Year 4 · Mathematics · Space
Shapes, angles and maps
Making and describing three-dimensional objects, comparing angles with a right angle, and using simple grid maps to describe locations and routes.
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These lessons were written around Australian Curriculum strands and matched to UK year groups by age (Year 1 is the year a child turns 6 in England). They are not mapped to the National Curriculum in England or the curricula of Scotland, Wales or Northern Ireland, so check them against your own plans.
Learning goals
Learners will
- Make and describe three-dimensional objects using faces, edges and vertices.
- Compare angles with a right angle, deciding if they are smaller, the same or larger.
- Use grid references on a simple map to describe locations and routes.
Success looks like
- I can build a cube or pyramid and count its faces, edges and vertices.
- I can use a paper right-angle tester to sort angles.
- I can say where something is on a grid map, like B3, and give directions for a route.
The big idea
Three-dimensional (3D) objects take up space. We describe them by their faces (flat or curved surfaces), edges (where faces meet) and vertices (corners where edges meet).
Build objects with toothpicks and play dough balls. A cube needs 12 toothpicks (edges) and 8 balls (vertices), and it has 6 square faces. A square pyramid needs 8 toothpicks and 5 balls, and it has 5 faces: a square base and 4 triangles. A triangular prism has 5 faces, 9 edges and 6 vertices.
Objects with curved surfaces, such as a cylinder (like a can), a cone and a sphere (like a ball), cannot be built from straight sticks. A cylinder has 2 flat circular faces and 1 curved surface; a sphere has one curved surface and no edges or vertices.
An angle is the amount of turn between two lines that meet. A right angle is a square corner. Fold a piece of paper in half and then in half again to make a right-angle tester. Hold it in angles around the home: the corner of a door, a book or a tile.
Compare each angle with the tester. If the angle fits inside the tester, it is smaller than a right angle (these are called acute angles). If it opens wider, it is larger than a right angle (obtuse). Clock hands make good examples: at 3 o'clock they make a right angle.
A grid map has letters along the bottom and numbers up the side. To find square C2, go along to column C, then up to row 2. A handy saying is 'along the corridor, then up the stairs'.
Routes are described with directions and distances: 'Start at A1. Move 3 squares right, then 2 squares up.' Your child can draw a grid map of a room or the backyard and plan routes between places.
- Cube: 6 faces, 12 edges, 8 vertices.
- Angles: smaller than, equal to or larger than a right angle.
- Grid reference: letter first (along), then number (up).
Worked examples
Describing a square pyramid
How many faces, edges and vertices does a square pyramid have?
- Faces: 1 square base and 4 triangle faces, so 5 faces.
- Edges: 4 around the base and 4 going up to the top, so 8 edges.
- Vertices: 4 at the base and 1 at the top, so 5 vertices.
Answer: A square pyramid has 5 faces, 8 edges and 5 vertices.
Comparing an angle with a right angle
The hands of a clock show 2 o'clock. Is the angle between them smaller or larger than a right angle?
- At 3 o'clock the hands make a right angle.
- At 2 o'clock the minute hand is on 12 and the hour hand is on 2, which is a smaller turn than to the 3.
- Check with the paper tester: the angle fits inside it.
Answer: The angle at 2 o'clock is smaller than a right angle.
Following a route on a grid map
Start at square A1. Move 2 squares right and 3 squares up. Where do you finish?
- Moving right changes the letter: A → B → C.
- Moving up changes the number: 1 → 2 → 3 → 4.
- Put the letter and number together.
Answer: You finish at C4.
Practice check
Have a go, then check your answers. Each answer comes with an explanation.
Answer guide for parents
How many faces does a cube have?
6 — A cube has 6 square faces, like a dice.
How many vertices does a square pyramid have?
5 — 4 vertices around the square base and 1 at the top make 5.
At 3 o'clock, what angle do the hands of a clock make?
a right angle — The minute hand on 12 and the hour hand on 3 make a quarter turn, which is a right angle.
Which object has no flat faces, no edges and no vertices?
sphere — A sphere, like a ball, has one curved surface only.
On a grid map with columns A, B, C, D, which square is 2 squares to the right of B4?
D4 — Moving right changes the letter: B → C → D. The number stays 4, so it is D4.
Is the angle between clock hands at 1 o'clock smaller or larger than a right angle?
smaller — At 1 o'clock the hands are close together, a much smaller turn than at 3 o'clock.
How many faces does a triangular prism have?
5 — A triangular prism has 2 triangle faces and 3 rectangle faces: 5 faces altogether.
You start at C3 and move 1 square left and 2 squares up. Where do you finish?
B5 — Left changes C to B. Up changes 3 to 4, then 5. You finish at B5.
Watch out for
- Counting only the faces or edges you can see in a picture. Use real objects and turn them over to count hidden ones.
- Thinking an angle is bigger because its lines are longer. Draw the same angle with short and long arms and test both with the right-angle tester.
- Reading grid references the wrong way round (number first). Practise 'along the corridor, then up the stairs': letter first, then number.
Tips for parents
- Use packaging from the recycling bin to explore 3D objects before building them.
- Make the right-angle tester together and go on an 'angle hunt' around the house.
- Board games played on a grid, such as battleship-style guessing games, are excellent grid-reference practice.
Go further
- Build a cube, a square pyramid and a triangular prism with toothpicks and play dough, and make a table of faces, edges and vertices.
- Draw a grid map of your bedroom or garden, mark five items, and write their grid references for someone else to find.
- Find five angles at home smaller than a right angle and five larger than a right angle, and sketch them.
About 40 minutes
You'll need
- Toothpicks or straws and small balls of play dough or blu-tack
- Boxes and household objects such as a can, a ball and an ice-cream cone
- A sheet of paper folded twice to make a right-angle tester
- Grid paper or a hand-drawn grid for a map
Key words
- face
- A flat or curved surface of a 3D object.
- edge
- A line where two faces meet.
- vertex
- A corner of a 3D object, where edges meet. The plural is vertices.
- angle
- The amount of turn between two lines that meet at a point.
- right angle
- A square corner, like the corner of a page; a quarter turn.
- grid reference
- A letter and number, such as C4, that names a square on a grid map.
Still tricky?
For parents
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