Year 5: 3-D shapes from 2-D pictures
Part of the Year 5 angles and shapes chapter. Chapter overview · whole chapter on one page
3-D shapes from 2-D pictures
A 3-D shape is a solid. It has faces, edges and vertices. A cube has 6 square faces. A cuboid has 6 rectangular faces. A cube is a special cuboid, where every face is a square.
We draw 3-D shapes on flat paper, so a drawing is a 2-D representation of a 3-D shape. A net is a flat pattern that folds up into a 3-D shape. If you can picture the net folding up, you can name the shape.
Key ideas
- A cube has 6 square faces, 12 edges and 8 vertices.
- A cuboid has 6 rectangular faces, 12 edges and 8 vertices.
- A net is flat. When it folds up, it makes a 3-D shape.
Key words. A face is a flat side of a 3-D shape. An edge is where two faces meet. A vertex is a corner (more than one is vertices). A net is a flat pattern that folds up into a 3-D shape.
Method. Count the faces of the net and look at their shapes. Then name the 3-D shape that it folds into.
- Count the squares. Each square becomes one face of the solid.6 squares
- Check the faces. All six faces are squares of the same size.six equal squares
- Name the solid. A 3-D shape with six equal square faces is a cube.cube
Check. The solid has 6 faces, the same as the net. ✓
Watch out. A cube has square faces. A cuboid has rectangular faces, and a cube is a special cuboid.
Key words. A face is a flat side of a 3-D shape. An edge is where two faces meet. A vertex is a corner (more than one is vertices). A net is a flat pattern that folds up into a 3-D shape.
Method. Picture the faces, the edges and the corners of a cuboid, then count each one.
- Count the faces. A cuboid has a top and a bottom, a front and a back, and two sides.2 + 2 + 2 = 6 faces
- Count the edges. Each face has 4 edges, and each edge is shared by 2 faces.6 × 4 ÷ 2 = 12 edges
- Count the vertices. Each corner is shared by 3 faces.6 × 4 ÷ 3 = 8 vertices
Check. The numbers match the cube: 6 faces, 12 edges and 8 vertices. ✓
Watch out. Faces, edges and vertices are different. An edge is a line, and a vertex is a corner.
Key words. A face is a flat side of a 3-D shape. An edge is where two faces meet. A vertex is a corner (more than one is vertices). A net is a flat pattern that folds up into a 3-D shape.
Method. Compare the faces of a cube with the faces of a cuboid.
- Say what a cuboid is. A cuboid is a 3-D shape with 6 rectangular faces.6 rectangular faces
- Say what a cube is. A cube has 6 square faces.6 square faces
- Decide. A square is a special rectangle, so a cube also has 6 rectangular faces.Yes, a cube is a cuboid
Check. Every cube is a cuboid, but not every cuboid is a cube. ✓
Watch out. A cuboid does not have to have square faces.
Watch out
A common mistake is to mix up faces, edges and vertices. A face is a flat side, an edge is a line where two faces meet, and a vertex is a corner. A cube has 6 faces, 12 edges and 8 vertices.
Exercise 9A Faces, edges and vertices of 3-D shapes
Non-calculatorKey words. A face is a flat side of a 3-D shape. An edge is where two faces meet. A vertex is a corner (more than one is vertices). A net is a flat pattern that folds up into a 3-D shape.
Method. Count the faces of the shape, one at a time.
- Picture the shape. A cube has six square faces, one on each side.
- Count the faces. Count each one once and do not miss any.6 faces
Check. Counting in a different order gives 6 again. ✓
Watch out. Faces, edges and vertices are different things. Read the question carefully.
Key words. A face is a flat side of a 3-D shape. An edge is where two faces meet. A vertex is a corner (more than one is vertices). A net is a flat pattern that folds up into a 3-D shape.
Method. Count the edges of the shape, one at a time.
- Picture the shape. An edge is a line where two faces meet. A cube has 4 edges on top, 4 on the bottom and 4 going up.
- Count the edges. Count each one once and do not miss any.12 edges
Check. Counting in a different order gives 12 again. ✓
Watch out. Faces, edges and vertices are different things. Read the question carefully.
Key words. A face is a flat side of a 3-D shape. An edge is where two faces meet. A vertex is a corner (more than one is vertices). A net is a flat pattern that folds up into a 3-D shape.
Method. Count the vertices of the shape, one at a time.
- Picture the shape. A vertex is a corner. A cuboid has 4 corners on the top and 4 on the bottom.
- Count the vertices. Count each one once and do not miss any.8 vertices
Check. Counting in a different order gives 8 again. ✓
Watch out. Faces, edges and vertices are different things. Read the question carefully.
Key words. A face is a flat side of a 3-D shape. An edge is where two faces meet. A vertex is a corner (more than one is vertices). A net is a flat pattern that folds up into a 3-D shape.
Method. Count the faces of the shape, one at a time.
- Picture the shape. A cuboid has six rectangular faces.
- Count the faces. Count each one once and do not miss any.6 faces
Check. Counting in a different order gives 6 again. ✓
Watch out. Faces, edges and vertices are different things. Read the question carefully.
Key words. A face is a flat side of a 3-D shape. An edge is where two faces meet. A vertex is a corner (more than one is vertices). A net is a flat pattern that folds up into a 3-D shape.
Method. Count the edges of the shape, one at a time.
- Picture the shape. A cuboid has 12 edges, the same as a cube.
- Count the edges. Count each one once and do not miss any.12 edges
Check. Counting in a different order gives 12 again. ✓
Watch out. Faces, edges and vertices are different things. Read the question carefully.
Key words. A face is a flat side of a 3-D shape. An edge is where two faces meet. A vertex is a corner (more than one is vertices). A net is a flat pattern that folds up into a 3-D shape.
Method. Count the vertices of the shape, one at a time.
- Picture the shape. A cuboid has 8 corners.
- Count the vertices. Count each one once and do not miss any.8 vertices
Check. Counting in a different order gives 8 again. ✓
Watch out. Faces, edges and vertices are different things. Read the question carefully.
Key words. A face is a flat side of a 3-D shape. An edge is where two faces meet. A vertex is a corner (more than one is vertices). A net is a flat pattern that folds up into a 3-D shape.
Method. List the faces, then find the one that matches the top face.
- List the faces. The top and bottom are 4 cm by 2 cm. The front and back are 4 cm by 3 cm. The sides are 2 cm by 3 cm.top 4 by 2, bottom 4 by 2, front and back 4 by 3, sides 2 by 3
- Find the match to the top. Only the bottom face is the same size and shape as the top face.bottom = top
- Write the answer. Apart from the top, only one face matches it.1 other face
Check. The front and back are 4 by 3, so they do not match the top. ✓
Watch out. Check the size of each face, not just its shape.
Key words. A face is a flat side of a 3-D shape. An edge is where two faces meet. A vertex is a corner (more than one is vertices). A net is a flat pattern that folds up into a 3-D shape.
Method. Count the faces of the net and look at their shapes. Then name the 3-D shape that it folds into.
- Count the squares. Each square becomes one face of the solid.6 squares
- Check the faces. All six faces are squares of the same size.six equal squares
- Name the solid. A 3-D shape with six equal square faces is a cube.cube
Check. The solid has 6 faces, the same as the net. ✓
Watch out. A cube has square faces. A cuboid has rectangular faces, and a cube is a special cuboid.
Key words. A face is a flat side of a 3-D shape. An edge is where two faces meet. A vertex is a corner (more than one is vertices). A net is a flat pattern that folds up into a 3-D shape.
Method. Count the faces of the net and look at their shapes. Then name the 3-D shape that it folds into.
- Count the rectangles. Each rectangle becomes one face of the solid.6 rectangles
- Look for matching faces. Opposite faces of a cuboid are the same size.the band has two pairs of equal faces, and the top and bottom match
- Name the solid. A 3-D shape with six rectangular faces is a cuboid.cuboid
Check. The solid has 6 faces, the same as the net. ✓
Watch out. A cube has square faces. A cuboid has rectangular faces, and a cube is a special cuboid.
Key words. A face is a flat side of a 3-D shape. An edge is where two faces meet. A vertex is a corner (more than one is vertices). A net is a flat pattern that folds up into a 3-D shape.
Method. Count the faces of a cube, then compare the answer with what each child says.
- Count the faces of a cube. A cube has six square faces, one on each side.6 faces
- Compare with what each child says. Ruby says 8, and Tom says 6.6 ≠ 8, and 6 = 6
- Decide. Tom is right, because a cube has 6 faces.Tom is right
Check. A cube has 6 faces, so the answer is 6. ✓
Watch out. Count the faces, do not guess the number.
Key words. A face is a flat side of a 3-D shape. An edge is where two faces meet. A vertex is a corner (more than one is vertices). A net is a flat pattern that folds up into a 3-D shape.
Method. Find the number of edges, then multiply by the length of one edge.
- Write the number of edges. A cube has 12 edges.12 edges
- Multiply by the length of one edge. All the edges of a cube are the same length.12 × 4 = 48
- Write the answer. 48 cm
Check. 48 ÷ 12 = 4. ✓
Watch out. Count the edges first. A cube has 12 of them.
Key words. A face is a flat side of a 3-D shape. An edge is where two faces meet. A vertex is a corner (more than one is vertices). A net is a flat pattern that folds up into a 3-D shape.
Method. Count the edges on the top, the bottom and the vertical edges.
- Count the edges on the top. The top face is a rectangle with 4 edges.4 edges
- Count the edges on the bottom. The bottom face is also a rectangle with 4 edges.4 edges
- Count the vertical edges. Four edges join the top corners to the bottom corners.4 edges
- Add them up. Add the three groups of 4.4 + 4 + 4 = 12 edges
- Decide. A cuboid has 12 edges, so Sam is wrong.No
Check. A cuboid has the same 12 edges as a cube. ✓
Watch out. Count every edge, including the ones on the bottom.
Key words. A face is a flat side of a 3-D shape. An edge is where two faces meet. A vertex is a corner (more than one is vertices). A net is a flat pattern that folds up into a 3-D shape.
Method. Write the three numbers, then add them together.
- Write the three numbers. A cube has 6 faces, 12 edges and 8 vertices.6 + 12 + 8
- Add the numbers. Add the first two, then add the third.6 + 12 = 18, and 18 + 8 = 26
- Write the answer. 26
Check. 26 − 8 = 18, and 18 − 12 = 6. ✓
Watch out. Add the three numbers. Do not write them as a number of angles.
Key words. A face is a flat side of a 3-D shape. An edge is where two faces meet. A vertex is a corner (more than one is vertices). A net is a flat pattern that folds up into a 3-D shape.
Method. Think about what a cube and a cuboid have in common.
- Is every cube a cuboid? A cube has 6 rectangular faces, so it is a cuboid.Yes
- Is every cuboid a cube? A cuboid only becomes a cube if all its edges are the same length.No, not always
- Write the answer. A cube is always a cuboid. A cuboid is only a cube if all its edges are equal.
Check. A cube is a special cuboid. ✓
Watch out. A cube is a special cuboid. Not every cuboid is a cube.