CCSS.Math.Content.7.G.A.3
The standard
Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.
Common Core State Standards for Mathematics · Geometry
What this standard means
Students need to picture a flat cut through a solid and name the shape made by that cut. They should work with rectangular prisms and rectangular pyramids, using words like horizontal, vertical, parallel to a face, and through a vertex.
Mastery means students can predict and sketch cross-sections without always seeing the model first. They can explain why a slice is a rectangle, triangle, trapezoid, or other polygon. Common trouble spots are thinking every slice of a prism is a rectangle, ignoring the angle of the cut, and confusing the solid with the flat shape made by the slice.
Ways to teach it
- Use clay rectangular prisms and pyramids, then cut them with dental floss to reveal and sketch the cross-sections.
- Ask students: How could you slice a rectangular prism to make a rectangle, a square, or a triangle?
- Show three slice diagrams and have students name each cross-section, then write one sentence explaining one choice.
- Connect to food by slicing a block of cheese or a sandwich at different angles and naming the flat faces created.
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