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Cambridge Primary Maths: Stage 6

Stage 6 of the Cambridge Primary Mathematics (0096) curriculum framework, usually Year 6 (ages 10 to 11). Here is what each part asks, a practice question for each, and the mistakes that cost the most marks.

Practise Stage 6 as a game

The 51 parts of Stage 6

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

Counting and sequences

Count on and back in constant steps, including fractions and decimals, through zero

What comes next?
2/3, 1, 4/3, 5/3, …

  1. 7/3
  2. 2
  3. 3/2
  4. 5/3
Show the answer

2. Count on in 3ths: 5/3 + 1/3 = 2 (a whole number).

Letters standing for quantities that vary

2n + 3 = 15
n = ?

  1. 13
  2. 9
  3. 6
  4. 12
Show the answer

6. Take away 3: 2n = 12. Then divide by 2: n = 6.

Find and use a position-to-term rule

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.

Generate terms of a sequence built on square numbers

What comes next?
25, 36, 49, 64, …

  1. 18
  2. 113
  3. 79
  4. 81
Show the answer

81. These are square numbers: 5², 6², 7², 8². Next is 9² = 81.

Integers and powers

Estimate, add and subtract integers

−2 − 2 = ?

  1. 0
  2. −5
  3. 4
  4. −4
Show the answer

−4. Start at −2 and count down 2 more: −4.

Use the laws of arithmetic and the order of operations to simplify

Work out 50 × 16 × 2 the easy way.

  1. 1610
  2. 802
  3. 1600
  4. 116
Show the answer

1600. Multiplying can be done in any order: 50 × 2 = 100 first, then 100 × 16 = 1600.

Brackets change the order of operations

(3 + 4) × 4 = ?

  1. 11
  2. 19
  3. 28
  4. 16
Show the answer

28. Brackets first: 3 + 4 = 7. Then 7 × 4 = 28.

Estimate and multiply numbers up to 10 000 by 1-digit or 2-digit numbers

Which is the best ESTIMATE of 436 × 22?

  1. 8 000
  2. 800
  3. 80 000
  4. 420
Show the answer

8 000. Round each number: 436 ≈ 400 and 22 ≈ 20. 400 × 20 = 8 000, so the answer is about 8 000.

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

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.

Common multiples and common factors

What is the highest common factor of 10 and 15?

  1. 30
  2. 5
  3. 1
  4. 10
Show the answer

5. 10 = 2 × 5 and 15 = 3 × 5. The biggest number that divides both is 5.

Tests of divisibility by 3, 6 and 9

Which number is divisible by 6?

  1. 732
  2. 476
  3. 278
  4. 908
Show the answer

732. A number divides by 6 when it is even AND its digits add up to a multiple of 3. 732 ÷ 6 = 122.

Recognise cube numbers from 1 to 125

Which of these is a cube number?

  1. 4
  2. 125
  3. 12
  4. 36
Show the answer

125. 125 = 5 × 5 × 5. The cube numbers up to 125 are 1, 8, 27, 64 and 125.

Place value, ordering and rounding

The value of each digit in decimals, to thousandths

What is the value of the digit 5 in 5.151?

  1. 0.005
  2. 0.5
  3. 5
  4. 0.05
Show the answer

0.05. After the point: tenths, hundredths, thousandths. The 5 is in the hundredths place, so it is worth 0.05.

Multiply and divide whole numbers and decimals 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.

Make, split and regroup numbers, including decimals to thousandths

How many hundredths are there in 1.57 altogether?

  1. 107
  2. 57
  3. 7
  4. 157
Show the answer

157. 1 ones is 100 hundredths, 5 tenths is 50 hundredths, and 7 more: 157.

Round numbers with two decimal places to the nearest tenth or whole number

Round 94.88 to the nearest whole number.

  1. 94
  2. 85
  3. 95
  4. 96
Show the answer

95. Look at the tenths digit, 8: it rounds up, so 94.88 becomes 95.

Fractions, decimals, percentages, ratio and proportion

A fraction as a division, proper and improper

Which fraction is the same as 7 ÷ 10?

  1. 3/10
  2. 10/7
  3. 7/10
  4. 7/17
Show the answer

7/10. A fraction IS a division: the top divided by the bottom. 7 ÷ 10 = 7/10.

Proper and improper fractions as operators

What is 4/5 of 20?

  1. 16
  2. 4
  3. 26
  4. 80
Show the answer

16. 20 ÷ 5 = 4. Then 4 × 4 = 16.

Write fractions in their simplest form

Write 25/30 in its simplest form.

  1. 5/7
  2. 21/26
  3. 5/6
  4. 6/5
Show the answer

5/6. Divide the top and bottom by their highest common factor, 5: 25 ÷ 5 = 5, 30 ÷ 5 = 6. 5/6 cannot be simplified any further.

Fractions, decimals to two places and percentages can be equal

Write 3/5 as a percentage.

  1. 40%
  2. 35%
  3. 15%
  4. 60%
Show the answer

60%. 3/5 = 60/100 = 60%.

Add and subtract fractions with different denominators

2/3 − 1/5 = ?
(simplest form)

  1. 1/2
  2. 13/15
  3. 7/15
  4. 1/15
Show the answer

7/15. Use 15 as the denominator: 10/15 − 3/15 = 7/15.

Multiply and divide proper fractions by whole numbers

3/4 ÷ 3 = ?
(simplest form)

  1. 1/2
  2. 3/7
  3. 9/4
  4. 1/4
Show the answer

1/4. Dividing by 3 makes each part 3 times smaller: 3/12, which is 1/4.

Percentages (1% and multiples of 5%) of shapes and whole numbers

What is 50% of 140?

  1. 50
  2. 35
  3. 70
  4. 90
Show the answer

70. 50% = 1/2. 1/2 of 140 is 70.

Compare and order decimals, fractions with different denominators and percentages

Which statement is true?

  1. 2/5 < 7/15
  2. 2/5 > 7/15
  3. 7/15 < 2/5
  4. 2/5 = 7/15
Show the answer

2/5 < 7/15. Make the denominators the same: 2/5 = 6/15. Now compare 6/15 with 7/15: 7/15 is bigger.

Add and subtract numbers with the same or different numbers of decimal places

7.83 + 5.74 = ?

  1. 13.47
  2. 13.67
  3. 13.57
  4. 13.58
Show the answer

13.57. Line up the decimal points: 7.83 + 5.74 = 13.57.

Multiply numbers with one or two decimal places by 1-digit and 2-digit numbers

0.2 × 0.5 = ?

  1. 10
  2. 0.01
  3. 0.1
  4. 0.7
Show the answer

0.1. 2 × 5 = 10. Two decimal places in the question, so 0.1.

Divide numbers with one or two decimal places by whole numbers

6.48 ÷ 3 = ?

  1. 21.6
  2. 2.16
  3. 2.17
  4. 0.216
Show the answer

2.16. 648 ÷ 3 = 216, and the decimal point stays where it was: 2.16.

Two quantities in direct proportion

3 pens cost $1.80.
How much do 5 pens cost?

  1. $3.80
  2. $0.60
  3. $3.00
  4. $9.00
Show the answer

$3.00. One costs $1.80 ÷ 3 = $0.60. So 5 cost 5 × $0.60 = $3.00.

Understand and use equivalent ratios

Share 24 sweets in the ratio 1 : 2.
How many are in the bigger share?

  1. 16
  2. 12
  3. 8
  4. 17
Show the answer

16. 1 + 2 = 3 parts. 24 ÷ 3 = 8 each. Bigger share: 2 × 8 = 16.

Time

Convert a time interval between a decimal and mixed units

4.75 hours = ? minutes

  1. 285
  2. 475
  3. 315
  4. 240
Show the answer

285. 4 hours = 240 minutes, and 0.75 of an hour is 45 minutes. 240 + 45 = 285.

Geometrical reasoning, shapes and measurements

Classify and sketch quadrilaterals: angles, symmetry, parallel sides, diagonals

Which quadrilateral has opposite sides parallel, but no right angles and not all sides equal?

  1. trapezium
  2. parallelogram
  3. rectangle
  4. kite
Show the answer

parallelogram. That describes a parallelogram.

Parts of a circle: centre, radius, diameter, circumference

The radius of a circle is 15 cm.
How long is its diameter?

  1. 31 cm
  2. 225 cm
  3. 17 cm
  4. 30 cm
Show the answer

30 cm. A diameter is two radii: 2 × 15 = 30 cm.

Area of a right-angled triangle from the area of a rectangle

A triangle has base 10 cm and height 10 cm.
What is its area?

  1. 20 cm²
  2. 40 cm²
  3. 50 cm²
  4. 100 cm²
Show the answer

50 cm². Area = ½ × base × height = ½ × 10 × 10 = 50 cm².

Identify and sketch compound 3D shapes

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

The difference between capacity and volume

A glass holds 250 ml when full. Which sentence is about its CAPACITY?

  1. It is 12 cm tall
  2. It can hold 250 ml of water
  3. It is made of 50 cm³ of glass
  4. It takes up space in the cupboard
Show the answer

It can hold 250 ml of water. Capacity is how much a container can HOLD. Volume is how much space something takes up, including the glass itself.

Nets for cubes, cuboids, prisms and pyramids

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

How the area of 2D shapes relates to the surface area of 3D shapes

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

Rotational symmetry up to order 4

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

Classify, estimate, measure and draw angles

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 in a triangle 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

Read and plot coordinates in all four quadrants, including fractions and decimals

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 all four quadrants

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 coordinate 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 vertical, horizontal and diagonal mirror lines

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

Rotate a shape 90° about a vertex

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, waffle and pie charts, frequency diagrams, line graphs, scatter 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, median, mean and range

What is the range?
10, 12, 7, 13, 3

  1. 10
  2. 13
  3. 9
  4. 3
Show the answer

10. Biggest − smallest = 13 − 3 = 10.

Interpret patterns within and between data sets, and check predictions

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

Probability

Describe and compare outcomes with the language of probability and proportion

A bag holds 7 red and 2 blue balls.
One is picked at random.
What is the probability it is red?

  1. 7/2
  2. 7/9
  3. 2/9
  4. 2/7
Show the answer

7/9. 7 red out of 9 balls altogether: 7/9.

Events that can and cannot happen together: mutually exclusive

A dice is rolled once.
The number CANNOT be both…

  1. even and odd
  2. even and more than four
  3. odd and a multiple of three
  4. even and prime
Show the answer

even and odd. No number on a dice is both even and odd: those two events are mutually exclusive. The other pairs can happen together (2 is even and prime).

Some probabilities can only be modelled by many trials

Which probability can be worked out WITHOUT an experiment?

  1. a bus being late tomorrow
  2. a seed growing into a plant
  3. a dropped cup breaking
  4. rolling a 6 on a fair dice
Show the answer

rolling a 6 on a fair dice. Rolling a 6 on a fair dice has equally likely outcomes you can count, so its probability can be worked out exactly.

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.

Gives the y-coordinate first

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

Adds the denominators too

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

Reflects in the wrong direction

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

Loses the negative sign

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

Puts the decimal point in the wrong place

Estimate first: 3.45 × 6 is about 3 × 6 = 18, so the answer is near 20.

Reads the digit, not its value

In 47 the 4 is four TENS. Say the number aloud in tens and ones.

Reads the angle as the number of people

The angle is a share of 360°. Turn it into a fraction of the whole first.

Reads a digit one place too far

Write the column names over the digits: ones, tens, hundreds, thousands...

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 5Year 5, ages 9 to 10

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