Statutory guidance
National curriculum in England:
mathematics programmes of study
Lower "Year 3" key stage 2  programme of study
Number  number and place value
Pupils should be taught to:

count from 0 in multiples of 4, 8, 50 and 100; find 10 or 100 more or less than a given number

recognise the place value of each digit in a 3digit number (100s, 10s, 1s)

compare and order numbers up to 1,000

identify, represent and estimate numbers using different representations

read and write numbers up to 1,000 in numerals and in words

solve number problems and practical problems involving these ideas
Notes and guidance (nonstatutory)
Pupils now use multiples of 2, 3, 4, 5, 8, 10, 50 and 100.
They use larger numbers to at least 1,000, applying partitioning related to place value using varied and increasingly complex problems, building on work in year 2 (for example, 146 = 100 + 40 + 6, 146 = 130 +16).
Using a variety of representations, including those related to measure, pupils continue to count in 1s, 10s and 100s, so that they become fluent in the order and place value of numbers to 1,000.
Number  addition and subtraction
Pupils should be taught to:

add and subtract numbers mentally, including:

a threedigit number and 1s

a threedigit number and 10s

a threedigit number and 100s


add and subtract numbers with up to 3 digits, using formal written methods of columnar addition and subtraction

estimate the answer to a calculation and use inverse operations to check answers

solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction
Notes and guidance (nonstatutory)
Pupils practise solving varied addition and subtraction questions. For mental calculations with twodigit numbers, the answers could exceed 100.
Pupils use their understanding of place value and partitioning, and practise using columnar addition and subtraction with increasingly large numbers up to 3 digits to become fluent (see Mathematics appendix 1).
Number  multiplication and division
Pupils should be taught to:

recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables

write and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for twodigit numbers times onedigit numbers, using mental and progressing to formal written methods

solve problems, including missing number problems, involving multiplication and division, including positive integer scaling problems and correspondence problems in which n objects are connected to m objects
Notes and guidance (nonstatutory)
Pupils continue to practise their mental recall of multiplication tables when they are calculating mathematical statements in order to improve fluency. Through doubling, they connect the 2, 4 and 8 multiplication tables.
Pupils develop efficient mental methods, for example, using commutativity and associativity (for example, 4 × 12 × 5 = 4 × 5 × 12 = 20 × 12 = 240) and multiplication and division facts (for example, using 3 × 2 = 6, 6 ÷ 3 = 2 and 2 = 6 ÷ 3) to derive related facts (30 × 2 = 60, 60 ÷ 3 = 20 and 20 = 60 ÷ 3).
Pupils develop reliable written methods for multiplication and division, starting with calculations of twodigit numbers by onedigit numbers and progressing to the formal written methods of short multiplication and division.
Pupils solve simple problems in contexts, deciding which of the 4 operations to use and why. These include measuring and scaling contexts, (for example 4 times as high, 8 times as long etc) and correspondence problems in which m objects are connected to n objects (for example, 3 hats and 4 coats, how many different outfits?; 12 sweets shared equally between 4 children; 4 cakes shared equally between 8 children).
Number  fractions
Pupils should be taught to:

count up and down in tenths; recognise that tenths arise from dividing an object into 10 equal parts and in dividing onedigit numbers or quantities by 10

recognise, find and write fractions of a discrete set of objects: unit fractions and nonunit fractions with small denominators

recognise and use fractions as numbers: unit fractions and nonunit fractions with small denominators

recognise and show, using diagrams, equivalent fractions with small denominators

add and subtract fractions with the same denominator within one whole [for example, + = ]

compare and order unit fractions, and fractions with the same denominators

solve problems that involve all of the above
Notes and guidance (nonstatutory)
Pupils connect tenths to place value, decimal measures and to division by 10.They begin to understand unit and nonunit fractions as numbers on the number line, and deduce relations between them, such as size and equivalence. They should go beyond the [0, 1] interval, including relating this to measure.Pupils understand the relation between unit fractions as operators (fractions of), and division by integers.They continue to recognise fractions in the context of parts of a whole, numbers, measurements, a shape, and unit fractions as a division of a quantity.Pupils practise adding and subtracting fractions with the same denominator through a variety of increasingly complex problems to improve fluency.
Measurement
Pupils should be taught to:

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

measure the perimeter of simple 2D shapes

add and subtract amounts of money to give change, using both £ and p in practical contexts

tell and write the time from an analogue clock, including using Roman numerals from I to XII, and 12hour and 24hour clocks

estimate and read time with increasing accuracy to the nearest minute; record and compare time in terms of seconds, minutes and hours; use vocabulary such as o’clock, am/pm, morning, afternoon, noon and midnight

know the number of seconds in a minute and the number of days in each month, year and leap year

compare durations of events [for example, to calculate the time taken by particular events or tasks]
Notes and guidance (nonstatutory)
Pupils continue to measure using the appropriate tools and units, progressing to using a wider range of measures, including comparing and using mixed units (for example, 1 kg and 200g) and simple equivalents of mixed units (for example, 5m = 500cm).The comparison of measures includes simple scaling by integers (for example, a given quantity or measure is twice as long or 5 times as high) and this connects to multiplication.Pupils continue to become fluent in recognising the value of coins, by adding and subtracting amounts, including mixed units, and giving change using manageable amounts. They record £ and p separately. The decimal recording of money is introduced formally in year 4.Pupils use both analogue and digital 12hour clocks and record their times. In this way they become fluent in and prepared for using digital 24hour clocks in year 4.
Geometry  properties of shapes
Pupils should be taught to:

draw 2D shapes and make 3D shapes using modelling materials; recognise 3D shapes in different orientations and describe them

recognise angles as a property of shape or a description of a turn

identify right angles, recognise that 2 right angles make a halfturn, 3 make threequarters of a turn and 4 a complete turn; identify whether angles are greater than or less than a right angle

identify horizontal and vertical lines and pairs of perpendicular and parallel lines
Notes and guidance (nonstatutory)
Pupils’ knowledge of the properties of shapes is extended at this stage to symmetrical and nonsymmetrical polygons and polyhedra. Pupils extend their use of the properties of shapes. They should be able to describe the properties of 2D and 3D shapes using accurate language, including lengths of lines and acute and obtuse for angles greater or lesser than a right angle.Pupils connect decimals and rounding to drawing and measuring straight lines in centimetres, in a variety of contexts.
Statistics
Pupils should be taught to:

interpret and present data using bar charts, pictograms and tables

solve onestep and twostep questions [for example ‘How many more?’ and ‘How many fewer?’] using information presented in scaled bar charts and pictograms and tables
Notes and guidance (nonstatutory)
Pupils understand and use simple scales (for example, 2, 5, 10 units per cm) in pictograms and bar charts with increasing accuracy.
They continue to interpret data presented in many contexts.