Math Background

Lesson: Finding Area and Volume
Developing the Concept

In this lesson the students will apply what they have learned about area to find the surface area of a solid figure. They will also learn how to find the volume of a rectangular prism.

Materials: tape, centimeter ruler, 4 cm x 3 cm x 2 cm rectangular box, 24 unit cubes (1 cm x 1 cm x 1 cm) for each group

Preparation: Use posterboard and tape to make the rectangular boxes. Label a face that measures 12 cm² Top. Label a face that measures 6 cm² Side. Label the face that measures 8 cm² Front. Distribute a ruler, 24 unit cubes, and a rectangular box to each group.

  • Say: Look at the box. I have 48 cm² of wrapping paper. How can I find out if this is enough paper to cover the box? (Add the areas of the faces of the box.)
  • Say: This box is a rectangular prism. A rectangular prism is made up of 6 faces. Each face is a rectangle. Measure the top of the box. What is the length and width? (The top is 4 cm by 3 cm.)
  • Ask: What is the area of the top of the box? (12 cm²) Does the bottom of the box have the same area? (yes)
    You may wish to have the students label each section as they find the area.
  • Say: Now measure the front of the box. What is the length and the width? (The front face is 2 cm by 4 cm.) What is the area of the front of the box? (8 cm²) Does the back of the box have the same area? (yes)
  • Say: Now measure the side of the box. What is the length and width? (The side is 2 cm by 3 cm.) What is the area of the side? (6 cm²)
  • Ask: Do both sides have the same area? (yes)
  • Say: Add the areas of each rectangular face. What is the sum? (52 cm²). Do I have enough wrapping paper to cover the box? (no)
  • Say: The surface area of a solid figure is the sum of the areas of all the faces of the figure. Surface area is measured in square units.
  • Say: Another way we can measure this box is to find its volume. Volume is a measure of the space inside a solid figure. Volume is measured in cubic units.
  • Say: Look at your unit cubes. Each unit cube is 1 cm x 1 cm x 1 cm. Place the cubes in the box.
  • Ask: How many layers of cubes are there? (2) How many cubes are in each layer? (12) How many unit cubes in all fill the box? (24) What is the volume of this box? (24 cubic units)
  • Say: You can also use a formula to find the volume of a rectangular prism.
    Write V (volume) = l (length) x w (width) x h (height) on the chalkboard. Have students find the volume using the formula.

Wrap-Up and Assessment Hints
Ask students how the number of cubes in the bottom layer relates to the length and width of the bottom of the box. They should understand that the length times the width equals the number of cubes. Then ask them how the number of layers relates to the height of the box. They should understand that they are equal. To informally assess their understanding of perimeter, area, surface area, and volume, you may wish to provide students with the dimensions of another rectangular prism (3 in. x 4 in. x 6 in.) and have them find the surface area (108 in.²) and volume (72 in.3) using the formulas. Have students work in groups and observe them as they work through the activity.

Houghton Mifflin Math Grade 4