← Back to Year 4 Maths

Term pack

Year 4 Maths

Name: ________________________

Skills in this pack

  • Multiplying two digits by one
  • Equivalent fractions
  • Numbers up to six digits
  • Decimal place value
  • Knowing our numbers
  • 6 times table
  • 7 times table
  • 8, 9 and 10 times tables
  • Patterns and tiling
  • Time and how long things last
  • Money problems
  • Perimeter: once round the outside
  • Area by counting squares
  • Line symmetry
  • Symmetry
  • Reading bar charts
  • Pictographs and bar graphs

Free at www.arenapublications.com/learn — no account, no ads, ever.

Year 4 Maths · 1 of 17

Multiplying two digits by one

Multiply a two-digit number by a single digit.

  1. 1.Put these multiplications in order, smallest answer first.

    • 21 × 4
    • 26 × 8
    • 14 × 3
    • 33 × 5

  2. 2.Sort these multiplications by whether the answer is below 200 or above it.

    Groups: Below 200 · Above 200

    • 47 × 5
    • 36 × 3
    • 29 × 8
    • 23 × 4
    • 52 × 6
    • 18 × 7

  3. 3.Which of these is another way of working out 24 × 5?

    • a) 2 × 5 + 4 × 5
    • b) 24 × 5 + 5
    • c) 20 × 5 + 4
    • d) 20 × 5 + 4 × 5

  4. 4.45 × 9 = ?

  5. 5.18 × 7 = ?

  6. 6.52 × 6 = ?

  7. 7.64 × 2 = ?

  8. 8.The line counts in 23s. Tap where 23 × 4 lands.

    Mark the line with an X.

    023466992115

Multiplying two digits by one · Year 4 Maths · www.arenapublications.com/learn

Year 4 Maths · 2 of 17

Equivalent fractions

Recognise fractions that are worth the same amount.

Before you start

Shade some of the bar, then cut it into more pieces. What happens to the shaded part?

123456789101112

Cutting the bar into more pieces never changes how much is shaded — only what you call it.

  1. 1.Match each fraction to another fraction worth exactly the same amount.

    • 1/4
    • 2/5
    • 3/8
    • 5/6
    • 4/10
    • 10/12
    • 3/12
    • 6/16

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

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

  3. 3.One bar shows 2/3 and the other shows 4/6. Which bar will show more when they are filled in?

    Which bar shows more when they are filled in? Circle one.

    2/34/6

    Top / The same / Bottom

  4. 4.Fill in the missing number: 2/3 = ?/9

  5. 5.Sort each fraction by whether it is worth the same as 2/3 or not.

    Groups: The same as 2/3 · Not the same as 2/3

    • 10/15
    • 5/8
    • 2/5
    • 3/5
    • 8/12
    • 4/6

  6. 6.Fill in the missing number: 3/4 = 15/?

  7. 7.Which fraction is NOT the same as 3/4?

    • a) 4/6
    • b) 6/8
    • c) 9/12
    • d) 12/16

  8. 8.Which fraction is the same as 5/10?

    • a) 1/2
    • b) 1/5
    • c) 5/5
    • d) 2/5

Equivalent fractions · Year 4 Maths · www.arenapublications.com/learn

Year 4 Maths · 3 of 17

Numbers up to six digits

Read, compare, order and round whole numbers up to six digits.

Before you start

This line runs from zero to one hundred thousand in steps of ten thousand. Look at where each number falls, and how far apart the steps are.

020000400006000080000100000

Every one of those steps is ten thousand. A six-digit number is a whole line like this one and then more.

  1. 1.Which digit is in the ten thousands place in 605218?

    • a) 0
    • b) 6
    • c) 2
    • d) 5

  2. 2.In 348617, what is the 4 worth?

    • a) 4 hundreds
    • b) 4 thousands
    • c) 4 ten thousands
    • d) 4 hundred thousands

  3. 3.What number is one more than 89999?

  4. 4.Round 47382 to the nearest thousand.

  5. 5.47382 lies between two hundreds. Tap the hundred it rounds to.

    Mark the line with an X.

    470004750048000

  6. 6.How many thousands make 60000?

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

    • a) 99099
    • b) 99909
    • c) 90909
    • d) 90999

  8. 8.Sort each number by how many digits it has.

    Groups: Five digits or fewer · Six digits

    • 87654
    • 100001
    • 150000
    • 98760
    • 99999
    • 234000

Numbers up to six digits · Year 4 Maths · www.arenapublications.com/learn

Year 4 Maths · 4 of 17

Decimal place value

Say what each digit is worth in a decimal number.

Before you start

This line runs from 0 to 1 in tenths. Look at where each tenth falls, and how much of the way along 0.7 really is.

0.00.10.20.30.40.50.60.70.80.91.0

Every decimal between 0 and 1 lives somewhere on this line. There is nothing beyond the ends of it, however many digits are written.

  1. 1.Which of these is the same as 0.6?

    • a) 0.006
    • b) 0.60
    • c) 6.0
    • d) 0.06

  2. 2.Match each number to what its 3 is worth.

    • 0.35
    • 0.53
    • 3.5
    • 0.053
    • 0.003
    • 3
    • 0.03
    • 0.3

  3. 3.What is 7.8 rounded to the nearest whole number?

    • a) 8
    • b) 80
    • c) 7
    • d) 7.5

  4. 4.In 5.062, what is the 6 worth?

    • a) 6 hundredths
    • b) 6 tenths
    • c) 6 thousandths
    • d) 6 ones

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

    • 2.3
    • 2.03
    • 2.31
    • 2.4

  6. 6.In 12.905, which digit is in the hundredths place?

    • a) 0
    • b) 5
    • c) 2
    • d) 9

  7. 7.Which number is the largest?

    • a) 0.5
    • b) 0.409
    • c) 0.4999
    • d) 0.45

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

    • 0.1
    • 0.2
    • 0.11
    • 0.21

Decimal place value · Year 4 Maths · www.arenapublications.com/learn

Year 4 Maths · 5 of 17

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

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

  3. 3.Which of these is the smallest number?

    • a) 30909
    • b) 30099
    • c) 30990
    • d) 39009

  4. 4.What is the predecessor of 40000?

  5. 5.Match each number to what it becomes when it is rounded to the nearest ten.

    • 4623
    • 4627
    • 4638
    • 4611
    • 4646
    • 4610
    • 4650
    • 4620
    • 4640
    • 4630

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

    Groups: Closer to 5000 · Closer to 6000

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

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

    • 9899
    • 98990
    • 9989
    • 98909
    • 98099

  8. 8.Round 4678 to the nearest hundred.

Knowing our numbers · Year 4 Maths · www.arenapublications.com/learn

Year 4 Maths · 6 of 17

6 times table

Recall the six times table up to 6 × 12.

  1. 1.6 × 9 = ?

  2. 2.6 × 4 = ?

    • a) 28
    • b) 24
    • c) 32
    • d) 20

  3. 3.6 × 7 = ?

  4. 4.Which one is 6 × 8?

    • a) 42
    • b) 48
    • c) 46
    • d) 54

  5. 5.6 × 11 = ?

  6. 6.Which times fact gives 54?

    • a) 6 × 8
    • b) 9 × 5
    • c) 8 × 7
    • d) 6 × 9

  7. 7.6 × 3 = ?

  8. 8.Match each times fact to its answer.

    • 6 × 2
    • 6 × 5
    • 6 × 8
    • 6 × 10
    • 48
    • 60
    • 12
    • 30

6 times table · Year 4 Maths · www.arenapublications.com/learn

Year 4 Maths · 7 of 17

7 times table

Recall the seven times table up to 7 × 12.

  1. 1.7 × 6 = ?

  2. 2.Match each times fact to its answer.

    • 7 × 2
    • 7 × 5
    • 7 × 6
    • 7 × 10
    • 14
    • 70
    • 35
    • 42

  3. 3.Which one is 7 × 7?

    • a) 47
    • b) 56
    • c) 49
    • d) 42

  4. 4.7 × 3 = ?

  5. 5.7 × 8 = ?

    • a) 54
    • b) 49
    • c) 63
    • d) 56

  6. 6.7 × 4 = ?

  7. 7.7 × 12 = ?

  8. 8.7 × 9 = ?

7 times table · Year 4 Maths · www.arenapublications.com/learn

Year 4 Maths · 8 of 17

8, 9 and 10 times tables

Recall the eight, nine and ten times tables up to 12.

  1. 1.8 × 7 = ?

  2. 2.Put these answers in order, smallest first.

    • 10 × 3
    • 9 × 3
    • 8 × 3
    • 8 × 6

  3. 3.Which one is 9 × 9?

    • a) 81
    • b) 99
    • c) 89
    • d) 72

  4. 4.Tap where 9 × 4 lands.

    Mark the line with an X.

    09182736455463728190

  5. 5.Match each times fact to its answer.

    • 9 × 3
    • 9 × 5
    • 9 × 7
    • 9 × 8
    • 45
    • 63
    • 27
    • 72

  6. 6.10 × 12 = ?

  7. 7.9 × 6 = ?

  8. 8.Tap where 8 × 5 lands.

    Mark the line with an X.

    08162432404856647280

8, 9 and 10 times tables · Year 4 Maths · www.arenapublications.com/learn

Year 4 Maths · 9 of 17

Patterns and tiling

Continue number and shape patterns, work out a later term in a pattern, and tell which shapes tile without leaving gaps.

  1. 1.A pattern goes 100, 90, 80, 70, ... What number comes next?

  2. 2.A pattern goes 3, 6, 9, 12, ... What number comes next?

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

    • A square
    • An isosceles triangle
    • A rectangle that is not a square
    • An equilateral triangle
    • A scalene triangle

  4. 4.Sort each shape by whether copies of it will tile a floor with no gaps.

    Groups: Tiles with no gaps · Leaves gaps

    • Regular octagon
    • Square
    • Equilateral triangle
    • Regular hexagon
    • Regular pentagon
    • Circle

  5. 5.A pattern goes 2, 4, 8, 16, ... What number comes next?

  6. 6.Which of these shapes will tile a floor with no gaps at all?

    • a) A regular octagon
    • b) A regular pentagon
    • c) A regular hexagon
    • d) A circle

  7. 7.Match each shape to how many lines of symmetry it has.

    • Square
    • Equilateral triangle
    • Rectangle that is not a square
    • Isosceles triangle
    • Scalene triangle
    • 4
    • 1
    • 0
    • 3
    • 2

  8. 8.A pattern of beads goes red, blue, green, red, blue, green, and keeps repeating in that order. What colour is the twelfth bead?

    • a) Green
    • b) Yellow
    • c) Blue
    • d) Red

Patterns and tiling · Year 4 Maths · www.arenapublications.com/learn

Year 4 Maths · 10 of 17

Time and how long things last

Work out how long something lasts, including when it runs past the hour, and find a start or finish time from a duration.

  1. 1.A clock shows 7:45. What time will it be in 40 minutes?

    • a) 8:25
    • b) 7:85
    • c) 8:05
    • d) 8:15

  2. 2.A lesson starts at 9:20 am and ends at 10:05 am. How many minutes long is it?

  3. 3.Sort each activity by whether it takes less than an hour or more than an hour.

    Groups: Less than an hour · More than an hour

    • A swim of 55 minutes
    • A train journey of 3 hours
    • A film of 90 minutes
    • A walk of 25 minutes
    • A lesson of 45 minutes
    • A match of 2 hours

  4. 4.A match starts at 2:15 pm and lasts 90 minutes. At what time does it end? Write it like 4:30.

  5. 5.Which of these is the longest time?

    • a) 95 minutes
    • b) 2 hours
    • c) 1 hour 30 minutes
    • d) 100 minutes

  6. 6.A shop opens at 8:30 am and closes at 8:30 pm. How many hours is it open?

  7. 7.How many minutes are there in 3 hours?

  8. 8.A bus journey takes 35 minutes and must arrive at 8:15 am. At what time must the bus leave? Write it like 7:05.

Time and how long things last · Year 4 Maths · www.arenapublications.com/learn

Year 4 Maths · 11 of 17

Money problems

Add, subtract and multiply amounts of money, and work out the change from a payment.

  1. 1.A box of 6 pencils costs $54. What does one pencil cost? Give just the number.

  2. 2.A shirt costs $450 and a cap costs $125. How much more does the shirt cost than the cap? Give just the number.

  3. 3.You start with $500, then spend $185 and after that $96. How much is left? Give just the number.

  4. 4.Which of these purchases costs the most?

    • a) 4 rulers at $18 each
    • b) 2 books at $35 each
    • c) 3 pens at $20 each
    • d) 5 erasers at $12 each

  5. 5.A book costs $135 and you pay with $200. How much change do you get? Give just the number.

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

    • $145
    • $450
    • $54
    • $405
    • $45

  7. 7.A juice costs $24.50 and a sandwich costs $35.50. What do they cost together? Give just the number.

  8. 8.A pen costs $18 and a notebook costs $25. What do the two cost together? Give just the number.

Money problems · Year 4 Maths · www.arenapublications.com/learn

Year 4 Maths · 12 of 17

Perimeter: once round the outside

Find the perimeter of any straight-sided shape by adding the lengths of its sides, and work backwards to a missing side.

Before you start

An L-shaped garden, with every side drawn as its own strip. Find all of them, and count how many there are.

123456
  1. 1. The top side
  2. 2. The short side going down
  3. 3. The step across
  4. 4. The long side going down
  5. 5. The bottom side
  6. 6. The tall side up the left

Six sides, not four — the step in the middle adds two more, and leaving one of those out is the commonest way a perimeter goes wrong.

  1. 1.Every side of every shape here is 6 centimetres long. Match each regular shape to its perimeter.

    • Triangle
    • Square
    • Pentagon
    • Hexagon
    • Octagon
    • 36
    • 48
    • 30
    • 24
    • 18

  2. 2.Every length here is in centimetres. Which shape has the largest perimeter?

    • a) A triangle with sides 7, 7 and 7
    • b) A regular pentagon of side 5
    • c) A rectangle 8 by 3
    • d) A square of side 6

  3. 3.A four-sided shape has sides of 3 cm, 7 cm, 4 cm and 9 cm. What is its perimeter, in centimetres? Give just the number.

  4. 4.A regular hexagon has sides of 5 cm. What is its perimeter, in centimetres? Give just the number.

  5. 5.Every length here is in centimetres. Sort each shape by whether its perimeter is below 30 or above 30.

    Groups: Perimeter below 30 · Perimeter above 30

    • A rectangle 10 by 4
    • A regular pentagon of side 7
    • A regular hexagon of side 6
    • A rectangle 9 by 7
    • A triangle with sides 8, 9 and 10
    • A square of side 6

  6. 6.A square has a perimeter of 32 cm. How long is each side, in centimetres? Give just the number.

  7. 7.A triangle has a perimeter of 24 cm. Two of its sides are 9 cm and 7 cm. How long is the third side, in centimetres? Give just the number.

  8. 8.A triangle has sides of 6 cm, 8 cm and 5 cm. What is its perimeter, in centimetres? Give just the number.

Perimeter: once round the outside · Year 4 Maths · www.arenapublications.com/learn

Year 4 Maths · 13 of 17

Area by counting squares

Measure the area of a shape on squared paper by counting the squares it covers, including half squares.

Before you start

Three shapes sit on the same grid of squares. Count the squares under each one and compare what you find with how big each shape looks.

123
  1. 1. Shape A
  2. 2. Shape B
  3. 3. Shape C

Shape B is the tallest and Shape C is the widest, but neither of those is what decides the area — only the count of squares does.

  1. 1.Two shapes look completely different, but each covers 12 squares. What can you say about them?

    • a) You cannot compare their areas
    • b) Their areas are the same
    • c) The taller one has the larger area
    • d) The wider one has the larger area

  2. 2.A rectangle on squared paper is 9 squares across and 5 squares down. How many squares does it cover?

  3. 3.Match each rectangle to the number of squares it covers.

    • 2 across and 3 down
    • 3 across and 3 down
    • 4 across and 5 down
    • 6 across and 6 down
    • 9
    • 36
    • 20
    • 6

  4. 4.A rectangle on squared paper is 7 squares across and 4 squares down. How many squares does it cover?

  5. 5.A shape drawn on squared paper covers 8 full squares in its upper part and 6 full squares in its lower part. What is its area, in squares?

  6. 6.An L-shape is made of a rectangle 5 squares by 3 squares joined to a rectangle 2 squares by 2 squares. How many squares does it cover altogether?

  7. 7.A rectangle covers 24 squares and is 6 squares across. How many squares tall is it?

  8. 8.Which rectangle covers the most squares?

    • a) 2 across and 8 down
    • b) 3 across and 6 down
    • c) 4 across and 4 down
    • d) 5 across and 3 down

Area by counting squares · Year 4 Maths · www.arenapublications.com/learn

Year 4 Maths · 14 of 17

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.How many lines of symmetry does a regular pentagon have?

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

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

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

    Groups: Has a line of symmetry · Has none

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

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

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

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

  7. 7.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
    • 5
    • 3
    • 1
    • 0
    • 2

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

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

Line symmetry · Year 4 Maths · www.arenapublications.com/learn

Year 4 Maths · 15 of 17

Symmetry

Count lines of symmetry, find the order of rotational symmetry, and work out the smallest turn that leaves a shape looking the same.

  1. 1.How many lines of symmetry does an equilateral triangle have?

  2. 2.Which of these has rotational symmetry of order 2 but no line of symmetry at all?

    • a) A square
    • b) The letter S
    • c) The letter A
    • d) An equilateral triangle

  3. 3.How many lines of symmetry does a square have?

  4. 4.Which capital letter has exactly one line of symmetry?

    • a) S
    • b) N
    • c) A
    • d) H

  5. 5.A shape has rotational symmetry of order 5. What is the smallest turn that leaves it looking the same, in degrees?

  6. 6.How many lines of symmetry does a regular hexagon have?

  7. 7.Match each shape to the number of lines of symmetry it has.

    • Scalene triangle
    • Isosceles triangle
    • Rectangle that is not a square
    • Equilateral triangle
    • Square
    • 3
    • 0
    • 2
    • 1
    • 4

  8. 8.Sort each shape by whether it has any line of symmetry at all.

    Groups: Has at least one line of symmetry · Has no line of symmetry

    • Parallelogram that is not a rhombus or a rectangle
    • Scalene triangle
    • The letter Z
    • Square
    • Rhombus
    • Regular pentagon

Symmetry · Year 4 Maths · www.arenapublications.com/learn

Year 4 Maths · 16 of 17

Reading bar charts

Read a bar chart, use its scale to turn a bar height into a number, and compare the bars.

  1. 1.On a bar chart each square of the scale stands for 2 children. A bar stands for 18 children. How many squares tall is it?

  2. 2.A chart shows 22 visitors on Monday, 15 on Tuesday, 30 on Wednesday and 18 on Thursday. Sort each day by whether it had fewer or more than 20 visitors.

    Groups: Fewer than 20 · More than 20

    • Tuesday
    • Monday
    • Wednesday
    • Thursday

  3. 3.On a bar chart one square of the scale stands for 10 people. A bar is four and a half squares tall. How many people does it stand for?

    • a) 50
    • b) 40
    • c) 410
    • d) 45

  4. 4.A chart shows 22 visitors on Monday, 15 on Tuesday, 30 on Wednesday and 18 on Thursday. Put the days in order, fewest visitors first.

    • Wednesday
    • Thursday
    • Monday
    • Tuesday

  5. 5.A bar chart shows 9, 14, 6 and 11 visitors across four days. How many visitors were there altogether?

  6. 6.Why does a bar chart need a scale up the side?

    • a) So that the chart has a title
    • b) So that every bar is the same width
    • c) So that the bars look neat
    • d) So that the height of a bar can be read as a number

  7. 7.On a bar chart each square of the scale stands for 5 books. A bar is 7 squares tall. How many books does it stand for?

  8. 8.On this chart each square of the scale stands for 4 cars. Match each bar height to the number of cars it shows.

    • 2 squares
    • 3 squares
    • 5 squares
    • 7 squares
    • 8
    • 28
    • 12
    • 20

Reading bar charts · Year 4 Maths · www.arenapublications.com/learn

Year 4 Maths · 17 of 17

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.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

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

  3. 3.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.

    • Monday
    • Tuesday
    • Thursday
    • Wednesday

  4. 4.Two of these bars are drawn already. Read how tall they are, then draw the other two.

    Some bars are drawn for you. Draw the rest.

    Cricket40
    Football30
    Hockey20
    Tennis50
    Each line up the side is worth 10.0102030405060CricketFootballHockeyTennis

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

  6. 6.Draw a pictograph of the cars counted in a car park. One symbol is not one car — check the key.

    Draw the symbols for every row of the table.

    Red40
    Blue20
    White60
    Each symbol stands for 20.RedBlueWhite

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

  8. 8.A shop sold 14 pens on Monday, 9 on Tuesday, 21 on Wednesday and 17 on Thursday. Sort each day by whether it sold fewer or more than 15 pens.

    Groups: Fewer than 15 pens · More than 15 pens

    • Thursday
    • Tuesday
    • Monday
    • Wednesday

Pictographs and bar graphs · Year 4 Maths · www.arenapublications.com/learn

Answer keys — Year 4 Maths

In the same order as the worksheets.

Multiplying two digits by one

  1. 1. 1. 14 × 3 2. 21 × 4 3. 33 × 5 4. 26 × 8
  2. 2. 23 × 4 → Below 200; 36 × 3 → Below 200; 47 × 5 → Above 200; 52 × 6 → Above 200; 18 × 7 → Below 200; 29 × 8 → Above 200
  3. 3. d) 20 × 5 + 4 × 5
  4. 4. 405
  5. 5. 126
  6. 6. 312
  7. 7. 128
  8. 8. 92

Equivalent fractions

  1. 1. 1/4 → 3/12; 2/5 → 4/10; 3/8 → 6/16; 5/6 → 10/12
  2. 2. d) 2/6
  3. 3. they show the same amount
  4. 4. 6
  5. 5. 4/6 → The same as 2/3; 3/5 → Not the same as 2/3; 10/15 → The same as 2/3; 5/8 → Not the same as 2/3; 8/12 → The same as 2/3; 2/5 → Not the same as 2/3
  6. 6. 20
  7. 7. a) 4/6
  8. 8. a) 1/2

Numbers up to six digits

  1. 1. a) 0
  2. 2. c) 4 ten thousands
  3. 3. 90000
  4. 4. 47000
  5. 5. 47400
  6. 6. 60
  7. 7. b) 99909
  8. 8. 98760 → Five digits or fewer; 100001 → Six digits; 87654 → Five digits or fewer; 234000 → Six digits; 99999 → Five digits or fewer; 150000 → Six digits

Decimal place value

  1. 1. b) 0.60
  2. 2. 0.35 → 0.3; 0.53 → 0.03; 3.5 → 3; 0.053 → 0.003
  3. 3. a) 8
  4. 4. a) 6 hundredths
  5. 5. 1. 2.03 2. 2.3 3. 2.31 4. 2.4
  6. 6. a) 0
  7. 7. a) 0.5
  8. 8. 1. 0.1 2. 0.11 3. 0.2 4. 0.21

Knowing our numbers

  1. 1. 2568
  2. 2. 9741
  3. 3. b) 30099
  4. 4. 39999
  5. 5. 4623 → 4620; 4627 → 4630; 4638 → 4640; 4611 → 4610; 4646 → 4650
  6. 6. 5120 → Closer to 5000; 5890 → Closer to 6000; 5499 → Closer to 5000; 5501 → Closer to 6000; 5045 → Closer to 5000; 5750 → Closer to 6000
  7. 7. 1. 9899 2. 9989 3. 98099 4. 98909 5. 98990
  8. 8. 4700

6 times table

  1. 1. 54
  2. 2. b) 24
  3. 3. 42
  4. 4. b) 48
  5. 5. 66
  6. 6. d) 6 × 9
  7. 7. 18
  8. 8. 6 × 2 → 12; 6 × 5 → 30; 6 × 8 → 48; 6 × 10 → 60

7 times table

  1. 1. 42
  2. 2. 7 × 2 → 14; 7 × 5 → 35; 7 × 6 → 42; 7 × 10 → 70
  3. 3. c) 49
  4. 4. 21
  5. 5. d) 56
  6. 6. 28
  7. 7. 84
  8. 8. 63

8, 9 and 10 times tables

  1. 1. 56
  2. 2. 1. 8 × 3 2. 9 × 3 3. 10 × 3 4. 8 × 6
  3. 3. a) 81
  4. 4. 36
  5. 5. 9 × 3 → 27; 9 × 5 → 45; 9 × 7 → 63; 9 × 8 → 72
  6. 6. 120
  7. 7. 54
  8. 8. 40

Patterns and tiling

  1. 1. 60
  2. 2. 15
  3. 3. 1. A scalene triangle 2. An isosceles triangle 3. A rectangle that is not a square 4. An equilateral triangle 5. A square
  4. 4. Square → Tiles with no gaps; Regular hexagon → Tiles with no gaps; Equilateral triangle → Tiles with no gaps; Regular pentagon → Leaves gaps; Circle → Leaves gaps; Regular octagon → Leaves gaps
  5. 5. 32
  6. 6. c) A regular hexagon
  7. 7. Square → 4; Equilateral triangle → 3; Rectangle that is not a square → 2; Isosceles triangle → 1; Scalene triangle → 0
  8. 8. a) Green

Time and how long things last

  1. 1. a) 8:25
  2. 2. 45
  3. 3. A walk of 25 minutes → Less than an hour; A film of 90 minutes → More than an hour; A lesson of 45 minutes → Less than an hour; A train journey of 3 hours → More than an hour; A swim of 55 minutes → Less than an hour; A match of 2 hours → More than an hour
  4. 4.
    • 3:45
    • 3.45
    • quarter to four
    • 3:45 pm
  5. 5. b) 2 hours
  6. 6. 12
  7. 7. 180
  8. 8.
    • 7:40
    • 7.40
    • twenty to eight
    • 7:40 am

Money problems

  1. 1. 9
  2. 2. 325
  3. 3. 219
  4. 4. a) 4 rulers at $18 each
  5. 5. 65
  6. 6. 1. $45 2. $54 3. $145 4. $405 5. $450
  7. 7. 60
  8. 8. 43

Perimeter: once round the outside

  1. 1. Triangle → 18; Square → 24; Pentagon → 30; Hexagon → 36; Octagon → 48
  2. 2. b) A regular pentagon of side 5
  3. 3. 23
  4. 4. 30
  5. 5. A square of side 6 → Perimeter below 30; A rectangle 10 by 4 → Perimeter below 30; A rectangle 9 by 7 → Perimeter above 30; A regular pentagon of side 7 → Perimeter above 30; A triangle with sides 8, 9 and 10 → Perimeter below 30; A regular hexagon of side 6 → Perimeter above 30
  6. 6. 8
  7. 7. 8
  8. 8. 19

Area by counting squares

  1. 1. b) Their areas are the same
  2. 2. 45
  3. 3. 2 across and 3 down → 6; 3 across and 3 down → 9; 4 across and 5 down → 20; 6 across and 6 down → 36
  4. 4. 28
  5. 5. 14
  6. 6. 19
  7. 7. 4
  8. 8. b) 3 across and 6 down

Line symmetry

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

Symmetry

  1. 1. 3
  2. 2. b) The letter S
  3. 3. 4
  4. 4. c) A
  5. 5. 72
  6. 6. 6
  7. 7. Scalene triangle → 0; Isosceles triangle → 1; Rectangle that is not a square → 2; Equilateral triangle → 3; Square → 4
  8. 8. Square → Has at least one line of symmetry; Scalene triangle → Has no line of symmetry; Rhombus → Has at least one line of symmetry; Parallelogram that is not a rhombus or a rectangle → Has no line of symmetry; Regular pentagon → Has at least one line of symmetry; The letter Z → Has no line of symmetry

Reading bar charts

  1. 1. 9
  2. 2. Monday → More than 20; Tuesday → Fewer than 20; Wednesday → More than 20; Thursday → Fewer than 20
  3. 3. d) 45
  4. 4. 1. Tuesday 2. Thursday 3. Monday 4. Wednesday
  5. 5. 40
  6. 6. d) So that the height of a bar can be read as a number
  7. 7. 35
  8. 8. 2 squares → 8; 3 squares → 12; 5 squares → 20; 7 squares → 28

Pictographs and bar graphs

  1. 1. 1 — Monday
  2. 2. 7
  3. 3. 1. Tuesday 2. Monday 3. Thursday 4. Wednesday
  4. 4. Cricket 40 (given), Football 30, Hockey 20 (given), Tennis 50
  5. 5. 35
  6. 6. Red 2 symbols, Blue 1 symbol, White 3 symbols
  7. 7. 40
  8. 8. Monday → Fewer than 15 pens; Tuesday → Fewer than 15 pens; Wednesday → More than 15 pens; Thursday → More than 15 pens

Year 4 Maths · www.arenapublications.com/learn