Unit 8, Lesson 12
Partition Rectangles into Squares
Grade 2
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The purpose of this Estimation Exploration is to practice the skill of making a reasonable estimate. Students consider how the placement of the first 2 squares can help them think about the total number of squares needed to fill the rectangle (MP7). These understandings will be helpful later when students need to partition rectangles into equal-size squares.
How many squares will fill the rectangle?
Record an estimate that is:
| too low | about right | too high |
|---|---|---|
The purpose of this activity is for students to partition rectangles to create rows and columns of equal-size squares. In the Launch, students build an array with tiles and then represent it on a rectangle with tick marks as guidance. They will partition rectangles without tick marks in the next activity.
Build a rectangle with 8 tiles in 2 rows. Use a ruler to partition this rectangle to match the rectangle you built.
Use a ruler. Partition the rectangle using the tick marks.
Use a ruler. Partition the rectangle using the tick marks.
The purpose of this activity is for students to partition rectangles into rows and columns of equal-size squares. They use tiles to help them see how to draw lines to partition the rectangles. Although it is important for students to use what they know about the structure of arrays and composing rectangles from squares to partition the rectangles (MP7), it is not necessary for students’ drawings to be perfect. It is more important that students clearly intended for the squares to be equal in size and they can articulate their reasoning. If their squares are significantly different or result in more squares in one column or row than another, offer a ruler and consider having students trace tiles for practice or guidance.
Use 12 tiles to make a rectangle. Then choose 1 of these 2 rectangles. Partition it into equal-size squares to match the rectangle you made with tiles.
Partition this rectangle into equal-size squares.
Write 2 equations to represent the total number of squares.
Partition this rectangle into equal-size squares.
“In this lesson, you learned about partitioning rectangles into equal-size squares to create arrays. You also wrote equations with equal addends to represent those arrays.”
“Which of these images looks most like a rectangle partitioned to create an array? What equations could you write to represent it?”
“Look at the rest of the images. Think about 1 thing you could say about each one. What are some things that are the same or different?”
We learned that an array is a group of objects arranged in rows and columns. Arrays have the same number of objects in each row and in each column.
In an array:
We practiced counting the objects in arrays. We used expressions with equal addends to show the total number objects in an array. We added the sum of each row or the sum of each column.
We also learned that rectangles can be composed of an array of equal-size squares. Then we partitioned rectangles into rows and columns of equal-size squares.
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