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Measurement: units, time, money and shape

Bea here! Measurement is maths you use every day: weighing a cake, catching a bus, paying at the shop. Let us get the units, the clock and the shapes under control.

1. Cheat sheet: Measurement

Everything you need on one page. Press the button to print it on one sheet of A4.

Metric units

  • 1 km = 1,000 m. 1 m = 100 cm. 1 cm = 10 mm.
  • 1 kg = 1,000 g. 1 l = 1,000 ml.
  • Big to small: multiply. Small to big: divide.
  • 3.5 kg = 3,500 g.

Imperial (about)

  • 1 inch ≈ 2.5 cm. 1 foot ≈ 30 cm.
  • 1 kg ≈ 2.2 pounds (lb). 1 litre ≈ 1¾ pints.
  • 5 miles ≈ 8 km.

Money

  • £1 = 100p. £2 and 5p is written £2.05. (£2.5 would mean £2.50.)
  • Change: count up from the price to what was paid.
  • Pay £10 for £6.35: 5p + 60p + £3 = £3.65.

Reading scales

  • Find what ONE gap is worth: gap value = difference ÷ number of gaps.
  • Then count gaps from a labelled mark.

Clocks

  • 60 seconds = 1 minute. 60 minutes = 1 hour.
  • pm: add 12 for 24-hour (3:40 pm = 15:40).
  • 12:00 pm = 12:00. 12:30 am = 00:30.

Durations and calendars

  • Bridge the hour: 2:40 to 3:25 = 20 + 25 = 45 min.
  • 0.25 h = 15 min. 1.5 h = 1 h 30 min.
  • 30 days: Sep, Apr, Jun, Nov. Feb has 28 (29 in a leap year, like 2028).

Perimeter and area

  • Perimeter: distance round (cm). Area: space inside (cm²).
  • Rectangle: P = 2 × (l + w), A = l × w.
  • Triangle: ½ × base × height. Parallelogram: base × height.
  • Composite: split, or take away.

Volume

  • Cuboid: length × width × height (cm³).
  • 1 litre = 1,000 cm³.
  • Count cubes layer by layer.

2. Mini lessons

Metric and imperial units

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Metric units use 10, 100 and 1,000 to change size, so converting is moving digits (or multiplying and dividing). Changing to a smaller unit means more of them, so multiply. Old imperial units, like miles and pounds, are only linked by approximate rules you have to remember.

kmmcmmm×1000×100×10kgg×1000lml×1000
Go right: multiply. Go left: divide.

Worked example: Change 3.5 kg to grams and 2,450 ml to litres. About how many km is 30 miles?

  1. kg to g: smaller unit, so multiply by 1,000. 3.5 × 1,000 = 3,500 g.
  2. ml to l: bigger unit, so divide by 1,000. 2,450 ÷ 1,000 = 2.45 l.
  3. 5 miles is about 8 km. 30 ÷ 5 = 6, so 6 × 8 = 48.

Answer: 3,500 g, 2.45 l and about 48 km

Money: totals and change

MEAS-03

Add the prices to find the total. To find change, count up from the price to the amount paid, in easy jumps. Always write money with two decimal places, like £3.05.

Animation: finding change by counting up

£6.35£6.40£7.00£10.00+5p+60p+£3Change: 5p + 60p + £3 = £3.65not to scale

Mia spends £6.35 and pays with a £10 note. Jump up to the next 10p: £6.35 + 5p = £6.40. Jump up to the next pound: £6.40 + 60p = £7. Jump to £10: £7 + £3. Add the jumps: 5p + 60p + £3 = £3.65 change.

Worked example: Mia buys a book for £4.80 and a pen for £1.55. She pays with a £10 note. How much change?

  1. Total: £4.80 + £1.55 = £6.35.
  2. Count up from £6.35: +5p to £6.40, +60p to £7, +£3 to £10.
  3. Add the jumps: 5p + 60p + £3 = £3.65.
  4. Check: £6.35 + £3.65 = £10.

Answer: £3.65

Reading measuring scales

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Not every scale goes up in ones. First find what one small gap is worth: take two labelled marks, find the difference, and divide by the number of gaps between them. Then count along from a labelled mark.

0102014
Between 0 and 10 there are 5 equal gaps, so each gap is 10 ÷ 5 = 2.

Worked example: The scale has labels at 0, 10 and 20 with 5 gaps between each label. The pointer is on the 7th small mark after 0. What is the reading?

  1. The gap between 0 and 10 is 10. It is split into 5 gaps.
  2. One gap = 10 ÷ 5 = 2.
  3. The 7th mark is 7 × 2 = 14.

Answer: 14

Telling the time: analogue, digital, 12- and 24-hour

MEAS-05MEAS-06

The short hand shows the hours and the long hand shows the minutes. On a 12-hour clock we add am or pm. The 24-hour clock has no am or pm: afternoon and evening hours are 12 more, so 3:40 pm is 15:40.

1234567891011123:40 pm15:40twenty to four
Short hand between 3 and 4. Long hand on 8 means 40 minutes. For the 24-hour clock, add 12 to pm hours.

Worked example: Write 20:15 using the 12-hour clock. Then write 8:05 am and 9:50 pm in 24-hour time.

  1. 20:15: take away 12: 20 − 12 = 8. So it is 8:15 pm.
  2. 8:05 am stays the same in 24-hour time: 08:05.
  3. 9:50 pm: add 12 to 9: 21:50.

Answer: 8:15 pm, 08:05 and 21:50

Durations and timetables

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To find how long something takes, bridge the hour: count on to the next whole hour, then whole hours, then the rest of the minutes. Add the pieces. Time is not decimal, so 100 minutes does not make an hour.

Animation: how long from 2:40 to 3:25?

1234567891011122:403:003:25start+20 minutes+20 + 25 more= 45 min

The clock shows 2:40. The red hand is the minute hand. Move the minute hand to 12: that bridges the hour in 20 minutes. Carry on to 25 past 3: 25 more minutes. 20 + 25 = 45 minutes. Time is not decimal: bridge to the next hour first.

Worked example: A train leaves at 09:25 and arrives at 11:10. How long does the journey take?

  1. 09:25 to 10:00 is 35 minutes.
  2. 10:00 to 11:00 is 1 hour = 60 minutes.
  3. 11:00 to 11:10 is 10 minutes.
  4. Add: 35 + 60 + 10 = 105 minutes = 1 hour 45 minutes.

Answer: 1 hour 45 minutes

Time units, decimal hours and calendars

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A decimal hour is a fraction of 60 minutes: 0.25 h is 15 minutes and 0.5 h is 30 minutes. For calendar questions, count to the end of the month first, then count the days in the next month. A leap year has 29 days in February.

15 min30 min45 min60 min0.25 h0.5 h0.75 h1 hMinutes ÷ 60 = hours as a decimal
0.25 h = 15 min. 0.5 h = 30 min. Never write 1.5 hours as 1 h 50 min.

Worked example: Write 2.25 hours in hours and minutes. How many days after 25 February 2027 is 5 March 2027?

  1. 0.25 hours = 15 minutes, so 2.25 hours = 2 hours 15 minutes.
  2. 2027 is not a leap year, so February has 28 days.
  3. 25 Feb to 28 Feb is 3 days. 28 Feb to 5 Mar is 5 more days.
  4. 3 + 5 = 8 days.

Answer: 2 hours 15 minutes and 8 days

Perimeter and area of rectangles

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Perimeter is the distance all the way round a shape, in cm or m. Area is the space inside, in square units like cm². For a rectangle, perimeter = 2 × (length + width) and area = length × width.

Animation: fence the edge, tile the inside

5 cm3 cm51015Perimeter = 5 + 3 + 5 + 3 = 16 cmArea = 5 × 3 = 15 cm²

A rectangle 5 cm long and 3 cm wide. Perimeter: walk round the edge (the fence). 5 + 3 + 5 + 3 = 16 cm. Area: cover the inside with 1 cm squares, row by row. 3 rows of 5 squares: 15 squares. Area = 15 cm². Perimeter is a length (cm). Area is a count of squares (cm²).

Worked example: A rectangular field is 14 m long and 8 m wide. Fencing costs £5 per metre. How much does it cost to fence all the way round, and what is the area?

  1. Perimeter: 2 × (14 + 8) = 2 × 22 = 44 m.
  2. Cost: 44 × £5 = £220.
  3. Area: 14 × 8 = 112 m².

Answer: £220, and area 112 m²

Area of triangles and parallelograms

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A parallelogram has the same area as a rectangle with the same base and height: base × height. A triangle is half of that: ½ × base × height. The height is measured straight up, at a right angle to the base.

base 16 cmh 5 cmbase 9 cmh 6 cm½ × 16 × 5 = 409 × 6 = 54
The height is measured straight up (at a right angle to the base), not along a slanted side.

Worked example: Find the area of a triangle with base 16 cm and height 5 cm, and of a parallelogram with base 9 cm and height 6 cm.

  1. Triangle: ½ × 16 × 5 = 8 × 5 = 40 cm².
  2. Parallelogram: 9 × 6 = 54 cm².

Answer: 40 cm² and 54 cm²

Composite shapes

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A composite shape is made of rectangles joined together. To find its area, either split it into rectangles and add, or complete the big rectangle and take away the missing piece. For the perimeter, add every outside edge, and work out any missing edge first.

558233Perimeter5+2+3+3+8+5= 26 cmArea = 40 − 6= 34 cm²
Area: the whole 8 by 5 rectangle, minus the missing 3 by 2 corner.

Worked example: Find the area and perimeter of the L-shape in the picture.

  1. Whole rectangle: 8 × 5 = 40 cm². Missing corner: 3 × 2 = 6 cm². Area: 40 − 6 = 34 cm².
  2. Perimeter: add all six edges: 5 + 2 + 3 + 3 + 8 + 5 = 26 cm.
  3. The L-shape has the same perimeter as the 8 by 5 rectangle: 2 × (8 + 5) = 26 cm.

Answer: 34 cm² and 26 cm

Same area, different perimeter

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Shapes with the same area can have different perimeters, and shapes with the same perimeter can have different areas. Long and thin shapes have a long perimeter. The nearer a shape is to a square, the shorter the perimeter for the same area.

1 × 12: perimeter 26 cm2 × 6: perimeter 16 cm3 × 4: perimeter 14 cm
All three have area 12 cm². The more square it is, the shorter the perimeter.

Worked example: Rectangles with whole-number sides all have area 12 cm². Find each perimeter and say which is shortest.

  1. 1 × 12: 2 × (1 + 12) = 26 cm.
  2. 2 × 6: 2 × (2 + 6) = 16 cm.
  3. 3 × 4: 2 × (3 + 4) = 14 cm.
  4. The 3 by 4 rectangle has the shortest perimeter.

Answer: 26 cm, 16 cm and 14 cm; the 3 × 4

Volume and packing cubes

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Volume is the space inside a 3-D shape, counted in cubes: cm³ for 1 cm cubes. For a cuboid, count the cubes in one layer, then multiply by the number of layers: length × width × height.

4 long3 high3 deepLayer: 4 × 3 = 123 layers: 12 × 3= 36 cubes
Volume = length × width × height. Count cubes layer by layer.

Worked example: A box is 12 cm long, 8 cm wide and 6 cm high. How many 2 cm cubes fit exactly inside? What is the volume of a cuboid 6 cm by 5 cm by 3 cm?

  1. Cubes along each side: 12 ÷ 2 = 6, 8 ÷ 2 = 4, 6 ÷ 2 = 3.
  2. Number of cubes: 6 × 4 × 3 = 72.
  3. Volume of the second cuboid: 6 × 5 × 3 = 90 cm³.

Answer: 72 cubes, and 90 cm³

3. Worked examples from easy to hard

Level 1 is Year 3, one step. Level 5 is a challenge with 3 to 5 steps. Try each one yourself before you read the steps.

Level 1One step

How many grams are there in 2 kg?

  1. 1 kg = 1,000 g.
  2. 2 × 1,000 = 2,000.

Answer: 2,000 g

Level 2One or two steps

A film starts at 14:35 and lasts 50 minutes. When does it end?

  1. 14:35 + 25 min = 15:00 (bridge the hour).
  2. 50 − 25 = 25 minutes left.
  3. 15:00 + 25 min = 15:25.

Answer: 15:25

Level 3Two steps

A rectangular playground is 15 m by 9 m. Edging costs £3 per metre. How much does it cost to edge all the way round?

  1. Perimeter: 2 × (15 + 9) = 2 × 24 = 48 m.
  2. Cost: 48 × £3 = £144.

Answer: £144

Level 4Exam standard

The 07:55 train takes 1 hour 50 minutes. Then Sara waits 25 minutes for a bus, and the bus takes 40 minutes. When does she arrive?

  1. 07:55 + 1 h 50 min = 09:45.
  2. Wait 25 min: 09:45 + 25 min = 10:10.
  3. Bus 40 min: 10:10 + 40 min = 10:50.

Answer: 10:50

Level 5Challenge

A tank is 60 cm long, 30 cm wide and 40 cm high. It is filled with water using a 1.5 litre jug. How many jugfuls fill the tank to the top? (1 litre = 1,000 cm³)

  1. Volume: 60 × 30 × 40 = 72,000 cm³.
  2. In litres: 72,000 ÷ 1,000 = 72 litres.
  3. Jugfuls: 72 ÷ 1.5 = 48.

Answer: 48 jugfuls

4. Common mistakes

Lots of children make these slips. Spot them early and you will win marks.

Reading every gap as 1

MEAS_SCALE_STEPS_AS_ONE

The mistake: Reading each small mark on a scale as 1.

Why it is wrong: The gaps are only worth 1 if the scale says so. The labels tell you what the gaps are worth.

How to avoid it: Find the value of ONE gap first: difference between labels ÷ number of gaps.

✗ Wrong: Scale 0 to 10 with 5 gaps. The pointer on the 2nd mark: "2".
✓ Right: Each gap is 10 ÷ 5 = 2, so the 2nd mark is 4.

The wrong conversion number

MEAS_CONVERSION_FACTOR

The mistake: Using × 100 instead of × 1,000 for kg, g, l and ml.

Why it is wrong: Kilo means a thousand. Centi means a hundredth, which is why only cm and m use 100.

How to avoid it: Learn the ladder: 1,000 for km, kg and l; 100 for m to cm; 10 for cm to mm.

✗ Wrong: 3.5 kg = 350 g.
✓ Right: 3.5 kg = 3,500 g.

Perimeter when area is asked

MEAS_AREA_PERIMETER_CONFUSED

The mistake: Adding the edges when the question wants the area, or the other way round.

Why it is wrong: Perimeter is the fence round the edge. Area is the tiles that cover the inside.

How to avoid it: Underline "area" or "perimeter" and write the unit (cm or cm²) before you start.

✗ Wrong: Area of the L-shape: 5 + 2 + 3 + 3 + 8 + 5 = 26 cm².
✓ Right: Area = 40 − 6 = 34 cm². (26 cm is the perimeter.)

Treating an hour as 100 minutes

TIME_100_MIN_HOUR

The mistake: Treating time as decimal, with 100 minutes in an hour.

Why it is wrong: There are 60 minutes in an hour, so you must bridge the hour on the clock.

How to avoid it: Draw a clock face or a timeline and jump to the next hour.

✗ Wrong: 3:10 − 25 min = 2:85. And 1.5 h = 1 h 50 min.
✓ Right: 3:10 − 25 min = 2:45. And 1.5 h = 1 h 30 min.

Wrong clock format

TIME_12_24_HOUR

The mistake: Answering in 12-hour time when the question wants 24-hour time.

Why it is wrong: The question tells you which format to use. For afternoon times the numbers differ by 12.

How to avoid it: Circle the format the question asks for, and add 12 to pm hours.

✗ Wrong: 3:15 pm in 24-hour time: "3:15".
✓ Right: 15:15.

Right number, wrong unit

TECH_UNITS

The mistake: Writing the correct digits with the wrong unit.

Why it is wrong: A length, an area and a volume are different kinds of quantity, so the units matter.

How to avoid it: Check the unit in the answer line, or the options, before you move on.

✗ Wrong: Area of a 12 cm by 9 cm rectangle: 108 cm.
✓ Right: 108 cm² (square centimetres).

5. Quick check

Five questions, easy to hard. Have a go on paper, then open the answer.

  1. How many metres are there in 2.4 km?

    Show answer

    2,400 m

    km to m: multiply by 1,000. 2.4 × 1,000 = 2,400.

  2. Zainab buys a scarf for £6.40 and gloves for £3.95. She pays with a £20 note. How much change does she get?

    Show answer

    £9.65

    £6.40 + £3.95 = £10.35. Count up from £10.35: +5p = £10.40, +60p = £11, +£9 = £20. 5p + 60p + £9 = £9.65.

  3. A coach leaves at 17:10. The journey takes 3 hours 15 minutes. When does it arrive?

    Show answer

    20:25

    17:10 + 3 h = 20:10. 20:10 + 15 min = 20:25.

  4. A triangle has a base of 14 cm and a height of 9 cm. What is its area?

    Show answer

    63 cm²

    ½ × 14 × 9 = 7 × 9 = 63 cm².

  5. A rectangle has an area of 70 cm² and a perimeter of 34 cm. What are the lengths of its sides?

    Show answer

    7 cm and 10 cm

    The two sides add up to half the perimeter: 34 ÷ 2 = 17. Two numbers that make 17 and multiply to 70 are 7 and 10. Check: 7 × 10 = 70.

6. For grown-ups

  • Use real scales. Ask your child to read the kitchen scales, a measuring jug and a ruler, and to say what ONE small mark is worth before reading the value.
  • Practise time with real timetables: "The bus leaves at 14:20 and takes 55 minutes. When do we arrive?" Bridging the hour on your fingers or a clock face works well.
  • Keep area and perimeter apart with a story: perimeter is the fence, area is the grass. Ask your child to draw a rectangle on squared paper and find both.