Teaching the Common Core Math Standards With Hands-On Activities, Grades 3-5 (72 page)

Activity 2: Tiling Rectangles with Fractions

Working in pairs or groups of three, students will find the areas of rectangles by tiling. They will then check their answers by multiplying the lengths of the sides.

Materials

Scissors; glue sticks; one large sheet of construction paper (in a color other than white, to provide a contrast with the unit squares used for tiling); reproducible, “Unit Squares for Constructing Rectangles,” for each pair or group of students.

Procedure

1.
Explain that the area of a rectangle can be found by multiplying length times width,
. This same method can be used whether the dimensions of the rectangle are whole numbers or fractions. Provide the following example:

A rectangle is 2 units long by
unit wide:
square unit.

2.
Explain that the area of a rectangle can also be found by tiling the rectangle with squares of the appropriate side length. Present the previous example of the rectangle that is 2 units long by
unit wide.

• Draw the rectangle.
  

  

• Tile the rectangle with squares that are
  unit by
  unit.
  

  

• Ask your students to find the area of each square that is
  unit long by
  unit wide. Students should realize that the area is
  square unit because
  . Ask your students to find the area of the rectangle by using the squares. Students should then realize that the area of the rectangle is 1 square unit, because the rectangle is covered with 4 squares and the area of each square is
  square unit (
  ).
  
• Instruct your students to find the area of the rectangle by using the formula. They should find that the area is 1 square unit because
  . Note that the area they found by tiling is the same as the area they found by using the formula.