Teaching the Common Core Math Standards With Hands-On Activities, Grades 3-5 (73 page)

3.
Hand out copies of the reproducible. Explain that it contains three sets of squares with the side lengths respectively:
unit,
unit, and
unit. (Note that the units are improvised units.) Students are to cut out the squares on the reproducible and use them to tile rectangles to show that the area found by tiling is the same as the area found by multiplying length times width.

4.
Write the dimensions of the following three rectangles on the board:

• Rectangle 1: 4 units long and
  unit wide. Students will use the
  -unit squares to tile this rectangle.
  
• Rectangle 2: 3 units long and
  unit wide. Students will use the
  -unit squares.
  
• Rectangle 3: 2 units long and
  unit wide. Students will use the
  -unit squares.
  

5.
Instruct your students to arrange the unit squares on their construction paper to create each rectangle. They should pay close attention to the dimensions. For example, for Rectangle 1, the length of 4 units is equal to eight
units. Note that students will not need to use all of the squares in each set to tile each rectangle.

6.
Explain that once they are sure the dimensions of the rectangle are correct, they should glue the squares on the paper to form a rectangle. They should then find the area of the rectangle by multiplying the number of tiles times the area of one tile, and confirm their answer by multiplying the length of the rectangle by its width.

Closure

Discuss students' answers. Ask your students to explain the strategies they used to complete this activity. Will tiling a rectangle to find its area always equal the area found by multiplying its length times its width?

Answers

The number of squares required to form each rectangle is listed, followed by the area of the rectangle.
(1)
Eight
-unit squares;
square units
(2)
Nine
-unit squares;
square unit
(3)
Eight
-unit squares;
square unit.