CCSS.Math.Content.HSG-GMD.B

CCSS.Math.Content.HSG-GMD.B is a cluster heading. These are the individual standards under it.

• 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...

01

What Students Need to Do

Students picture and describe the flat shape created when a plane slices a solid. They also determine the three-dimensional solid formed by rotating a flat figure around a line.

02

What Mastery Looks Like

Students correctly sketch and name cross-sections made by planes cutting prisms, pyramids, cylinders, cones, and spheres. They also predict the solid formed when a two-dimensional figure rotates around a given line.

03

Common Misconceptions

Students often assume every slice of a solid matches its base. They may confuse the axis of rotation with an outside edge or misjudge how distance from the axis affects the resulting solid.

04

How to Assess It

Give students two prompts: draw the cross-section of a cone cut parallel to its base, then sketch the solid formed by rotating a right triangle around one leg.

1. 01

   Slice clay cylinders and cones with dental floss, then trace and label each exposed face.

2. 02

   Show three cuts through a cone and ask, “How does the cutting angle change the cross-section?”

3. 03

   Match cards showing solids, cutting planes, cross-sections, and rotation axes, then justify each set to a partner.

4. 04

   Use stacked CT scan images to sketch the three-dimensional shape they represent and explain why the slices vary.

• 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 ...