This is a level 3 measurement strand activity from the Figure It Out series.
A PDF of the student activity is included.
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find the volume of rectangular prisms
unit place value blocks
square grid paper
scissors and tape
This activity investigates measuring the volume of rectangular prisms. It is an ideal opportunity to use and compare a variety of problem-solving strategies such as guess and check, draw a diagram, make a table, and look for a pattern.
Question 1 clarifies the conditions for the investigation and tests whether the student understands the problem. Let students use a variety of strategies to find the volume of unit place value blocks. After students share these strategies, discuss the efficiency of using the l x w x d rule.
Question 2 encourages students to investigate the most efficient open box, namely the one that holds the most unit cubes. Point out that different size cut-out squares will result in different combinations of length, width, and depth measures and hence different volumes. The students could work individually or in pairs. It may be necessary to clarify the meaning of “set of small corner squares”.
It may help to ask “What size squares can be cut from each corner of the 18 x 18 grid?” This would show that it is possible to cut out squares ranging from 1 x 1 to 8 x 8.
Ask the students to discuss and report on possible strategies for answering the question. You may wish to assign different strategies to different groups and use an observer to report and discuss the most efficient strategy. Make sure a group uses a systematic approach and makes records using a table such as:
They may stop after the fourth box is recorded if the pattern has become obvious.
The investigation explores sides based on fractions. This could result in varying solutions. The practical solution using blocks will be different from the solution reached using the l x w x d rule because the rule assumes that you can split the cubes into halves. Those who use blocks may claim that it is sensible to stack the top layer of cubes with a half cube standing above the box edge. This will give a very different result.
Answers to Activity
1. 392
2. When a 3 x 3 square is cut from the paper, the volume is 12 x 12 x 3 = 432 cm3. This gives the maximum number of unit place value blocks (432).
Investigation
Answers will vary. (The volume of a is 3371/2 cm3 and b is 422 1/2cm 3 .)