Construction of 3D Objects
Warm-up
Mystery object: pass around a closed box. Feel it without looking. How many faces? Edges? Corners (vertices)? Open and reveal. Were your counts correct? This activates tactile geometry knowledge before visual construction.
Explore
Net construction: students choose one 3D shape, fold a pre-drawn net to construct it, then build the same shape as a skeleton with straws and clay. Compare: what does the net show that the skeleton does not? (Faces.) What does the skeleton show that the net does not? (Spatial structure without distraction of surfaces.)
Formalize
Properties chart: as a class, build a chart of all 3D shapes studied (cube, rectangular prism, triangular prism, cone, cylinder, sphere). For each: faces, edges, vertices. Notice: some shapes have curved surfaces that are not counted as faces in the usual sense. A sphere: 0 flat faces, 0 edges, 0 vertices. A cone: 1 flat face, 1 curved surface, 1 edge (the circle), 1 vertex (the tip).
Construction of 3D Objects
Cultural connection: examine images of a pithouse. What 3D shapes compose it? (Cylinder or cone on top of a rectangular depression.) Why might this shape have been chosen? (Insulation, structural stability, natural building materials.) How does the geometry serve the function?
Practice
Students construct nets for 3 different 3D objects, record faces/edges/vertices for each, and sketch 2 cultural objects identifying the 3D shapes they contain. Exit ticket: how many faces does a cube have, and what shape are they?
Exit ticket
Students construct nets for 3 different 3D objects, record faces/edges/vertices for each, and sketch 2 cultural objects identifying the 3D shapes they contain. Exit ticket: how many faces does a cube have, and what shape are they?
Step 1: Distribute toothpicks (edges) and clay balls (vertices). The build order that works: make the square base first — 4 sticks, 4 balls.
Step 2: Plant 4 vertical sticks, one rising from each base ball.
Step 3: Cap with the top square: 4 more sticks joining the tops, 4 more balls at the corners.
Step 4: Audit the inventory AGAINST the built object, touching each part: sticks used — 4 (base) + 4 (posts) + 4 (top) = 12 edges. Balls — 4 + 4 = 8 vertices. The 6 faces are the empty square windows (count them: top, bottom, 4 walls).
Step 5: The insight the skeleton makes visible that a solid block hides: a cube is STRUCTURE — the faces are just the spaces the frame encloses. Now predict the skeleton for a triangular prism BEFORE building: 2 triangles need 6 edges + 3 posts = 9 edges, 6 vertices. Build to confirm.
Step 1: Show four flat arrangements of 6 squares (nets and fake-nets): the cross shape; an L of 6; a 2×3 block; a T shape.
Step 2: PREDICT each — fold it in your head only, commit yes/no in writing with a reason. (The mental folding is the actual geometry workout; cutting first skips the exercise.)
Step 3: Cut and fold to test. The cross folds neatly into a cube ✓. The 2×3 block collapses with overlapping squares and a gaping hole ✗. The T works ✓. The L of 6 in a line wraps around leaving two faces doubled ✗.
Step 4: Do the autopsy on the failures — where exactly did squares collide? Which face never got covered? Failure analysis teaches more spatial reasoning than the successes do.
Extension for early finishers: there are exactly 11 distinct cube nets. Find a new one nobody in class has drawn yet — and prove it folds.
Setup: solids hidden in a cloth bag — cube, sphere, cylinder, cone, square pyramid, rectangular prism. A student reaches in (no peeking) and must name the object BEFORE withdrawing it.
Step 1: Teach the interrogation order: first, does it ROLL in your fingers? Any curved surface says sphere / cylinder / cone territory. All flat? It's a prism-or-pyramid.
Step 2: If curved: sphere rolls every direction (no flat anywhere); cylinder has two flat circle ends; cone has one flat end and a point.
Step 3: If flat-faced: count vertices by touch. 8 corners with all-square faces → cube; 8 corners with long faces → rectangular prism; a point on top with a square base → pyramid.
Step 4: The student announces the name AND the deciding evidence: "pyramid — I felt one sharp apex and a flat square bottom." Evidence-based naming is the point; a lucky guess without the property-talk scores zero.
Why touch beats sight here: eyes recognize; fingers must ANALYZE properties one at a time. It's the properties we're teaching.