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Term pack

Grade 6 Math

Name: ________________________

Skills in this pack

  • Whole numbers
  • Integers
  • HCF and LCM
  • Ratio and proportion
  • How much for one?
  • Percentages
  • Letters for numbers
  • Solving equations
  • Nets of solids
  • Area of triangles and parallelograms
  • Mean, median and mode
  • Data handling

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Grade 6 Math · 1 of 12

Whole numbers

Use the order, identity, grouping and splitting properties of whole numbers to make arithmetic easier.

Before you start

Move along the whole numbers. Notice that each one has a next one, and that only zero has nothing before it.

0123456789101112

The line stops at 0 on the left because that is where the whole numbers start — but it never has to stop on the right.

  1. 1.Match each calculation to its answer.

    • 25 × 4
    • 25 + 4
    • 25 - 4
    • 100 ÷ 4
    • 4 × 4
    • 16
    • 21
    • 29
    • 25
    • 100

  2. 2.8 × 106 = ?

  3. 3.Which pair gives the same answer both ways round?

    • a) 9 + 4 and 4 + 9
    • b) 9 ÷ 4 and 4 ÷ 9
    • c) 9 - 4 and 4 + 9
    • d) 9 - 4 and 4 - 9

  4. 4.Work out each one, then sort it by whether the answer is a whole number. (The whole numbers are 0, 1, 2, 3, …)

    Groups: Is a whole number · Is not a whole number

    • 12 ÷ 4
    • 3 - 8
    • 7 - 7
    • 9 ÷ 2
    • 12 ÷ 5
    • 6 × 0

  5. 5.Which of these is NOT a whole number? (The whole numbers are 0, 1, 2, 3, …)

    • a) 0
    • b) -4
    • c) 206
    • d) 17

  6. 6.What is the successor of 6099?

  7. 7.7 × 98 = ?

  8. 8.37 + 65 + 63 = ?

Whole numbers · Grade 6 Math · www.arenapublications.com/learn

Grade 6 Math · 2 of 12

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.-10 - (-4) = ?

  2. 2.5 - 12 = ?

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

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

  4. 4.-4 + 11 = ?

  5. 5.-7 + 3 = ?

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

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

  7. 7.-8 - 6 = ?

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

    Groups: Negative · Positive

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

Integers · Grade 6 Math · www.arenapublications.com/learn

Grade 6 Math · 3 of 12

HCF and LCM

Find the highest common factor and the lowest common multiple of two numbers, and use them to answer sharing and repeating problems.

Before you start

Every mark here is a multiple of 4 and a multiple of 6 at the same time. Move from one to the next.

01224364860

Zero is a multiple of everything, so it never counts. The first mark after it is 12, and that is what the LCM of 4 and 6 means — the earliest place their two lists of multiples meet.

  1. 1.What is the LCM of 5 and 8?

  2. 2.What is the HCF of 12 and 18?

  3. 3.One bell rings every 6 minutes and another rings every 8 minutes. They have just rung together. In how many minutes will they next ring together?

  4. 4.What is the HCF of 7 and 13?

  5. 5.Work out the LCM of each pair, then sort by whether it is below 30 or above 30.

    Groups: LCM below 30 · LCM above 30

    • 9 and 12
    • 6 and 9
    • 5 and 8
    • 7 and 10
    • 4 and 6
    • 3 and 8

  6. 6.Which of these is 60 written as a product of prime factors?

    • a) 4 × 15
    • b) 2 × 2 × 3 × 5
    • c) 2 × 5 × 6
    • d) 2 × 3 × 10

  7. 7.What is the LCM of 9 and 12?

  8. 8.Two ropes are 12 inches and 18 inches long. Both are cut into equal pieces, as long as possible, with nothing left over. How long is each piece, in inches? Give just the number.

HCF and LCM · Grade 6 Math · www.arenapublications.com/learn

Grade 6 Math · 4 of 12

Ratio and proportion

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

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

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

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

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

  4. 4.A recipe uses 2 cups of rice to 5 cups of water. How many cups of water are needed for 6 cups of rice?

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

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

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

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

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

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

Ratio and proportion · Grade 6 Math · www.arenapublications.com/learn

Grade 6 Math · 5 of 12

How much for one?

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

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

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

  2. 2.Which of these is better value?

    • a) There is no way to tell
    • b) They cost the same each
    • c) 5 pencils for $30
    • d) 8 pencils for $40

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

  4. 4.6 identical books weigh 18 lb altogether. What does 1 book weigh, in pounds? Give just the number.

  5. 5.9 apples cost $72. What does one apple cost?

    • a) 6
    • b) 7
    • c) 9
    • d) 8

  6. 6.5 tickets cost $200. What do 3 tickets cost? Give just the number.

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

  8. 8.4 pens cost $60. What do 7 pens cost? Give just the number.

How much for one? · Grade 6 Math · www.arenapublications.com/learn

Grade 6 Math · 6 of 12

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.What is 3/4 written as a percentage?

    • a) 75%
    • b) 34%
    • c) 43%
    • d) 25%

  2. 2.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.

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

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

  4. 4.What is 50% of 96?

  5. 5.What is 10% of 250?

  6. 6.What is 20% of 45?

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

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

  8. 8.A book costs $200. The price goes up by 10%. What is the new price? Give just the number.

Percentages · Grade 6 Math · www.arenapublications.com/learn

Grade 6 Math · 7 of 12

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

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

    Circle weights from the tray to make the scale level.

    127532

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

    The scale is balanced. Write what one box weighs.

    xx19

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

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

  5. 5.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
    • 7m
    • m - 7
    • m + 7

  6. 6.A square has sides of length s. Which expression gives its perimeter?

    • a) s × s
    • b) s + 4
    • c) 4s
    • d) 2s

  7. 7.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

  8. 8.Which expression means 'three times a number n'?

    • a) n - 3
    • b) n + 3
    • c) 3n
    • d) n ÷ 3

Letters for numbers · Grade 6 Math · www.arenapublications.com/learn

Grade 6 Math · 8 of 12

Solving equations

Solve a linear equation in one variable by keeping both sides balanced.

Before you start

Two mystery boxes and some weights, and the beam is level. See how much you can take away without it moving.

517

Take the 5 off both sides and the two boxes stand against what is left; one box is half of that. The scale has just walked you through the whole solution without a line of working.

  1. 1.I think of a number, double it and add 5. The answer is 17. What was my number?

  2. 2.3x = 21. What is x?

  3. 3.4(x + 2) = 20. What is x?

  4. 4.5x - 7 = 18. What is x?

  5. 5.2x + 3 = 11. What is x?

  6. 6.What is the right first move to solve 7x = 56?

    • a) Divide both sides by 7
    • b) Add 7 to both sides
    • c) Multiply both sides by 7
    • d) Subtract 7 from both sides

  7. 7.x + 5 = 12. What is x?

  8. 8.3x - 4 = 2x + 6. What is x?

Solving equations · Grade 6 Math · www.arenapublications.com/learn

Grade 6 Math · 9 of 12

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.A net folds up into a cuboid. How many rectangles does the net have?

  2. 2.A net is made of one square and four triangles. Which solid does it fold into?

    • a) Triangular prism
    • b) Cylinder
    • c) Cube
    • d) Square-based pyramid

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

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

  4. 4.A net is made of one circle and one curved piece. Which solid does it fold into?

    • a) Cuboid
    • b) Cone
    • c) Triangular prism
    • d) Cylinder

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

  6. 6.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

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

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

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

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

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

Nets of solids · Grade 6 Math · www.arenapublications.com/learn

Grade 6 Math · 10 of 12

Area of triangles and parallelograms

Find the area of a parallelogram, a triangle and a rhombus, and the perimeter of a straight-sided shape.

  1. 1.Sort each rule by what it works out.

    Groups: Area · Perimeter

    • all the sides added together
    • 4 × side
    • 2 × (length + width)
    • length × width
    • 1/2 × base × height
    • base × height

  2. 2.A path runs all the way round a rectangular garden 20 ft long and 15 ft wide. How far is it once round the garden, in feet?

  3. 3.A rhombus has diagonals of 8 inches and 6 inches. What is its area, in square inches?

  4. 4.A rectangle 14 inches by 9 inches has a triangle of base 14 inches and height 9 inches cut out of it. What area is left, in square inches?

  5. 5.A parallelogram has a base of 8 inches and a height of 5 inches. What is its area, in square inches?

  6. 6.A triangle has a base of 10 inches and a height of 6 inches. What is its area, in square inches?

  7. 7.A parallelogram has an area of 60 square inches and a base of 10 inches. What is its height, in inches?

  8. 8.A triangle and a parallelogram share the same base and the same height. The triangle's area is...

    • a) twice the parallelogram's area
    • b) half the parallelogram's area
    • c) impossible to compare
    • d) the same as the parallelogram's area

Area of triangles and parallelograms · Grade 6 Math · www.arenapublications.com/learn

Grade 6 Math · 11 of 12

Mean, median and mode

Find the mean, median, mode and range of a small set of numbers.

  1. 1.Find the median of 12, 5, 9, 3 and 7.

  2. 2.Find the median of 3, 7, 9, 11 and 15.

  3. 3.Find the mean of 10, 20, 30 and 40.

  4. 4.Find the mode of 2, 3, 3, 5, 7 and 3.

  5. 5.Find the range of 12, 4, 9 and 20.

  6. 6.Match each word to what it tells you about a set of numbers.

    • Mean
    • Median
    • Mode
    • Range
    • The value that turns up most often
    • The middle value, once in order
    • The gap between the largest and the smallest
    • The total shared out equally

  7. 7.Find the mode of 5, 8, 8, 2, 9, 8 and 1.

  8. 8.Find the mean of 4, 8, 6, 10 and 2.

Mean, median and mode · Grade 6 Math · www.arenapublications.com/learn

Grade 6 Math · 12 of 12

Data handling

Find the mean, median, mode and range of a set of data, and read information off a bar chart.

  1. 1.A bar graph shows 7 blue cars and 5 white cars. How many more blue cars are there than white ones?

  2. 2.Sort each statement by whether it describes the mean or the mode.

    Groups: The mean · The mode

    • A list can have more than one of them
    • One unusually large value pulls it upwards
    • It is always a value taken from the list itself
    • The value that appears most often
    • Every value in the list changes it
    • Add every value up and divide by how many there are

  3. 3.A bar graph shows 4 red cars, 7 blue cars, 5 white cars and 4 black cars. How many cars are there altogether?

  4. 4.This bar chart shows how many books a library lent out on four days. Tap the bar for the day it lent the fewest.

    Write the number of the part.

    1234

  5. 5.This bar chart shows how many books a library lent out on four days. Tap the bar for the day it lent the most.

    Write the number of the part.

    1234

  6. 6.The mean of five numbers is 14. What do the five numbers add up to?

  7. 7.Match each set of numbers to its mean.

    • 2, 4, 6
    • 10, 20, 30, 40
    • 5, 5, 5, 5
    • 1, 2, 3, 4, 5
    • 8, 12
    • 5
    • 10
    • 3
    • 4
    • 25

  8. 8.Find the range of 33, 18, 47 and 22.

Data handling · Grade 6 Math · www.arenapublications.com/learn

Answer keys — Grade 6 Math

In the same order as the worksheets.

Whole numbers

  1. 1. 25 × 4 → 100; 25 + 4 → 29; 25 - 4 → 21; 100 ÷ 4 → 25; 4 × 4 → 16
  2. 2. 848
  3. 3. a) 9 + 4 and 4 + 9
  4. 4. 12 ÷ 4 → Is a whole number; 12 ÷ 5 → Is not a whole number; 7 - 7 → Is a whole number; 3 - 8 → Is not a whole number; 6 × 0 → Is a whole number; 9 ÷ 2 → Is not a whole number
  5. 5. b) -4
  6. 6. 6100
  7. 7. 686
  8. 8. 165

Integers

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

HCF and LCM

  1. 1. 40
  2. 2. 6
  3. 3. 24
  4. 4. 1
  5. 5. 4 and 6 → LCM below 30; 3 and 8 → LCM below 30; 6 and 9 → LCM below 30; 5 and 8 → LCM above 30; 9 and 12 → LCM above 30; 7 and 10 → LCM above 30
  6. 6. b) 2 × 2 × 3 × 5
  7. 7. 36
  8. 8. 6

Ratio and proportion

  1. 1. 25
  2. 2. 15
  3. 3. 1. 1:4 2. 1:2 3. 2:3 4. 3:4 5. 5:4
  4. 4. 15
  5. 5. a) 6:8
  6. 6. 105
  7. 7. 8:12 → 2:3; 10:4 → 5:2; 9:27 → 1:3; 16:20 → 4:5; 18:24 → 3:4
  8. 8. 2:3

How much for one?

  1. 1. 2 for $18 → 9; 3 for $18 → 6; 4 for $20 → 5; 5 for $60 → 12; 6 for $90 → 15
  2. 2. d) 8 pencils for $40
  3. 3. 21
  4. 4. 3
  5. 5. d) 8
  6. 6. 120
  7. 7. 270
  8. 8. 105

Percentages

  1. 1. a) 75%
  2. 2. 25
  3. 3. 1. 1/5 2. 30% 3. 0.4 4. 1/2 5. 60%
  4. 4. 48
  5. 5. 25
  6. 6. 9
  7. 7. 50% → 1/2; 25% → 1/4; 20% → 1/5; 75% → 3/4; 10% → 1/10
  8. 8. 220

Letters for numbers

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

Solving equations

  1. 1. 6
  2. 2. 7
  3. 3. 3
  4. 4. 5
  5. 5. 4
  6. 6. a) Divide both sides by 7
  7. 7. 7
  8. 8. 10

Nets of solids

  1. 1. 6
  2. 2. d) Square-based pyramid
  3. 3. b) 6
  4. 4. b) Cone
  5. 5. 3
  6. 6. 2 — Third in the row
  7. 7. 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
  8. 8. 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

Area of triangles and parallelograms

  1. 1. base × height → Area; 1/2 × base × height → Area; 2 × (length + width) → Perimeter; 4 × side → Perimeter; length × width → Area; all the sides added together → Perimeter
  2. 2. 70
  3. 3. 24
  4. 4. 63
  5. 5. 40
  6. 6. 30
  7. 7. 6
  8. 8. b) half the parallelogram's area

Mean, median and mode

  1. 1. 7
  2. 2. 9
  3. 3. 25
  4. 4. 3
  5. 5. 16
  6. 6. Mean → The total shared out equally; Median → The middle value, once in order; Mode → The value that turns up most often; Range → The gap between the largest and the smallest
  7. 7. 8
  8. 8. 6

Data handling

  1. 1. 2
  2. 2. Add every value up and divide by how many there are → The mean; The value that appears most often → The mode; Every value in the list changes it → The mean; A list can have more than one of them → The mode; One unusually large value pulls it upwards → The mean; It is always a value taken from the list itself → The mode
  3. 3. 20
  4. 4. 3 — Wednesday
  5. 5. 2 — Tuesday
  6. 6. 70
  7. 7. 2, 4, 6 → 4; 10, 20, 30, 40 → 25; 5, 5, 5, 5 → 5; 1, 2, 3, 4, 5 → 3; 8, 12 → 10
  8. 8. 29

Grade 6 Math · www.arenapublications.com/learn