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Term pack

Class 6 Maths

Name: ________________________

Skills in this pack

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

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Class 6 Maths · 1 of 16

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.Round 4678 to the nearest hundred.

  2. 2.Make the largest number you can from the digits 4, 7, 1 and 9, using each digit once.

  3. 3.Round 25361 to the nearest thousand.

  4. 4.What is the predecessor of 40000?

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

    Groups: Closer to 5000 · Closer to 6000

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

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

    • 9989
    • 98099
    • 98909
    • 9899
    • 98990

  7. 7.What is the successor of 78999?

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

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

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

Class 6 Maths · 2 of 16

Lakh, crore and the Indian number system

Read, write and compare large numbers in the Indian system of numeration, and place its commas.

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

    • Nine thousand
    • Ninety lakh
    • Nine crore
    • Nine lakh
    • Ninety thousand

  2. 2.Which of these is 4560000 with its commas in the international system?

    • a) 45,600,00
    • b) 45,60,500
    • c) 4,56,0000
    • d) 4,560,000

  3. 3.Write six lakh forty thousand in figures.

  4. 4.This line runs from zero to ten lakh, with a mark at every lakh. Tap seven lakh.

    Mark the line with an X.

    05000001000000

  5. 5.How is 5,00,00,000 said in the Indian system?

    • a) Fifty lakh
    • b) Five crore
    • c) Fifty crore
    • d) Five lakh

  6. 6.Write three crore fifteen lakh in figures.

  7. 7.Every number below is written correctly. Sort each one by which system its commas belong to.

    Groups: Indian system · International system

    • 500,000
    • 7,320,159
    • 40,500,000
    • 5,00,000
    • 4,05,00,000
    • 73,20,159

  8. 8.A district records 2500000 voters. How many lakh is that? Give just the number.

Lakh, crore and the Indian number system · Class 6 Maths · www.arenapublications.com/learn

Class 6 Maths · 3 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.Match each calculation to its answer.

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

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

    Mark the line with an X.

    303540455055606570

  4. 4.7 × 98 = ?

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

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

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

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

  7. 7.25 × 17 × 4 = ?

  8. 8.What is the successor of 6099?

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

Class 6 Maths · 4 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. 1.5 - 12 = ?

  2. 2.-15 + 15 = ?

  3. 3.-4 + 11 = ?

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

    Groups: Negative · Positive

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

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

  6. 6.-7 + 3 = ?

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

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

  8. 8.-8 - 6 = ?

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

Class 6 Maths · 5 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.Exactly one number on this line is a multiple of 6. Tap it.

    Mark the line with an X.

    20212223242526272829

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

    • 16
    • 9
    • 12
    • 8
    • 13

  3. 3.How many prime numbers are there between 10 and 20?

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

  5. 5.Which of these numbers is prime?

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

  6. 6.What is the smallest prime number?

  7. 7.Match each number to how many factors it has.

    • 7
    • 8
    • 16
    • 12
    • 36
    • 2
    • 4
    • 5
    • 6
    • 9

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

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

Class 6 Maths · 6 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.What is the LCM of 4 and 6?

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

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

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

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

  5. 5.Match each pair of numbers to their HCF.

    • 6 and 9
    • 8 and 12
    • 10 and 15
    • 14 and 21
    • 16 and 24
    • 3
    • 7
    • 4
    • 5
    • 8

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

  7. 7.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

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

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

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

Class 6 Maths · 7 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.Which of these fractions is NOT equivalent to 2/3?

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

  2. 2.What fraction of an hour is 45 minutes? Write it in its simplest form.

  3. 3.Match each fraction to an equivalent one with a larger bottom number.

    • 1/2
    • 1/3
    • 2/5
    • 3/4
    • 2/3
    • 8/20
    • 4/12
    • 9/12
    • 10/15
    • 5/10

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

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

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

  6. 6.Tap where 7/4 sits.

    Mark the line with an X.

    0.001.002.003.00

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

    Groups: Less than 1 · More than 1

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

  8. 8.Tap where 3/4 sits.

    Mark the line with an X.

    0.001.00

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

Class 6 Maths · 8 of 16

Adding and subtracting fractions

Add and subtract fractions, including ones with different denominators.

  1. 1.2/3 + 1/6 = ? Write your answer as a fraction.

  2. 2.1/3 + 1/4 = ? Write your answer as a fraction.

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

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

  4. 4.1/2 + 1/4 = ? Write your answer as a fraction.

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

  6. 6.7/10 - 3/10 = ? Write your answer as a fraction.

  7. 7.5/6 - 1/3 = ? Write your answer as a fraction.

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

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

Class 6 Maths · 9 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.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.

  2. 2.Tap where 2.75 sits.

    Mark the line with an X.

    2.002.252.502.753.00

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

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

  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.Which of these decimals is the largest?

    • a) 0.609
    • b) 0.7
    • c) 0.68
    • d) 0.5

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

    Groups: Closer to 0 · Closer to 1

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

  7. 7.3.4 + 2.75 = ?

  8. 8.8.6 - 3.75 = ?

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

Class 6 Maths · 10 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.An angle is made where two rays meet at a point. How many arms does one angle have?

  2. 2.Sort each name by whether it describes a part of a circle or a part of an angle.

    Groups: Part of a circle · Part of an angle

    • Diameter
    • Chord
    • Centre
    • Radius
    • Arm
    • Vertex

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

    Write the number of the part.

    123

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

  5. 5.Three straight lines have been drawn on this circle. Tap the chord that is not a diameter.

    Write the number of the part.

    123

  6. 6.A line has no ends, a ray has one end, and a line segment has two. Which of the three has a length you could measure with a ruler?

    • a) A ray
    • b) All three of them
    • c) A line
    • d) A line segment

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

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

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

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

Class 6 Maths · 11 of 16

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

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

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

    Groups: Flat shape · Solid shape

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

  4. 4.An angle of 200° is which kind of angle?

    • a) Obtuse
    • b) Straight
    • c) Acute
    • d) Reflex

  5. 5.Match each angle to the name for its size.

    • 45°
    • 90°
    • 120°
    • 180°
    • 300°
    • Obtuse
    • Straight
    • Right
    • Reflex
    • Acute

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

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

    Write the number of the part.

    123

  8. 8.A full turn is 360° and splits into four equal right angles. How many degrees is one right angle?

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

Class 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 shape drawn on squared paper covers 12 full squares and 6 half squares. What is its area, in squares?

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

  3. 3.Match each square to its area.

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

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

  5. 5.Which of these rectangles has the largest area?

    • a) 7 by 4
    • b) 6 by 5
    • c) 9 by 2
    • d) 8 by 3

  6. 6.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.

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

  8. 8.A rectangle has an area of 48 square centimetres and a length of 8 cm. How wide is it, in centimetres? Give just the number.

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

Class 6 Maths · 13 of 16

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.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

  2. 2.On a pictograph one whole symbol stands for 8 cars, and half a symbol is drawn at the end of a row. How many cars does that half symbol stand for?

  3. 3.A bar graph shows 6, 11, 9 and 4 goals across four matches. In how many of the matches were fewer than 8 goals scored?

  4. 4.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?

  5. 5.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

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

  7. 7.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.

    • Thursday
    • Tuesday
    • Wednesday
    • Monday

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

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

Class 6 Maths · 14 of 16

Ratio and proportion

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

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

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

  2. 2.A tray holds 4 red beads and 6 blue beads. What is the ratio of red to blue in its simplest form? Write it like 4:5.

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

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

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

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

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

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

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

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

Class 6 Maths · 15 of 16

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.Take n = 5. Work out each expression, then sort it by its value.

    Groups: Equals 10 · Equals 15

    • 2n
    • n + 5
    • 3n
    • n + 10
    • n × 2
    • 20 - n

  3. 3.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
    • 7m
    • m + 7
    • m ÷ 7
    • m - 7

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

    The scale is balanced. Write what one box weighs.

    xx19

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

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

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

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

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

Class 6 Maths · 16 of 16

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.A regular shape has 8 lines of symmetry. How many sides does it have?

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

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

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

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

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

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

    Groups: Has a line of symmetry · Has none

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

  6. 6.This kite has one line of symmetry. Three lines have been drawn on it. Tap the one that is a line of symmetry.

    Write the number of the part.

    123

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

  8. 8.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
    • 3
    • 1
    • 2
    • 0
    • 5

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

Answer keys — Class 6 Maths

In the same order as the worksheets.

Knowing our numbers

  1. 1. 4700
  2. 2. 9741
  3. 3. 25000
  4. 4. 39999
  5. 5. 5120 → Closer to 5000; 5890 → Closer to 6000; 5499 → Closer to 5000; 5501 → Closer to 6000; 5045 → Closer to 5000; 5750 → Closer to 6000
  6. 6. 1. 9899 2. 9989 3. 98099 4. 98909 5. 98990
  7. 7. 79000
  8. 8. d) 46875

Lakh, crore and the Indian number system

  1. 1. 1. Nine thousand 2. Ninety thousand 3. Nine lakh 4. Ninety lakh 5. Nine crore
  2. 2. d) 4,560,000
  3. 3. 640000
  4. 4. 700000
  5. 5. b) Five crore
  6. 6. 31500000
  7. 7. 73,20,159 → Indian system; 7,320,159 → International system; 5,00,000 → Indian system; 500,000 → International system; 4,05,00,000 → Indian system; 40,500,000 → International system
  8. 8. 25

Whole numbers

  1. 1. 25 × 4 → 100; 25 + 4 → 29; 25 - 4 → 21; 100 ÷ 4 → 25; 4 × 4 → 16
  2. 2. b) 9 + 4 and 4 + 9
  3. 3. 50
  4. 4. 686
  5. 5. 1. 0 2. 1 3. 19 4. 91 5. 109 6. 190
  6. 6. b) -4
  7. 7. 1700
  8. 8. 6100

Integers

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

Factors and multiples

  1. 1. 24
  2. 2. 1. 13 2. 9 3. 8 4. 16 5. 12
  3. 3. 4
  4. 4. 28
  5. 5. b) 29
  6. 6. 2
  7. 7. 7 → 2; 8 → 4; 16 → 5; 12 → 6; 36 → 9
  8. 8. 15

HCF and LCM

  1. 1. 12
  2. 2. b) 8 and 15
  3. 3. 24
  4. 4. a) 2 × 2 × 3 × 5
  5. 5. 6 and 9 → 3; 8 and 12 → 4; 10 and 15 → 5; 14 and 21 → 7; 16 and 24 → 8
  6. 6. 1
  7. 7. 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
  8. 8. 40

Understanding fractions

  1. 1. d) 6/8
  2. 2.
    • 3/4
    • 3 / 4
    • three quarters
    • three-quarters
  3. 3. 1/2 → 5/10; 1/3 → 4/12; 2/5 → 8/20; 3/4 → 9/12; 2/3 → 10/15
  4. 4. c) 5/8
  5. 5.
    • 13/5
    • 13 / 5
  6. 6. 1.75
  7. 7. 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
  8. 8. 0.75

Adding and subtracting fractions

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

Decimals

  1. 1. 1.7
  2. 2. 2.75
  3. 3. 1/2 → 0.5; 1/4 → 0.25; 3/4 → 0.75; 1/5 → 0.2; 3/10 → 0.3
  4. 4. 0.4
  5. 5. b) 0.7
  6. 6. 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
  7. 7. 6.15
  8. 8. 4.85

Basic geometrical ideas

  1. 1. 2
  2. 2. Radius → Part of a circle; Diameter → Part of a circle; Chord → Part of a circle; Centre → Part of a circle; Vertex → Part of an angle; Arm → Part of an angle
  3. 3. 2 — the line right across through the centre
  4. 4. 6
  5. 5. 3 — the line across the top
  6. 6. d) A line segment
  7. 7. 2
  8. 8. Triangle → 3; Quadrilateral → 4; Pentagon → 5; Hexagon → 6; Octagon → 8

Understanding elementary shapes

  1. 1. 60
  2. 2. 2
  3. 3. Square → Flat shape; Cube → Solid shape; Circle → Flat shape; Sphere → Solid shape; Triangle → Flat shape; Cylinder → Solid shape
  4. 4. d) Reflex
  5. 5. 45° → Acute; 90° → Right; 120° → Obtuse; 180° → Straight; 300° → Reflex
  6. 6. 60
  7. 7. 2 — the bottom left corner
  8. 8. 90

Perimeter and area

  1. 1. 15
  2. 2. 6
  3. 3. side 2 → 4; side 3 → 9; side 5 → 25; side 6 → 36; side 9 → 81
  4. 4. 49
  5. 5. b) 6 by 5
  6. 6. 31
  7. 7. 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
  8. 8. 6

Pictographs and bar graphs

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

Ratio and proportion

  1. 1. d) 6:8
  2. 2. 2:3
  3. 3. 15
  4. 4. 15
  5. 5. 105
  6. 6. 2:3
  7. 7. d) Yes
  8. 8. 1. 1:4 2. 1:2 3. 2:3 4. 3:4 5. 5:4

Letters for numbers

  1. 1. 5 on the right pan
  2. 2. 2n → Equals 10; 3n → Equals 15; n + 5 → Equals 10; n + 10 → Equals 15; 20 - n → Equals 15; n × 2 → Equals 10
  3. 3. 7 less than m → m - 7; m shared equally between 7 → m ÷ 7; 7 times m → 7m; 7 more than m → m + 7
  4. 4. box = 5
  5. 5. x = 4
  6. 6. c) 3n
  7. 7. 14
  8. 8. 21

Line symmetry

  1. 1. 8
  2. 2. a) R
  3. 3. 1
  4. 4. a) Isosceles triangle
  5. 5. 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
  6. 6. 3 — the upright line
  7. 7. 2
  8. 8. The letter F → 0; The letter T → 1; The letter H → 2; Equilateral triangle → 3; Regular pentagon → 5

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