3D shapes
🎯 In this topic you will
- Explain what prisms are and compare their properties with pyramids.
- Build and correctly name different 3D shapes.
- Describe the features of 3D shapes and sketch them accurately.
🧠 Key Words
- apex
- prism
Show Definitions
- apex: The pointed top of a 3D shape, where several faces meet at a single vertex (common in pyramids).
- prism: A 3D shape with two identical, parallel faces called bases, connected by rectangular side faces.
🔷 Discovering 3D Shapes
You will have seen 3D shapes all around you, but do you really know what they are? Do you know what a prism is? You might even be able to find prisms both at school and at home. In this section, you will learn how to recognise prisms and pyramids and how to use other familiar 3D shapes in different puzzles and activities.
❓ EXERCISES
1. Put a ring around the prisms.
a. How do you know they are prisms?
b. Why aren’t the other shapes prisms?
👀 Show answer
a. They are prisms because they each have exactly two matching ends and all the side faces are flat rectangles.
b. The other shapes are not prisms because they either come to a point (pyramids and cones), have curved surfaces (cylinders and spheres), or do not have two equal parallel ends.
2. Write the name of the shape and say whether it is a prism, a pyramid or neither.
For each shape, give the number of edges, faces and vertices.
👀 Show answer
Cylinder – neither – $2$ curved edges, $3$ faces, $0$ vertices.
Triangular prism – prism – $9$ edges, $5$ faces, $6$ vertices.
Hexagonal prism – prism – $18$ edges, $8$ faces, $12$ vertices.
Pyramid – pyramid – number of edges, faces and vertices depends on the base (for a square pyramid: $8$ edges, $5$ faces, $5$ vertices).
3.
You will need a die and a set of coloured counters in two different colours.
Take turns to roll the die and check your shape using the key.
Place a counter on the shape that matches the key.
Keep playing until all the shapes are covered.
The winner is the player with the most counters on the shapes.
👀 Show answer
4. Work with a partner.
Sketch $3$D shapes.
Sketch a cuboid.
Sketch two cubes joined together.
Choose another $3$D shape to sketch. Name it.
👀 Show answer
🧠 Think like a Mathematician
Task: How many bricks would you need to make each of these rectangular prisms?
Method:
- Carefully count the number of small cubes (bricks) in prism a.
- Repeat for prisms b, c, and d.
- Record your totals.
- Look for a pattern or rule connecting length, width, height, and total bricks.
- Choose a different number of bricks and try to build as many different rectangular prisms as possible.
- Observe any number patterns you notice.
Follow-up Questions:
👀 Show Answers
- 1. Each prism uses $\text{length} \times \text{width} \times \text{height}$ cubes. Counting layer by layer gives the total number of bricks.
- 2. The rule is: $\text{Number of cubes} = l \times w \times h$. You multiply how many cubes are along each direction.
- 3. For example, using $12$ bricks you could make prisms of size $1 \times 1 \times 12$, $1 \times 2 \times 6$, or $2 \times 2 \times 3$. Each different factor arrangement gives a new prism.
- 4. The possible prisms depend on the factors of the number. Numbers with more factors allow more different rectangular prisms, while prime numbers only make one long thin prism.