CCSS.Math.Content.HSG-GMD.B
The standard
Visualize relationships between two-dimensional and three-dimensional objects
Common Core State Standards for Mathematics · High School — Geometry
What this standard means
Students need to connect flat drawings, slices, nets, and projections to the solid figures they represent. They should predict cross-sections, match nets to solids, and describe how changing a view changes what they know about the object.
Mastery looks like moving both ways, from 3D model to 2D representation and from 2D clues back to a possible solid. Students often get stuck when a drawing hides depth, when a net has extra or missing faces, or when a slanted slice creates an unexpected shape.
Ways to teach it
- Use clay or foam solids and dental floss to cut cross-sections, then sketch each slice before and after the cut.
- Show a cube net and ask, Which faces will touch when folded, and how do you know?
- Give three solids and four top-view drawings, then have students match them and explain one choice in writing.
- Bring in a cereal box, soup can, and traffic cone image, then identify their nets, views, and possible cross-sections.
Plan a lesson for CCSS.Math.Content.HSG-GMD.B
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Related standards
- CCSS.Math.Content.K.G.A.3
Identify shapes as two-dimensional (lying in a plane, "flat") or three-dimensional ("solid").
- CCSS.Math.Content.K.G.B.4
Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences,...
- CCSS.Math.Content.7.G.A.3
Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular ...
- CCSS.Math.Content.HSG-GMD.B.4
Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensi...