Describe a Solid Made from Smaller Solids

Supplied materials

• Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
• Supplied worked-case record: A model has two layers, each with three cubes in a row.
• All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.

Learn the idea

A solid model can be composed of matching cubes. Count every cube, including cubes in the stated hidden layer. The number of component cubes describes the model’s construction; it is different from the number of flat faces on one cube.

Use the supplied layer description. Draw or list the cubes in one layer and repeat for each stated layer. Count components without counting a shared boundary or a visible face as another cube.

Use the supplied full-layer count even when a sketch hides a cube. A cube’s faces are not separate component cubes. Represent each layer as its own row of cube labels.

1. Represent each layer as its own row of cube labels.
2. Follow the worked example. Point to each number or shape feature and say what it tells you.
3. Use the supplied layer description.
4. Try the question and then the three practice questions. Check your answers and explain any change you make.

Check your reasoning

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Take it further

Three layers of four cubes use 12 cubes. Draw or explain all three layers.

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