Task Teacher Guide

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Students will engage in warm up activities that will encourage them to think about units as well as consider the effect of doubling a dimension of a rectangular prism on the magnitude of its volume. They will explore composite shapes made up of non-overlapping rectangular prisms and develop strategies to find their volume.

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The purpose of Day 4 activities is to reinforce and extend concepts from Day 3. Students will engage in warm up activities that will encourage them to consider appropriate units and the effect of doubling an edge length on the volume.

Students will also have an opportunity to complete a purposeful practice that will serve to develop a deeper understanding of the following big ideas:

• The volume of a rectangular prism is related to the edge lengths
• The volume of a rectangular prism can be determined by finding the area of the base and multiplying by the number of layers
• The volume of a rectangular prism can be determined by multiplying length, width and height
• The volume of a composite shape made up of non-overlapping rectangular prisms can be determined by breaking it apart into rectangular prisms, multiplying length, width and height of each prism, and adding the products
• Doubling one of the dimensions of a rectangular prism results in doubling the volume.

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A variety of tools for students to use to think through the problems, such as:

• Linking cubes or Omnifix cubes
• Isometric dot paper & colored pencils or markers
• Grid paper
• Whiteboards & markers
• Teaching remotely? NCTM’s Isometric Drawing Tool can be used to build and manipulate cube structures

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Math Talk #1

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A unit talk encourages students to consider the relationship between the size of the object being measured and the size of the unit of measurement. It can be useful to have physical models of the units to help students visualize and select an appropriate unit of measurement (centimeter cubes, or inch cubes, for example). You may consider using units from different measurement systems to build flexibility. The goal is to encourage discussion about the relationship between sizes, and more than one answer may be possible.

Consider using the following prompt:

Which unit would you use (cubic centimeters, cubic meters) or (cubic inches, cubic feet, cubic yards) to measure:

• your lunchbox?
• your bedroom?
• a cereal box?
• a moving van?

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[accordion-item title=”What Comes Next #1?”]

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Purposeful Practice

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[accordion-item title=”Questions: Finding the Volume of Composite Shapes and Doubling Dimensions”]

Allow students the opportunity to engage in purposeful practice without the use of a calculator to promote their fluency and flexibility with these concepts and to model their thinking:

Question #1:

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Question #2:

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Question #3:

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Question #4:

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Question #5:

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Question #6:

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We suggest collecting this reflection as an additional opportunity to engage in the formative assessment process to inform next steps for individual students as well as how the whole class will proceed.

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Resources and Downloads

Explore The Entire Unit of Study

This Make Math Moments Task was designed to spark curiosity for a multi-day unit of study with built in purposeful practice, and extensions to elicit and emerge mathematical models and strategies.

Click the links at the top of this task to head to the other related lessons created for this unit of study.