Cuboid Construction

This activity focuses on measuring the volume of rectangular prisms.
At this point, the key to this activity is the “How do you know?” part of question 1. This is when the technique for determining volume by multiplying the length, width, and depth should become clear. If students do not come up with this technique themselves, you could then demonstrate with the multilink cubes.

Use patterning to help students see the connection between length, width, depth, and volume. (Note that length and height refer to the same dimension.) Have the students make a chart to help them see the pattern. A spreadsheet will be a useful tool here if students know how to enter a formula in the Volume column.

Discuss the pattern on the chart and make explicit the l x w x d = V rule for finding the volume of a rectangular prism. Highlight the connection between the area rule and the volume rule by comparing them: “The area rule is length multiplied by width, and this gives square units. The volume rule is length multiplied by width multiplied by depth, and this gives cubic units. So volume is the area multiplied by the depth.” This can be written as the rules:
A = l x w
V = l x w x d
so V = A x d.
Students could then explore the cuboids made with 30 cubes and make their own volume chart.

Answers to Activity

1. a. Yes.
Iosefa 9 x 2 x 2 = 36 blocks
Roma 12 x 3 x 1 = 36 blocks
Liam 1 x 6 x 6 = 36 blocks
Bee Har 3 x 4 x 3 = 36 blocks
b. 2 x 1 x 18; 1 x 1 x 36; 9 x 1 x 4; 3 x 2 x 6
2. Answers will vary. Some examples are: