CCSS.Math.Content.HSG-GMD.B.4
The standard
Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
Common Core State Standards for Mathematics
What this standard means
Students need to picture how a flat slice cuts through a solid, then name the shape of that slice. They also need to imagine a flat shape spinning around a line and identify the solid it creates.
Mastery looks like matching slices and rotations to shapes without guessing. Students can explain why a cylinder can have circular or rectangular cross-sections, depending on the cut. Common sticking points are diagonal slices, confusing surface views with cross-sections, and not tracking the axis of rotation.
Ways to teach it
- Use play dough and dental floss to slice cubes, cylinders, cones, and spheres, then sketch and label each cross-section.
- Ask students to explain what solid forms when a right triangle rotates around each leg, and why the results differ.
- Show three quick diagrams of sliced solids and have students name each cross-section on mini whiteboards.
- Connect to CT scan images by showing how stacked circular cross-sections can model a sphere or cylinder.
Plan a lesson for CCSS.Math.Content.HSG-GMD.B.4
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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.HSG-GMD.B
Visualize relationships between two-dimensional and three-dimensional objects
- CCSS.Math.Content.K.G.A
Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).