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Cambridge Primary Maths: Stage 5

Stage 5 of the Cambridge Primary Mathematics (0096) curriculum framework, usually Year 5 (ages 9 to 10). Here is what each part asks, a practice question for each, and the mistakes that cost the most marks.

Practise Stage 5 as a game

The 49 parts of Stage 5

Each part with one practice question, made by the same engine your child plays.

Counting and sequences

Count on and back in constant steps, through zero

What comes next?
25, 17, 9, 1, …

  1. −8
  2. 7
  3. −7
  4. 9
Show the answer

−7. The numbers go down in 8s, past zero. 1 − 8 = −7.

Symbols standing for two unknowns in addition and subtraction

△ + □ = 12 and △ − □ = 8.
What number is △?

  1. 10
  2. 8
  3. 12
  4. 2
Show the answer

10. △ is the bigger one. Adding the two facts: △ + △ = 20, so △ = 10 (and □ = 2).

Find any term of a linear sequence by multiplying

5, 9, 13, 17, …
What is the 10th term?

  1. 21
  2. 45
  3. 40
  4. 41
Show the answer

41. It goes up in 4s. 10th term = 5 + 9 × 4 = 41.

The spatial pattern of square and triangular numbers

Which of these is a TRIANGULAR number?

  1. 9
  2. 25
  3. 10
  4. 49
Show the answer

10. Triangular numbers make a triangle of dots: 3, 6, 10, 15, 21, 28...

Integers and powers

Estimate, add and subtract integers, one of them negative

The temperature is 8°C.
It falls by 9°C. What is it now?

  1. 1°C
  2. −17°C
  3. 17°C
  4. −1°C
Show the answer

−1°C. Count down 9 from 8: you pass 0 and reach −1°C.

Choose the law of arithmetic that simplifies a calculation

Which is equal to 4 × 21?

  1. 4 × 20 + 4 × 1
  2. 4 + 20 × 1
  3. 4 × 20 × 1
  4. 4 × 20 + 1
Show the answer

4 × 20 + 4 × 1. Split 21 into 20 + 1 and multiply each part (the distributive law): 4 × 20 + 4 × 1 = 80 + 4 = 84.

The four operations follow a set order

30 − 12 ÷ 3 = ?

  1. 27
  2. 18
  3. 26
  4. 6
Show the answer

26. Divide first: 12 ÷ 3 = 4. Then 30 − 4 = 26.

Estimate and multiply numbers up to 1000 by 1-digit or 2-digit numbers

Which is the best ESTIMATE of 173 × 17?

  1. 40 000
  2. 220
  3. 4 000
  4. 400
Show the answer

4 000. Round each number: 173 ≈ 200 and 17 ≈ 20. 200 × 20 = 4 000, so the answer is about 4 000.

Estimate and divide numbers up to 1000 by a 1-digit number

10 ÷ 3 = ?

  1. 3 r 1
  2. 3 r 2
  3. 2 r 1
  4. 4 r 1
Show the answer

3 r 1. 3 × 3 = 9, and 10 − 9 = 1 left over.

Prime and composite numbers

Which of these is a prime number?

  1. 33
  2. 9
  3. 5
  4. 51
Show the answer

5. 5 has exactly two factors: 1 and 5.

Tests of divisibility by 4 and 8

Which number is divisible by 8?

  1. 906
  2. 908
  3. 132
  4. 728
Show the answer

728. A number divides by 8 when you can halve it three times and stay whole. 728 ÷ 8 = 91.

Recognise square numbers from 1 to 100

What is 7²?

  1. 49
  2. 42
  3. 56
  4. 14
Show the answer

49. 7² means 7 × 7 = 49.

Place value, ordering and rounding

The value of each digit in decimals: tenths and hundredths

What is the value of the 9 in 5.92?

  1. 9
  2. 0.09
  3. 90
  4. 0.9
Show the answer

0.9. The 9 is in the tenths place, so it is worth 9 tenths: 0.9.

Multiply and divide whole numbers by 10, 100 and 1000

0.64 × 1,000 = ?

  1. 640
  2. 64
  3. 6.4
  4. 64000
Show the answer

640. Multiplying by 1,000 moves each digit 3 places to the left.

Multiply and divide decimals by 10 and 100

0.65 × 100 = ?

  1. 6500
  2. 650
  3. 65
  4. 0.65
Show the answer

65. Multiplying by 100 moves each digit 2 places to the left.

Make, split and regroup numbers, including decimals

3.73 = 3 + ? tenths + 3 hundredths

  1. 70
  2. 7
  3. 4
  4. 3
Show the answer

7. The digit after the point is the tenths: 7.

Round numbers with one decimal place to the nearest whole number

Round 27.4 to the nearest whole number.

  1. 30
  2. 27
  3. 28
  4. 29
Show the answer

27. 27.4 is between 27 and 28. The tenths digit is 4, so it rounds down to 27.

Fractions, decimals, percentages, ratio and proportion

A fraction as a division, including tenths and hundredths

Which fraction is the same as 2 ÷ 3?

  1. 2/5
  2. 2/3
  3. 3/2
  4. 1/3
Show the answer

2/3. A fraction IS a division: the top divided by the bottom. 2 ÷ 3 = 2/3.

Proper fractions as operators

What is 8/10 of 30?

  1. 3
  2. 240
  3. 24
  4. 22
Show the answer

24. 30 ÷ 10 = 3. Then 3 × 8 = 24.

Improper fractions and mixed numbers can be equal

Write 1 1/2 as an improper fraction.

  1. 1
  2. 3/2
  3. 2/3
  4. 5/2
Show the answer

3/2. 1 wholes are 1 × 2 = 2 2ths. Add the 1: 3/2.

Proper fractions, one-place decimals and percentages can be equal

Write 6/10 as a decimal.

  1. 6
  2. 0.06
  3. 0.6
  4. 1.6
Show the answer

0.6. 6 tenths is 0.6.

Add and subtract fractions: same denominator, or one a multiple of the other

6/8 + 1/8 = ?
(simplest form)

  1. 7/16
  2. 7/8
  3. 1
  4. 3/4
Show the answer

7/8. Same denominator, so add the tops: 7/8.

Multiply and divide unit fractions by a whole number

1/2 ÷ 2 = ?

  1. 1/5
  2. 1/4
  3. 1
  4. 1/2
Show the answer

1/4. Cutting one 2th into 2 equal pieces makes each piece 2 times smaller: 1/4.

Percentages of shapes; a percentage as a fraction out of 100

A shape is cut into 5 equal parts and 3 are shaded.
What percentage is shaded?

  1. 60%
  2. 30%
  3. 3%
  4. 40%
Show the answer

60%. 3/5 of the shape is shaded. As hundredths: 3/5 = 60/100 = 60%.

Compare and order one-place decimals, same-denominator fractions and percentages

Which statement is true?

  1. 9.7 < 1.6
  2. 1.6 = 9.7
  3. 1.6 < 9.7
  4. 1.6 > 9.7
Show the answer

1.6 < 9.7. Compare the whole numbers first, then the tenths. 9.7 is bigger than 1.6.

Add and subtract numbers with the same number of decimal places

3.41 − 1.94 = ?

  1. 1.47
  2. 2.47
  3. 1.37
  4. 1.48
Show the answer

1.47. Line up the decimal points: 3.41 − 1.94 = 1.47.

Multiply a number with one decimal place by a 1-digit number

3.1 × 2 = ?

  1. 6.2
  2. 6
  3. 7.2
  4. 0.62
Show the answer

6.2. 31 × 2 = 62. One decimal place, so 6.2.

Proportion compares part to whole; ratio compares part to part

A bag has 2 red and 3 blue counters.
What PROPORTION of the counters are red?

  1. 3/5
  2. 2/5
  3. 2/3
  4. 2:3
Show the answer

2/5. A proportion compares the part with the WHOLE: 2 red out of 5 counters altogether is 2/5.

Time

Time intervals shorter than one second

A stopwatch shows 10.05 seconds.
How many hundredths of a second is that?

  1. 1005
  2. 10
  3. 101
  4. 10050
Show the answer

1005. 1 second is 100 hundredths, so 10.05 s is 1005 hundredths.

Compare times across time zones

It is 10:00 in Kuala Lumpur.
Tokyo is 1 hour AHEAD.
What time is it in Tokyo?

  1. 11:00
  2. 12:00
  3. 23:00
  4. 09:00
Show the answer

11:00. Ahead means later, so add 1 hours: 11:00.

Time intervals that bridge through 60

A show starts at 9:40 and ends at 10:35.
How many minutes long is it?

  1. 5 min
  2. 55 min
  3. 60 min
  4. 65 min
Show the answer

55 min. From 9:40 to 10:35 is 55 minutes.

A time interval as a decimal or in mixed units

4.5 hours = ? minutes

  1. 290
  2. 240
  3. 450
  4. 270
Show the answer

270. 4 hours = 240 minutes, and 0.5 of an hour is 30 minutes. 240 + 30 = 270.

Geometrical reasoning, shapes and measurements

Classify and sketch isosceles, equilateral and scalene triangles

How many lines of symmetry does an isosceles triangle have?

  1. 3
  2. 0
  3. 2
  4. 1
Show the answer

1. An equilateral triangle has 3 lines of symmetry, an isosceles triangle has 1 (between its two equal sides), and a scalene triangle has none.

Same perimeter, different area, and the other way round

A rectangle is 6 cm by 3 cm.
Which rectangle has the SAME perimeter but a BIGGER area?

  1. 7 cm by 3 cm
  2. 5 cm by 4 cm
  3. 6 cm by 4 cm
  4. 7 cm by 2 cm
Show the answer

5 cm by 4 cm. The perimeter is 2 × (6 + 3) = 18 cm, so the length and the width must still add up to 9. 5 cm by 4 cm does, and its area is 20 cm² against 18 cm². (7 cm by 2 cm keeps the perimeter too, but its area is smaller: the nearer to a square, the more area.)

Perimeter and area of compound shapes made of rectangles

The questions for this part come with a picture or are played as a game, so they are best tried in Huh Lab.

Identify and sketch 3D shapes in different orientations

The questions for this part come with a picture or are played as a game, so they are best tried in Huh Lab.

Different nets for a cube

The questions for this part come with a picture or are played as a game, so they are best tried in Huh Lab.

Complete symmetrical patterns

The questions for this part come with a picture or are played as a game, so they are best tried in Huh Lab.

Estimate, compare and classify angles: acute, right, obtuse, reflex

An angle of 90° is…

  1. obtuse
  2. acute
  3. right angle
  4. reflex
Show the answer

right angle. Acute is less than 90°. Obtuse is between 90° and 180°. Reflex is more than 180°.

Angles on a straight line add to 180°; find the missing one

The questions for this part come with a picture or are played as a game, so they are best tried in Huh Lab.

Position and transformation

Compare the relative position of coordinates

The questions for this part come with a picture or are played as a game, so they are best tried in Huh Lab.

Plot points to form lines and shapes in the first quadrant

The questions for this part come with a picture or are played as a game, so they are best tried in Huh Lab.

Translate 2D shapes on a square grid

The questions for this part come with a picture or are played as a game, so they are best tried in Huh Lab.

Reflect 2D shapes in horizontal and vertical mirror lines to make patterns

The questions for this part come with a picture or are played as a game, so they are best tried in Huh Lab.

Statistics

Record and show data: Venn, Carroll, tally, frequency tables, bar charts, waffle diagrams, frequency diagrams, line graphs, dot plots

The questions for this part come with a picture or are played as a game, so they are best tried in Huh Lab.

Find and interpret the mode and the median

What is the median?
16, 7, 18, 4, 19

  1. 19
  2. 7
  3. 18
  4. 16
Show the answer

16. Put them in order: 4, 7, 16, 18, 19. The middle one is 16.

Interpret patterns within and between data sets

The questions for this part come with a picture or are played as a game, so they are best tried in Huh Lab.

Probability

Language of likelihood and risk, including equally likely outcomes

You roll a normal dice.
Game A: you LOSE if you roll 5 numbers: 1 to 5.
Game B: you LOSE if you roll a 6.
Which game is riskier?

  1. Game A
  2. They are equally risky
  3. You cannot tell with dice
  4. Game B
Show the answer

Game A. Losing in Game A is 5 out of 6, in Game B 1 out of 6. The more likely it is to lose, the riskier the game: Game A.

Some outcomes are equally likely, others more or less likely

A bag holds 1 red, 3 blue, 4 green, 6 yellow counters.
One is picked without looking.
Which colour is LEAST likely?

  1. blue
  2. yellow
  3. red
  4. green
Show the answer

red. There are fewer red counters (1) than any other colour, so red is the least likely.

The mistakes that cost the most marks

Huh Lab checks every wrong answer against known mistakes like these, and goes back to the step behind the one your child keeps making.

Reflects in the wrong direction

A reflection goes straight ACROSS the mirror line, never along it.

Slides the point instead of reflecting it

The image is the same distance from the mirror, on the OTHER side.

Gives the y-coordinate first

Along the corridor, THEN up the stairs: x comes before y.

Puts an answer in the wrong place value

Estimate first: 672 ÷ 24 is about 700 ÷ 25, so near 28, not 280.

Loses the negative sign

Use a number line: below zero the numbers keep counting, in the other direction.

Adds the denominators too

Quarters plus quarters are still quarters. Only the tops are added.

Mixes up perimeter and area

Perimeter is the fence around it. Area is the grass inside.

Takes a triangular number for a square one (or the other way)

Try to make it as a square of dots, then as a triangle: only one of them works.

Other Cambridge Primary Maths stages

Stage 1Year 1, ages 5 to 6 Stage 2Year 2, ages 6 to 7 Stage 3Year 3, ages 7 to 8 Stage 4Year 4, ages 8 to 9 Stage 6Year 6, ages 10 to 11

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