Grade by Grade
E. Spatial Sense · 3D Objects, Directions and Measurement

Sorting and Building 3D Objects

E1.1 A1About 35 minutes
Learning goals
  • I can tell the difference between a prism and a pyramid.
  • I can sort 3D objects using a rule and explain my rule.
  • I can figure out someone else's sorting rule.
  • I can build a skeleton of a 3D object and predict how many sticks and balls I need.

Words to know

prism
A 3D object with 2 matching bases that face each other, joined by rectangle faces. It is named after the shape of its bases.
pyramid
A 3D object with 1 base and triangle faces that all meet at one vertex. It is named after the shape of its base.
apex
The vertex at the top of a pyramid or cone, where the faces or curved surface come to a point.
sorting rule
The reason we put objects into groups, like "has a curved surface".
skeleton
A model that shows only the edges and vertices of a 3D object, like a frame made of sticks.

Let's start with recycling day

It's recycling day! The blue bin is full of cereal boxes, soup cans, a tissue box and a cone-shaped paper cup. Your job is to sort them into groups.

There are many ways to sort. You could sort by what the objects look like, by how they move (roll, slide or stack), or by counting their faces, edges or vertices. The important part is to say your rule.

Prism or pyramid?

Prisms and pyramids are families of 3D objects.

  • A prism has 2 matching bases, one at each end. Rectangles join the bases. It looks the same all the way through, like a loaf of bread you could slice.
  • A pyramid has 1 base. Triangles go up from each side of the base and meet at one point at the top, called the apex.

Both are named after the shape of their base. A prism with triangle bases is a triangular prism. A pyramid with a square base is a square-based pyramid.

pentagonal prismpentagonal pyramid
Left: a pentagonal prism has 2 pentagon bases joined by 5 rectangles. Right: a pentagonal pyramid has 1 pentagon base and 5 triangles that meet at the apex.

Is a cube a prism?

Yes! A cube has 2 matching square bases (top and bottom) joined by 4 faces. It is a rectangular prism whose faces are all squares. A cylinder is a bit like a prism too (2 matching circle bases), but it has a curved surface instead of rectangles, so it is not a prism.

Worked example

Example 1: Sort by faces

Sort these: cube, cone, cylinder, triangular prism, square-based pyramid, rectangular prism. Use the rule "only flat faces" or "has a curved surface".

  1. Check each object. Does any part curve?
  2. Cube, triangular prism, square-based pyramid and rectangular prism have only flat faces.
  3. The cone and the cylinder each have a curved surface.

Only flat faces: cube, triangular prism, square-based pyramid, rectangular prism. Has a curved surface: cone, cylinder.

Worked example

Example 2: What's my rule?

Maya sorted some objects.

  • Group A: cube, rectangular prism, triangular prism, cylinder
  • Group B: cone, square-based pyramid, triangular pyramid

What is her sorting rule?

  1. Look for something every object in Group B has. The cone and both pyramids come to a point at the top (an apex).
  2. Check Group A. The cube and the prisms have 2 matching bases. The cylinder has 2 matching circles. None of them comes to a point.
  3. Make sure the rule works for every object.

Group A has 2 matching bases (one at each end). Group B has 1 base and comes to a point (an apex).

Has a vertexHas no vertex
Can rollconecylinder
Cannot rollcube, rectangular prism, triangular prism, square-based pyramid, triangular pyramidnone of our objects
Sorting with two rules at once. A ball (sphere) could also go in "can roll, has no vertex".

Sorting by angles

You can also sort by angles. Look at the corners of the faces.

  • All square corners: cube and rectangular prism. Every corner of every face is a square corner.
  • Some corners are not square corners: pyramids and triangular prisms, because a triangle face has corners that are smaller or bigger than a square corner. (In a triangular prism, the rectangle faces still have square corners.)

Building 3D objects

One way to build a 3D object is to make a skeleton. Sticks (like straws or toothpicks) are the edges. Small balls of modelling clay are the vertices.

Before you build, predict: How many sticks will you need? How many balls?

cube: 12 sticks, 8 ballspyramid: 8 sticks, 5 balls
Skeletons. A cube needs 12 sticks (edges) and 8 balls (vertices). A square-based pyramid needs 8 sticks and 5 balls.
Worked example

Example 3: Plan a skeleton

How many sticks and clay balls do you need to build a triangular prism skeleton?

  1. Sticks are edges. A triangular prism has 3 edges on each triangle and 3 joining edges: 3 + 3 + 3 = 9 sticks.
  2. Clay balls are vertices. It has 3 corners on each triangle: 3 + 3 = 6 balls.
  3. To build: make 2 triangles with 3 sticks each. Stand them up facing each other and join the matching corners with 3 more sticks.

You need 9 sticks and 6 clay balls.

Worked example

Example 4: Build with faces

Noor wants to build a cube out of paper squares taped together. How many squares does she need? Must they be the same size?

  1. A cube has 6 faces, and every face is a square.
  2. All the edges of a cube are the same length, so all the squares must be the same size.

She needs 6 squares, all the same size.

Thinking like a mathematician

When you sort or build, predict first, then check. If your prediction was off, that's fine. Ask yourself: "What did I miss?" Explaining your rule clearly is just as important as sorting correctly.

Just for fun

What did the cone say to the cylinder?

"Let's roll!" (They both have a curved surface, so they both can roll.)

Hands-on activity

Build skeletons

You need: drinking straws cut into pieces (or toothpicks), and modelling clay or play dough.

Grown-up note: a grown-up should cut the straws. Toothpicks have sharp points, so use them carefully. Keep clay balls away from babies and toddlers.

  1. Roll small balls of clay. These are the vertices.
  2. Predict: How many sticks and balls will a cube need? Write it down.
  3. Build a square for the bottom (4 sticks, 4 balls). Stand 4 sticks up from the corners. Add 4 balls and 4 more sticks for the top.
  4. Count: Were you right? (12 sticks, 8 balls.)
  5. Now predict and build a square-based pyramid and a triangular prism.
  6. Sort your skeletons: which have only square corners?

Math talk: "How did you know how many sticks to use?"

Your turn

1

How many bases does a prism have? How many does a pyramid have?

2

A pyramid has a hexagon base. What is its name?

3

Sort these into prisms and pyramids: triangular pyramid, cube, triangular prism, square-based pyramid.

4

Name the two objects we studied that can roll.

5

How many sticks and clay balls do you need for a square-based pyramid skeleton?

6

What shape are the faces that join the two bases of a prism?

7

Which objects have only square corners on their faces?

More practice: warm-up

1

What is the apex of a pyramid?

2

Does a cylinder have a curved surface?

3

A prism has 2 triangle bases. What is its name?

4

How many sticks do you need for a cube skeleton?

5

Can a cube roll?

More practice: on your own

1

Sam's groups: Group 1: cube, rectangular prism. Group 2: cone, triangular pyramid, square-based pyramid. What is his rule?

2

Sort into more than 5 vertices and 5 or fewer vertices: cube, cone, triangular prism, square-based pyramid, triangular pyramid.

3

Leo has 6 sticks and 4 clay balls. Which skeleton can he build? Explain.

4

Why is a cylinder not a prism?

5

You want to build a rectangular prism that is long, not a cube. Do all 12 sticks need to be the same length? Explain.

Challenge

1

How many sticks and clay balls do you need for a hexagonal prism skeleton?

2

Find a rule that puts the cone and the square-based pyramid in one group and the cylinder and cube in the other.

3

Ana built a skeleton with 8 sticks and 5 balls, but it is not a square-based pyramid. Its base has 4 sides that are not all equal. What could it be?

Check your understanding

Quiz

1.

How many bases does a prism have?

2.

Which object is a pyramid?

3.

Group A: cylinder, cone. Group B: cube, square-based pyramid. What is the rule?

4.

How many sticks do you need to build a triangular prism skeleton?

5.

How many clay balls (vertices) does a cube skeleton need?

6.

Which object has only square corners on all its faces?

For parents and teachers

Big idea: Children sort 3D objects by their properties (faces, edges, vertices, angles, curved or flat) and build them (Ontario E1.1). Explaining a sorting rule and checking predictions are key mathematical processes (strand A1).

Common difficulties:

  • Prism vs pyramid. A quick test: "Does it come to a point?" Pyramids do; prisms have a matching base at each end.
  • Rules that don't fit every object. Ask: "Does your rule work for every object in this group, and for none in the other group?"
  • Skeleton counts. Link the parts: sticks = edges, balls = vertices. Encourage predicting before building.

Safety: A grown-up should cut straws. Toothpicks are sharp, and small balls of clay or mini marshmallows are a choking risk for younger siblings.

How to help: Play "guess my rule" with things from the recycling bin. You sort; your child guesses the rule, then switch.