Measurement
KS2MA-Y3-D005
Measuring and comparing lengths, mass and volume/capacity using mixed units, measuring perimeter of 2-D shapes, money calculations, and telling time using Roman numerals, analogue clocks and 12/24-hour notation.
National Curriculum context
In Year 3, the measurement domain significantly extends KS1 knowledge by introducing millimetres, mixed units (e.g. 1 m and 50 cm), simple metric equivalents, and calculating the perimeter of 2-D shapes for the first time. The non-statutory guidance indicates that pupils continue to measure using a range of instruments, read scales with increasing accuracy in a range of contexts, and that they should be able to carry out additions and subtractions with measurements in the same units. Money work progresses to include formal £ and p notation and giving change, while time is extended to Roman numerals on clock faces, 12- and 24-hour clocks, and reading the time to the nearest minute. These practical measurement skills reinforce pupils' number understanding in applied contexts and connect directly to the formal calculation methods being developed in the number domains.
6
Concepts
2
Clusters
1
Prerequisites
6
With difficulty levels
Lesson Clusters
Measure in mixed units and calculate perimeter
introduction CuratedMixed-unit measurement and perimeter are both applied measurement skills that connect to number work and shape. They form the practical measurement cluster.
Calculate with money and read the time accurately
practice CuratedMoney calculations, Roman numerals on clock faces, 24-hour clock and duration of time are co-taught as a cluster (C032, C034, C035 mutually co-teach; C033 co-teaches with C035). Time and money together form the real-world applications cluster.
Teaching Suggestions (1)
Study units and activities that deliver concepts in this domain.
Measurement: Length, Mass, Capacity and Time
Mathematics Worked Example SetPedagogical rationale
Y3 measurement brings together practical measuring skills with the formal calculation methods being learned in number. Converting between units (e.g., knowing that 1 m = 100 cm) reinforces place value understanding. Measurement contexts provide the most natural application for addition and subtraction of three-digit numbers. Time remains a significant challenge because it is the only non-decimal system children encounter, and the analogue clock face requires simultaneous reading of two different scales.
Prerequisites
Concepts from other domains that pupils should know before this domain.
Concepts (6)
Measuring in mixed units (length, mass, volume)
skill AI FacilitatedMA-Y3-C030
In Year 3, pupils work with measurements given in mixed units — for example, 1 m 45 cm, 2 kg 300 g, 1 l 250 ml — and perform calculations with such measurements. They also recognise simple equivalents (e.g. 1 km = 1000 m, 1 m = 100 cm, 1 m = 1000 mm, 1 kg = 1000 g, 1 l = 1000 ml). Mastery means pupils can read measuring instruments accurately, record measurements in appropriate units, and carry out addition and subtraction with measurements.
Teaching guidance
Use real measuring instruments: rulers in mm/cm/m, kitchen scales in g/kg, measuring jugs in ml/l. The curriculum specifies mm is introduced in Year 3, so ensure this unit is covered. Simple equivalents: use the pattern that kilo- means 1000, so 1 kilogram = 1000 grams, 1 kilometre = 1000 metres. Connect to place value: 1 m 45 cm = 145 cm (multiply metres by 100 and add centimetres). Practise reading scales with non-standard intervals.
Common misconceptions
Pupils confuse mm and cm (writing 45 mm as 45 cm). They may add mixed units without converting (1 m 70 cm + 50 cm = 1 m 120 cm rather than 2 m 20 cm). Converting between units requires the multiplication/division knowledge from the number domain, and pupils often use the wrong conversion factor (multiplying by 10 rather than 100 for cm to mm).
Difficulty levels
Measuring objects using a ruler (cm and mm) and a set of kitchen scales (g/kg), recording the measurement in the correct unit.
Example task
Measure this pencil to the nearest centimetre. Weigh this bag of rice on the scales.
Model response: The pencil is 14 cm long. The rice weighs 500 g.
Recording measurements in mixed units and knowing simple equivalences (1 m = 100 cm, 1 kg = 1000 g, 1 l = 1000 ml).
Example task
A table is 1 m and 35 cm long. Write this in centimetres only.
Model response: 1 m 35 cm = 135 cm because 1 m = 100 cm, so 100 + 35 = 135 cm.
Adding and subtracting measurements in mixed units, converting to a single unit first.
Example task
A bag weighs 2 kg 400 g. Another bag weighs 1 kg 750 g. What is their total weight?
Model response: 2 kg 400 g + 1 kg 750 g: 400 g + 750 g = 1150 g = 1 kg 150 g. 2 kg + 1 kg + 1 kg 150 g = 4 kg 150 g.
Solving multi-step measurement problems involving comparison and conversion between units.
Example task
A ribbon is 2 m 30 cm long. I cut off 85 cm. How much is left? Give your answer in metres and centimetres.
Model response: 2 m 30 cm = 230 cm. 230 - 85 = 145 cm = 1 m 45 cm.
CPA Stages
concrete
Measuring real objects using rulers (mm/cm/m), kitchen scales (g/kg) and measuring jugs (ml/l), recording measurements in mixed units and practising unit conversions with physical equipment
Transition: Child reads measuring instruments accurately in mixed units and converts between units using the ×1000 relationship (1 kg = 1000 g, 1 l = 1000 ml, 1 km = 1000 m)
pictorial
Drawing scales on number lines showing conversions between units, recording measurements in tables, and using bar models to add and subtract mixed-unit measurements
Transition: Child records conversions and calculations on paper without measuring equipment, correctly converting between mixed units and single units
abstract
Converting between metric units mentally, adding and subtracting measurements in mixed units, and selecting appropriate units for different contexts
Transition: Child converts between metric units fluently and selects the most appropriate unit for any given measurement context
Delivery rationale
Primary maths (Y3) with concrete stage requiring physical manipulatives (30 cm rulers (mm markings), metre sticks). AI delivers instruction; facilitator sets up materials.
Perimeter of simple 2-D shapes
knowledge AI FacilitatedMA-Y3-C031
Perimeter is the distance around the boundary of a flat (2-D) shape, found by adding the lengths of all its sides. In Year 3, pupils measure the perimeter of simple rectilinear shapes. Mastery means pupils understand perimeter as a length measurement (in mm, cm or m), can measure sides accurately and add them, and can distinguish perimeter from area.
Teaching guidance
Introduce perimeter physically: pupils walk the perimeter of the playground or run a finger around the edge of a shape. Measure sides using a ruler and record each length before adding. Simple rectilinear shapes (made from squares on squared paper) allow pupils to count squares along each side before measuring. Emphasise: perimeter is the total length around the outside, not the space inside (which is area). Use the formula for a rectangle (2 × length + 2 × width) informally at this stage.
Common misconceptions
Pupils frequently confuse perimeter (length around the outside) with area (space inside). They may count the squares of a shape (area) rather than measuring around its edge (perimeter). When measuring rectilinear shapes, pupils sometimes miss a side or count a vertex rather than a side. On shapes with equal opposite sides, pupils may only measure two sides and forget to double them.
Difficulty levels
Tracing around a shape on squared paper and counting the unit lengths along each side to find the perimeter.
Example task
A rectangle on squared paper is 4 squares long and 2 squares wide. Trace around the outside and count the units.
Model response: Top: 4, Right: 2, Bottom: 4, Left: 2. Perimeter = 4 + 2 + 4 + 2 = 12 units.
Measuring the sides of simple shapes with a ruler and adding the lengths to find the perimeter.
Example task
Measure each side of this triangle with a ruler and find its perimeter.
Model response: Sides: 5 cm, 4 cm, 3 cm. Perimeter = 5 + 4 + 3 = 12 cm.
Calculating the perimeter of rectilinear shapes where some side lengths are given and others must be deduced.
Example task
A rectangle has a length of 8 cm and a width of 3 cm. What is its perimeter?
Model response: Perimeter = 8 + 3 + 8 + 3 = 22 cm. Or: 2 x (8 + 3) = 2 x 11 = 22 cm.
Finding the perimeter of compound rectilinear shapes (L-shapes) where missing side lengths must be calculated.
Example task
An L-shape has outer dimensions 6 cm by 4 cm, with a 2 cm by 2 cm square cut from one corner. Find the perimeter.
Model response: The L-shape has 6 sides. Working around the outside: 6 + 2 + 4 + 2 + 2 + 4 = 20 cm. The missing sides are 6-2=4 and 4-2=2.
CPA Stages
concrete
Walking the perimeter of the classroom, playground and large shapes taped on the floor, then measuring the perimeter of smaller shapes using string laid along edges and a ruler
Transition: Child measures all sides of a shape and adds them to find the perimeter without being reminded to include every side
pictorial
Drawing rectilinear shapes on squared paper and counting/adding side lengths to calculate perimeter, labelling each side measurement on the diagram
Transition: Child labels all sides of any rectilinear shape and calculates perimeter correctly, clearly distinguishing perimeter (distance around) from area (space inside)
abstract
Calculating perimeters of shapes from given dimensions without drawing, including finding missing side lengths of rectilinear shapes
Transition: Child calculates perimeters from given measurements and works backwards from a perimeter to find unknown side lengths
Delivery rationale
Primary maths (Y3) with concrete stage requiring physical manipulatives (string, rulers). AI delivers instruction; facilitator sets up materials.
Money calculations with £ and p
skill AI FacilitatedMA-Y3-C032
In Year 3, pupils add and subtract amounts of money expressed in both pounds and pence (e.g. £3.45 + £1.27 = £4.72) and calculate change. This requires understanding the notation £x.pp, relating pounds and pence to the decimal place value system. Mastery means pupils can fluently perform calculations in mixed £/p notation and give change by counting up from the purchase price to the amount tendered.
Teaching guidance
Connect to decimal notation: £1.45 means 1 pound and 45 pence, paralleling 1 whole and 45 hundredths. Use play money in practical shopkeeper role-plays as the primary concrete context. Teach giving change as 'counting up' (complementary addition): from £1.37 to £2.00, count up 3p to £1.40, then 60p to £2.00, giving change of 63p. This strategy is more intuitive than subtraction. Connect to columnar addition/subtraction for written calculations.
Common misconceptions
Pupils confuse £ and p notation — writing £45 to mean 45 pence, or 45p to mean £4.50. They may add pounds and pence in separate columns without converting: £1.45 + 75p is handled as 1.45 + 0.75 = 2.20 by some but as 1.45 + 75 = 76.45 by others. The conversion between pence and pounds (÷ 100) is often unreliable.
Difficulty levels
Adding amounts of money using play coins and notes in a shopkeeper role-play.
Example task
A toy costs £2.35. You have a £2 coin, a 20p coin, a 10p coin and a 5p coin. Do you have enough?
Model response: £2 + 20p + 10p + 5p = £2.35. Yes, that is exactly enough.
Adding and subtracting money amounts using the pounds and p notation, with pictorial support.
Example task
A book costs £3.75. A pen costs £1.50. What is the total cost?
Model response: £3.75 + £1.50: 75p + 50p = 125p = £1.25. £3 + £1 + £1.25 = £5.25.
Calculating change from a given amount using counting up (complementary addition).
Example task
An apple costs £1.37. You pay with a £2 coin. How much change do you get?
Model response: Count up from £1.37: +3p to £1.40, +60p to £2.00. Change = 63p.
Solving multi-step money problems involving total cost, change, and comparison.
Example task
Jack buys 3 pencils at 45p each and a rubber for 68p. He pays with £5. How much change does he receive?
Model response: 3 x 45p = £1.35. £1.35 + 68p = £2.03. Change: £5.00 - £2.03 = £2.97.
CPA Stages
concrete
Using play money (£1, £2 coins; 1p, 2p, 5p, 10p, 20p, 50p coins; £5, £10 notes) to set up shopkeeper role-plays, making totals and giving change by counting up
Transition: Child makes totals and gives change using coins fluently, selecting efficient coin combinations and counting up from the price to the amount paid
pictorial
Recording money calculations in columnar format with the decimal point aligned, drawing number lines to show counting-up change, and converting between pounds and pence on paper
Transition: Child sets up money calculations in columns with the decimal point correctly aligned and uses number lines for change without play money
abstract
Adding and subtracting money amounts mentally and in written form, converting fluently between pounds and pence, and solving multi-step money word problems
Transition: Child solves multi-step money problems fluently, converting between £ and p notation and calculating change without visual aids
Delivery rationale
Primary maths (Y3) with concrete stage requiring physical manipulatives (play money (full coin and note set), price labels). AI delivers instruction; facilitator sets up materials.
Time: Roman numerals I–XII and analogue clock
Keystone knowledge AI FacilitatedMA-Y3-C033
Roman numerals I through XII are used on traditional clock faces. Pupils must recognise these symbols and translate them to Hindu-Arabic numerals to read the time. The curriculum also requires pupils to tell and write the time from analogue clocks to the nearest minute. Mastery means pupils can read any time shown on a Roman numeral clock face and accurately report the time to the nearest minute in both words and 12-hour notation.
Teaching guidance
Display Roman numerals I–XII alongside their Hindu-Arabic equivalents. Focus on the additive (I, II, III, VI, VII, VIII, XI, XII) and subtractive (IV = 4, IX = 9) notations. Use real clocks with Roman numerals or large printed clock faces. Practise reading times to the nearest minute — the minute hand requires reading a scale of 60 (each minute mark is worth 1 minute), while the hour hand's position between two Roman numerals indicates the hour.
Common misconceptions
Pupils sometimes read Roman numeral IV as 6 (confusing VI and IV). They may read the hour hand position when it is between two numbers by always rounding to the nearer number rather than the number it has passed. The minute hand scale (each interval of 5 minutes marked but individual minutes unmarked between) requires careful interpretation.
Difficulty levels
Matching Roman numerals I to XII with Hindu-Arabic numerals 1 to 12 using a clock face for reference.
Example task
Look at this clock face. What number does VI represent? What about IX?
Model response: VI = 6. IX = 9.
Reading the time from a Roman numeral clock face to the nearest 5 minutes.
Example task
The hour hand is between VIII and IX, and the minute hand points to III. What time is it?
Model response: VIII = 8 and III = 15 minutes. The time is 8:15 or quarter past eight.
Reading any time to the nearest minute from an analogue clock with Roman numerals, writing in 12-hour notation.
Example task
The hour hand is just past XI and the minute hand points to the 7th minute mark past VI. What time is it?
Model response: XI = 11. The minute hand is at 30 + 7 = 37 minutes. The time is 11:37.
CPA Stages
concrete
Handling real or large demonstration clocks with Roman numerals I-XII, matching Roman numeral cards to Hindu-Arabic number cards, and reading times on analogue clocks with moveable hands
Transition: Child reads all Roman numerals I-XII instantly and tells the time to the nearest minute on a Roman numeral clock face
pictorial
Drawing clock faces with Roman numerals, recording times in words and in 12-hour digital notation, and labelling the minute scale (0-60) around the clock
Transition: Child draws accurate clock faces and reads/records any time to the nearest minute without a reference chart for Roman numerals
abstract
Reading and writing times in Roman numeral and analogue contexts without a clock, converting between words and notation, and answering time questions mentally
Transition: Child converts between Roman numerals, analogue positions and digital time notation fluently without any visual reference
Delivery rationale
Primary maths (Y3) with concrete stage requiring physical manipulatives (demonstration clock with Roman numerals, Roman numeral cards (I-XII)). AI delivers instruction; facilitator sets up materials.
24-hour clock
skill AI FacilitatedMA-Y3-C034
The 24-hour clock system represents times from midnight (00:00) through midnight of the following day (23:59), avoiding the a.m./p.m. ambiguity of the 12-hour system. Afternoon hours are expressed as 13:00–23:59. Mastery means pupils can convert between 12-hour (with a.m./p.m.) and 24-hour notation and can read and write times in both systems correctly.
Teaching guidance
Establish: for a.m. times, the 24-hour time is the same as the 12-hour time but written with a leading zero (09:00). For p.m. times, add 12 to the 12-hour hour (3:00 p.m. = 15:00). Use a number line of 24 hours to show how p.m. continues the count past 12. Display a conversion table initially. Digital clocks showing 24-hour times provide a practical context. Connect to timetables (train, bus, television) which commonly use 24-hour notation.
Common misconceptions
Pupils frequently forget to add 12 for p.m. times (recording 3 p.m. as 03:00 instead of 15:00). They may think 12:00 midnight is 00:00 correctly but treat 12:00 noon as 00:00 (confusing noon with midnight). The format 00:00 for midnight (rather than 24:00) can be counterintuitive.
Difficulty levels
Understanding that a.m. means morning and p.m. means afternoon/evening, and identifying times as a.m. or p.m.
Example task
Is 3 o'clock in the afternoon written as 3 a.m. or 3 p.m.? What about 8 o'clock in the morning?
Model response: 3 o'clock in the afternoon is 3 p.m. 8 o'clock in the morning is 8 a.m.
Converting simple times between 12-hour and 24-hour format using the rule 'add 12 for p.m.'
Example task
Convert these times to 24-hour format: 2:30 p.m., 9:15 a.m., 6:00 p.m.
Model response: 2:30 p.m. = 14:30. 9:15 a.m. = 09:15. 6:00 p.m. = 18:00.
Converting fluently between 12-hour and 24-hour notation in both directions, including noon and midnight.
Example task
Convert to 12-hour time: 17:45, 00:30, 12:00. Convert to 24-hour time: 11:50 p.m.
Model response: 17:45 = 5:45 p.m. 00:30 = 12:30 a.m. 12:00 = 12:00 p.m. (noon). 11:50 p.m. = 23:50.
Using 24-hour times in context to solve problems, such as reading timetables.
Example task
A bus leaves at 15:45 and arrives at 16:20. How long is the journey? Another bus leaves at 09:50 and takes the same amount of time. When does it arrive?
Model response: 15:45 to 16:20: from 15:45 to 16:00 is 15 minutes, from 16:00 to 16:20 is 20 minutes. Total = 35 minutes. Second bus: 09:50 + 35 minutes = 10:25.
CPA Stages
concrete
Using a 24-hour number line from 00:00 to 23:59, sliding a marker along to show how 12-hour times map to 24-hour times, with analogue and digital clocks side by side
Transition: Child converts a.m. times (same number, add leading zero) and p.m. times (add 12) correctly without the number line
pictorial
Drawing a circular 24-hour diagram or parallel number lines (12-hour above, 24-hour below) and recording conversions in a two-column table
Transition: Child completes 12-hour to 24-hour conversions on paper without the parallel number line, correctly handling midnight (00:00) and noon (12:00)
abstract
Converting between 12-hour and 24-hour notation mentally, reading bus and train timetables in 24-hour format, and solving problems involving both systems
Transition: Child converts any time between 12-hour and 24-hour format within 3 seconds and reads real timetables without errors
Delivery rationale
Primary maths (Y3) with concrete stage requiring physical manipulatives (24-hour number line (wall display), analogue clock). AI delivers instruction; facilitator sets up materials.
Comparing durations of time
skill AI FacilitatedMA-Y3-C035
Comparing durations involves calculating how much time has passed between two events or which of two events took longer. This requires converting between seconds, minutes and hours as necessary. Mastery means pupils can calculate time durations using a number line or counting-on strategy, compare durations expressed in different units, and solve problems involving start and end times.
Teaching guidance
Use a number line timeline as the primary tool: mark the start time, mark the end time, and find the gap. For durations crossing the hour: e.g. from 2:45 to 3:20, count on 15 minutes to 3:00 then 20 more minutes = 35 minutes. Connect to subtraction in the time domain. Use real-life contexts: cooking times, journey times, the length of school lessons. The curriculum requires knowledge that there are 60 seconds in a minute, 60 minutes in an hour, 24 hours in a day — these conversion facts are essential for duration calculations.
Common misconceptions
Pupils often treat time as a base-10 system: subtracting 2:45 from 3:20 as 3.20 – 2.45 = 0.75, giving 75 minutes rather than 35 minutes. This is the single most common error in time calculations and arises from treating time notation as a decimal. Pupils also frequently confuse 1 hour 30 minutes with 1.3 hours or 130 minutes.
Difficulty levels
Comparing the durations of two events by looking at a timeline or counting on from start to end time on a clock.
Example task
Maths starts at 9:00 and finishes at 10:00. PE starts at 1:30 and finishes at 2:15. Which lesson is longer?
Model response: Maths is 1 hour = 60 minutes. PE is 45 minutes. Maths is longer.
Calculating the duration between two times using counting on, where the duration does not cross an hour boundary.
Example task
A film starts at 3:20 and finishes at 3:55. How long is the film?
Model response: From 3:20 to 3:55 = 35 minutes.
Calculating durations that cross hour boundaries using the bridging-through-the-hour strategy.
Example task
A journey starts at 2:45 and ends at 4:10. How long is the journey?
Model response: 2:45 to 3:00 = 15 minutes. 3:00 to 4:00 = 60 minutes. 4:00 to 4:10 = 10 minutes. Total = 85 minutes = 1 hour 25 minutes.
Solving multi-step duration problems involving conversions between seconds, minutes and hours.
Example task
A race takes 2 minutes and 45 seconds. Another race takes 195 seconds. Which race is longer? By how many seconds?
Model response: 2 minutes 45 seconds = 120 + 45 = 165 seconds. 195 seconds is longer. 195 - 165 = 30 seconds longer.
CPA Stages
concrete
Using a demonstration clock to physically move the hands from a start time to an end time, counting the minutes in jumps, and using sand timers to experience durations
Transition: Child calculates durations by counting on from the start time across the hour boundary, without moving the clock hands
pictorial
Drawing timeline number lines to show durations, marking the start time, end time and jumps across hours, and recording calculations
Transition: Child draws timeline jumps efficiently, bridging across hours, and converts between minutes and hours correctly (60 min = 1 hour, not 100)
abstract
Calculating durations mentally using the counting-on strategy, converting between seconds/minutes/hours, and comparing durations expressed in different units
Transition: Child calculates durations mentally without drawing timelines, never treating time as base-10, and converts between time units fluently
Delivery rationale
Primary maths (Y3) with concrete stage requiring physical manipulatives (demonstration clock, sand timers (1-minute, 5-minute)). AI delivers instruction; facilitator sets up materials.