have? ______
 How many columns does your rectangle have? ______
 How many tiles are in your rectangle? ______
 Write 2 equations to represent the number of squares in your rectangle.
Student Response
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Activity Synthesis
 Display student work.
 “Describe this rectangle.” (It has _____ rows of squares. It has _____ columns of squares. It has _____ squares in all.)
 If needed, ask:
 “How many squares are in each row?”
 “How many squares are in each column?”
 “What equations could we write to represent the number of squares in this rectangle?”
Activity 2: Make Equalsize Squares (20 minutes)
Narrative
The purpose of this activity is for students to finish partitioning a rectangle into equalsize squares. This work will prepare students for partitioning rectangles on their own in later lessons. In the synthesis, students are invited to use what they know about the structure of arrays to anticipate how many equalsize squares will fill the rectangle without drawing any lines (MP8).
Advances: Speaking, Conversing, Representing
Required Materials
Materials to Gather
Launch
 Give each student at least 2 different colors of colored pencils or crayons and a ruler.
Activity
 “In the first activity, you used tiles to make a rectangle and shaded in squares to represent it. In this activity, you will start with a rectangle and decompose it into small equalsize squares by drawing lines with a ruler. For each rectangle, there will be some squares already outlined. Draw lines to continue making equalsize squares inside each rectangle.”
 “After making the squares, use colored pencils or crayons to show patterns in the rows or columns.”
 10 minutes: independent work time
Student Facing


Draw lines so that the rectangle is completely filled with equalsize squares.
 Color the rows different colors.
 How many rows of equalsize squares are there?
 How many squares are in each row?
 Write an equation to represent the sum of the squares in each row.



Draw lines so that the rectangle is completely filled with equalsize squares.
 Color the columns different colors.
 How many columns of equalsize squares are there?
 How many squares are in each column?
 Write an equation that represents the sum of squares in each column.



Draw lines so that the rectangle is completely filled with equalsize squares.
 How many columns of equalsize squares are there? How many squares are in each column?
 How many rows of equalsize squares are there? How many squares are in each row?
 Write 2 equations to represent the number of equalsize squares in the rectangle.

Student Response
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Advancing Student Thinking
Activity Synthesis
 Display the rectangle that has 4 squares in the first row, but is missing squares in each column.
 “How could you find the total number of squares that would fill this rectangle without drawing the lines?” (I can tell there will be 4 columns based on the top row. I can tell there will be 5 rows based on the first column, even though it is missing 1 square.)
Lesson Synthesis
Lesson Synthesis
“Today you learned that we can partition a rectangle into equalsized squares.”
Create or draw a rectangle with inch tiles to show:
“How would you describe this rectangle?” (It has 4 rows of squares. There are 5 squares in each row. It has 5 columns. There are 4 squares in each column.)
“What is the total number of equalsize squares inside the rectangle?” (20)
Cooldown: Partition Rectangles into Squares (5 minutes)
CoolDown
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