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Maths Year 4 42 questions with answers

Year 4 maths: a question for each objective

The national curriculum lists what children are taught in maths in Year 4. Here is each objective in its own words, by strand, with one question on it, its answer and how to find it.

Questions written by Remelia for the objectives of the national curriculum for England; not taken from any test paper.

The strands

Try each question before opening its answer. Printed, the questions come first and the answers on a sheet of their own.

Number & place value

  1. Objective: Count in multiples of 6, 7, 9, 25 and 1,000

    One number is in the wrong place in the Carroll diagram.

    Which one?

    Carroll diagramA Carroll diagram: a table of four boxes. The two columns are headed ‘multiple of 6’ and ‘not a multiple of 6’; the two rows ‘multiple of 9’ and ‘not a multiple of 9’. Under ‘multiple of 6’, beside ‘multiple of 9’: 84 and 72. Under ‘not a multiple of 6’, beside ‘multiple of 9’: 45 and 99. Under ‘multiple of 6’, beside ‘not a multiple of 9’: 12 and 78. Under ‘not a multiple of 6’, beside ‘not a multiple of 9’: 29 and 55.multiple of 6not a multipleof 6multipleof 9not amultipleof 91284294572785599
    • A 78
    • B 55
    • C 45
    • D 84
    Show the answer to question 1

    Answer: D · 84

    Why:

    84 is under ‘multiple of 6’, beside ‘multiple of 9’. 84 = 14 × 6, so it is a multiple of 6. 84 is 3 more than 81 = 9 × 9, so it is not a multiple of 9.

    So 84 belongs under ‘multiple of 6’, beside ‘not a multiple of 9’. Every other number is where it belongs.

  2. Objective: Find 1,000 more or less than a given number

    Leo thinks of a number.

    1,000 less than it is 2,359.

    What is Leo's number?

    Show the answer to question 2

    Answer: 3,359

    Why:

    Undo it: add 1,000 back. 2,359 + 1,000 = 3,359.

  3. Objective: Count backwards through 0 to include negative numbers

    Two freezers are at -4°C and -2°C.

    Which is colder?

    • A -4°C
    • B -2°C
    Show the answer to question 3

    Answer: A · -4°C

    Why:

    Below zero, the bigger the number after the minus sign, the colder it is. -4°C is colder.

  4. Objective: Recognise the place value of each digit in a 4-digit number

    Write the number that has 3 thousands, 6 tens, 5 ones and 6 hundreds.

    Show the answer to question 4

    Answer: 3,665

    Why:

    Put each digit in its own column: thousands, hundreds, tens, ones → 3,665.

  5. Objective: Order and compare numbers beyond 1,000

    Which is the largest?

    • A 2,141
    • B 9,306
    • C 7,675
    • D 5,256
    Show the answer to question 5

    Answer: B · 9,306

    Why:

    Look at the thousands digit first. 9,306 is the largest.

  6. Objective: Identify, represent and estimate numbers using different representations

    On a pictogram, one symbol stands for 20 children.

    A row has 3 symbols.

    How many children is that?

    Show the answer to question 6

    Answer: 60

    Why:

    3 symbols × 20 children each = 60.

    Always read the key first: the symbol almost never means 1.

  7. Objective: Round any number to the nearest 10, 100 or 1,000

    Three of these round to 600 to the nearest 100. Which one does not?

    • A 647
    • B 623
    • C 663
    • D 640
    Show the answer to question 7

    Answer: C · 663

    Why:

    Anything from 550 up to 649 rounds to 600. 663 is outside that, so it rounds to 700.

  8. Objective: Solve number and practical problems with increasingly large positive numbers

    Which of these numbers is closest to 5,000?

    • A 4,321
    • B 5,343
    • C 5,088
    • D 4,948
    Show the answer to question 8

    Answer: D · 4,948

    Why:

    4,948 is 52 below 5,000; 5,088 is 88 above 5,000; 5,343 is 343 above 5,000; 4,321 is 679 below 5,000.

    The smallest gap is 52, so 4,948 is closest.

  9. Objective: Read Roman numerals to 100 (I to C); the numeral system later gained 0 and place value

    Which sign goes in the box: <, > or =?

    89 □ LXXXIX

    • A =
    • B >
    • C <
    Show the answer to question 9

    Answer: A · =

    Why:

    LXXXIX = 89.

    So 89 = LXXXIX.

Addition & subtraction

  1. Objective: Add and subtract numbers with up to 4 digits using formal columnar methods Explained, with a worked example

    5,174 + 6,771 = ?

    Round each number to the nearest hundred, then add. Which is the estimate?

    • A 12,000
    • B 12,200
    • C 12,100
    • D 12,300
    Show the answer to question 10

    Answer: A · 12,000

    Why:

    5,174 rounds to 5,200 and 6,771 to 6,800.

    5,200 + 6,800 = 12,000. (The exact answer is 11,945.)

  2. Objective: Estimate and use inverse operations to check answers

    Leo worked out 1,644 + 2,364 and got 5,008.

    Round both numbers to the nearest 100. Is Leo's answer about right, far too big or far too small?

    • A Far too big
    • B Far too small
    • C About right
    Show the answer to question 11

    Answer: A · Far too big

    Why:

    1,644 ≈ 1,600 and 2,364 ≈ 2,400, so the answer should be about 4,000.

    5,008 is about 1,000 more than that. Far too big.

  3. Objective: Solve addition and subtraction two-step problems in context, deciding which operations and methods to use and why

    A warehouse has 4,437 parcels.

    1,396 parcels arrive, then 866 parcels are sent out.

    Which calculation gives the number of parcels now?

    • A 4,437 + 1,396 + 866
    • B 4,437 + 1,396 − 866
    • C 4,437 − 1,396 + 866
    • D 4,437 − 1,396 − 866
    Show the answer to question 12

    Answer: B · 4,437 + 1,396 − 866

    Why:

    Going out takes away; coming in adds. Start with 4,437, add 1,396, then take away 866: 4,437 + 1,396 − 866 = 4,967.

Multiplication & division

  1. Objective: Recall multiplication and division facts for tables up to 12 × 12

    What number goes in the box?

    □ × 8 = 40

    Show the answer to question 13

    Answer: 5

    Why:

    5 × 8 = 40, so the missing number is 5.

  2. Objective: Use place value, known and derived facts to × and ÷ mentally, including × 0, × 1, ÷ 1, multiplying three numbers together

    5 × 6 × 3 = ?

    Show the answer to question 14

    Answer: 90

    Why:

    You can multiply in any order. 5 × 6 = 30, then × 3 = 90. Choosing an easy pair first makes it quicker.

  3. Objective: Recognise and use factor pairs and commutativity in mental calculations

    Three of these are factors of 24. Which one is not?

    • A 12
    • B 13
    • C 3
    • D 2
    Show the answer to question 15

    Answer: B · 13

    Why:

    2, 12, 3 all divide into 24 exactly. 24 ÷ 13 leaves a remainder, so 13 is not a factor.

  4. Objective: Multiply 2-digit and 3-digit numbers by a 1-digit number using formal written layout

    173 × 5 = ?

    Round 173 to the nearest hundred, then multiply. Which is the estimate?

    • A 1,000
    • B 1,400
    • C 1,200
    • D 600
    Show the answer to question 16

    Answer: A · 1,000

    Why:

    173 rounds to 200.

    200 × 5 = 1,000. (The exact answer is 865.)

  5. Objective: Solve problems involving multiplying and adding, including the distributive law, integer scaling and harder correspondence problems

    A box holds 39 pencils.

    Which calculations give the number of pencils in 3 boxes?

    Tick every one that is right.

    • A (30 × 3) + (9 × 4)
    • B (30 × 3) + 9
    • C 39 + 3
    • D (40 × 3) − (1 × 3)
    • E 39 × 3
    Show the answer to question 17

    Answer: D, E · (40 × 3) − (1 × 3), 39 × 3

    Why:

    The number of pencils in 3 boxes: 39 × 3 = 117.

    39 × 3 = 117 ✓

    (40 × 3) − (1 × 3) = 117 ✓

    (30 × 3) + (9 × 4) = 126

    (30 × 3) + 9 = 99

    39 + 3 = 42

    Splitting 39 into 30 + 9 works only when both parts are multiplied by 3.

Fractions, decimals & %

Six Year 4 fractions questions with the common mistakes

  1. Objective: Recognise and show, using diagrams, families of common equivalent fractions Explained, with a worked example

    Three of these are in the same family as 3/5. Which one is not?

    • A 13/20
    • B 12/20
    • C 15/25
    • D 6/10
    Show the answer to question 18

    Answer: A · 13/20

    Why:

    3/5 = 6/10 = 12/20 = 15/25. 13/20 does not simplify to 3/5.

  2. Objective: Count up and down in hundredths; hundredths arise from dividing by 100 and dividing tenths by 10

    Count up in hundredths from 0.11, 5 at a time.

    What comes next?

    Show the answer to question 19

    Answer: 0.16

    Why:

    11 hundredths + 5 = 16 hundredths = 0.16.

  3. Objective: Solve problems with harder fractions to calculate and to divide quantities, including non-unit fractions where the answer is a whole number Explained, with a worked example

    To find 2/5 of 70, what do you do?

    • A Divide by 5, then multiply by 2
    • B Subtract 2 from 70 and divide by 5
    • C Multiply by 5, then divide by 2
    • D Divide by 2, then multiply by 5
    Show the answer to question 20

    Answer: A · Divide by 5, then multiply by 2

    Why:

    Divide by the bottom to get one part (70 ÷ 5 = 14), then multiply by the top (× 2 = 28).

  4. Objective: Add and subtract fractions with the same denominator Explained, with a worked example

    What is the missing numerator?

    5/10 − ?/10 makes 3/10

    Show the answer to question 21

    Answer: 2

    Why:

    The denominators all stay 10, so only the numerators count: 5 − 2 = 3. The missing numerator is 2.

  5. Objective: Recognise and write decimal equivalents of any number of tenths or hundredths Explained, with a worked example

    Write 73 hundredths as a decimal.

    Show the answer to question 22

    Answer: 0.73 (also accept .73)

    Why:

    100 hundredths make one whole, so 73 hundredths = 73 ÷ 100 = 0.73.

    The last digit of 73 goes in the hundredths column, the second place after the point.

  6. Objective: Recognise and write decimal equivalents to ¼, ½, ¾

    Kai says: 3/4 written as a decimal is 3.4.

    Kai is wrong. Which reason shows why?

    • A 3/4 means 3 ÷ 4, which is less than 1.
    • B The top number goes before the point and the bottom one after it.
    • C In 3/4, the 3 is the numerator and the 4 is the denominator.
    • D A fraction becomes a decimal by putting a point between its two numbers.
    Show the answer to question 23

    Answer: A · 3/4 means 3 ÷ 4, which is less than 1.

    Why:

    3/4 means 3 ÷ 4, which is less than 1.

    "In 3/4, the 3 is the numerator and the 4 is the denominator." is true, but it does not show Kai is wrong.

  7. Objective: Find the effect of dividing a 1- or 2-digit number by 10 and 100; identify ones, tenths, hundredths Explained, with a worked example

    How many tenths are there in 8.7?

    Show the answer to question 24

    Answer: 87

    Why:

    8.7 × 10 = 87 tenths.

  8. Objective: Round decimals with 1 decimal place to the nearest whole number

    Round 9.3 to the nearest whole number.

    Show the answer to question 25

    Answer: 9

    Why:

    The tenths digit is 3, so round down → 9.

  9. Objective: Compare numbers with the same number of decimal places up to 2 d.p.

    Which sign goes in the box: <, > or =?

    9.32 □ 9.23

    • A >
    • B <
    • C =
    Show the answer to question 26

    Answer: A · >

    Why:

    The whole numbers are the same, so compare the tenths digits: 3 and 2.

    So 9.32 > 9.23.

  10. Objective: Solve simple measure and money problems involving fractions and decimals to 2 d.p.

    A parcel weighs 1 kg and another weighs 750 g.

    How much is that altogether, in kilograms? Write it like 3.75

    Show the answer to question 27

    Answer: 1.75 (also accept 1.75kg, 1750g)

    Why:

    750 g = 0.75 kg. 1 + 0.75 = 1.75 kg.

Measurement

Six Year 4 measurement questions with the common mistakes

  1. Objective: Convert between different units of measure (km→m; hour→minute) Explained, with a worked example

    A bag of sand is on the kitchen scale.

    How many grams does it weigh?

    Kitchen scaleA kitchen scale with a round dial. The marks round the dial are numbered in kilograms from 0 to 5, one every kilogram. Between each numbered mark and the next there is one unnumbered mark. The pointer is on the first unnumbered mark after 3. 012345kilograms
    Show the answer to question 28

    Answer: 3,500 g

    Why:

    The numbered marks go up in 1 kg, which is 1,000 g. One unnumbered mark splits each gap in half, so each mark is 1,000 ÷ 2 = 500 g.

    The pointer is one mark past 3 kg (3,000 g): 3,000 + 1 × 500 = 3,500 g.

  2. Objective: Measure and calculate the perimeter of a rectilinear figure (including squares) in cm and m

    A rectangle is 14 cm long and 6 cm wide.

    What is its perimeter?

    Show the answer to question 29

    Answer: 40 cm

    Why:

    Perimeter = 2 × (14 + 6) = 2 × 20 = 40 cm.

  3. Objective: Find the area of rectilinear shapes by counting squares

    An L-shape is drawn on squared paper.

    It is a rectangle 9 squares long and 7 squares wide, with a corner cut away: 1 square along its length and 3 squares along its width.

    How many squares is its area?

    L-shapeA rectangle with a smaller rectangle cut out of one corner, making an L.
    Show the answer to question 30

    Answer: 60 squares

    Why:

    The whole rectangle: 9 × 7 = 63 squares.

    The corner cut away: 1 × 3 = 3 squares.

    63 − 3 = 60 squares.

  4. Objective: Estimate, compare and calculate different measures, including money in pounds and pence

    Three pieces of ribbon are 122 cm, 141 cm and 112 cm long.

    Round each length to the nearest 10 cm to estimate the total length. Which is the estimate?

    • A 360 cm
    • B 350 cm
    • C 370 cm
    • D 340 cm
    Show the answer to question 31

    Answer: C · 370 cm

    Why:

    122 cm, 141 cm, 112 cm round to 120 cm, 140 cm and 110 cm.

    120 + 140 + 110 = 370 cm. (The exact total length is 375 cm.)

  5. Objective: Read, write and convert time between analogue and digital 12- and 24-hour clocks

    The clock shows the time Ines sits down to eat in the evening.

    What time is it in the 24-hour clock? Write it like 16:25.

    ClockAn analogue clock with the numbers 1 to 12 round the face and a mark for every minute: the short hour hand is between the 9 and the 10, and the long minute hand points to the second minute mark after the 8. 121234567891011
    Show the answer to question 32

    Answer: 21:42 (also accept 21.42, 2142)

    Why:

    The short hand is between 9 and 10, so it is after 9 o'clock. The long hand is 2 minute marks past the 8: 8 × 5 + 2 = 42 minutes past.

    It is in the evening, so add 12 to the hour: 9 + 12 = 21. 21:42.

  6. Objective: Solve problems converting hours→minutes, minutes→seconds, years→months, weeks→days

    The clocks show when a school trip left and when it arrived, both in the morning.

    How long did the journey take? Give your answer in minutes.

    Two clocksTwo analogue clocks, each with the numbers 1 to 12 round the face and a mark for every minute. The first, labelled Start: the short hour hand is between the 7 and the 8, and the long minute hand points straight at the 1. The second, labelled Finish: the short hour hand is between the 9 and the 10, and the long minute hand points straight at the 6. 121234567891011 Start 121234567891011 Finish
    Show the answer to question 33

    Answer: 145 minutes

    Why:

    From 7:05 am to 9:30 am is 2 hours 25 minutes.

    2 hours is 2 × 60 = 120 minutes, and 120 + 25 = 145: 145 minutes.

Geometry

  1. Objective: Compare and classify geometric shapes, including quadrilaterals and triangles, by properties and sizes

    Is this true or false?

    Every rhombus is also a square.

    • A True
    • B False
    Show the answer to question 34

    Answer: B · False

    Why:

    A square needs four right angles. A rhombus that leans over has no right angles, so not every rhombus is a square.

  2. Objective: Identify acute and obtuse angles; compare and order angles up to 2 right angles

    Which list is in order, smallest first?

    • A 15°, 30°, 135°, 60°
    • B 15°, 30°, 60°, 135°
    • C 135°, 60°, 30°, 15°
    • D 30°, 15°, 60°, 135°
    Show the answer to question 35

    Answer: B · 15°, 30°, 60°, 135°

    Why:

    In order, smallest first: 15°, 30°, 60°, 135°.

  3. Objective: Identify lines of symmetry in 2-D shapes in different orientations

    How many lines of symmetry does the capital letter P have?

    Show the answer to question 36

    Answer: 0

    Why:

    P has no line of symmetry: however you fold it, the two halves do not match.

  4. Objective: Complete a simple symmetric figure with respect to a specific line of symmetry

    A symmetric shape is drawn on a grid. Its mirror line goes straight across the grid through (0, 7) and (10, 7).

    One corner of the shape is at (5, 8). Where is the matching corner on the other side of the mirror line? Write it like (2, 6).

    Show the answer to question 37

    Answer: (5,6) (also accept 5,6)

    Why:

    The corner is 1 square above the mirror line, so its match is 1 square below it: 7 − 1 = 6.

    The first number stays 5: a reflection in this line moves the corner only up or down.

  5. Objective: Describe positions on a 2-D grid as coordinates in the first quadrant

    Which point is at (5, 2)?

    Coordinate gridA coordinate grid. The x-axis is numbered from 0 to 8 and the y-axis from 0 to 8, with a gridline for every whole number and every gridline numbered. Points C, F, B and A are marked where gridlines cross, each with its letter beside it.xy012345678012345678CFBA
    • A
    • B
    • F
    • C
    Show the answer to question 38

    Answer: C

    Why:

    (5, 2) means 5 to the right of 0, then 2 up: across first, then up or down.

    Point C is there. Point F is at (2, 5): the same numbers the other way round.

  6. Objective: Describe movements between positions as translations left/right, up/down

    The rectangle moves 5 right and 4 down.

    Where is corner D now? Write it like (5, 2).

    Coordinate gridA coordinate grid. The x-axis is numbered from 0 to 10 and the y-axis from 0 to 10, with a gridline for every whole number and every gridline numbered. Points A at (1, 9), B at (4, 9), C at (4, 5) and D at (1, 5) are marked where gridlines cross. A quadrilateral is drawn, its corners at A, B, C and D.xy012345678910012345678910ABCD
    Show the answer to question 39

    Answer: (6, 1) (also accept 6, 1)

    Why:

    D is at (1, 5).

    Right changes the x-coordinate: 1 + 5 = 6.

    Down changes the y-coordinate: 5 − 4 = 1.

    D is now at (6, 1). The rectangle is the same size and shape: only its place has changed.

  7. Objective: Plot specified points and draw sides to complete a given polygon

    Three corners of a square are plotted at (7, 3), (7, 7) and (3, 7).

    Where is the fourth corner? Write it like (2, 6).

    Show the answer to question 40

    Answer: (3,3) (also accept 3,3)

    Why:

    Its sides go straight across and straight up, so the fourth corner is in line with (7, 3) one way and with (3, 7) the other: (3, 3).

Statistics

  1. Objective: Interpret and present discrete and continuous data using bar charts and time graphs

    The line graph shows the temperature in a playground each hour of a school day.

    How much warmer was it at 11:00 than at 09:00?

    Line graph: Temperature in the playgroundA line graph. Temperature (°C) is up the side, from 0 to 18, with a line every 2, each line labelled; Time along the bottom: 09:00, 10:00, 11:00, 12:00, 13:00, 14:00, 15:00. A point is marked at each, joined by straight lines. At 09:00 the point is halfway between 6 and 8; At 10:00 the point is halfway between 8 and 10; At 11:00 the point is on the line marked 12; At 12:00 the point is on the line marked 14; At 13:00 the point is halfway between 16 and 18; At 14:00 the point is halfway between 16 and 18; At 15:00 the point is halfway between 16 and 18.Temperature in the playground 02468101214161809:0010:0011:0012:0013:0014:0015:00 TimeTemperature (°C)
    • A 8°C
    • B 3°C
    • C 6°C
    • D 5°C
    Show the answer to question 41

    Answer: D · 5°C

    Why:

    At 11:00 the point is on the 12 line: 12°C.

    At 09:00 the point is halfway between 6 and 8: 7°C.

    12 − 7 = 5.

  2. Objective: Solve comparison, sum and difference problems from bar charts, pictograms, tables and other graphs

    The pictogram shows how many books were borrowed from a library each day.

    On which day were the most books borrowed?

    Pictogram: Books borrowed from the libraryA pictogram. Key: one circle stands for 4 books. Mon: two and three quarters circles; Tue: seven and a half circles; Wed: one circle; Thu: five circles; Fri: half a circle.Books borrowed from the library MonTueWedThuFri Key: stands for 4 books
    • A Monday
    • B Thursday
    • C Tuesday
    • D Wednesday
    Show the answer to question 42

    Answer: C · Tuesday

    Why:

    Monday: 2 circles × 4 = 8, and three quarters of a circle stands for 3: 8 + 3 = 11.

    Tuesday: 7 circles × 4 = 28, and half a circle stands for 2: 28 + 2 = 30.

    Wednesday: 1 circle × 4 = 4.

    Thursday: 5 circles × 4 = 20.

    Friday: half a circle, which stands for half of 4: 2.

    The largest is 30: Tuesday.

Answers

  1. 1. D · 84
  2. 2. 3,359
  3. 3. A · -4°C
  4. 4. 3,665
  5. 5. B · 9,306
  6. 6. 60
  7. 7. C · 663
  8. 8. D · 4,948
  9. 9. A · =
  10. 10. A · 12,000
  11. 11. A · Far too big
  12. 12. B · 4,437 + 1,396 − 866
  13. 13. 5
  14. 14. 90
  15. 15. B · 13
  16. 16. A · 1,000
  17. 17. D, E · (40 × 3) − (1 × 3), 39 × 3
  18. 18. A · 13/20
  19. 19. 0.16
  20. 20. A · Divide by 5, then multiply by 2
  21. 21. 2
  22. 22. 0.73 (also accept .73)
  23. 23. A · 3/4 means 3 ÷ 4, which is less than 1.
  24. 24. 87
  25. 25. 9
  26. 26. A · >
  27. 27. 1.75 (also accept 1.75kg, 1750g)
  28. 28. 3,500 g
  29. 29. 40 cm
  30. 30. 60 squares
  31. 31. C · 370 cm
  32. 32. 21:42 (also accept 21.42, 2142)
  33. 33. 145 minutes
  34. 34. B · False
  35. 35. B · 15°, 30°, 60°, 135°
  36. 36. 0
  37. 37. (5,6) (also accept 5,6)
  38. 38. C
  39. 39. (6, 1) (also accept 6, 1)
  40. 40. (3,3) (also accept 3,3)
  41. 41. D · 5°C
  42. 42. C · Tuesday

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