Which of the following shapes has only flat faces and no curved surfaces at all?
ACylinder — it has two flat circles on top and bottom
BCone — it has one flat circle at the base
CRectangular prism — all six faces are flat rectangles or squares
DSphere — it is completely smooth and round
A rectangular prism (like a cereal box or brick) has six flat faces and no curves anywhere. Cylinders and cones are tricky wrong answers because they do have at least one flat face — but both also have a curved surface. The sphere has no flat faces at all. The sorting question 'flat only, curved only, or both?' is what distinguishes these shapes.
Question 2 Multiple Choice
Your friend says a cylinder and a sphere must be the same kind of shape because they both roll. What is the most important difference between them?
AA cylinder is bigger than a sphere
BA cylinder has two flat circular faces and a curved side, while a sphere has no flat faces at all
CA sphere can roll but a cylinder cannot
DThey are actually the same shape — just different sizes
Both shapes roll because both have curved surfaces, but the similarity ends there. A sphere is entirely curved — every point on its surface is curved. A cylinder combines a curved side with two flat circular ends. This is why a cylinder can balance upright on a table (resting on a flat end) while a sphere cannot — it will always roll. Shape identity is about surfaces, not just behaviors.
Question 3 True / False
A cube and a rectangular prism are mostly different kinds of shapes because a cube has equal sides and a rectangular prism does not.
TTrue
FFalse
Answer: False
A cube is actually a special type of rectangular prism — one where all edges happen to be the same length. Both shapes have exactly 6 flat faces, 8 corners, and 12 edges, and neither has any curved surfaces. The cube is a rectangular prism with equal dimensions. Saying they are 'completely different' overstates a subtle distinction in one attribute.
Question 4 True / False
The reason a cylinder can stand upright on a table but cannot stand on its curved side is directly related to its shape attributes.
TTrue
FFalse
Answer: True
This is shape attributes working in the physical world. A cylinder's two flat circular ends provide a stable, level surface to rest on — that flat face is why it stands. Its curved side has no flat contact point, so it rolls instead of standing. This connection between named attributes (flat faces vs. curved surfaces) and physical behavior (standing vs. rolling) is exactly what makes learning shape properties useful.
Question 5 Short Answer
How would you use the ideas of 'flat faces' and 'curved surfaces' to sort a cube, sphere, cylinder, and cone into groups? Describe your sorting rule and which shapes go together.
Think about your answer, then reveal below.
Model answer: Sort into three groups: (1) Only flat faces — cube and rectangular prism. (2) Only curved surfaces — sphere. (3) Both flat and curved — cylinder (two flat circles + curved side) and cone (one flat circle + curved surface). The cube has 6 flat faces and nothing curved. The sphere has no flat faces. The cylinder and cone each have at least one flat face plus a curved surface.
The flat/curved sorting rule captures the essential structural difference between these shapes. A student who can apply this rule correctly has understood shape attributes as meaningful properties — not just labels to memorize — and can reason about any new 3D shape they encounter using the same framework.