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Maths Year 3 32 questions with answers

Year 3 maths: a question for each objective

The national curriculum lists what children are taught in maths in Year 3. 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

Six Year 3 place value questions with the common mistakes

  1. Objective: Count from 0 in multiples of 4, 8, 50 and 100; find 10 or 100 more or less than a given number

    Count in 100s from 0. Which of these numbers do you say?

    Tick every one that is right.

    • A 810
    • B 180
    • C 450
    • D 400
    • E 900
    Show the answer to question 1

    Answer: D, E · 400, 900

    Why:

    Counting in 100s from 0 you say the multiples of 100: 400 = 4 × 100, 900 = 9 × 100. 180 is 80 past 100; 450 is 50 past 400; 810 is 10 past 800, so you do not say them.

  2. Objective: Recognise the place value of each digit in a 3-digit number (100s, 10s, 1s) Explained, with a worked example

    In which number is the digit 2 worth 200?

    • A 828
    • B 722
    • C 482
    • D 249
    Show the answer to question 2

    Answer: D · 249

    Why:

    A digit 2 is worth 200 when it is in the hundreds place (2 × 100 = 200).

    In 249 the 2 is in the hundreds place.

  3. Objective: Compare and order numbers up to 1,000

    Use each of the digits 8, 9, 2 once to make 3-digit numbers.

    Write down every one that is greater than 900, smallest first, with commas between them.

    Show the answer to question 3

    Answer: 928, 982

    Why:

    Every 3-digit number from 8, 9, 2, in order: 289, 298, 829, 892, 928, 982.

    The ones greater than 900: 928, 982.

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

    A number is made of 8 hundreds, 0 tens and 7 ones.

    What is the number?

    Show the answer to question 4

    Answer: 807

    Why:

    8 × 100 + 0 × 10 + 7 = 807.

  5. Objective: Read and write numbers up to 1,000 in numerals and in words

    Write 395 in words.

    (Use "and", and hyphens like "twenty-four".)

    Show the answer to question 5

    Answer: three hundred and ninety-five

    Why:

    395 = three hundred and ninety-five.

  6. Objective: Solve number problems and practical problems involving these ideas

    Rosa's number is 10 more than 663.

    Elif's number is 1 more than Rosa's number.

    What is Elif's number?

    Show the answer to question 6

    Answer: 674

    Why:

    Rosa's number: 663 + 10 = 673.

    Elif's number: 673 + 1 = 674.

Addition & subtraction

  1. Objective: Add and subtract numbers mentally: 3-digit ± 1s, ± 10s, ± 100s

    Ines adds 60 to a number and gets 722.

    What number did Ines start with?

    Show the answer to question 7

    Answer: 662

    Why:

    Undo it: take away 60.

    722 − 60 = 662.

    Check: 662 + 60 = 722.

  2. Objective: Add and subtract numbers up to 3 digits using formal columnar methods Explained, with a worked example

    You work out 321 + 188 in columns.

    In which columns do you exchange 10 for 1 in the next column?

    • A Neither column
    • B The ones and the tens columns
    • C Only the ones column
    • D Only the tens column
    Show the answer to question 8

    Answer: D · Only the tens column

    Why:

    Ones: 1 + 8 = 9, nothing to exchange.

    Tens: 2 + 8 = 10, so exchange 10 tens for 1 hundred.

    321 + 188 = 509.

  3. Objective: Estimate the answer to a calculation and use inverse operations to check answers

    Estimate 591 − 233 by rounding each number to the nearest hundred.

    Which estimate do you get?

    • A 300
    • B 400
    • C 100
    • D 200
    Show the answer to question 9

    Answer: B · 400

    Why:

    591 rounds to 600 and 233 rounds to 200.

    600 − 200 = 400.

    The exact answer, 358, is close to 400.

  4. Objective: Solve problems, including missing-number problems, using number facts and place value

    Find the missing number:

    793 + ? = 862

    Show the answer to question 10

    Answer: 69

    Why:

    Subtraction undoes addition: 862 − 793 = 69.

Multiplication & division

  1. Objective: Recall and use multiplication and division facts for the 3, 4 and 8 tables

    2 × 3 = 6.

    Use this to work out 4 × 3.

    Show the answer to question 11

    Answer: 12

    Why:

    4 is double 2, so 4 × 3 is double 6: 4 × 3 = 12.

  2. Objective: Write and calculate statements for × and ÷, including 2-digit × 1-digit, mental progressing to formal written

    16 × 8 = 128

    Which of these is also true?

    • A 128 ÷ 8 = 16
    • B 128 × 8 = 16
    • C 128 ÷ 16 = 7
    • D 16 × 128 = 8
    Show the answer to question 12

    Answer: A · 128 ÷ 8 = 16

    Why:

    From 16 × 8 = 128 come 8 × 16 = 128 (multiplying in any order), and 128 ÷ 8 = 16 and 128 ÷ 16 = 8 (division undoes multiplication).

    128 ÷ 8 = 16 is the one here.

  3. Objective: Solve problems including missing-number, positive integer scaling and correspondence problems (n objects connected to m objects)

    Sana's bean plant is 9 cm tall.

    Ines's bean plant is 10 times as tall.

    How tall is Ines's bean plant?

    Show the answer to question 13

    Answer: 90 cm

    Why:

    10 times as tall: 9 × 10 = 90.

Fractions, decimals & %

Six Year 3 fractions questions with the common mistakes

  1. Objective: Count up and down in tenths; tenths arise from dividing into 10 equal parts

    These fractions go up in tenths:

    1/10, 2/10, 3/10, 4/10, ?

    What comes next?

    Show the answer to question 14

    Answer: 5/10 (also accept 1/2)

    Why:

    Each step adds one tenth: 4/10 + 1/10 = 5/10.

  2. Objective: Recognise, find and write fractions of a discrete set of objects (unit and non-unit fractions, small denominators)

    Ava gives away 3/8 of a bag of balloons.

    That is 12 balloons.

    How many balloons were in the bag at the start?

    Show the answer to question 15

    Answer: 32

    Why:

    3/8 is 12, so 1/8 is 12 ÷ 3 = 4.

    The whole bag is 8/8: 4 × 8 = 32.

  3. Objective: Recognise and use fractions as numbers

    How many quarters make 3 wholes?

    Show the answer to question 16

    Answer: 12

    Why:

    4 quarters make 1 whole, so 3 wholes need 3 × 4 = 12.

  4. Objective: Recognise and show, using diagrams, equivalent fractions with small denominators Explained, with a worked example

    Which of these is the same as 3/4?

    • A 3/16
    • B 12/16
    • C 12/17
    • D 7/8
    Show the answer to question 17

    Answer: B · 12/16

    Why:

    3/4 = 12/16: both parts multiplied by 4. Adding the same number to top and bottom does not work.

  5. Objective: Add and subtract fractions with the same denominator within one whole Explained, with a worked example

    Rosa works out 1/5 + 4/5 and writes 5/5.

    What mistake, if any, did Rosa make?

    • A They made no mistake
    • B They added the denominators as well as the numerators
    • C They took the numerators away instead of adding them
    • D They multiplied the numerators
    Show the answer to question 18

    Answer: A · They made no mistake

    Why:

    1/5 + 4/5 = 5/5: add the numerators, and keep the denominator.

    Rosa's answer is right.

  6. Objective: Compare and order unit fractions, and fractions with the same denominator

    Which list is in order, smallest first?

    • A 2/6, 3/6, 5/6, 4/6
    • B 3/6, 2/6, 4/6, 5/6
    • C 2/6, 3/6, 4/6, 5/6
    • D 5/6, 4/6, 3/6, 2/6
    Show the answer to question 19

    Answer: C · 2/6, 3/6, 4/6, 5/6

    Why:

    Same bottom number: just compare the tops.

Measurement

Six Year 3 measurement questions with the common mistakes

  1. Objective: Measure, compare, add and subtract: lengths (m/cm/mm); mass (kg/g); volume/capacity (l/ml)

    How long is the worm, in millimetres?

    A ruler and a wormA ruler numbered in centimetres from 0 to 4, with a small mark for every millimetre and a longer mark halfway between each centimetre and the next. A worm lies along it. Its left end lines up with the mark numbered 0; its right end lines up with the sixth small mark after 2. 01234 cm
    Show the answer to question 20

    Answer: 26 mm

    Why:

    Each centimetre is split into 10 millimetres. The right end is at 2 cm and 6 small marks, which is 26 mm.

    So it is 26 mm long.

  2. Objective: Measure the perimeter of simple 2-D shapes

    The marks show that all the sides of this octagon are the same length.

    What is its perimeter?

    OctagonAn octagon with eight straight sides, drawn to scale. Going round from the bottom left-hand corner, its sides go: right, 4 cm, with one small mark across it; up and to the right, not labelled, with one small mark across it; up, not labelled, with one small mark across it; up and to the left, not labelled, with one small mark across it; left, not labelled, with one small mark across it; down and to the left, not labelled, with one small mark across it; down, not labelled, with one small mark across it; down and to the right, not labelled, with one small mark across it. Sides with the same number of small marks across them are equal. 4 cm
    Show the answer to question 21

    Answer: 32 cm

    Why:

    It has 8 sides, each 4 cm.

    4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 = 8 × 4 = 32 cm.

  3. Objective: Add and subtract amounts of money to give change, using pounds and pence

    What is the smallest number of coins that make exactly 98p?

    You can use any UK coins, as many of each as you like.

    Show the answer to question 22

    Answer: 6 coins

    Why:

    Take the biggest coin that fits each time: 50p + 20p + 20p + 5p + 2p + 1p = 98p. That is 6 coins.

  4. Objective: Tell and write the time from an analogue clock, including Roman numerals I–XII, and 12- and 24-hour clocks

    The clock shows the time Kai gets to the park in the afternoon.

    What time is it?

    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 3 and the 4, and the long minute hand points straight at the 11. 121234567891011
    • A 3:50 pm
    • B 4:00 pm
    • C 3:55 pm
    • D 3:11 pm
    Show the answer to question 23

    Answer: C · 3:55 pm

    Why:

    The short hand is between 3 and 4, so it is after 3 o'clock. The long hand is on the 11: 11 × 5 = 55 minutes past.

    It is in the afternoon, so it is pm: 3:55 pm.

  5. Objective: Estimate and read time to the nearest minute; compare time in seconds, minutes, hours; am/pm, noon, midnight

    It is 07:25.

    What time will it be in 25 minutes? Write it like 14:05.

    Show the answer to question 24

    Answer: 07:50 (also accept 07.50, 0750, 7:50 am)

    Why:

    07:25 + 25 minutes: go up to the next hour first if you need to. → 07:50.

  6. Objective: Know seconds in a minute, days in each month, year and leap year

    How many days are there in September?

    Show the answer to question 25

    Answer: 30

    Why:

    There are 30 days in September.

  7. Objective: Compare durations of events / calculate time taken

    A film starts at the time on the digital clock. It ends at the time on the clock face, the same afternoon or evening.

    How long is the film? Write it like "1 hour 25 minutes".

    A clock and a digital 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 7 and the 8, and the long minute hand points straight at the 2. Beside it, labelled Film starts, a digital clock showing 17:20. 121234567891011 17:20 Film starts
    Show the answer to question 26

    Answer: 1 hour 50 minutes (also accept 110 minutes, 110, 1h 50 minutes)

    Why:

    The digital clock says 17:20, which is 5:20 pm. The clock face shows 7:10, in the evening.

    40 minutes to 6 o'clock, then 1 hour (60 minutes) to 7 o'clock, then 10 more: 40 + 60 + 10 = 110 minutes. That is 1 hour 50 minutes.

Geometry

  1. Objective: Draw 2-D shapes and make 3-D shapes; recognise 3-D shapes in different orientations

    How many edges does a square-based pyramid have?

    Show the answer to question 27

    Answer: 8

    Why:

    A square-based pyramid has 5 faces, 8 edges and 5 vertices.

  2. Objective: Recognise angles as a property of shape or a description of a turn

    How many faces does a cube have?

    Show the answer to question 28

    Answer: 6

    Why:

    A cube has 6 faces, 12 edges and 8 vertices.

  3. Objective: Identify right angles; 2 = half turn, 3 = three-quarter turn, 4 = complete turn; greater/less than a right angle

    Yusuf faces west and makes a quarter turn clockwise.

    Which way is Yusuf facing now?

    • A east
    • B south
    • C north
    • D west
    Show the answer to question 29

    Answer: C · north

    Why:

    A quarter turn is 1 right angle. Clockwise goes north, east, south, west.

    From west, 1 quarter turn clockwise ends facing north.

  4. Objective: Identify horizontal and vertical lines, and pairs of perpendicular and parallel lines

    Which pair of lines is perpendicular?

    • A Two lines of different lengths
    • B Two lines that meet, but not at a right angle
    • C Two lines that stay the same distance apart and never meet
    • D Two lines that meet or cross at a right angle
    Show the answer to question 30

    Answer: D · Two lines that meet or cross at a right angle

    Why:

    Parallel = never meet, always the same gap. Perpendicular = meet or cross at 90°.

Statistics

  1. Objective: Interpret and present data using bar charts, pictograms and tables

    The pictogram shows the birds seen in a garden one morning.

    How many birds were robins?

    Pictogram: Birds seen in the gardenA pictogram. Key: one circle stands for 4 birds. robin: two and a quarter circles; sparrow: three and a half circles; magpie: four and a quarter circles; pigeon: half a circle.Birds seen in the garden robinsparrowmagpiepigeon Key: stands for 4 birds
    Show the answer to question 31

    Answer: 9

    Why:

    Robin: 2 circles × 4 = 8, and a quarter of a circle stands for 1: 8 + 1 = 9.

  2. Objective: Solve one-step and two-step questions ("How many more?", "How many fewer?") from scaled bar charts, pictograms and tables

    The bar chart shows the favourite colours of a group of children.

    How many fewer children chose green than yellow?

    Bar chart: Favourite coloursA bar chart. Number of children is on the scale up the side, from 0 to 40, with a line every 5, each line labelled. yellow: the bar ends on the line marked 20; red: the bar ends on the line marked 40; green: the bar ends on the line marked 5; blue: the bar ends on the line marked 35.Favourite colours 0510152025303540 yellowredgreenblue Number of children
    Show the answer to question 32

    Answer: 15

    Why:

    The yellow bar ends on the 20 line: 20.

    The green bar ends on the 5 line: 5.

    20 − 5 = 15. "How many fewer" means find the difference.

Answers

  1. 1. D, E · 400, 900
  2. 2. D · 249
  3. 3. 928, 982
  4. 4. 807
  5. 5. three hundred and ninety-five
  6. 6. 674
  7. 7. 662
  8. 8. D · Only the tens column
  9. 9. B · 400
  10. 10. 69
  11. 11. 12
  12. 12. A · 128 ÷ 8 = 16
  13. 13. 90 cm
  14. 14. 5/10 (also accept 1/2)
  15. 15. 32
  16. 16. 12
  17. 17. B · 12/16
  18. 18. A · They made no mistake
  19. 19. C · 2/6, 3/6, 4/6, 5/6
  20. 20. 26 mm
  21. 21. 32 cm
  22. 22. 6 coins
  23. 23. C · 3:55 pm
  24. 24. 07:50 (also accept 07.50, 0750, 7:50 am)
  25. 25. 30
  26. 26. 1 hour 50 minutes (also accept 110 minutes, 110, 1h 50 minutes)
  27. 27. 8
  28. 28. 6
  29. 29. C · north
  30. 30. D · Two lines that meet or cross at a right angle
  31. 31. 9
  32. 32. 15

More Year 3 maths

Remelia practises maths for the child's own year group, in short sessions, and brings back on later days what they got wrong.

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