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Term pack

Year 6 Maths

Name: ________________________

Skills in this pack

  • Knowing our numbers
  • Whole numbers
  • Integers
  • Factors and multiples
  • HCF and LCM
  • Understanding fractions
  • Adding and subtracting fractions
  • Decimals
  • Ratio and proportion
  • Letters for numbers
  • Perimeter and area
  • Basic geometrical ideas
  • Understanding elementary shapes
  • Line symmetry
  • Pictographs and bar graphs

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Year 6 Maths · 1 of 15

Knowing our numbers

Compare, order, round and estimate with numbers of four digits and more.

Before you start

Move between four thousand and five thousand, a hundred at a time. Watch which end of the line you are nearer.

400045005000

Halfway is 4500. Everything to the left of it is nearer 4000 and everything to the right is nearer 5000 — which is the whole of rounding to the nearest thousand, and why 4783 goes up rather than down.

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

    • 9989
    • 9899
    • 98099
    • 98909
    • 98990

  2. 2.Which of these is the largest number?

    • a) 46587
    • b) 46857
    • c) 46785
    • d) 46875

  3. 3.Make the smallest number you can from the digits 5, 2, 8 and 6, using each digit once.

  4. 4.Sort each number by whether it is closer to 5000 or to 6000.

    Groups: Closer to 5000 · Closer to 6000

    • 5120
    • 5501
    • 5045
    • 5750
    • 5499
    • 5890

  5. 5.Estimate 297 + 405 by rounding each number to the nearest hundred, then tap the estimate.

    Mark the line with an X.

    4005006007008009001000

  6. 6.What is the predecessor of 40000?

  7. 7.Round 4678 to the nearest hundred, then tap it on the line.

    Mark the line with an X.

    4400450046004700480049005000

  8. 8.What is the successor of 78999?

Knowing our numbers · Year 6 Maths · www.arenapublications.com/learn

Year 6 Maths · 2 of 15

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 · 3 of 15

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 · 4 of 15

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 · 5 of 15

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 · 6 of 15

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 · 7 of 15

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 · 8 of 15

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 · 9 of 15

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

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

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

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

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

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

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

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

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

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

Year 6 Maths · 10 of 15

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

    The scale is balanced. Write what one box weighs.

    xx19

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

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

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

    Circle weights from the tray to make the scale level.

    127532

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

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

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

  6. 6.If x = 5, what is the value of x + 12?

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

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

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

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

Year 6 Maths · 11 of 15

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 · 12 of 15

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 · 13 of 15

Understanding elementary shapes

Classify angles by size, triangles by their sides and their angles, and tell flat shapes from solid ones.

Before you start

Four angles, drawn side by side and getting wider as you go. Find out what each one is called.

1234
  1. 1. Acute
  2. 2. Right angle
  3. 3. Obtuse
  4. 4. Straight

Acute is under 90°, obtuse is over it, and the straight one is a half turn — 180°, which is why it stopped looking like a corner at all.

  1. 1.Put these kinds of angle in order by size, smallest first.

    • Obtuse
    • Right
    • Acute
    • Straight
    • Reflex

  2. 2.This triangle has one right angle. Tap the corner where it is.

    Write the number of the part.

    123

  3. 3.The angles of a triangle add up to 180°. Two of them are 55° and 65°. How big is the third, in degrees?

  4. 4.Two right angles side by side make a straight angle. How many degrees is a straight angle?

  5. 5.All three angles of an equilateral triangle are equal, and they add up to 180°. How big is each one, in degrees?

  6. 6.A triangle with one angle of exactly 90° is called which kind of triangle?

    • a) Right-angled
    • b) Obtuse-angled
    • c) Equilateral
    • d) Acute-angled

  7. 7.Sort each shape by whether it is flat or solid.

    Groups: Flat shape · Solid shape

    • Sphere
    • Triangle
    • Cylinder
    • Circle
    • Square
    • Cube

  8. 8.A triangle has sides of 5 cm, 5 cm and 8 cm. How many of its sides are equal in length?

Understanding elementary shapes · Year 6 Maths · www.arenapublications.com/learn

Year 6 Maths · 14 of 15

Line symmetry

Find the lines of symmetry of shapes and letters, and tell a mirror line from a line that only looks like one.

  1. 1.Sort each capital letter by whether it has a line of symmetry.

    Groups: Has a line of symmetry · Has none

    • R
    • T
    • M
    • F
    • A
    • P

  2. 2.How many lines of symmetry does the capital letter H have?

  3. 3.How many lines of symmetry does the capital letter F have?

  4. 4.Match each of these to the number of lines of symmetry it has.

    • The letter F
    • The letter T
    • The letter H
    • Equilateral triangle
    • Regular pentagon
    • 1
    • 0
    • 2
    • 3
    • 5

  5. 5.Put these in order by how many lines of symmetry they have, fewest first.

    • Equilateral triangle
    • The letter T
    • Square
    • Rectangle that is not a square
    • Scalene triangle
    • Regular hexagon

  6. 6.Which of these capital letters has no line of symmetry?

    • a) M
    • b) R
    • c) X
    • d) E

  7. 7.How many lines of symmetry does the capital letter T have?

  8. 8.Which of these shapes has exactly one line of symmetry?

    • a) Scalene triangle
    • b) Square
    • c) Rectangle that is not a square
    • d) Isosceles triangle

Line symmetry · Year 6 Maths · www.arenapublications.com/learn

Year 6 Maths · 15 of 15

Pictographs and bar graphs

Record data with tallies, read pictographs and bar graphs where one unit stands for many, and answer questions from them.

Before you start

Every line across this graph is worth 5 books. Look at how far up each bar reaches and work out what it is worth.

1234
  1. 1. Monday — 30 books
  2. 2. Tuesday — 15 books
  3. 3. Wednesday — 40 books
  4. 4. Thursday — 25 books

Count the lines, not the bars. Monday reaches six lines up and each line is worth 5 books, which is why it is 30 and not 6 — that is the whole job a scale does.

Move the bars up and down, and watch the number each one stands for.

Each line up the side is worth 5.0510152025303540MondayTuesdayWednesday

One line up is not one book. Every line you cross is worth 5, so a bar that grows by one line grows by five — that is the scale doing its job.

  1. 1.In a pictograph, one symbol stands for 10 cars. How many symbols are needed to show 70 cars?

  2. 2.On a bar graph each square of the scale stands for 4 children. A bar is 6 squares tall. How many children does that bar stand for?

  3. 3.This bar chart shows how many apples a stall sold on four days. Tap the bar for the day it sold the fewest.

    Write the number of the part.

    1234

  4. 4.In a pictograph, one symbol stands for 5 books. How many books do 7 symbols stand for?

  5. 5.A bar graph shows 12 red, 8 blue, 15 green and 5 yellow counters. How many counters are there altogether?

  6. 6.A bar graph shows 12 red counters and 5 yellow counters. How many more red counters are there than yellow?

  7. 7.A library counted the books borrowed each day. Draw a bar for every day in the table.

    Draw a bar for every row of the table.

    Monday30
    Tuesday15
    Wednesday40
    Thursday25
    Each line up the side is worth 5.0510152025303540MondayTuesdayWednesdayThursday

  8. 8.A shop sold 14 pens on Monday, 9 on Tuesday, 21 on Wednesday and 17 on Thursday. Put the days in order, fewest pens first.

    • Wednesday
    • Tuesday
    • Monday
    • Thursday

Pictographs and bar graphs · Year 6 Maths · www.arenapublications.com/learn

Answer keys — Year 6 Maths

In the same order as the worksheets.

Knowing our numbers

  1. 1. 1. 9899 2. 9989 3. 98099 4. 98909 5. 98990
  2. 2. d) 46875
  3. 3. 2568
  4. 4. 5120 → Closer to 5000; 5890 → Closer to 6000; 5499 → Closer to 5000; 5501 → Closer to 6000; 5045 → Closer to 5000; 5750 → Closer to 6000
  5. 5. 700
  6. 6. 39999
  7. 7. 4700
  8. 8. 79000

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

Ratio and proportion

  1. 1. 16
  2. 2. 1. 1:4 2. 1:2 3. 2:3 4. 3:4 5. 5:4
  3. 3. 2:3
  4. 4. 15
  5. 5. 105
  6. 6. 25
  7. 7. a) Yes
  8. 8. 15

Letters for numbers

  1. 1. x = 4
  2. 2. d) 4s
  3. 3. 5 on the right pan
  4. 4. a) x + 5
  5. 5. 21
  6. 6. 17
  7. 7. 36
  8. 8. b) 3n

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

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

Understanding elementary shapes

  1. 1. 1. Acute 2. Right 3. Obtuse 4. Straight 5. Reflex
  2. 2. 2 — the bottom left corner
  3. 3. 60
  4. 4. 180
  5. 5. 60
  6. 6. a) Right-angled
  7. 7. Square → Flat shape; Cube → Solid shape; Circle → Flat shape; Sphere → Solid shape; Triangle → Flat shape; Cylinder → Solid shape
  8. 8. 2

Line symmetry

  1. 1. A → Has a line of symmetry; F → Has none; M → Has a line of symmetry; P → Has none; T → Has a line of symmetry; R → Has none
  2. 2. 2
  3. 3. 0
  4. 4. The letter F → 0; The letter T → 1; The letter H → 2; Equilateral triangle → 3; Regular pentagon → 5
  5. 5. 1. Scalene triangle 2. The letter T 3. Rectangle that is not a square 4. Equilateral triangle 5. Square 6. Regular hexagon
  6. 6. b) R
  7. 7. 1
  8. 8. d) Isosceles triangle

Pictographs and bar graphs

  1. 1. 7
  2. 2. 24
  3. 3. 1 — Monday
  4. 4. 35
  5. 5. 40
  6. 6. 7
  7. 7. Monday 30, Tuesday 15, Wednesday 40, Thursday 25
  8. 8. 1. Tuesday 2. Monday 3. Thursday 4. Wednesday

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