Term pack
Year 5 Maths
Name: ________________________
Skills in this pack
- Numbers up to six digits
- Multiplying and dividing larger numbers
- Factor pairs and multiples
- Unlike fractions and mixed numbers
- Decimal place value
- Adding and subtracting decimals
- How much for one?
- Number patterns
- Area and perimeter
- Volume with unit cubes
- Angles and the protractor
- Nets of solids
- Averages
- Bar graphs with scales
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Year 5 Maths · 1 of 14
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.
Every one of those steps is ten thousand. A six-digit number is a whole line like this one and then more.
1.What number is one more than 89999?
2.Put these in order, smallest first.
- 48520
- 84205
- 84025
- 48250
3.Round 47382 to the nearest thousand.
4.Sort each number by how many digits it has.
Groups: Five digits or fewer · Six digits
- 87654
- 234000
- 98760
- 99999
- 100001
- 150000
5.Round 152649 to the nearest hundred.
6.In 348617, what is the 4 worth?
- a) 4 ten thousands
- b) 4 thousands
- c) 4 hundred thousands
- d) 4 hundreds
7.Which digit is in the ten thousands place in 605218?
- a) 5
- b) 6
- c) 0
- d) 2
8.What is the value of the 7 in 273481?
Numbers up to six digits · Year 5 Maths · www.arenapublications.com/learn
Year 5 Maths · 2 of 14
Multiplying and dividing larger numbers
Multiply by a two-digit number, divide with a remainder, and multiply or divide by 10, 100 and 1000.
1.7200 ÷ 10 = ?
2.23 × 14 = ?
3.What is the remainder when 47 is divided by 6?
4.Which of these is 48 × 25?
- a) 1250
- b) 960
- c) 1000
- d) 1200
5.125 × 12 = ?
6.96 ÷ 8 = ?
7.56 × 1000 = ?
8.Work each one out, then put them in order, smallest answer first.
- 12 × 12
- 18 × 10
- 23 × 9
- 15 × 11
Multiplying and dividing larger numbers · Year 5 Maths · www.arenapublications.com/learn
Year 5 Maths · 3 of 14
Factor pairs and multiples
Find the factor pairs of a number, list its multiples, and spot factors and multiples two numbers share.
1.What is the smallest number that is a multiple of both 4 and 6?
2.What is the fifth multiple of 8?
3.What is the largest number that is a factor of both 12 and 18?
4.20 tiles are laid out in equal rows of 4. How many rows are there?
5.Exactly one number on this line is a multiple of 9. Tap it.
Mark the line with an X.
6.Which of these numbers is a factor of 24?
- a) 8
- b) 9
- c) 7
- d) 5
7.Put these numbers in order, starting with the one that has the fewest factors.
- 7
- 9
- 12
- 24
8.12 = 3 × ? What is the missing factor?
Factor pairs and multiples · Year 5 Maths · www.arenapublications.com/learn
Year 5 Maths · 4 of 14
Unlike fractions and mixed numbers
Add and subtract fractions with different denominators, and swap between mixed numbers and improper fractions.
1.Put these fractions in order, smallest first.
- 1/2
- 1/3
- 1/6
- 2/3
2.A film lasts 3 1/2 hours, and 1 1/4 hours of it have been watched. How much is left? Write your answer as a mixed number.
3.Three eighths of a cake are eaten in the morning and two eighths in the afternoon. What fraction of the cake has been eaten? Write your answer as a fraction.
4.3/4 - 1/8 = ? Write your answer as a fraction.
5.1/2 + 1/5 = ? Write your answer as a fraction.
6.2/3 + 1/6 = ? Write your answer as a fraction.
7.One job takes 1 1/4 hours and another takes 1/2 an hour. How long do they take altogether? Write your answer as a mixed number.
8.Write 7/4 as a mixed number.
Unlike fractions and mixed numbers · Year 5 Maths · www.arenapublications.com/learn
Year 5 Maths · 5 of 14
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.
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.One point on this line is 4 tenths and 7 hundredths. Which point is it?
Mark the line with an X.
2.In 3.47, what is the 4 worth?
- a) 4 hundredths
- b) 4 tenths
- c) 4 tens
- d) 4 ones
3.What is 7.8 rounded to the nearest whole number?
- a) 7
- b) 80
- c) 7.5
- d) 8
4.Put these in order, smallest first.
- 0.75
- 1.2
- 0.09
- 0.4
5.How many thousandths are the same as 0.46?
6.Put these in order, smallest first.
- 2.31
- 2.03
- 2.3
- 2.4
7.Put these in order, smallest first.
- 0.1
- 0.11
- 0.21
- 0.2
8.Match each number to what its 3 is worth.
- 0.35
- 0.53
- 3.5
- 0.053
- 0.03
- 3
- 0.003
- 0.3
Decimal place value · Year 5 Maths · www.arenapublications.com/learn
Year 5 Maths · 6 of 14
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.
Ten hundredths make one tenth. That is why 0.5 is far bigger than 0.05, even though both are written with a 5.
1.4.6 + 2.35 = ?
2.2.5 + 1.3 = ?
3.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
- 0.6
- 0.75
4.5.8 - 2.3 = ?
5.7.2 - 3.45 = ?
6.6 - 0.4 = ?
7.One jug holds 1.5 litres and another holds 0.75 litres. How much do they hold together, in litres? Give just the number.
8.Work each one out, then put them in order, smallest answer first.
- 1.2 + 0.3
- 2.5 - 0.4
- 3.6 - 0.7
- 1.9 + 0.5
Adding and subtracting decimals · Year 5 Maths · www.arenapublications.com/learn
Year 5 Maths · 7 of 14
How much for one?
Find what one thing costs or weighs, then use it to work out any number of them.
1.4 pens cost $60. What does 1 pen cost? Give just the number.
2.6 identical books weigh 18 kg altogether. What does 1 book weigh, in kilograms? Give just the number.
3.A machine makes 120 bottles in 4 hours. How many does it make in 9 hours?
4.Work out what one costs in each deal, then sort the deals.
Groups: One costs less than $10 · One costs $10 or more
- 4 for $80
- 6 for $42
- 3 for $27
- 2 for $30
- 4 for $24
- 5 for $60
5.4 pens cost $60. What do 7 pens cost? Give just the number.
6.Which of these is better value?
- a) There is no way to tell
- b) 8 pencils for $40
- c) They cost the same each
- d) 5 pencils for $30
7.9 apples cost $72. What does one apple cost?
- a) 9
- b) 8
- c) 6
- d) 7
8.1 notebook costs $25. What do 6 notebooks cost? Give just the number.
How much for one? · Year 5 Maths · www.arenapublications.com/learn
Year 5 Maths · 8 of 14
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.
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.What is the rule for 2, 5, 8, 11, 14?
- a) Multiply by 2
- b) Add 4
- c) Add 3
- d) Add 2
2.What comes next? 1, 4, 9, 16, ?
3.What comes next? 100, 90, 81, 73, ?
4.What comes next? 3, 7, 11, 15, ?
5.Sort each pattern by what its rule does.
Groups: Adds the same amount each time · Doubles each time
- 1, 2, 4, 8
- 4, 8, 16, 32
- 2, 4, 6, 8
- 3, 6, 12, 24
- 7, 12, 17, 22
- 5, 10, 15, 20
6.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
- Add 2
- Multiply by 3
- Add 10
7.What comes next? 1, 1, 2, 3, 5, 8, ?
8.A pattern of squares grows: 1 square, then 4, then 9. How many squares are in the next step?
- a) 12
- b) 16
- c) 20
- d) 14
Number patterns · Year 5 Maths · www.arenapublications.com/learn
Year 5 Maths · 9 of 14
Area and perimeter
Work out the area and perimeter of a rectangle.
1.Every rectangle here is measured in centimetres. Which one has the largest perimeter?
- a) 3 by 9
- b) 4 by 7
- c) 2 by 6
- d) 5 by 5
2.A rectangle is 8 m by 4 m. What is its area, in square metres?
3.Every rectangle here is measured in centimetres. Match each rectangle to its area, in square centimetres.
- 4 by 5
- 3 by 9
- 6 by 6
- 7 by 4
- 20
- 27
- 28
- 36
4.A rectangle is 5 cm long and 3 cm wide. What is its area, in square centimetres?
5.A rectangle is 8 m by 4 m. What is its perimeter, in metres?
6.Every rectangle here is measured in centimetres. Put them in order, smallest perimeter first.
- 5 by 4
- 4 by 3
- 2 by 3
- 8 by 3
7.A rectangle is 6 cm by 4 cm. Which point on the line is its perimeter, in centimetres?
Mark the line with an X.
8.Every rectangle here is measured in centimetres. Sort them by whether the area is below 30 square centimetres or above it.
Groups: Below 30 · Above 30
- 4 by 9
- 6 by 6
- 7 by 5
- 2 by 8
- 5 by 5
- 3 by 4
Area and perimeter · Year 5 Maths · www.arenapublications.com/learn
Year 5 Maths · 10 of 14
Volume with unit cubes
Find the volume of a box by counting the unit cubes that fill it.
1.A cuboid is built from 2 layers. Each layer is 6 cubes long and 2 cubes wide. How many cubes are there altogether?
2.A box is 5 cubes long, 2 cubes wide and 3 cubes tall. How many unit cubes fill it?
3.A cube measures 3 unit cubes along every edge. How many unit cubes is it built from?
- a) 27
- b) 81
- c) 9
- d) 18
4.A box is 4 cubes long, 3 cubes wide and 2 cubes tall. How many unit cubes fill it?
5.Match each box to the number of unit cubes that fill it.
- 2 by 2 by 2
- 2 by 3 by 2
- 3 by 3 by 2
- 4 by 3 by 2
- 5 by 4 by 2
- 24
- 8
- 40
- 12
- 18
6.A cuboid is 6 cm long, 3 cm wide and 2 cm tall. What is its volume, in cubic centimetres? Give just the number.
7.Work out each box, then sort it by how many unit cubes it holds.
Groups: Fewer than 24 cubes · 24 cubes or more
- 2 by 2 by 4
- 4 by 4 by 2
- 5 by 5 by 1
- 1 by 3 by 6
- 3 by 4 by 2
- 2 by 2 by 5
8.A box holds 20 unit cubes in a single layer. Filled 4 layers deep, how many unit cubes does it hold?
Volume with unit cubes · Year 5 Maths · www.arenapublications.com/learn
Year 5 Maths · 11 of 14
Angles and the protractor
Name an angle as acute, right, obtuse or straight, and measure one with a protractor.
1.Three angles are drawn below. Tap the obtuse one.
Write the number of the part.
2.How many degrees are there in a right angle?
3.An angle measures 45°. What kind of angle is it?
- a) Straight
- b) Acute
- c) Right
- d) Obtuse
4.How many right angles make a full turn?
5.An angle is measured with a protractor. One arm reads 20 and the other reads 75. How many degrees is the angle?
6.Put these angles in order, smallest first.
- 25°
- 90°
- 170°
- 70°
- 135°
7.Match each angle to what it is called.
- 40°
- 90°
- 120°
- 180°
- Straight
- Right
- Obtuse
- Acute
8.How many degrees are there in a half turn?
Angles and the protractor · Year 5 Maths · www.arenapublications.com/learn
Year 5 Maths · 12 of 14
Nets of solids
Say which solid a net folds into, and which flat shapes a solid's net is made from.
Before you start
Here is a cube opened out flat. Find out which face of the finished cube each flat square folds up to become.
- 1. The top
- 2. The left-hand face
- 3. The front
- 4. The right-hand face
- 5. The back
- 6. The bottom
The front stays where it is and the other five fold up around it. Six squares and six faces, each appearing exactly once — a net with a square missing or a square repeated folds into nothing at all.
1.Match each solid to what its net is made of.
- Cube
- Cylinder
- Cone
- Square-based pyramid
- Triangular prism
- 6 squares
- 2 triangles and 3 rectangles
- 2 circles and 1 rectangle
- 1 square and 4 triangles
- 1 circle and 1 curved piece
2.A net has six rectangles and not one of them is a square. Write the name of the solid it folds into.
3.A net is made of two circles and one rectangle. Which solid does it fold into?
- a) Sphere
- b) Cylinder
- c) Cone
- d) Cube
4.A net is made of one circle and one curved piece. Which solid does it fold into?
- a) Cylinder
- b) Triangular prism
- c) Cuboid
- d) Cone
5.A cylinder is unfolded into its net. Write the name of the flat shape that appears twice in it.
6.The net of a square-based pyramid has four triangles and one square. How many faces will the pyramid have?
7.A net is made of one square and four triangles. Which solid does it fold into?
- a) Cylinder
- b) Square-based pyramid
- c) Cube
- d) Triangular prism
8.A net folds up into a cuboid. How many rectangles does the net have?
Nets of solids · Year 5 Maths · www.arenapublications.com/learn
Year 5 Maths · 13 of 14
Averages
Find the average of a small set of numbers by sharing the total out equally.
1.Three parcels weigh 2 kg, 5 kg and 8 kg. What is their average mass, in kilograms? Give just the number.
2.Work out each average, then sort it by size.
Groups: Average is less than 10 · Average is 10 or more
- 8, 10, 12
- 2, 4, 6
- 9, 11, 13
- 5, 6, 7
- 14, 16, 18
- 1, 2, 3
3.Find the average of 10, 12, 14 and 16.
4.Work out each average, then put the sets in order, smallest average first.
- 1, 2, 3
- 2, 4, 6
- 5, 6, 7
- 8, 10, 12
5.Which of these sets of numbers has an average of 5?
- a) 4, 6, 8
- b) 2, 4, 6
- c) 3, 5, 8
- d) 1, 5, 9
6.Five numbers have an average of 6. A sixth number, 12, is added to the set. What happens to the average?
- a) It goes down
- b) It becomes 12
- c) It goes up
- d) It stays the same
7.A player scores 20, 30 and 40 points in three games. What is the average score?
8.Two numbers have an average of 9. One of them is 6. What is the other?
Averages · Year 5 Maths · www.arenapublications.com/learn
Year 5 Maths · 14 of 14
Bar graphs with scales
Read values off a bar graph whose scale counts in steps of more than one, and choose a sensible scale of your own.
1.This bar graph shows how many people visited a library on four days. Tap the bar for the day with the fewest visitors.
Write the number of the part.
2.A bar graph's scale counts in fives. Match each bar to the number it shows.
- 2 lines up
- 3 lines up
- 5 lines up
- 8 lines up
- 12 lines up
- 40
- 10
- 25
- 15
- 60
3.A bar graph's scale counts in threes. A bar shows 21. How many lines tall is it?
4.A bar graph's scale counts in fours. Put these bars in order, shortest first.
- 3 lines up
- 7 lines up
- 2 lines up
- 5 lines up
5.A bar graph's scale counts in tens. A bar reaches exactly halfway between 30 and 40. What number does it show?
6.A bar graph's scale counts in twos. A bar is level with the seventh line above zero. What number does it show?
7.A bar graph has four bars, showing 60, 45, 30 and 25. What is the difference between the tallest bar and the shortest?
8.A bar graph has four bars, showing 60, 45, 30 and 25. What do the four bars add up to?
Bar graphs with scales · Year 5 Maths · www.arenapublications.com/learn
Answer keys — Year 5 Maths
In the same order as the worksheets.
Numbers up to six digits
- 1. 90000
- 2. 1. 48250 2. 48520 3. 84025 4. 84205
- 3. 47000
- 4. 98760 → Five digits or fewer; 100001 → Six digits; 87654 → Five digits or fewer; 234000 → Six digits; 99999 → Five digits or fewer; 150000 → Six digits
- 5. 152600
- 6. a) 4 ten thousands
- 7. c) 0
- 8. 70000
Multiplying and dividing larger numbers
- 1. 720
- 2. 322
- 3. 5
- 4. d) 1200
- 5. 1500
- 6. 12
- 7. 56000
- 8. 1. 12 × 12 2. 15 × 11 3. 18 × 10 4. 23 × 9
Factor pairs and multiples
- 1. 12
- 2. 40
- 3. 6
- 4. 5
- 5. 27
- 6. a) 8
- 7. 1. 7 2. 9 3. 12 4. 24
- 8. 4
Unlike fractions and mixed numbers
- 1. 1. 1/6 2. 1/3 3. 1/2 4. 2/3
- 2. 2 1/4
- 3. 5/8
- 4. 5/8
- 5. 7/10
- 6. 5/6
- 7. 1 3/4
- 8. 1 3/4
Decimal place value
- 1. 0.47
- 2. b) 4 tenths
- 3. d) 8
- 4. 1. 0.09 2. 0.4 3. 0.75 4. 1.2
- 5. 460
- 6. 1. 2.03 2. 2.3 3. 2.31 4. 2.4
- 7. 1. 0.1 2. 0.11 3. 0.2 4. 0.21
- 8. 0.35 → 0.3; 0.53 → 0.03; 3.5 → 3; 0.053 → 0.003
Adding and subtracting decimals
- 1. 6.95
- 2. 3.8
- 3. 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
- 4. 3.5
- 5. 3.75
- 6. 5.6
- 7. 2.25
- 8. 1. 1.2 + 0.3 2. 2.5 - 0.4 3. 1.9 + 0.5 4. 3.6 - 0.7
How much for one?
- 1. 15
- 2. 3
- 3. 270
- 4. 4 for $24 → One costs less than $10; 5 for $60 → One costs $10 or more; 3 for $27 → One costs less than $10; 2 for $30 → One costs $10 or more; 6 for $42 → One costs less than $10; 4 for $80 → One costs $10 or more
- 5. 105
- 6. b) 8 pencils for $40
- 7. b) 8
- 8. 150
Number patterns
- 1. c) Add 3
- 2. 25
- 3. 66
- 4. 19
- 5. 2, 4, 6, 8 → Adds the same amount each time; 3, 6, 12, 24 → Doubles each time; 5, 10, 15, 20 → Adds the same amount each time; 1, 2, 4, 8 → Doubles each time; 7, 12, 17, 22 → Adds the same amount each time; 4, 8, 16, 32 → Doubles each time
- 6. 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
- 7. 13
- 8. b) 16
Area and perimeter
- 1. a) 3 by 9
- 2. 32
- 3. 4 by 5 → 20; 3 by 9 → 27; 6 by 6 → 36; 7 by 4 → 28
- 4. 15
- 5. 24
- 6. 1. 2 by 3 2. 4 by 3 3. 5 by 4 4. 8 by 3
- 7. 20
- 8. 3 by 4 → Below 30; 5 by 5 → Below 30; 2 by 8 → Below 30; 6 by 6 → Above 30; 4 by 9 → Above 30; 7 by 5 → Above 30
Volume with unit cubes
- 1. 24
- 2. 30
- 3. a) 27
- 4. 24
- 5. 2 by 2 by 2 → 8; 2 by 3 by 2 → 12; 3 by 3 by 2 → 18; 4 by 3 by 2 → 24; 5 by 4 by 2 → 40
- 6. 36
- 7. 2 by 2 by 5 → Fewer than 24 cubes; 3 by 4 by 2 → 24 cubes or more; 1 by 3 by 6 → Fewer than 24 cubes; 4 by 4 by 2 → 24 cubes or more; 2 by 2 by 4 → Fewer than 24 cubes; 5 by 5 by 1 → 24 cubes or more
- 8. 80
Angles and the protractor
- 1. 3 — Angle C
- 2. 90
- 3. b) Acute
- 4. 4
- 5. 55
- 6. 1. 25° 2. 70° 3. 90° 4. 135° 5. 170°
- 7. 40° → Acute; 90° → Right; 120° → Obtuse; 180° → Straight
- 8. 180
Nets of solids
- 1. Cube → 6 squares; Cylinder → 2 circles and 1 rectangle; Cone → 1 circle and 1 curved piece; Square-based pyramid → 1 square and 4 triangles; Triangular prism → 2 triangles and 3 rectangles
- 2.
- cuboid
- rectangular prism
- 3. b) Cylinder
- 4. d) Cone
- 5.
- circle
- circles
- 6. 5
- 7. b) Square-based pyramid
- 8. 6
Averages
- 1. 5
- 2. 2, 4, 6 → Average is less than 10; 8, 10, 12 → Average is 10 or more; 1, 2, 3 → Average is less than 10; 9, 11, 13 → Average is 10 or more; 5, 6, 7 → Average is less than 10; 14, 16, 18 → Average is 10 or more
- 3. 13
- 4. 1. 1, 2, 3 2. 2, 4, 6 3. 5, 6, 7 4. 8, 10, 12
- 5. d) 1, 5, 9
- 6. c) It goes up
- 7. 30
- 8. 12
Bar graphs with scales
- 1. 2 — Tuesday
- 2. 2 lines up → 10; 3 lines up → 15; 5 lines up → 25; 8 lines up → 40; 12 lines up → 60
- 3. 7
- 4. 1. 2 lines up 2. 3 lines up 3. 5 lines up 4. 7 lines up
- 5. 35
- 6. 14
- 7. 35
- 8. 160
Year 5 Maths · www.arenapublications.com/learn