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Primary Maths · Year 2Chapter 8 · 2-D and 3-D shapes
Year 2 · Chapter 8

2-D and 3-D shapes

By the end of this chapter you will be able to

  • Name a flat (2-D) shape and count its straight sides and corners
  • Say whether a shape has a vertical line of symmetry
  • Name a solid (3-D) shape and count its faces, edges and vertices
  • Name the flat (2-D) shape of each face of a solid
  • Sort shapes and everyday objects by their shape

You should already know

  • Recognising and naming 2-D and 3-D shapes (Year 1, Chapter 3)
  • Counting in ones and twos to 20 (Year 1, Chapter 4)
  • Adding within 20 (Chapter 2)

Where this leads

  • Drawing 2-D shapes and making 3-D shapes; right angles and angles (Year 3)
  • Lines of symmetry and reflection with more precision (Year 3)

National Curriculum for England, Key Stage 1 mathematics, Year 2. Content: Identify and describe the properties of 2-D shapes, including the number of sides and line symmetry in a vertical line, Identify and describe the properties of 3-D shapes, including the number of edges, vertices and faces, Identify 2-D shapes on the surface of 3-D shapes, Compare and sort common 2-D and 3-D shapes and everyday objects.

Exercise P  Do you remember?

Non-calculator
1
FWhat shape is this?
2
FThis ball is shaped like which 3-D shape? Write its name.
3
FWhich shape is round? Write its name.
ABC
4
FHow many corners does a square have?
5
PSRuby has 2 square tiles. She gets 3 more square tiles. How many square tiles does she have now?
8.1

Naming 2-D shapes and counting sides

Year 2
Identify and describe 2-D shapes, including the number of sides
Video lesson: Naming 2-D shapes and counting sidesComing soon
A classroom. Shapes are all around us.

A 2-D shape is flat. It has length and width, but no depth.

A side is a straight edge. A corner is a sharp point where two sides meet.

A triangle has 3 sides. A square has 4 sides. A pentagon has 5 sides.

A hexagon has 6 sides. A pentagon and a hexagon are shapes with 5 and 6 corners.

A circle and an oval have no straight sides. A semicircle has one straight side and 2 corners.

A square turned on its corner is a diamond. It still has 4 equal sides.

Key ideas

  • A triangle has 3 sides.
  • A square and a rectangle have 4 sides.
  • A pentagon has 5 sides, a hexagon has 6.
  • A circle and an oval have no straight sides.
  • A semicircle has one straight side and 2 corners.
Worked example 8.1.1
How many sides does this triangle have? Trace the sides with your finger.

Method. Trace each straight side with your finger, and count it once.

  1. Trace the edge with your finger. Go round the outside of the shape once.
    one trip round the shape
  2. Count the straight sides. Count each straight side once.
    3 straight sides
  3. Write the answer.
    3

Check. Count the corners too: there are 3. ✓

Watch out. A curved edge is not a side. Count only the straight parts.

Worked example 8.1.2
Which shape has no straight sides? Write its name.
ABC

Method. Check the number of straight sides of each shape. Then pick the one that matches.

  1. Look at each shape. Check the number of straight sides of each one.
    A: square has 4 sides; B: circle has 0 sides; C: triangle has 3 sides
  2. Find the one that matches. A circle has no straight sides, so it is the answer.
    circle matches
  3. Write the answer.
    circle

Check. Check each of the other shapes too. Only circle matches. ✓

Watch out. Check every shape, not only the first one you see.

Worked example 8.1.3
How many corners does this semicircle have?

Method. Find every sharp point on the outside of the shape. Count each one once.

  1. Find each corner. A corner is a sharp point where two sides meet.
    mark each sharp point
  2. Count the corners. Each corner is counted once.
    2 corners
  3. Write the answer.
    2

Check. Count the straight sides as well: there are 1. ✓

Watch out. A corner is sharp. A curved part has no corners.

Watch out

Watch out: a circle has no sides at all. Its edge is one curve, not a straight side. A semicircle has one straight side, not two.

Exam tip

Grown-up tip. Trace each shape with a finger, round the outside. Say the count out loud: “one side, two sides, three sides.” Then count the corners. A curved part has no corners.

Exercise 8A  Naming 2-D shapes and sides

Non-calculator
1
FWhat is the name of this shape?
2
FWhat is the name of this shape?
3
FHow many sides does this triangle have?
4
FHow many sides does this hexagon have?
5
FHow many sides does this pentagon have?
6
FCount the sides of each shape.
ABC
(a)Shape A
(b)Shape B
(c)Shape C
7
PSWhich shape has 6 sides? Write its name.
ABC
8
PSWhich shape has 4 sides that are all the same length? Write its name.
ABCD
9
FDoes a circle have any straight sides? Write Yes or No.
10
FHow many straight sides does an oval have?
11
PSHow many straight sides does a semicircle have?
12
PSCount the straight sides of each shape.
ABC
(a)Shape A
(b)Shape B
(c)Shape C
13
RMia says a diamond has 4 sides, so it cannot be a square. Is she right? Write Yes or No.
14
RAli counts the sides of this rectangle. He says it has 2 sides. Is he right? Write Yes or No.
8.2

Vertical lines of symmetry

Year 2
Identify line symmetry in a vertical line
Video lesson: Vertical lines of symmetryComing soon
A garden on a sunny day.

A shape has a line of symmetry if you can fold it so that the two halves match.

In this chapter we look at a vertical line. It goes straight up and down through the middle.

A square has a vertical line of symmetry. A triangle standing up has one too.

A shape turned on its side may not fold up and down. Then it has no vertical line of symmetry.

The dashed line goes straight up and down. The two halves match.

Key ideas

  • A line of symmetry folds a shape into two matching halves.
  • A vertical line goes straight up and down.
  • Turn a shape round in your head to check the fold.
  • A sideways or slanting line is not a vertical line.
Worked example 8.2.1
Does this rectangle have a vertical line of symmetry? Write Yes or No.

Method. Imagine folding the shape in half, down the middle from top to bottom.

  1. Imagine a vertical fold. The fold line goes straight up and down.
    a straight up-and-down fold
  2. Check the two halves. Folded along a straight up-and-down line, the two halves match exactly.
    Do the two halves match?
  3. Write the answer.
    Yes

Check. Trace one half, then the other. They are the same shape. ✓

Watch out. A vertical line goes straight up and down. A sideways or slanting line does not count here.

Worked example 8.2.2
This triangle is turned on its side. Does it have a vertical line of symmetry? Write Yes or No.

Method. Imagine folding the shape in half, down the middle from top to bottom.

  1. Imagine a vertical fold. The fold line goes straight up and down.
    a straight up-and-down fold
  2. Check the two halves. Folded along a straight up-and-down line, the two halves do not match.
    Do the two halves match?
  3. Write the answer.
    No

Check. The shape is turned, so its line of symmetry slopes or goes sideways. A vertical fold does not match.

Watch out. A vertical line goes straight up and down. A sideways or slanting line does not count here.

Worked example 8.2.3
How many vertical lines of symmetry does this square have?

Method. Look for a straight up-and-down fold line where the two halves match.

  1. Look for a vertical fold line. Draw it straight up and down through the middle.
    one vertical line
  2. Check the fold. The two halves match, so the line is a line of symmetry.
    halves match
  3. Write the answer.
    1

Check. There is only one vertical direction, so only one vertical line can be a line of symmetry. ✓

Watch out. A shape can have other lines of symmetry. Only the up-and-down line counts here.

Watch out

Watch out: a shape can have other lines of symmetry, which slope or go sideways. In this section we only look at the line that goes straight up and down.

Exam tip

Grown-up tip. Cut out a paper shape and fold it in half, straight up and down. If the two halves match, the fold is a vertical line of symmetry. Try the same shape turned on its side.

Exercise 8B  Vertical lines of symmetry

Non-calculator
1
FDoes this square have a vertical line of symmetry? Write Yes or No.
2
FDoes this circle have a vertical line of symmetry? Write Yes or No.
3
FDoes this rectangle have a vertical line of symmetry? Write Yes or No.
4
FDoes this triangle, standing up, have a vertical line of symmetry? Write Yes or No.
5
FDoes this pentagon have a vertical line of symmetry? Write Yes or No.
6
FDoes this hexagon have a vertical line of symmetry? Write Yes or No.
7
FDoes this oval have a vertical line of symmetry? Write Yes or No.
8
PSThe triangle is turned on its side. Does it have a vertical line of symmetry? Write Yes or No.
9
PSThe semicircle is turned on its side. Does it have a vertical line of symmetry? Write Yes or No.
10
PSThe rectangle is tilted. Does it have a vertical line of symmetry? Write Yes or No.
11
PSWhich shapes have a vertical line of symmetry? Write the letters.
ABCD
12
FDoes this diamond have a vertical line of symmetry? Write Yes or No.
13
FHow many vertical lines of symmetry does this rectangle have?
14
RMia says a shape has a vertical line of symmetry only if it is a circle. Is she right? Write Yes or No.
8.3

Faces, edges and vertices of 3-D shapes

Year 2
Identify and describe the properties of 3-D shapes, including the number of edges, vertices and faces
Video lesson: Faces, edges and vertices of 3-D shapesComing soon
A shop. Many things in a shop are 3-D shapes.

A 3-D shape is solid. It has length, width and depth.

A face is a flat surface. An edge is a straight line where two faces meet.

A vertex is a corner. More than one vertex is vertices.

A cube has 6 faces, 12 edges and 8 vertices.

A sphere has no flat faces, no edges and no vertices.

Key ideas

  • A face is a flat surface.
  • An edge is a straight line where two faces meet.
  • A vertex is a corner.
  • A cube has 6 faces, 12 edges and 8 vertices.
Worked example 8.3.1
How many faces does this cube have? Count the flat surfaces.

Method. Count the flat faces of the cube. Count the ones you cannot see, like the bottom.

  1. Look at the shape. A face is a flat surface.
    a cube
  2. Count the flat faces. There are 6 flat faces on a cube.
    6 flat faces
  3. Write the answer.
    6

Check. Faces plus vertices equals edges plus 2: 6 + 8 = 12 + 2. ✓

Watch out. Turn the shape in your mind. Hidden faces, like the base, still count.

Worked example 8.3.2
How many vertices does this cuboid have? Count its corners.

Method. Count the vertices (corners) of the cuboid. Count the ones you cannot see, like the bottom.

  1. Look at the shape. A vertex is a sharp corner point.
    a cuboid
  2. Count the vertices (corners). There are 8 vertices (corners) on a cuboid.
    8 vertices (corners)
  3. Write the answer.
    8

Check. Faces plus vertices equals edges plus 2: 6 + 8 = 12 + 2. ✓

Watch out. Turn the shape in your mind. Hidden faces, like the base, still count.

Worked example 8.3.3
This pyramid has a triangle base. How many edges does it have?

Method. Count the edges of the pyramid. Count the ones you cannot see, like the bottom.

  1. Look at the shape. An edge is a straight line where two faces meet.
    a pyramid
  2. Count the edges. There are 6 edges on a pyramid.
    6 edges
  3. Write the answer.
    6

Check. Faces plus vertices equals edges plus 2: 4 + 4 = 6 + 2. ✓

Watch out. Turn the shape in your mind. Hidden faces, like the base, still count.

Watch out

Watch out: a face is flat. The curved side of a cylinder is not a flat face, and a sphere has no flat faces.

Exam tip

Grown-up tip. Use a cereal box. Count the faces first, then the edges, then the corners. Run your finger along each edge. Ask: “How many corners can you find?”

Exercise 8C  3-D shapes: faces, edges and vertices

Non-calculator
1
FWhat solid shape is this?
2
FWhat solid shape is this?
3
FWhat solid shape is this?
4
FWhat solid shape is this?
5
FHow many faces does this cuboid have?
6
FHow many edges does this cube have?
7
FHow many vertices does this cube have?
8
FThis cylinder has a curved side. Answer both parts.
(a)How many flat faces?
(b)How many vertices?
9
FThis pyramid has a triangle base. How many faces does it have altogether? Remember the faces you cannot see.
10
FHow many flat faces does this cone have?
11
PSHow many vertices does this cone have?
12
PSWhich solid has no flat faces, no edges and no vertices? Write its name.
ABC
13
PSLook at shapes A, B and C. Which one has 8 vertices? Write its name.
ABC
14
RSam says a cylinder has 2 faces and 1 edge. Is he right? Write Yes or No.
8.4

2-D shapes on the faces of 3-D shapes

Year 2
Identify 2-D shapes on the surface of 3-D shapes
Video lesson: 2-D shapes on the faces of 3-D shapesComing soon
A kitchen. Many things in a kitchen are 3-D shapes.

Solid shapes have faces. Each flat face is a 2-D shape.

A cube has 6 square faces. A cuboid has rectangle faces.

A cylinder has 2 flat ends. Each end is a circle.

A pyramid with a triangle base has triangle faces.

A sphere has no flat faces, so no 2-D shape is on it.

Key ideas

  • A cube has 6 square faces.
  • A cuboid has rectangle faces.
  • A cylinder has 2 circle ends.
  • A pyramid has triangle faces.
  • A sphere has no flat faces.
Worked example 8.4.1
What 2-D shape is each face of this cube?

Method. Look at one flat face of the cube. Then name its shape.

  1. Look at one flat face. A cube has flat faces that are squares.
    one flat face of the cube
  2. Check its sides. Count the straight sides, or check if the face is round.
    4 equal straight sides
  3. Name the shape. This flat face is a square.
    square

Check. Every flat face of this cube is the same kind of shape. ✓

Watch out. A face is flat, so it is a 2-D shape. The solid itself is 3-D.

Worked example 8.4.2
What 2-D shape is the flat end of this cylinder?

Method. Look at one flat face of the cylinder. Then name its shape.

  1. Look at one flat face. A cylinder has flat faces that are circles.
    one flat face of the cylinder
  2. Check its sides. Count the straight sides, or check if the face is round.
    round, with no straight sides
  3. Name the shape. This flat face is a circle.
    circle

Check. Every flat face of this cylinder is the same kind of shape. ✓

Watch out. A face is flat, so it is a 2-D shape. The solid itself is 3-D.

Worked example 8.4.3
What 2-D shape is one of the faces of this pyramid?

Method. Look at one flat face of the pyramid. Then name its shape.

  1. Look at one flat face. A pyramid has flat faces that are triangles.
    one flat face of the pyramid
  2. Check its sides. Count the straight sides, or check if the face is round.
    3 straight sides
  3. Name the shape. This flat face is a triangle.
    triangle

Check. Every flat face of this pyramid is the same kind of shape. ✓

Watch out. A face is flat, so it is a 2-D shape. The solid itself is 3-D.

Watch out

Watch out: a face of a cube is a square, not a cube. A cube is 3-D. A square is 2-D. The curved side of a cylinder is not a flat 2-D shape.

Exam tip

Grown-up tip. Find a box, a tin and a ball at home. Ask: “What shape is the flat side?” Then ask: “Does the ball have a flat side?”

Exercise 8D  2-D shapes on the faces of 3-D shapes

Non-calculator
1
FWhat 2-D shape is each face of this cube?
2
FWhat 2-D shape is each face of this cuboid?
3
FWhat 2-D shape is the flat end of this cylinder?
4
FWhat 2-D shape is a face of this pyramid?
5
FWhat 2-D shape is the flat base of this cone?
6
PSWhich 2-D shape is a face of the cube? Write its letter.
ABC
7
PSWhich 2-D shape is a flat face of the cuboid? Write its letter.
ABC
8
PSWhich 2-D shape is on the flat end of the cylinder? Write its letter.
ABC
9
FName the 2-D shape on the flat face of each solid.
ABC
(a)Solid A
(b)Solid B
(c)Solid C
10
FCan a sphere have a flat face? Write Yes or No.
11
PSWhich 3-D shape has triangle faces? Write its name.
ABC
12
PSBen says a cube has triangle faces. Is he right? Write Yes or No.
13
PSWhich 3-D shape has 2 flat circle ends? Write its name.
AB
14
RA shape has 6 square faces. Is it always a cube? Write Yes or No.
8.5

Comparing and sorting shapes and everyday objects

Year 2
Compare and sort common 2-D and 3-D shapes and everyday objects
Video lesson: Comparing and sorting shapes and everyday objectsComing soon
A school. Shapes are all around us.

We can sort shapes into groups. We can sort them by flat or solid.

We can also sort them by sides, corners, faces or vertices.

A ball is shaped like a sphere. A tin is shaped like a cylinder.

A book is shaped like a cuboid. A clock face is a flat circle.

Key ideas

  • Flat shapes are 2-D. Solid shapes are 3-D.
  • Sort shapes by their sides, corners, faces and vertices.
  • A ball is a sphere. A tin is a cylinder.
  • A book is a cuboid.
Worked example 8.5.1
Look at shapes A, B and C. Which one is solid? Write the letter.
ABC

Method. Check the flat or solid of each shape. Then pick the one that matches.

  1. Look at each shape. Check the flat or solid of each one.
    A: square is flat; B: cube is solid; C: circle is flat
  2. Find the one that matches. A cube has depth, so it is solid. The square and circle are flat.
    B matches
  3. Write the answer.
    B

Check. Check each of the other shapes too. Only B matches. ✓

Watch out. Check every shape, not only the first one you see.

Worked example 8.5.2
Which shape has more sides: a triangle or a pentagon? Write the name.
AB

Method. Count the sides of each shape. Then compare the two numbers.

  1. Count the sides of triangle. The triangle has 3 sides.
    triangle: 3
  2. Count the sides of pentagon. The pentagon has 5 sides.
    pentagon: 5
  3. Compare the numbers. The shape with more sides is the answer.
    5 is more than 3
  4. Write the answer.
    pentagon

Check. The other shape has more sides, so pentagon is right. ✓

Watch out. Count both shapes before you decide.

Worked example 8.5.3
A tin is shaped like which 3-D shape? Write its name.

Method. Think about the shape of the whole object, not one small part.

  1. Look at the object. Think about its flat parts and curved parts.
    a tin
  2. Match it to a shape. A tin has 2 flat circle ends and a curved side, so it is a cylinder.
    tin = cylinder
  3. Write the name.
    cylinder

Check. Name the flat faces or the curved part to check. ✓

Watch out. Many objects are not perfect shapes, so think about the main shape.

Watch out

Watch out: a book is not a cube. A book has rectangle faces, not square faces.

Exam tip

Grown-up tip. Gather a ball, a tin, a box and a block from home. Ask: “Which one can roll?” and “Which one has flat faces?”

Exercise 8E  Comparing and sorting shapes and objects

Non-calculator
1
FIs this shape flat or solid? Write flat or solid.
2
FIs this shape flat or solid? Write flat or solid.
3
FLook at shapes A, B and C. Which one is solid? Write its letter.
ABC
4
PSWhich shape has more sides: a square or a triangle? Write the name.
AB
5
PSWhich shape has fewer corners: a circle or a hexagon? Write the name.
AB
6
PSWhich shape has the most sides? Write the name.
ABC
7
FA ball is shaped like which 3-D shape? Write its name.
8
FA tin is shaped like which 3-D shape? Write its name.
9
FA book is shaped like which 3-D shape? Write its name.
10
FMatch each object to its 3-D shape.
ABC
(a)Object A (ball)
(b)Object B (tin)
(c)Object C (block)
11
PSWhich shapes have a curved surface? Write the letters.
ABCD
12
FWhich shape has no corners: a square or a circle? Write the name.
AB
13
RRuby says a cuboid has 4 corners, like a rectangle. Is she right? Write Yes or No.
14
ROdd one out: which shape is different from the others? Write its name.
ABCD

Chapter summary

SkillMethod
2-D shapesA flat shape has length and width. A side is a straight edge. A corner is a sharp point.
SidesTriangle 3, square 4, rectangle 4, pentagon 5, hexagon 6. A circle or an oval has no straight sides.
Vertical line of symmetryThe two halves match when folded along a straight up-and-down line.
3-D shapesA face is flat. An edge is a straight line where faces meet. A vertex is a corner.
Cube and cuboidEach has 6 faces, 12 edges and 8 vertices.
2-D shapes on 3-D shapesA cube has square faces. A cuboid has rectangle faces. A cylinder has circle ends.
SortingSort shapes by flat or solid, by sides, or by curved surfaces. A ball is a sphere; a tin is a cylinder.

Can you…?

  • I can name a 2-D shape and count its sides.
  • I can say whether a shape has a vertical line of symmetry.
  • I know that a circle and an oval have no straight sides.
  • I can name a 3-D shape.
  • I can count the faces, edges and vertices of a cube.
  • I can name the 2-D shape of a face of a 3-D shape.
  • I can sort shapes and everyday objects by their shape.

Key terms

2-D shape
a flat shape with length and width, but no depth.
3-D shape
a solid shape with length, width and depth.
side
a straight edge of a flat shape.
corner
a sharp point where two sides of a flat shape meet.
line of symmetry
a line where a shape folds so that the two halves match.
vertical
straight up and down.
face
a flat surface of a solid shape.
edge
a straight line where two faces of a solid shape meet.
vertex
a corner of a solid shape. More than one is vertices.
cube
a solid shape with 6 equal square faces.
cuboid
a solid box shape with 6 rectangle faces.
sphere
a round solid shape, like a ball, with no flat faces.
cylinder
a solid shape with 2 flat circle ends and a curved side.
cone
a solid shape with a round flat base and one point at the top.
pyramid
a solid shape with a flat base and triangle faces that meet at a point.

Exercise 8Z  Check-up

Non-calculator
1
What shape is this?
2
How many sides does this pentagon have?
3
What solid shape is this?
4
How many faces does this cube have?
5
How many vertices does this cuboid have?
6
The rectangle is tilted. Does it have a vertical line of symmetry? Write Yes or No.
7
What 2-D shape is the flat end of this cylinder?
8
Which solid has a point at the top and a round flat base: cone, cylinder or sphere? Write its name.
9
Look at shapes A, B and C. Which one is flat? Write its letter.
ABC
10
Sam says a square turned on its corner is not a square. Is he right? Write Yes or No.

Total 13 marks. Allow about 13 minutes.

Exercise 8X  End-of-chapter quiz

Non-calculator
1
FWhat shape is this?[1 mark]
2
FWhat solid shape is this?[1 mark]
3
FHow many corners does this semicircle have?[1 mark]
4
PSAli says a cube has 8 faces. Is he right? Write Yes or No.[1 mark]
5
FLook at shapes A and B. Which one has no straight sides? Write its name.[1 mark]
AB
6
FDoes this square have a vertical line of symmetry? Write Yes or No.[1 mark]
7
FWhat 2-D shape is one of the faces of this cuboid? Write its name.[1 mark]
8
PSLook at the diamond. How many of its sides are the same length? Write the number.[2 marks]
9
PSWhich 3-D shape has 6 faces, 12 edges and 8 vertices? Write its name.[2 marks]
AB
10
RRuby says a rectangle turned on its side still has a vertical line of symmetry. Is she right? Write Yes or No.[2 marks]
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