Chapter 7 of 8

All 8 chapters
  1. 1Straight lines and parallel lines, readunderstood
  2. 2Polygons, readunderstood
  3. 3Right angles and turns, readunderstood
  4. 4Measuring angles in degrees, readunderstood
  5. 5Triangles and four sided shapes, readunderstood
  6. 6Lines of symmetry, readunderstood
  7. 7Solid shapes and nets, readunderstood
  8. 8Grids and directions, readunderstood

M2.5.7 Chapter 7

Solid shapes and nets

Will any 6 squares joined together fold into a cube?

Your guess

Pick one before you read on. It is fine to be wrong.

Your guess

  • You picked A. Read on. At the end, the chapter comes back to your guess.

  • You picked B. Read on. At the end, the chapter comes back to your guess.

  • You picked C. Read on. At the end, the chapter comes back to your guess.

By the end you can

  • Count the faces, edges and corners of a cube and a prism
  • Fold a net into an open box
  • Match a solid shape to its net

Pick up a box. It has flat sides, straight lines and sharp points.

Draw it first

Faces, edges and corners of a cube

  1. A cube drawn with its hidden edges dashed. Step 2 outlines the front side and labels it face. Step 3 outlines the left front line and labels it edge. Step 4 puts a dot on the top right back point and labels it corner.

    1 Draw a cube. Dashed lines are edges you cannot see.

  2. A cube drawn with its hidden edges dashed. Step 2 outlines the front side and labels it face. Step 3 outlines the left front line and labels it edge. Step 4 puts a dot on the top right back point and labels it corner.face

    2 A flat side is a face. A cube has 6 faces.

  3. A cube drawn with its hidden edges dashed. Step 2 outlines the front side and labels it face. Step 3 outlines the left front line and labels it edge. Step 4 puts a dot on the top right back point and labels it corner.faceedge

    3 A line where two faces meet is an edge. A cube has 12 edges.

  4. A cube drawn with its hidden edges dashed. Step 2 outlines the front side and labels it face. Step 3 outlines the left front line and labels it edge. Step 4 puts a dot on the top right back point and labels it corner.faceedgecorner

    4 A point where edges meet is a corner. A cube has 8 corners.

Some books call a corner a vertex. Two or more are vertices.

A cube and a triangular prism with their counts. The cube: 6 faces, 12 edges, 8 corners. The triangular prism: 5 faces, 9 edges, 6 corners. The labels are cube, 6 faces, 12 edges, 8 corners, triangular prism, 5 faces, 9 edges and 6 corners.cube6 faces12 edges8 cornerstriangular prism5 faces9 edges6 corners
A box like a matchbox has the same counts as a cube.

A prism has the same shape all along its length. A triangular prism has 2 triangle faces and 3 rectangle faces.

A square based pyramid has 5 faces, 8 edges and 5 corners.

Take a box apart and lay it flat. The flat shape is a net. A net folds up into the solid.

Only some shapes of 6 squares are nets of a cube. Look at these three.

Three shapes made of 6 squares, with dashed fold lines. The first is a cross shape and folds into a cube, labelled yes. The second is a row of 6 and does not, labelled no. The third is a block of 2 by 3 and does not, labelled no.yesnono
Dashed lines are folds. The row of 6 wraps round into a tube.

See it three ways

With things

Hold a box, such as a matchbox. Touch each face, edge and corner as you count.

As a picture

A cube drawn with hidden edges dashed. The labels are 6 faces, 12 edges and 8 corners.6 faces12 edges8 corners

In symbols

Faces 6. Edges 12. Corners 8. The top has 4 edges and the bottom has 4. Four edges go up.

Try it

Fold a net into an open box

You need: a square of paper that is 15 cm wide, a ruler, a pencil, scissors.

Be safe: Ask a grown up to help with the scissors.

  1. Mark every 5 cm along each side. Join the marks with a ruler. You get 9 squares.
  2. Cut out the 4 corner squares. A cross of 5 squares is left.
  3. Fold up along the 4 sides of the middle square. The 4 arms stand up.
  4. Hold the upright sides together at the corners. You have an open box.

What you will see: The net has 5 squares, and the box has 5 faces. It is open on top, so it has no sixth face.

If you cannot try it, this is what happens.
A cross of 5 squares with dashed fold lines. The middle square is the base. The four arms fold up as sides. The labels are base and side.baseside

A wrong idea many people have

Any 6 squares joined edge to edge fold into a cube.

Why it feels right: A cube has 6 faces. A net has 6 squares.

The test that breaks it: Draw 6 squares in a row. Fold them. Four squares make a tube. The last two land on top of the first two.

What is true: No two faces may land in the same place. A cube has 11 different nets. A row of 6 is not one of them.

Key words

face
a flat side of a solid shape.
edge
a line where two faces meet.
corner
a point where edges meet.
net
a flat shape that folds up into a solid.

Back to your guess

The answer is B: No. Only some joined squares fold into a cube.

Only some work. When you fold, no two squares may land in the same place. A cube has 11 different nets.

Check yourself

Try each one before you look. A wrong answer tells you where to go next.

  1. A cube has 6 faces. Each face has 4 edges. Each edge joins 2 faces. How many edges does a cube have?

    See the answer

    12

    6 faces with 4 edges each is 24. Each edge was counted twice, so 24 ÷ 2 = 12.

  2. A triangular prism has two triangle ends. A triangle has 3 corners. How many corners does the prism have?

    See the answer

    6

    Each triangle end has 3 corners. 3 + 3 = 6. There are no other corners.

  3. Which solid folds up from this net?

    A net made of three rectangles in a row, with a triangle joined above and below the middle rectangle. Dashed lines show the folds.
    Tap your answer.

    1. Not this one. A cube net has 6 squares. This net has triangles and rectangles. Try another.

    2. Yes, that is right. The net has 2 triangles and 3 rectangles. That is 5 faces, the faces of a triangular prism.

    3. Not this one. A pyramid net has a square and 4 triangles. This net has 3 rectangles. Try another.

    See the answer

    a triangular prism

    The net has 2 triangles and 3 rectangles. That is 5 faces, the faces of a triangular prism.

    • If you chose A: A cube net has 6 squares. This net has triangles and rectangles.
    • If you chose C: A pyramid net has a square and 4 triangles. This net has 3 rectangles.

  4. Which shape folds into a cube?

    Two shapes made of 6 squares. Shape A is a row of 6 squares. Shape B is a cross shape with a row of 4 and one square above and below. The labels are A and B.AB
    Tap your answer.

    1. Not this one. Six in a row wrap into a tube. The last squares land on the first ones. Two faces are missing. Try another.

    2. Yes, that is right. B folds so every square lands in a different place. A does not.

    3. Not this one. Both have 6 squares. But a row of 6 wraps into a tube. Try another.

    See the answer

    Shape B

    B folds so every square lands in a different place. A does not.

    • If you chose A: Six in a row wrap into a tube. The last squares land on the first ones. Two faces are missing.
    • If you chose C: Both have 6 squares. But a row of 6 wraps into a tube.

  5. A square based pyramid has a square base with 4 edges. 4 more edges go up to the top corner. How many edges?

    See the answer

    8

    4 edges on the base and 4 edges going up. 4 + 4 = 8.

  6. From an earlier chapter

    Mei measures a line with a ruler. Where should the start of the line be?

    Tap your answer.

    1. Yes, that is right. Put one end of the line at the 0 mark. Read the number at the other end.

    2. Not this one. Many rulers have a gap before 0. Start at the 0 mark, not at the edge. Go to M2.5.1. Try another.

    3. Not this one. The line would read 1 cm too long. Measuring starts at 0. Go to M2.5.1. Try another.

    See the answer

    At the 0 mark

    Put one end of the line at the 0 mark. Read the number at the other end.

    • If you chose B: Many rulers have a gap before 0. Start at the 0 mark, not at the edge. Go to M2.5.1.
    • If you chose C: The line would read 1 cm too long. Measuring starts at 0. Go to M2.5.1.

  7. How many faces does this triangular prism have?

    A triangular prism lying on a rectangle, with its hidden edges dashed. The label is triangular prism.triangular prism
    Tap your answer.

    1. Yes, that is right. It has 2 triangle ends and 3 rectangle sides. 2 + 3 = 5 faces.

    2. Not this one. You counted the 3 rectangle sides. The 2 triangle ends are faces too. Try another.

    3. Not this one. A cube has 6 faces. A prism with triangle ends has 2 triangles and 3 rectangles. Try another.

    See the answer

    5

    It has 2 triangle ends and 3 rectangle sides. 2 + 3 = 5 faces.

    • If you chose B: You counted the 3 rectangle sides. The 2 triangle ends are faces too.
    • If you chose C: A cube has 6 faces. A prism with triangle ends has 2 triangles and 3 rectangles.

  8. Lucía folds this net into a box with no lid. How many faces does the box have?

    A cross of squares with dashed fold lines. The label is net.net
    Tap your answer.

    1. Not this one. You counted the sides only. The middle square is the base, and it is a face too. Try another.

    2. Not this one. A box with a lid has 6 faces. This net has no square for a lid. Try another.

    3. Yes, that is right. Each square of the net becomes one face. The net has 5 squares, so the box has 5 faces.

    See the answer

    5

    Each square of the net becomes one face. The net has 5 squares, so the box has 5 faces.

    • If you chose A: You counted the sides only. The middle square is the base, and it is a face too.
    • If you chose B: A box with a lid has 6 faces. This net has no square for a lid.

  9. How many corners does this cube have?

    A cube drawn with its hidden edges dashed. The label is cube.cube
    Tap your answer.

    1. Not this one. That is the number of edges. A corner is a point where edges meet. Try another.

    2. Yes, that is right. The front face has 4 corners and the back face has 4. 4 + 4 = 8.

    3. Not this one. That is the number of faces. A corner is a point, not a flat side. Try another.

    See the answer

    8

    The front face has 4 corners and the back face has 4. 4 + 4 = 8.

    • If you chose A: That is the number of edges. A corner is a point where edges meet.
    • If you chose C: That is the number of faces. A corner is a point, not a flat side.

Keep it

Copy this into your exercise book.

A cube has 6 faces, 12 edges and 8 corners. A triangular prism has 5, 9 and 6. A net is a solid laid flat. Not every 6 squares make a cube net.

Draw: A cube with its hidden edges dashed. Label a face, an edge and a corner.

Reading with a child? A short page for the adult: what this chapter teaches and three questions to ask.

No internet tomorrow? Save the whole book as one file (773 KB). It opens on any phone.