Students will reinforce concepts related to the volume of rectangular prisms and how volume relates to multiplication and addition, as well as the commutative property.

The purpose of Day 2 activities is to reinforce concepts from Day 1. Students will engage in warm up activities that will encourage them to consider different ways to describe the volume of rectangular prisms as well as making connections to the commutative property and how it can be leveraged to determine the volume of rectangular prisms.

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

• Volume is an attribute of a three-dimensional space;
• The volume of a rectangular prism is related to the edge lengths;
• The volume of a rectangular prism can be found by counting the cubes in one layer and multiplying it by the number of layers;
• The volume of a rectangular prism can be determined by finding the area of the base and multiplying by the number of layers;
• Both volume formulas relate to counting the cubes in one layer and multiplying that value by the number of layers (height);
• The product remains unchanged, no matter how the numbers being multiplied are ordered (commutative property of multiplication).

Coming Soon

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

On this day, there are a variety of Math Talk options to select from. You might consider utilizing a single math talk, or possibly more than one. Alternatively, you might consider using these math talks over the next week or as a means to interleave and spiral throughout the school year.

Consider utilizing the following image with the prompt:

Which one doesn’t belong?

If you have not used a Which One Doesn’t Belong prompt before, note that the options in the image are crafted in such a way where one might be able to argue one or more reasons why any of the options do not belong based on different attributes, properties, characteristics, etc.

Some possible observations students might share include:

• D doesn’t belong because it’s the only one that doesn’t have a volume of 24 cubic units
• A doesn’t belong because it’s the only one that has a single layer
• B doesn’t belong because it’s the only tall one
• A doesn’t belong because you can rotate B and C into D, but A doesn’t fit

Of course, these are just some possible observations and many more ideas may be highlighted by your students.

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These prompts promote students reasoning and proving as they connect visual representations to symbolic representations.

Connecting Representations #1:

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Connecting Representations #2:

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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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