Materials: Per pair: 36 centimeter cubes, pencils; Volume of 36 worksheet
Procedure 1. Introduction (10 minutes, whole group and pairs) Distribute cubes and ask pairs of students to use 12 of them to make a rectangle.
After a moment, gather the group to share how they approached the task. Record the dimensions of rectangles that they found on the board in a chart such as:
Next, ask students to add a second layer so that they have a rectangular prism that is two cubes high.
Again, gather the group to share strategies and dimensions. Add a “height” column to the chart and record:
Establish that each figure has a base of 12 cm2 and a volume of 36 cm3.
2. Volume of Right Rectangular Prisms (10 minutes, pairs) Distribute the worksheet and review the instructions. Mention that pairs will have time to find only a few of the many possible solutions (and they may not end up filling up the sheet).
Once pairs have found several rectangular prisms, call the group together to share strategies. Prompt for strategies based on factors, multiples, area, and doubling/halving.
3. Video and Conclusion (10 minutes, whole group) Ask pairs to attempt a problem they will see in the video: A rectangular prism has a 3 by 4 base and a height of 6. What is its volume?
After a few minutes, show students the video. Pause at 1:10 and ask:
Did anyone solve the problem as demonstrated in the video?
Are there other ways to solve the problem?
When the video is over, engage the group in a brief discussion. Ask students:
What other three-dimensional (3D) figures composed of quadrilaterals did you see in the video?
What real-life objects are in those shapes?
Note that the base • height volume formula applies to any 3D shape composed of six quadrilateral faces, with at least two faces that are parallel and congruent. (See the Activity Extension for a suggestion involving trapezoidal prisms.)
To wrap up, engage students in reflecting on and explaining the volume formula. Ask, How would you respond if someone said to you, “I need to see all the cubes to know how many there are. Convince me that the formula will give always me the right answer”?
Activity Extension: If students know how to find the area of a trapezoid, have them calculate the volume of a real-life object in a trapezoidal prism shape. Otherwise, provide students with small boxes and have them determine the volume by packing with unit cubes and by using the volume formula.