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Term pack

Year 6 Maths

Name: ________________________

Skills in this pack

  • Whole numbers
  • Integers
  • Factors and multiples
  • HCF and LCM
  • Understanding fractions
  • Adding and subtracting fractions
  • Decimals
  • Percentages
  • Discount and tax
  • Adding and subtracting decimals
  • Number patterns
  • Perimeter and area
  • Changing between units of measure
  • Basic geometrical ideas
  • Coordinate geometry
  • Chance and probability

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Year 6 Maths · 1 of 16

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.What is the predecessor of 3000?

  2. 2.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

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

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

  4. 4.Tap the whole number that is halfway between 40 and 60.

    Mark the line with an X.

    303540455055606570

  5. 5.7 × 98 = ?

  6. 6.Put these whole numbers in order, smallest first.

    • 190
    • 109
    • 1
    • 91
    • 0
    • 19

  7. 7.Match each calculation to its answer.

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

  8. 8.8 × 106 = ?

Whole numbers · Year 6 Maths · www.arenapublications.com/learn

Year 6 Maths · 2 of 16

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

    Groups: Negative · Positive

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

  2. 2.6 + (-9) = ?

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

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

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

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

  5. 5.-10 - (-4) = ?

  6. 6.5 - 12 = ?

  7. 7.-15 + 15 = ?

  8. 8.-8 - 6 = ?

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

Year 6 Maths · 3 of 16

Factors and multiples

Find factors and multiples, use divisibility tests, and tell a prime number from a composite one.

Before you start

Every mark on this line is a multiple of 3. Move along them and see how many you already know from the 3 times table.

061218243036

The line could carry on for ever, because a number has no last multiple. Factors go the other way: 36 has exactly nine of them and then they run out.

  1. 1.What is the fourth number in the seven times table?

  2. 2.Put these numbers in order by how many factors they have, fewest first.

    • 13
    • 16
    • 12
    • 9
    • 8

  3. 3.Which of these numbers is prime?

    • a) 91
    • b) 49
    • c) 29
    • d) 39

  4. 4.What is the smallest prime number?

  5. 5.What is the largest factor of 45, apart from 45 itself?

  6. 6.Which number between 20 and 30 is a multiple of 9?

  7. 7.Sort each number by whether it is prime or composite.

    Groups: Prime · Composite

    • 27
    • 17
    • 31
    • 23
    • 21
    • 33

  8. 8.Exactly one number on this line is a multiple of 6. Tap it.

    Mark the line with an X.

    20212223242526272829

Factors and multiples · Year 6 Maths · www.arenapublications.com/learn

Year 6 Maths · 4 of 16

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.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

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

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

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

  4. 4.What is the HCF of 24 and 36?

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

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

  6. 6.Put these pairs in order by their HCF, smallest first.

    • 6 and 8
    • 8 and 9
    • 10 and 15
    • 12 and 16
    • 9 and 12

  7. 7.Which pair of numbers has an HCF of 1?

    • a) 9 and 15
    • b) 8 and 15
    • c) 8 and 12
    • d) 10 and 15

  8. 8.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?

HCF and LCM · Year 6 Maths · www.arenapublications.com/learn

Year 6 Maths · 5 of 16

Understanding fractions

Place fractions on a number line, find equivalent fractions, compare them, and switch between mixed numbers and improper fractions.

Before you start

Move along the line and watch the quarters go past. See which fractions land on a whole number and which land between two of them.

0.001.002.00

Every fourth step lands on a whole number, because four quarters make one whole. That is the same fact as 4/4 = 1.

  1. 1.Tap where 3/4 sits.

    Mark the line with an X.

    0.001.00

  2. 2.Write 17/5 as a mixed number.

  3. 3.Fill in the missing number: 2/5 = ?/20

  4. 4.Write 18/24 in its simplest form.

  5. 5.Which fraction is larger, 3/5 or 5/8?

    • a) They are equal
    • b) You cannot compare them
    • c) 3/5
    • d) 5/8

  6. 6.Which of these fractions is NOT equivalent to 2/3?

    • a) 10/15
    • b) 6/8
    • c) 8/12
    • d) 4/6

  7. 7.Tap where 7/4 sits.

    Mark the line with an X.

    0.001.002.003.00

  8. 8.Sort each fraction by whether it is less than 1 or more than 1.

    Groups: Less than 1 · More than 1

    • 3/4
    • 7/8
    • 9/7
    • 8/3
    • 5/4
    • 5/9

Understanding fractions · Year 6 Maths · www.arenapublications.com/learn

Year 6 Maths · 6 of 16

Adding and subtracting fractions

Add and subtract fractions, including ones with different denominators.

  1. 1.5/8 - 2/8 = ? Write your answer as a fraction.

  2. 2.Match each fraction to the same amount written as a decimal.

    • 1/2
    • 1/4
    • 3/4
    • 1/5
    • 1/10
    • 0.5
    • 0.1
    • 0.75
    • 0.2
    • 0.25

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

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

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

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

  5. 5.1/3 + 1/4 = ? Write your answer as a fraction.

  6. 6.1/2 + 1/4 = ? Write your answer as a fraction.

  7. 7.2/3 + 1/6 = ? Write your answer as a fraction.

  8. 8.1/5 + 2/5 = ? Write your answer as a fraction.

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

Year 6 Maths · 7 of 16

Decimals

Compare and order decimals, add and subtract them, and switch between decimals and fractions.

Before you start

Move between 3 and 4 in tenths. A whole line of numbers is hiding between two whole ones.

3.03.13.23.33.43.53.63.73.83.94.0

Nothing says the line has to stop at tenths. Chop each of these gaps into ten again and hundredths appear — 3.14, 3.15 — and you could keep chopping for ever.

  1. 1.Match each fraction to the decimal that is worth the same.

    • 1/2
    • 1/4
    • 3/4
    • 1/5
    • 3/10
    • 0.5
    • 0.25
    • 0.75
    • 0.3
    • 0.2

  2. 2.What is 0.6 + 0.45?

  3. 3.Which fraction is the same as 0.05?

    • a) 5/10
    • b) 1/25
    • c) 1/20
    • d) 1/5

  4. 4.Tap where 0.4 sits.

    Mark the line with an X.

    0.00.10.20.30.40.50.60.70.80.91.0

  5. 5.Sort each decimal by whether it is closer to 0 or closer to 1.

    Groups: Closer to 0 · Closer to 1

    • 0.7
    • 0.91
    • 0.09
    • 0.45
    • 0.2
    • 0.55

  6. 6.A pencil is 12.5 cm long and a pen is 14.2 cm long. How much longer is the pen, in centimetres? Give just the number.

  7. 7.8.6 - 3.75 = ?

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

    • 0.5
    • 1.05
    • 0.09
    • 0.41
    • 0.4

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

Year 6 Maths · 8 of 16

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 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.

  2. 2.What is 20% of 45?

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

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

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

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

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

  6. 6.What is 3/4 written as a percentage?

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

  7. 7.What is 25% of 80?

  8. 8.What is 10% of 250?

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

Year 6 Maths · 9 of 16

Discount and tax

Work out a discount, a sale price, and the price once tax has been added.

  1. 1.A bag is marked $1200 and is sold at a discount of 25 per cent. What is the sale price? Give just the number.

  2. 2.A shop takes 10 per cent off an item marked $500, then adds tax of 10 per cent to the reduced price. What is the final price? Give just the number.

  3. 3.Match each marked price to its sale price after a discount of 20 per cent.

    • $150
    • $250
    • $400
    • $600
    • $900
    • $320
    • $480
    • $120
    • $200
    • $720

  4. 4.Sort each change by whether it makes the price go up or down.

    Groups: Price goes up · Price goes down

    • A service charge of 5 per cent added
    • Tax of 8 per cent added
    • A discount of 10 per cent
    • Tax of 12 per cent added
    • A quarter off
    • A third off

  5. 5.Which of these offers takes the most off an item marked $1000?

    • a) A discount of one fifth
    • b) 10 per cent off, and then 10 per cent off again
    • c) $250 off
    • d) A discount of 30 per cent

  6. 6.A book costs $250 and tax of 8 per cent is added. How much is the tax? Give just the number.

  7. 7.A discount of 20 per cent followed by a further 20 per cent off the new price is the same as one single discount of how much?

    • a) 30 per cent
    • b) 36 per cent
    • c) 40 per cent
    • d) 44 per cent

  8. 8.A shirt is marked $800 and is sold at a discount of 15 per cent. How much is taken off the marked price? Give just the number.

Discount and tax · Year 6 Maths · www.arenapublications.com/learn

Year 6 Maths · 10 of 16

Adding and subtracting decimals

Add and subtract numbers with tenths and hundredths by keeping the columns lined up.

Before you start

This line runs from 0 to 1. The numbered ticks are tenths, and the plain ticks between them fall halfway again. Look at how far apart 0.05 and 0.5 really are.

0.000.100.200.300.400.500.600.700.800.901.00

Ten hundredths make one tenth. That is why 0.5 is far bigger than 0.05, even though both are written with a 5.

  1. 1.6 - 0.4 = ?

  2. 2.5.8 - 2.3 = ?

  3. 3.Work each one out, then sort it by how the answer compares with 1.

    Groups: Less than 1 · More than 1

    • 0.6 + 0.7
    • 0.4 + 0.3
    • 0.35 + 0.4
    • 0.9 + 0.2
    • 0.25 + 0.5
    • 0.8 + 0.45

  4. 4.0.75 + 0.25 = ?

  5. 5.7.2 - 3.45 = ?

  6. 6.Tap where 2.6 + 0.7 lands.

    Mark the line with an X.

    2.02.53.03.54.0

  7. 7.A notebook costs $12.50 and a pencil costs $4.25. What do they cost together? Give just the number.

  8. 8.Match each subtraction to its answer.

    • 1 - 0.4
    • 1 - 0.25
    • 1 - 0.05
    • 1 - 0.9
    • 1 - 0.5
    • 0.1
    • 0.5
    • 0.95
    • 0.75
    • 0.6

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

Year 6 Maths · 11 of 16

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 missing number? 6, 12, ?, 24, 30

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

  3. 3.What comes next? 3, 7, 11, 15, ?

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

    Mark the line with an X.

    1012141618202224262830

  5. 5.A pattern of squares grows: 1 square, then 4, then 9. How many squares are in the next step?

    • a) 14
    • b) 12
    • c) 16
    • d) 20

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

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

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

  8. 8.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
    • Subtract 3
    • Multiply by 2
    • Multiply by 3
    • Add 10
    • Add 2

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

Year 6 Maths · 12 of 16

Perimeter and area

Find the perimeter and the area of rectangles, squares and shapes built from them, and measure area by counting squares.

  1. 1.A square has sides of 7 cm. What is its area, in square centimetres? Give just the number.

  2. 2.Every rectangle here is measured in centimetres. Sort each one by whether its perimeter is below 20 or above 20.

    Groups: Perimeter below 20 · Perimeter above 20

    • 3 by 5
    • 4 by 7
    • 6 by 6
    • 5 by 6
    • 2 by 6
    • 1 by 8

  3. 3.An L-shape is made from a rectangle 10 cm by 4 cm with a square of side 3 cm cut out of one corner. What is its area, in square centimetres? Give just the number.

  4. 4.Match each square to its area.

    • side 2
    • side 3
    • side 5
    • side 6
    • side 9
    • 4
    • 81
    • 25
    • 36
    • 9

  5. 5.A rectangle is 9 cm long and 4 cm wide. What is its area, in square centimetres? Give just the number.

  6. 6.Put these rectangles in order by area, smallest first.

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

  7. 7.A rectangle has a perimeter of 30 cm and a length of 9 cm. How wide is it, in centimetres? Give just the number.

  8. 8.A square has sides of 7 cm. What is its perimeter, in centimetres? Give just the number.

Perimeter and area · Year 6 Maths · www.arenapublications.com/learn

Year 6 Maths · 13 of 16

Changing between units of measure

Change a measurement from a larger unit to a smaller one and back again, and add measurements written in mixed units.

  1. 1.A parcel has a mass of 3 kg and 400 g. What is its mass in g altogether? Give just the number.

  2. 2.A rope 5 metres long is cut into pieces each 50 centimetres long. How many pieces are there? Give just the number.

  3. 3.There are 1,000 g in 1 kg. How many g are there in 2 kg? Give just the number.

  4. 4.Which unit would you choose to measure the length of a pencil?

    • a) metres
    • b) centimetres
    • c) kilograms
    • d) kilometres

  5. 5.There are 1,000 metres in 1 kilometres. How many metres are there in 3 kilometres? Give just the number.

  6. 6.A ribbon is 2 metres and 35 centimetres long. How long is it in centimetres altogether? Give just the number.

  7. 7.Which of these is the same length as 250 centimetres?

    • a) 2 metres and 5 centimetres
    • b) 2 metres and 50 centimetres
    • c) 20 metres and 50 centimetres
    • d) 25 metres

  8. 8.Put these lengths in order, shortest first.

    • 350 centimetres
    • 1 kilometres
    • 50 centimetres
    • 2 metres
    • 9 metres

Changing between units of measure · Year 6 Maths · www.arenapublications.com/learn

Year 6 Maths · 14 of 16

Basic geometrical ideas

Tell points, lines, rays and line segments apart, name the parts of an angle and a circle, and count the sides and diagonals of a polygon.

Before you start

Three lines are drawn on this circle. Take them in turn and find out what each one is called, looking at where each one starts and where it ends.

123
  1. 1. Radius — centre to edge
  2. 2. Diameter — right across, through the centre
  3. 3. Chord — edge to edge, missing the centre

Every diameter is also a chord — it is simply the longest one, and the only kind that passes through the centre.

  1. 1.Put these shapes in order by how many sides they have, fewest first.

    • Octagon
    • Pentagon
    • Triangle
    • Quadrilateral
    • Hexagon

  2. 2.Match each shape to the number of sides it has.

    • Triangle
    • Quadrilateral
    • Pentagon
    • Hexagon
    • Octagon
    • 6
    • 3
    • 4
    • 5
    • 8

  3. 3.Three straight lines have been drawn on this circle. Tap the diameter.

    Write the number of the part.

    123

  4. 4.An angle is made where two rays meet at a point. How many arms does one angle have?

  5. 5.Three points are marked, and no two of them are in the same place. How many different line segments can be drawn joining pairs of them?

  6. 6.How many line segments make up the sides of a hexagon?

  7. 7.A circle has a radius of 7 cm. How long is its diameter, in centimetres?

    • a) 21
    • b) 3.5
    • c) 7
    • d) 14

  8. 8.How many diagonals can be drawn inside a quadrilateral?

Basic geometrical ideas · Year 6 Maths · www.arenapublications.com/learn

Year 6 Maths · 15 of 16

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

  2. 2.In which quadrant does the point (5, -1) lie?

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

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

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

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

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

  5. 5.What is the x-coordinate of the point (7, -3)?

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

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

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

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

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

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

Year 6 Maths · 16 of 16

Chance and probability

Say how likely an event is, and write its probability as a fraction.

Before you start

Every chance there is sits somewhere on this line, from impossible at one end to certain at the other. Move along it.

0.00.51.0

0.5 in the middle is an even chance — as likely to happen as not. To the left of it things are unlikely and to the right they are likely, and nothing at all lives past the two ends.

  1. 1.A fair die numbered 1 to 6 is rolled. Match each event to its probability.

    • Rolling a 3
    • Rolling an odd number
    • Rolling a number above 4
    • Rolling a number below 7
    • Rolling a 9
    • 1/2
    • 1/3
    • 1/6
    • 0
    • 1

  2. 2.The probability that it rains tomorrow is 3/10. What is the probability that it does not rain? Write your answer as a fraction.

  3. 3.A fair coin is tossed. What is the probability of getting a head? Write your answer as a fraction.

  4. 4.A fair die numbered 1 to 6 is rolled. What is the probability of getting a 4? Write your answer as a fraction.

  5. 5.A spinner has 8 equal sections numbered 1 to 8. What is the probability of landing on a number greater than 5? Write your answer as a fraction.

  6. 6.An event that is certain to happen has which probability?

    • a) 1
    • b) 1/2
    • c) 0
    • d) 100

  7. 7.Sort each event by how likely it is.

    Groups: Impossible · Possible but not certain · Certain

    • Rolling an even number on a die numbered 1 to 6
    • Drawing a red ball from a bag of only red balls
    • Rolling a 7 on a die numbered 1 to 6
    • Rolling a number below 7 on a die numbered 1 to 6
    • Drawing a blue ball from a bag of only red balls
    • Tossing a fair coin and getting a tail

  8. 8.Put these events in order, least likely first.

    • Rolling a number below 7 on a die numbered 1 to 6
    • Rolling a 5 on a die numbered 1 to 6
    • Rolling a number above 4 on a die numbered 1 to 6
    • Tossing a fair coin and getting a head
    • Rolling a 7 on a die numbered 1 to 6

Chance and probability · Year 6 Maths · www.arenapublications.com/learn

Answer keys — Year 6 Maths

In the same order as the worksheets.

Whole numbers

  1. 1. 2999
  2. 2. d) 9 + 4 and 4 + 9
  3. 3. b) -4
  4. 4. 50
  5. 5. 686
  6. 6. 1. 0 2. 1 3. 19 4. 91 5. 109 6. 190
  7. 7. 25 × 4 → 100; 25 + 4 → 29; 25 - 4 → 21; 100 ÷ 4 → 25; 4 × 4 → 16
  8. 8. 848

Integers

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

Factors and multiples

  1. 1. 28
  2. 2. 1. 13 2. 9 3. 8 4. 16 5. 12
  3. 3. c) 29
  4. 4. 2
  5. 5. 15
  6. 6. 27
  7. 7. 17 → Prime; 21 → Composite; 23 → Prime; 27 → Composite; 31 → Prime; 33 → Composite
  8. 8. 24

HCF and LCM

  1. 1. 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
  2. 2. 6
  3. 3. 6
  4. 4. 12
  5. 5. c) 2 × 2 × 3 × 5
  6. 6. 1. 8 and 9 2. 6 and 8 3. 9 and 12 4. 12 and 16 5. 10 and 15
  7. 7. b) 8 and 15
  8. 8. 24

Understanding fractions

  1. 1. 0.75
  2. 2.
    • 3 2/5
    • 3 2 / 5
  3. 3. 8
  4. 4.
    • 3/4
    • 3 / 4
    • three quarters
    • three-quarters
  5. 5. d) 5/8
  6. 6. b) 6/8
  7. 7. 1.75
  8. 8. 3/4 → Less than 1; 5/4 → More than 1; 7/8 → Less than 1; 9/7 → More than 1; 5/9 → Less than 1; 8/3 → More than 1

Adding and subtracting fractions

  1. 1. 3/8
  2. 2. 1/2 → 0.5; 1/4 → 0.25; 3/4 → 0.75; 1/5 → 0.2; 1/10 → 0.1
  3. 3. a) 3/6
  4. 4. 1. 1/6 2. 1/4 3. 1/3 4. 1/2 5. 2/3 6. 3/4
  5. 5. 7/12
  6. 6. 3/4
  7. 7. 5/6
  8. 8. 3/5

Decimals

  1. 1. 1/2 → 0.5; 1/4 → 0.25; 3/4 → 0.75; 1/5 → 0.2; 3/10 → 0.3
  2. 2. 1.05
  3. 3. c) 1/20
  4. 4. 0.4
  5. 5. 0.2 → Closer to 0; 0.7 → Closer to 1; 0.45 → Closer to 0; 0.55 → Closer to 1; 0.09 → Closer to 0; 0.91 → Closer to 1
  6. 6. 1.7
  7. 7. 4.85
  8. 8. 1. 0.09 2. 0.4 3. 0.41 4. 0.5 5. 1.05

Percentages

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

Discount and tax

  1. 1. 900
  2. 2. 495
  3. 3. $150 → $120; $250 → $200; $400 → $320; $600 → $480; $900 → $720
  4. 4. A discount of 10 per cent → Price goes down; Tax of 8 per cent added → Price goes up; A quarter off → Price goes down; A service charge of 5 per cent added → Price goes up; A third off → Price goes down; Tax of 12 per cent added → Price goes up
  5. 5. d) A discount of 30 per cent
  6. 6. 20
  7. 7. b) 36 per cent
  8. 8. 120

Adding and subtracting decimals

  1. 1. 5.6
  2. 2. 3.5
  3. 3. 0.4 + 0.3 → Less than 1; 0.6 + 0.7 → More than 1; 0.25 + 0.5 → Less than 1; 0.9 + 0.2 → More than 1; 0.35 + 0.4 → Less than 1; 0.8 + 0.45 → More than 1
  4. 4. 1
  5. 5. 3.75
  6. 6. 3.3
  7. 7. 16.75
  8. 8. 1 - 0.4 → 0.6; 1 - 0.25 → 0.75; 1 - 0.05 → 0.95; 1 - 0.9 → 0.1; 1 - 0.5 → 0.5

Number patterns

  1. 1. 18
  2. 2. 66
  3. 3. 19
  4. 4. 24
  5. 5. c) 16
  6. 6. b) Add 3
  7. 7. 35
  8. 8. 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

Perimeter and area

  1. 1. 49
  2. 2. 2 by 6 → Perimeter below 20; 3 by 5 → Perimeter below 20; 4 by 7 → Perimeter above 20; 5 by 6 → Perimeter above 20; 1 by 8 → Perimeter below 20; 6 by 6 → Perimeter above 20
  3. 3. 31
  4. 4. side 2 → 4; side 3 → 9; side 5 → 25; side 6 → 36; side 9 → 81
  5. 5. 36
  6. 6. 1. 2 by 6 2. 3 by 5 3. 4 by 4 4. 3 by 6 5. 5 by 4
  7. 7. 6
  8. 8. 28

Changing between units of measure

  1. 1. 3400
  2. 2. 10
  3. 3. 2000
  4. 4. b) centimetres
  5. 5. 3000
  6. 6. 235
  7. 7. b) 2 metres and 50 centimetres
  8. 8. 1. 50 centimetres 2. 2 metres 3. 350 centimetres 4. 9 metres 5. 1 kilometres

Basic geometrical ideas

  1. 1. 1. Triangle 2. Quadrilateral 3. Pentagon 4. Hexagon 5. Octagon
  2. 2. Triangle → 3; Quadrilateral → 4; Pentagon → 5; Hexagon → 6; Octagon → 8
  3. 3. 2 — the line right across through the centre
  4. 4. 2
  5. 5. 3
  6. 6. 6
  7. 7. d) 14
  8. 8. 2

Coordinate geometry

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

Chance and probability

  1. 1. Rolling a 3 → 1/6; Rolling an odd number → 1/2; Rolling a number above 4 → 1/3; Rolling a number below 7 → 1; Rolling a 9 → 0
  2. 2. 7/10
  3. 3. 1/2
  4. 4. 1/6
  5. 5. 3/8
  6. 6. a) 1
  7. 7. Rolling a 7 on a die numbered 1 to 6 → Impossible; Tossing a fair coin and getting a tail → Possible but not certain; Rolling a number below 7 on a die numbered 1 to 6 → Certain; Drawing a red ball from a bag of only red balls → Certain; Drawing a blue ball from a bag of only red balls → Impossible; Rolling an even number on a die numbered 1 to 6 → Possible but not certain
  8. 8. 1. Rolling a 7 on a die numbered 1 to 6 2. Rolling a 5 on a die numbered 1 to 6 3. Rolling a number above 4 on a die numbered 1 to 6 4. Tossing a fair coin and getting a head 5. Rolling a number below 7 on a die numbered 1 to 6

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