Multiple Attributes of 2D Shapes and 3D Objects
Warm-up
Hold up a cylinder. What 2D shapes can you find on it? (Two circles, one rectangle if unrolled.) Hold up a triangular prism. (Two triangles, three rectangles.) This activates the 2D-in-3D connection before the main activity.
Explore
Venn challenge: left circle = 4 or more sides; right circle = at least one pair of equal sides. Sort 12 shape cards. Which shapes are in the overlap? Which are outside both circles? Compare sorts with a partner and discuss any disagreements.
Formalize
Construction from description: make a shape with 3 sides where two sides are equal length. How many different shapes satisfy this? (Many isosceles triangles of different sizes and angles.) Make one that also has a right angle. This narrows it to isosceles right triangles only.
Multiple Attributes of 2D Shapes and 3D Objects
Examine a Northwest Coast formline image. Identify every ovoid and U-form. What are the geometric attributes of an ovoid compared to a regular rectangle? (Rounded corners, sides that taper slightly.) How does the artist use these shapes to suggest animal anatomy?
Practice
Students complete a two-attribute Venn sort with 10 shapes, construct 3 shapes from written descriptions on dot paper, and label the faces of 2 different 3D objects. Exit ticket: name a shape in each of the four regions of a Venn diagram (left only, right only, overlap, outside).
Exit ticket
Students complete a two-attribute Venn sort with 10 shapes, construct 3 shapes from written descriptions on dot paper, and label the faces of 2 different 3D objects. Exit ticket: name a shape in each of the four regions of a Venn diagram (left only, right only, overlap, outside).
Step 1: Set up two overlapping sorting hoops (a Venn diagram before naming it): hoop A = "has 4 sides," hoop B = "has at least one square corner."
Step 2: Sort a shape pile. A tilted square: 4 sides ✓ AND square corners ✓ → it lives in the OVERLAP. A right triangle: square corner ✓ but 3 sides → hoop B only. A hexagon: neither → outside both hoops.
Step 3: The overlap is the day's idea: a shape can satisfy TWO rules at once, and the overlap region is exactly the "yes-and-yes" club.
Step 4: Run the reverse game: point to a region and ask students to INVENT a shape that belongs there. Inventing for the overlap ("4 sides and a square corner… a rectangle!") is harder — and more revealing — than sorting ever is.
Watch for: students who sort by overall look ("pointy things") instead of checking each attribute separately. Require a two-part verdict for every shape: sides? corners?
Step 1: Hand out real cubes and define by touch: a FACE is a flat surface you can press your palm on; an EDGE is a line where two faces meet (run a finger along it); a VERTEX is a sharp corner point.
Step 2: Count faces systematically, not randomly: top and bottom (2), front and back (2), left and right (2) → 6 faces. Pairing opposite faces prevents the classic recount-forever loop.
Step 3: Count edges by layers: 4 around the top face, 4 around the bottom, 4 vertical posts connecting them → 12 edges.
Step 4: Count vertices by layers too: 4 corners up top, 4 below → 8 vertices.
Record the cube's ID card: 6 faces, 12 edges, 8 vertices. Then verify the same numbers on a rectangular box (a cereal box) — same counts, stretched shape. That surprise (same structure, different look) is the start of thinking about CLASSES of objects.
The moment: a triangle drawn point-down gets rejected by half the class. They've only ever met triangles sitting flat on a horizontal base.
Step 1: Return to the definition — the checklist, not the vibe: 3 straight sides? Count them: yes. 3 corners? Yes. Closed (no gaps)? Yes. Then it IS a triangle. Orientation is not on the checklist.
Step 2: Prove it with rotation: cut the shape out and slowly spin it. Ask the class to shout when it STOPS being a triangle. It never does — turning a shape doesn't change its sides or corners.
Step 3: Diagnose the source: books and posters that always draw shapes in one "pose" teach the pose instead of the shape. Counter it deliberately: draw skinny triangles, obtuse ones, point-down ones — and tilted squares (which students will try to rename "diamonds").
Step 4: The habit to leave with: judge shapes by their PROPERTIES (sides, corners, closed), never by which way they happen to be sitting.