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Term pack

Year 6 Maths

Name: ________________________

Skills in this pack

  • Integers
  • Multiplying and dividing larger numbers
  • Unlike fractions and mixed numbers
  • Adding and subtracting fractions
  • Percentages
  • Ratio and proportion
  • How much for one?
  • Letters for numbers
  • Number patterns
  • Volume with unit cubes
  • Nets of solids
  • Coordinate geometry
  • Averages

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Year 6 Maths · 1 of 13

Integers

Add and subtract positive and negative whole numbers.

Before you start

Have a wander along the line — nothing here is right or wrong. See how far each number sits from zero, and which side of it.

-6-5-4-3-2-10123456

Zero is not a wall. Going from -3 up to 2 walks straight through it and out the other side.

  1. 1.-7 + 3 = ?

  2. 2.Work out each one, then sort it by whether the answer is negative or positive.

    Groups: Negative · Positive

    • -5 - 5
    • 4 - 10
    • -6 + 2
    • -2 + 8
    • -9 + 12
    • 7 - 3

  3. 3.6 + (-9) = ?

  4. 4.5 - 12 = ?

  5. 5.Put these integers in order, smallest first.

    • -1
    • -5
    • 0
    • -12
    • 3
    • 9

  6. 6.-8 - 6 = ?

  7. 7.Which number is greater: -3 or -9?

    • a) -3
    • b) You cannot compare negative numbers
    • c) -9
    • d) They are equal

  8. 8.-10 - (-4) = ?

Integers · Year 6 Maths · www.arenapublications.com/learn

Year 6 Maths · 2 of 13

Multiplying and dividing larger numbers

Multiply by a two-digit number, divide with a remainder, and multiply or divide by 10, 100 and 1000.

  1. 1.96 ÷ 8 = ?

  2. 2.125 × 12 = ?

  3. 3.Work each one out, then put them in order, smallest answer first.

    • 12 × 12
    • 15 × 11
    • 23 × 9
    • 18 × 10

  4. 4.56 × 1000 = ?

  5. 5.23 × 14 = ?

  6. 6.Sort each division by whether anything is left over.

    Groups: Divides exactly · Leaves a remainder

    • 73 ÷ 9
    • 90 ÷ 6
    • 84 ÷ 7
    • 50 ÷ 8
    • 43 ÷ 5
    • 60 ÷ 5

  7. 7.7200 ÷ 10 = ?

  8. 8.A box holds 24 pencils. How many pencils are in 15 boxes?

Multiplying and dividing larger numbers · Year 6 Maths · www.arenapublications.com/learn

Year 6 Maths · 3 of 13

Unlike fractions and mixed numbers

Add and subtract fractions with different denominators, and swap between mixed numbers and improper fractions.

  1. 1.One job takes 1 1/4 hours and another takes 1/2 an hour. How long do they take altogether? Write your answer as a mixed number.

  2. 2.Sort each fraction by how it compares with a half.

    Groups: Less than a half · More than a half

    • 7/10
    • 2/5
    • 1/3
    • 5/8
    • 3/4
    • 1/6

  3. 3.3/4 - 1/8 = ? Write your answer as a fraction.

  4. 4.Match each mixed number to the improper fraction worth the same.

    • 1 1/2
    • 2 1/3
    • 1 3/4
    • 2 1/2
    • 3 1/3
    • 5/2
    • 10/3
    • 7/4
    • 3/2
    • 7/3

  5. 5.Write 2 1/3 as an improper fraction.

  6. 6.Three eighths of a cake are eaten in the morning and two eighths in the afternoon. What fraction of the cake has been eaten? Write your answer as a fraction.

  7. 7.Put these fractions in order, smallest first.

    • 1/3
    • 2/3
    • 1/2
    • 1/6

  8. 8.A film lasts 3 1/2 hours, and 1 1/4 hours of it have been watched. How much is left? Write your answer as a mixed number.

Unlike fractions and mixed numbers · Year 6 Maths · www.arenapublications.com/learn

Year 6 Maths · 4 of 13

Adding and subtracting fractions

Add and subtract fractions, including ones with different denominators.

  1. 1.Put these fractions in order, smallest first.

    • 1/4
    • 3/4
    • 2/3
    • 1/3
    • 1/6
    • 1/2

  2. 2.Which fraction is worth the same as 1/2?

    • a) 3/6
    • b) 2/5
    • c) 5/12
    • d) 4/6

  3. 3.1/3 + 1/4 = ? Write your answer as a fraction.

  4. 4.7/10 - 3/10 = ? Write your answer as a fraction.

  5. 5.3/4 - 1/2 = ? Write your answer as a fraction.

  6. 6.1/5 + 2/5 = ? Write your answer as a fraction.

  7. 7.5/8 - 2/8 = ? Write your answer as a fraction.

  8. 8.1/2 + 1/4 = ? Write your answer as a fraction.

Adding and subtracting fractions · Year 6 Maths · www.arenapublications.com/learn

Year 6 Maths · 5 of 13

Percentages

Find a percentage of an amount, and change between fractions and percentages.

Before you start

This line is the whole of something, split into a hundred. Move along it and read the percentages off.

020406080100

50 sits exactly halfway, 25 is halfway again, and 10 is a tenth of the way along. Those three are worth knowing by sight, because nearly every other percentage is built out of them.

  1. 1.A shirt costs £500 and is reduced by 20% in a sale. What is the sale price? Give just the number.

  2. 2.What is 50% of 96?

  3. 3.What is 25% of 80?

  4. 4.A shopkeeper buys a bag for £400 and sells it for £500. What is the profit as a percentage of the cost? Give just the number.

  5. 5.Match each percentage to the same amount written as a fraction.

    • 50%
    • 25%
    • 20%
    • 75%
    • 10%
    • 1/4
    • 1/10
    • 3/4
    • 1/5
    • 1/2

  6. 6.What is 20% of 45?

  7. 7.What is 10% of 250?

  8. 8.Put these amounts in order, smallest first.

    • 0.4
    • 60%
    • 30%
    • 1/5
    • 1/2

Percentages · Year 6 Maths · www.arenapublications.com/learn

Year 6 Maths · 6 of 13

Ratio and proportion

Write and simplify ratios, and use them to share amounts and scale recipes.

  1. 1.The ratio of boys to girls in a class is 5:4. There are 20 boys. How many girls are there?

  2. 2.Simplify the ratio 10:15. Write it like 4:5.

  3. 3.Are 2:3 and 8:12 in proportion?

    • a) Only if you swap them round
    • b) No
    • c) There is not enough information
    • d) Yes

  4. 4.These ratios are all written as first:second. Put them in order, smallest first.

    • 1:2
    • 5:4
    • 2:3
    • 1:4
    • 3:4

  5. 5.Share 40 sweets between two children in the ratio 3:5. How many does the first child get?

  6. 6.Match each ratio to its simplest form.

    • 8:12
    • 10:4
    • 9:27
    • 16:20
    • 18:24
    • 2:3
    • 3:4
    • 5:2
    • 4:5
    • 1:3

  7. 7.If 3 pens cost £45, what do 7 pens cost? Give just the number.

  8. 8.Which ratio is equivalent to 3:4?

    • a) 6:8
    • b) 9:16
    • c) 4:3
    • d) 7:8

Ratio and proportion · Year 6 Maths · www.arenapublications.com/learn

Year 6 Maths · 7 of 13

How much for one?

Find what one thing costs or weighs, then use it to work out any number of them.

  1. 1.4 pens cost £60. What does 1 pen cost? Give just the number.

  2. 2.A machine makes 120 bottles in 4 hours. How many does it make in 1 hour?

  3. 3.5 tickets cost £200. What do 3 tickets cost? Give just the number.

  4. 4.A machine makes 120 bottles in 4 hours. How many does it make in 9 hours?

  5. 5.Work out what one costs in each deal, then put the deals in order, cheapest for one first.

    • 4 for £24
    • 3 for £21
    • 2 for £20
    • 6 for £30

  6. 6.Work out what one costs in each deal, then sort the deals.

    Groups: One costs less than £10 · One costs £10 or more

    • 4 for £80
    • 4 for £24
    • 6 for £42
    • 2 for £30
    • 5 for £60
    • 3 for £27

  7. 7.A recipe uses 12 spoons of sugar for 4 cakes. How many spoons are needed for 7 cakes?

  8. 8.Match each deal to what one item costs.

    • 2 for £18
    • 3 for £18
    • 4 for £20
    • 5 for £60
    • 6 for £90
    • 12
    • 6
    • 9
    • 5
    • 15

How much for one? · Year 6 Maths · www.arenapublications.com/learn

Year 6 Maths · 8 of 13

Letters for numbers

Write simple algebraic expressions and work out their value.

Before you start

The scale is level. Move the weights about and see what keeps it that way.

38

Take the same amount off both sides and it stays level. Take it off one side only and the scale says so at once — which is the whole rule for solving an equation, felt before it is written down.

  1. 1.Add weights from the shelf until both sides are equal.

    Circle weights from the tray to make the scale level.

    127532

  2. 2.Match each description to the expression that says the same thing.

    • 7 less than m
    • m shared equally between 7
    • 7 times m
    • 7 more than m
    • m ÷ 7
    • m - 7
    • 7m
    • m + 7

  3. 3.If a = 6, what is the value of a × a?

  4. 4.The scale is level and every box holds the same. What does one box weigh?

    The scale is balanced. Write what one box weighs.

    353

  5. 5.If y = 9, what is the value of 2y - 4?

  6. 6.If n = 7, what is the value of 3n?

  7. 7.Which expression means '5 more than x'?

    • a) 5x
    • b) x - 5
    • c) x + 5
    • d) 5 - x

  8. 8.Two boxes, and x is what one of them weighs. Find x.

    The scale is balanced. Write what one box weighs.

    xx19

Letters for numbers · Year 6 Maths · www.arenapublications.com/learn

Year 6 Maths · 9 of 13

Number patterns

Work out the rule behind a pattern of numbers and carry the pattern on.

Before you start

This line starts at 1 and every mark along it is 4 further on. Move from mark to mark and see which numbers the pattern lands on.

1917253341

Once you know what happens between two neighbouring marks you know every number on the line, however far along it you go. Finding the rule is the work; the next number then costs nothing.

  1. 1.What is the rule for 2, 5, 8, 11, 14?

    • a) Add 4
    • b) Add 3
    • c) Add 2
    • d) Multiply by 2

  2. 2.What comes next? 100, 90, 81, 73, ?

  3. 3.What is the missing number? 6, 12, ?, 24, 30

  4. 4.A pattern goes 7, 14, 21, 28 and carries on the same way. What is its tenth number?

  5. 5.What comes next? 1, 4, 9, 16, ?

  6. 6.Match each pattern to its rule.

    • 2, 4, 6, 8
    • 10, 20, 30, 40
    • 1, 3, 9, 27
    • 20, 17, 14, 11
    • 1, 2, 4, 8
    • Add 10
    • Subtract 3
    • Add 2
    • Multiply by 2
    • Multiply by 3

  7. 7.What is the missing number? 45, 40, ?, 30, 25

  8. 8.A pattern goes 12, 16, 20 and carries on. Tap the number that comes next.

    Mark the line with an X.

    1012141618202224262830

Number patterns · Year 6 Maths · www.arenapublications.com/learn

Year 6 Maths · 10 of 13

Volume with unit cubes

Find the volume of a box by counting the unit cubes that fill it.

  1. 1.Put these boxes in order, starting with the one that holds the fewest unit cubes.

    • 3 by 4 by 3
    • 2 by 3 by 3
    • 3 by 3 by 3
    • 2 by 2 by 3

  2. 2.Which of these boxes holds the most unit cubes?

    • a) 2 by 2 by 6
    • b) 3 by 3 by 3
    • c) 1 by 5 by 5
    • d) 2 by 3 by 4

  3. 3.A box holds 20 unit cubes in a single layer. Filled 4 layers deep, how many unit cubes does it hold?

  4. 4.A cuboid is built from 2 layers. Each layer is 6 cubes long and 2 cubes wide. How many cubes are there altogether?

  5. 5.Match each box to the number of unit cubes that fill it.

    • 2 by 2 by 2
    • 2 by 3 by 2
    • 3 by 3 by 2
    • 4 by 3 by 2
    • 5 by 4 by 2
    • 40
    • 8
    • 12
    • 24
    • 18

  6. 6.A cuboid is 6 cm long, 3 cm wide and 2 cm tall. What is its volume, in cubic centimetres? Give just the number.

  7. 7.Work out each box, then sort it by how many unit cubes it holds.

    Groups: Fewer than 24 cubes · 24 cubes or more

    • 3 by 4 by 2
    • 1 by 3 by 6
    • 2 by 2 by 5
    • 5 by 5 by 1
    • 4 by 4 by 2
    • 2 by 2 by 4

  8. 8.A cuboid is built from 36 unit cubes in 3 equal layers. How many cubes are in each layer?

Volume with unit cubes · Year 6 Maths · www.arenapublications.com/learn

Year 6 Maths · 11 of 13

Nets of solids

Say which solid a net folds into, and which flat shapes a solid's net is made from.

Before you start

Here is a cube opened out flat. Find out which face of the finished cube each flat square folds up to become.

123456
  1. 1. The top
  2. 2. The left-hand face
  3. 3. The front
  4. 4. The right-hand face
  5. 5. The back
  6. 6. The bottom

The front stays where it is and the other five fold up around it. Six squares and six faces, each appearing exactly once — a net with a square missing or a square repeated folds into nothing at all.

  1. 1.Sort each solid by whether any part of its net is curved.

    Groups: Net is all straight-sided · Net has a curved piece

    • Cuboid
    • Cone
    • Cylinder
    • Square-based pyramid
    • Cube
    • Triangular prism

  2. 2.The net of a square-based pyramid has four triangles and one square. How many faces will the pyramid have?

  3. 3.A net is made of two circles and one rectangle. Which solid does it fold into?

    • a) Cylinder
    • b) Sphere
    • c) Cone
    • d) Cube

  4. 4.How many squares are there in the net of a cube?

    • a) 5
    • b) 4
    • c) 6
    • d) 8

  5. 5.A net has six rectangles and not one of them is a square. Write the name of the solid it folds into.

  6. 6.Match each solid to what its net is made of.

    • Cube
    • Cylinder
    • Cone
    • Square-based pyramid
    • Triangular prism
    • 6 squares
    • 2 circles and 1 rectangle
    • 1 square and 4 triangles
    • 2 triangles and 3 rectangles
    • 1 circle and 1 curved piece

  7. 7.The net of a triangular prism has two triangles and some rectangles. How many rectangles does it have?

  8. 8.This net folds up into a cube. The first square in the row is marked. Tap the square that will end up opposite the marked one.

    Write the number of the part.

    12345

Nets of solids · Year 6 Maths · www.arenapublications.com/learn

Year 6 Maths · 12 of 13

Coordinate geometry

Read and plot points on the coordinate plane and name the quadrant they lie in.

Before you start

The two axes cut the page into four quarters. Find out what each one is called — all four, in any order, nothing to get right.

1234
  1. 1. First quadrant
  2. 2. Second quadrant
  3. 3. Third quadrant
  4. 4. Fourth quadrant

They are numbered anticlockwise from the top right. Both coordinates are positive in the first and both are negative in the third.

  1. 1.Where does the point (0, 4) lie?

    • a) On the y-axis
    • b) On the x-axis
    • c) At the origin
    • d) In the first quadrant

  2. 2.How far is the point (6, 8) from the y-axis? Give just the number.

  3. 3.How far is the point (6, 8) from the x-axis? Give just the number.

  4. 4.In which quadrant does the point (-2, -6) lie?

    • a) Fourth
    • b) Third
    • c) First
    • d) Second

  5. 5.In which quadrant does the point (3, 5) lie?

    • a) First
    • b) Second
    • c) Fourth
    • d) Third

  6. 6.What are the coordinates of the origin?

    • a) (1, 1)
    • b) (1, 0)
    • c) (0, 0)
    • d) (0, 1)

  7. 7.Match each point to where it lies.

    • (2, 3)
    • (-2, 3)
    • (-2, -3)
    • (2, -3)
    • (0, 0)
    • The origin
    • Fourth quadrant
    • Third quadrant
    • Second quadrant
    • First quadrant

  8. 8.In which quadrant does the point (-4, 2) lie?

    • a) Fourth
    • b) First
    • c) Second
    • d) Third

Coordinate geometry · Year 6 Maths · www.arenapublications.com/learn

Year 6 Maths · 13 of 13

Averages

Find the average of a small set of numbers by sharing the total out equally.

  1. 1.Find the average of 10, 12, 14 and 16.

  2. 2.Match each pair of numbers to its average.

    • 2, 4
    • 4, 6
    • 6, 10
    • 10, 14
    • 14, 20
    • 12
    • 3
    • 17
    • 8
    • 5

  3. 3.The average of four numbers is 7. What do the four numbers add up to?

  4. 4.Five numbers have an average of 6. A sixth number, 12, is added to the set. What happens to the average?

    • a) It stays the same
    • b) It becomes 12
    • c) It goes up
    • d) It goes down

  5. 5.Find the average of 4, 6 and 8.

  6. 6.A player scores 20, 30 and 40 points in three games. What is the average score?

  7. 7.Three children have 5, 8 and 11 stickers. They share them all out equally. How many does each child end up with?

  8. 8.Work out each average, then put the sets in order, smallest average first.

    • 2, 4, 6
    • 1, 2, 3
    • 8, 10, 12
    • 5, 6, 7

Averages · Year 6 Maths · www.arenapublications.com/learn

Answer keys — Year 6 Maths

In the same order as the worksheets.

Integers

  1. 1. -4
  2. 2. -6 + 2 → Negative; 7 - 3 → Positive; -5 - 5 → Negative; -9 + 12 → Positive; 4 - 10 → Negative; -2 + 8 → Positive
  3. 3. -3
  4. 4. -7
  5. 5. 1. -12 2. -5 3. -1 4. 0 5. 3 6. 9
  6. 6. -14
  7. 7. a) -3
  8. 8. -6

Multiplying and dividing larger numbers

  1. 1. 12
  2. 2. 1500
  3. 3. 1. 12 × 12 2. 15 × 11 3. 18 × 10 4. 23 × 9
  4. 4. 56000
  5. 5. 322
  6. 6. 60 ÷ 5 → Divides exactly; 43 ÷ 5 → Leaves a remainder; 84 ÷ 7 → Divides exactly; 50 ÷ 8 → Leaves a remainder; 90 ÷ 6 → Divides exactly; 73 ÷ 9 → Leaves a remainder
  7. 7. 720
  8. 8. 360

Unlike fractions and mixed numbers

  1. 1. 1 3/4
  2. 2. 1/3 → Less than a half; 5/8 → More than a half; 2/5 → Less than a half; 3/4 → More than a half; 1/6 → Less than a half; 7/10 → More than a half
  3. 3. 5/8
  4. 4. 1 1/2 → 3/2; 2 1/3 → 7/3; 1 3/4 → 7/4; 2 1/2 → 5/2; 3 1/3 → 10/3
  5. 5. 7/3
  6. 6. 5/8
  7. 7. 1. 1/6 2. 1/3 3. 1/2 4. 2/3
  8. 8. 2 1/4

Adding and subtracting fractions

  1. 1. 1. 1/6 2. 1/4 3. 1/3 4. 1/2 5. 2/3 6. 3/4
  2. 2. a) 3/6
  3. 3. 7/12
  4. 4. 2/5
  5. 5. 1/4
  6. 6. 3/5
  7. 7. 3/8
  8. 8. 3/4

Percentages

  1. 1. 400
  2. 2. 48
  3. 3. 20
  4. 4. 25
  5. 5. 50% → 1/2; 25% → 1/4; 20% → 1/5; 75% → 3/4; 10% → 1/10
  6. 6. 9
  7. 7. 25
  8. 8. 1. 1/5 2. 30% 3. 0.4 4. 1/2 5. 60%

Ratio and proportion

  1. 1. 16
  2. 2. 2:3
  3. 3. d) Yes
  4. 4. 1. 1:4 2. 1:2 3. 2:3 4. 3:4 5. 5:4
  5. 5. 15
  6. 6. 8:12 → 2:3; 10:4 → 5:2; 9:27 → 1:3; 16:20 → 4:5; 18:24 → 3:4
  7. 7. 105
  8. 8. a) 6:8

How much for one?

  1. 1. 15
  2. 2. 30
  3. 3. 120
  4. 4. 270
  5. 5. 1. 6 for £30 2. 4 for £24 3. 3 for £21 4. 2 for £20
  6. 6. 4 for £24 → One costs less than £10; 5 for £60 → One costs £10 or more; 3 for £27 → One costs less than £10; 2 for £30 → One costs £10 or more; 6 for £42 → One costs less than £10; 4 for £80 → One costs £10 or more
  7. 7. 21
  8. 8. 2 for £18 → 9; 3 for £18 → 6; 4 for £20 → 5; 5 for £60 → 12; 6 for £90 → 15

Letters for numbers

  1. 1. 5 on the right pan
  2. 2. 7 less than m → m - 7; m shared equally between 7 → m ÷ 7; 7 times m → 7m; 7 more than m → m + 7
  3. 3. 36
  4. 4. box = 5
  5. 5. 14
  6. 6. 21
  7. 7. c) x + 5
  8. 8. x = 4

Number patterns

  1. 1. b) Add 3
  2. 2. 66
  3. 3. 18
  4. 4. 70
  5. 5. 25
  6. 6. 2, 4, 6, 8 → Add 2; 10, 20, 30, 40 → Add 10; 1, 3, 9, 27 → Multiply by 3; 20, 17, 14, 11 → Subtract 3; 1, 2, 4, 8 → Multiply by 2
  7. 7. 35
  8. 8. 24

Volume with unit cubes

  1. 1. 1. 2 by 2 by 3 2. 2 by 3 by 3 3. 3 by 3 by 3 4. 3 by 4 by 3
  2. 2. b) 3 by 3 by 3
  3. 3. 80
  4. 4. 24
  5. 5. 2 by 2 by 2 → 8; 2 by 3 by 2 → 12; 3 by 3 by 2 → 18; 4 by 3 by 2 → 24; 5 by 4 by 2 → 40
  6. 6. 36
  7. 7. 2 by 2 by 5 → Fewer than 24 cubes; 3 by 4 by 2 → 24 cubes or more; 1 by 3 by 6 → Fewer than 24 cubes; 4 by 4 by 2 → 24 cubes or more; 2 by 2 by 4 → Fewer than 24 cubes; 5 by 5 by 1 → 24 cubes or more
  8. 8. 12

Nets of solids

  1. 1. Cube → Net is all straight-sided; Cylinder → Net has a curved piece; Cuboid → Net is all straight-sided; Cone → Net has a curved piece; Triangular prism → Net is all straight-sided; Square-based pyramid → Net is all straight-sided
  2. 2. 5
  3. 3. a) Cylinder
  4. 4. c) 6
  5. 5.
    • cuboid
    • rectangular prism
  6. 6. Cube → 6 squares; Cylinder → 2 circles and 1 rectangle; Cone → 1 circle and 1 curved piece; Square-based pyramid → 1 square and 4 triangles; Triangular prism → 2 triangles and 3 rectangles
  7. 7. 3
  8. 8. 2 — Third in the row

Coordinate geometry

  1. 1. a) On the y-axis
  2. 2. 6
  3. 3. 8
  4. 4. b) Third
  5. 5. a) First
  6. 6. c) (0, 0)
  7. 7. (2, 3) → First quadrant; (-2, 3) → Second quadrant; (-2, -3) → Third quadrant; (2, -3) → Fourth quadrant; (0, 0) → The origin
  8. 8. c) Second

Averages

  1. 1. 13
  2. 2. 2, 4 → 3; 4, 6 → 5; 6, 10 → 8; 10, 14 → 12; 14, 20 → 17
  3. 3. 28
  4. 4. c) It goes up
  5. 5. 6
  6. 6. 30
  7. 7. 8
  8. 8. 1. 1, 2, 3 2. 2, 4, 6 3. 5, 6, 7 4. 8, 10, 12

Year 6 Maths · www.arenapublications.com/learn