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Cambridge Primary Maths: Stage 4

Stage 4 of the Cambridge Primary Mathematics (0096) curriculum framework, usually Year 4 (ages 8 to 9). Here is what each part asks, a practice question for each, and the mistakes that cost the most marks.

Practise Stage 4 as a game

The 44 parts of Stage 4

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

Counting and sequences

Count on and back in steps of a 1-digit number, tens, hundreds or thousands, 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.

What happens when odd and even numbers are added and subtracted

An odd number plus an even number is…

  1. always even
  2. always odd
  3. sometimes odd, sometimes even
  4. never a whole number
Show the answer

always odd. Try one: 23 + 4 = 27, which is odd. Two of the same kind always give even; one of each always gives odd.

Shapes or symbols standing for unknowns in addition and subtraction

81 − △ = 44
What number is △?

  1. 81
  2. 125
  3. 37
  4. 44
Show the answer

37. 81 − 44 = 37, so △ is 37.

Extend linear and non-linear sequences and give the term-to-term rule

What comes next?
16, 8, 4, 2, …

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

1. Each number is HALF the one before. 2 ÷ 2 = 1.

The spatial pattern of square numbers

What comes next?
16, 25, 36, 49, …

  1. 16
  2. 85
  3. 64
  4. 62
Show the answer

64. These are square numbers: 4², 5², 6², 7². Next is 8² = 64.

Integers and powers

Read and write numbers and number names above 1000 and below 0

Which number is "nineteen thousand, three hundred and seventy-seven"?

  1. 1,937
  2. 19,387
  3. 91,377
  4. 19,377
Show the answer

19,377. nineteen thousand, three hundred and seventy-seven is written 19,377.

Estimate, add and subtract numbers with up to three digits

621 + 272 = ?

  1. 883
  2. 893
  3. 793
  4. 993
Show the answer

893. 621 + 272 = 893.

Multiplication is associative; use this to simplify

Which is the smartest way to work out 28 + 68 + 2?

  1. (28 + 68) × 2
  2. 28 × 68 + 2
  3. 28 + (68 − 2)
  4. (28 + 2) + 68
Show the answer

(28 + 2) + 68. Addition can be done in any order (it is commutative and associative). 28 + 2 = 30, a tidy number, and then + 68 = 98.

All the times tables from 1 to 10

6 × 3 = ?

  1. 18
  2. 24
  3. 15
  4. 21
Show the answer

18. 6 × 3 = 18.

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

990 × 4 = ?

  1. 660
  2. 3 960
  3. 3 956
  4. 4 950
Show the answer

3 960. Multiply each digit by 4, carrying as you go: 3 960.

Estimate and divide numbers up to 100 by a 1-digit number

60 ÷ 10 = ?

  1. 50
  2. 10
  3. 7
  4. 6
Show the answer

6. 6 × 10 = 60, so 60 ÷ 10 = 6.

How multiples and factors relate

Which number is a factor of 28?

  1. 8
  2. 14
  3. 16
  4. 9
Show the answer

14. 14 × 2 = 28, so 14 is a factor of 28.

Tests of divisibility by 2, 5, 10, 25, 50 and 100

Which number is divisible by 5?

  1. 583
  2. 325
  3. 172
  4. 442
Show the answer

325. A number divides by 5 when it ends in 0 or 5. 325 ÷ 5 = 65.

Place value, ordering and rounding

The value of each digit in any whole number

What is the value of the digit 2 in 762 024?

  1. 2 000
  2. 20 000
  3. 2
  4. 200
Show the answer

2 000. Counting from the right: ones, tens, hundreds, thousands... The 2 is in the thousands place, so it is worth 2 000.

Multiply and divide whole numbers by 10 and 100 using place value

41 × 10 = ?

  1. 410
  2. 41000
  3. 4.1
  4. 4100
Show the answer

410. Multiplying by 10 moves each digit 1 place to the left.

Make, split and regroup whole numbers

424 = 3 hundreds + ? tens + 4 ones

  1. 12
  2. 2
  3. 3
  4. 102
Show the answer

12. One of the hundreds is regrouped as 10 tens: 4 hundreds is 3 hundreds and 10 tens, so 2 + 10 = 12 tens.

Compare and order positive and negative numbers with =, > and <

Put in order, smallest first:
0, 8, −9, −4

  1. −9, −4, 0, 8
  2. 0, −4, 8, −9
  3. −4, −9, 0, 8
  4. 8, 0, −4, −9
Show the answer

−9, −4, 0, 8. Picture a number line: the most negative is furthest left, so it comes first. −9, −4, 0, 8.

Round to the nearest 10, 100, 1000, 10 000 or 100 000

Round 4,655 to the nearest 10.

  1. 5,000
  2. 4,700
  3. 4,660
  4. 4,650
Show the answer

4,660. 4,655 is between 4,650 and 4,660. It is closer to 4,660.

Fractions, decimals, percentages, ratio and proportion

The more parts a whole is cut into, the smaller each part

Which statement is true?

  1. 1/8 < 1/2
  2. 1/8 > 1/2
  3. 1/2 < 1/8
  4. 1/8 = 1/2
Show the answer

1/8 < 1/2. The more equal parts a whole is cut into, the smaller each part. 1/8 is smaller than 1/2.

A fraction as numerator divided by denominator (unit fractions, three-quarters)

Which fraction is the same as 1 ÷ 4?

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

1/4. A fraction IS a division: the top divided by the bottom. 1 ÷ 4 = 1/4.

Unit fractions as operators

What is 1/3 of 9?

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

3. 9 ÷ 3 = 3. Then 3 × 1 = 3.

Two proper fractions can be equal

Which fraction is equal to 1/5?

  1. 2/15
  2. 3/7
  3. 2/10
  4. 3/10
Show the answer

2/10. Multiply top and bottom by 2: 1/5 = 2/10.

Estimate, add and subtract fractions with the same denominator

9/11 − 8/11 = ?

  1. 1/22
  2. 1/11
  3. 17/11
  4. 2/11
Show the answer

1/11. The parts are the same size (11ths), so just subtract how many there are: 9 − 8 = 1. The denominator stays 11.

Percentage as parts in each hundred; the % symbol

Write 7/10 as a percentage.

  1. 30%
  2. 7%
  3. 70%
  4. 100%
Show the answer

70%. 7/10 = 70/100 = 70%.

Compare and order proper fractions with =, > and <

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

Time

How units of time relate; convert between them

How many months are there in 4 years?

  1. 48
  2. 16
  3. 40
  4. 400
Show the answer

48. 1 year = 12 months, so 4 × 12 = 48.

Read and record time accurately, 12-hour and 24-hour, digital and analogue

What is 2:55 pm in 24-hour time?

  1. 12:55
  2. 02:55
  3. 13:55
  4. 14:55
Show the answer

14:55. After midday, add 12 to the hour: 2 + 12 = 14.

Read and use 12-hour and 24-hour timetables

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

Time intervals: days to years, and seconds to hours without bridging 60

How many weeks are there in 3 years? (1 year = 52 weeks)

  1. 1095
  2. 208
  3. 156
  4. 36
Show the answer

156. 3 × 52 = 156 weeks.

Geometrical reasoning, shapes and measurements

Combine shapes and analyse the result; tessellation

Tiles that TESSELLATE fit together with no gaps and no overlaps.
Which of these shapes tessellates on its own?

  1. square
  2. regular pentagon
  3. regular octagon
  4. circle
Show the answer

square. Squares meet at each corner with angles that add up to exactly 360°, so there are no gaps. Circles always leave gaps; regular pentagons and octagons cannot fill 360° exactly.

Perimeter and area of 2D shapes; areas add for a compound shape

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

Rectangles and squares on a grid; formulae for their area and perimeter

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

Estimate the area of an irregular shape on a grid, with part squares

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

The 2D faces 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.

Match nets to 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.

All lines of symmetry: horizontal, vertical and diagonal

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

An angle of 90° is…

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

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

Read a measuring scale using fractions

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

Describe position, direction and movement with the eight compass points

Which direction is exactly half way between south and west?

  1. south-east
  2. north-west
  3. south-west
  4. north-east
Show the answer

south-west. Half way between south and west is south-west: the name is made from the two it sits between.

Read and plot coordinates in the first quadrant

Start at (0, 0). Go 6 along and 7 up.
What are the coordinates of the point you reach?

  1. (6, 7)
  2. (6, 8)
  3. (7, 7)
  4. (7, 6)
Show the answer

(6, 7). Along first, then up: 6 along the x-axis and 7 up the y-axis is (6, 7).

Reflect 2D shapes in a horizontal or vertical mirror line on a grid

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, pictograms, bar charts, 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.

Interpret data 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 chance: maybe, likely, certain, impossible

A bag holds 4 red and 2 blue balls.
One is picked without looking.
Picking a red ball is…

  1. certain
  2. likely
  3. impossible
  4. an even chance
Show the answer

likely. More than half of the balls are red.

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.

Mixes up perimeter and area

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

Gives the y-coordinate first

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

Adds only two sides for perimeter

Trace all the way round the shape with a finger while counting sides.

Reads a digit one place too far

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

Rounds to the wrong place value

Underline the digit in the place you are rounding to before you start.

Reads the digit, not its value

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

Mixes up factors and multiples

Factors go INTO a number (small). Multiples are in its times table (big).

Adds the denominators too

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

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 5Year 5, ages 9 to 10 Stage 6Year 6, ages 10 to 11

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Short rounds on any topic, a new question every time, the exact mistake found, and a report to you after every session.

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