g10-10-01 · Syllabus supplement
Classify by structure, not by viewpoint
Does rotating a solid change its type?
1 MIN · PREDICT ON PAPER
Compare a prism,pyramid,cylinder,cone,frustum andsphere; decide which have parallel bases and which have a common apex.
Discuss or write first. No typed answer is required to continue.
Rotation changes the image, not the structural classification.
2 MIN · EXPLAIN AND REVISE
Which condition does your claim need?
Compare at least two cases. Write a reason, then check the explanation together.
Reveal explanation and conditions
Structure determines the class: parallel congruent bases describe prisms or cylinders; a common apex describes pyramids or cones; cutting off a smaller cone gives a frustum. A sphere has no flat base.
Conditions: Use nondegenerate solids. A curved surface is not a polygonal face, and the apparent outline changes with viewpoint.
Mathematical justification: Rotation preserves incidence, parallelism and congruence of the defining bases; it changes projected coordinates but not the solid structure.
1 MIN · EXIT CHECK
A solid has two parallel congruent circular bases and a curved side. Name it.
Check after answering
A circular cylinder.
Teacher guidance and extension
Before: Plane area, Pythagoras and units.
Ask: Which defining feature can you still identify after rotating the view?
Watch for: Classifying a tilted cylinder as a cone because its image looks narrow.
Challenge: Explain why a sphere cannot be classified as a many-sided prism.
Suggested timing: predict 1 min, compare 3 min, explain 2 min, exit check 1 min. Observations can suggest a claim; they do not prove it for every input.
Optional local notebook
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