Teaching the Common Core Math Standards With Hands-On Activities, Grades 3-5 (87 page)

Activity 1: Finding the Volume of a Rectangular Prism

Working in groups, students will fill a rectangular prism with centimeter cubes to find the volume. They will also find the volume of the rectangular prism by finding the product of the area of the base and the height.

Materials

About 200 1-centimeter cubes; scissors; glue sticks; metric rulers; reproducible, “Rectangular Prism Net,” for each group of students. (
Note:
The reproducible should be copied on card stock because it is sturdier than paper.) Optional: A cardboard box to show the dimensions of a rectangular prism.

Preparation

Make a copy of the net, contained on the reproducible, cut it out, and demonstrate the procedure for making the rectangular prism.

Preparation

1.
Explain that the volume of a rectangular prism can be found by using formulas:
or
. Note what each variable represents. Also note that an example of a rectangular prism is a cardboard box. If you have a model of a rectangular prism, point out the dimensions to show what each variable represents.

2.
Hand out copies of the reproducible. Explain that it contains a net, which is a figure that can be cut out and then folded to form a rectangular prism.

3.
Instruct your students to cut out the net along the solid lines. Demonstrate how they should do this by working with your own figure. After cutting the net out, they should fold it along the dotted lines to form an “open” rectangular prism.

4.
After students have formed the prism, they should glue its sides together where indicated on the tabs. Again, demonstrate this to students with your own prism.

5.
Instruct your students to position their prisms so that the height is 4 centimeters. They are to then fill their prisms with centimeter cubes. Suggest that they place one layer of cubes at the bottom of their prism, and then count and record the number of cubes in that layer. They are to continue filling the prism by adding more layers. They should record the number of cubes in each layer.

6.
After their prisms are filled, explain that students are to find the total number of cubes they used to fill the prism. Note that the number of cubes times the volume of each cube is equal to the volume of the prism.

7.
Instruct your students to use metric rulers to measure the dimensions of the base of the prism and then find the area of the base by multiplying its length by its width. Next they should measure the height of their prism. Finally, they should use the formula,
, to find the volume of the prism.

Closure

Ask your students questions such as the following: How many 1-centimeter cubes did you need to fill your prism? (192) What is the volume of your prism? (192 cubic centimeters) What is the length of the base? (8 centimeters) What is the width of the base? (6 centimeters) What is the area of the base? (48 square centimeters) What is the height of the prism? (4 centimeters) How does the volume you found by packing cubes compare to the volume you found by multiplying the area of the prism's base by its height? (The volumes are the same.)

(
Note:
If you assign Activity 2 for this Standard, maintain the same groups and instruct students to keep their prisms.)

Activity 2: Using Formulas to Find the Volume of Rectangular Prisms

Working in groups, students will use the rectangular prisms they constructed in Activity 1 to find the volume of a rectangular prism. (
Note:
If students did not complete Activity 1, they must construct the rectangular prism before starting this activity.)

Materials

Rectangular prisms constructed previously; metric rulers for each group of students.

Procedure

1.
Explain that the volume of a rectangular prism can be found by multiplying the area of the base by the height.
, where
stands for the area of the base and
stands for the height of the prism.

2.
Remind students that the volume of the prisms they previously constructed was 192 cubic centimeters. The area of the base was 48 square centimeters (8 centimeters by 6 centimeters) and the height was 4 centimeters.

3.
Instruct your students to position their prisms so that the base measures 6 centimeters by 4 centimeters. This will require them to turn their prisms and place them on their sides. Ask them to find the area of the base. (24 square centimeters) Ask them to find the height. (8 centimeters) Ask them to find the volume by multiplying the area of the base by the height of the prism. (192 cubic centimeters)

4.
Now instruct your students to position their prisms so that the base measures 8 centimeters by 4 centimeters. Ask your students to find the area of the base. (32 square centimeters) Ask them to find the height of the prism. (6 centimeters) Ask them to find the volume by multiplying the area of the base by the height of the prism. (
)