Lesson 12 Partition Rectangles Into Squares

    • Let’s partition rectangles into squares.

Warm-up Estimation Exploration: Fill it Up

How many little squares would fill the rectangle?

Rectangle partially partitioned to show the beginning of one row. Two equal sized squares.

Record an estimate that is:

too low

about right

too high

Activity 1 How Many Squares?

Problem 1

Build a rectangle with 8 tiles arranged in 2 rows. Use a ruler to partition the rectangle to match the rectangle you made.

Rectangle. Length sides, 3 evenly spaced tick marks each. Width sides, 1 tick mark each.

Problem 2

  1. Use a ruler to partition the rectangle using the tick marks as a guide.

    Rectangle. Length sides, 4 evenly spaced tick marks. Width sides, 2 evenly spaced tick marks.

  2. How many rows of equal-size squares did you make?

  3. How many columns did you make?

  4. Write 2 equations to represent the total number of equal-size squares.

Problem 3

  1. Use a ruler to partition the rectangle using the tick marks as a guide.

    Rectangle. Length sides, 3 evenly spaced tick marks each. Width sides, 2 evenly spaced tick marks each. 

  2. How many rows of equal-size squares did you make?

  3. How many columns did you make?

  4. Write 2 equations to represent the total number of equal-size squares.

Activity 2 Partition Rectangles

Problem 1

  1. Use 12 tiles to make a rectangle. Split one of the rectangles into equal-size squares to match your rectangle made of tiles.

    Rectangle.
    Rectangle.

  2. Write 2 equations to represent the total number of squares.

Problem 2

Split this rectangle into equal-size squares.

  1. Square.

  2. Write 2 equations to represent the total number of squares.

Problem 3

  1. Split this rectangle into equal-size squares.

    Rectangle.

  2. Write 2 equations to represent the total number of squares.

Practice Problem

Problem 1

  1. Split the rectangle into equal-size squares.

    Rectangle. Length, 5. Width, 2.

  2. Write 2 equations that represent the number of squares in the array.