Year 3 Mathematics

Step 1 Represent numbers to 100

Step 2 Partition numbers to 100

Step 3 Number line to 100

Step 4 Hundreds

Step 5 Represent numbers to 1,000

Step 6 Partition numbers to 1,000

Step 7 Flexible partitioning of numbers to 1,000

Step 8 Hundreds, tens and ones

Step 9 Find 1, 10 or 100 more or less

Step 10 Number line to 1,000

Step 11 Estimate on a number line to 1,000

Step 12 Compare numbers to 1,000

Step 13 Order numbers to 1,000

Step 14 Count in 50s

National Curriculum Links:

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 3-digit 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

Step 1 Apply number bonds within 10

Step 2 Add and subtract 1s

Step 3 Add and subtract 10s

Step 4 Add and subtract 100s

Step 5 Spot the pattern

Step 6 Add 1s across a 10

Step 7 Add 10s across a 100

Step 8 Subtract 1s across a10

Step 9 Subtract 10s across a 100

Step 10 Make connections

Step 11 Add two numbers (no exchange)

Step 12 Subtract two numbers (no exchange)

Step 13 Add two numbers (across a 10)

Step 14 Add two numbers (across a 100)

Step 15 Subtract two numbers (across a 10)

Step 16 Subtract two numbers (across a 100)

Step 17 Add 2-digit and 3-digit numbers

Step 18 Subtract a 2-digit number from a 3-digit number

Step 19 Complements to 100

Step 20 Estimate answers

Step 21 Inverse operations

Step 22 Make decisions

National Curriculum Links:

Pupils should be taught to:

• add and subtract numbers mentally, including:

  • a three-digit number and 1s

  • a three-digit number and 10s

  • a three-digit 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

Step 1 Multiplication – equal groups

Step 2 Use arrays

Step 3 Multiples of 2

Step 4 Multiples of 5 and 10

Step 5 Sharing and grouping

Step 6 Multiply by 3

Step 7 Divide by 3

Step 8 The 3 times-table

Step 9 Multiply by 4

Step 10 Divide by 4

Step 11 The 4 times-table

Step 12 Multiply by 8

Step 13 Divide by 8

Step 14 The 8 times-table

Step 15 The 2, 4 and 8 times-tables

National Curriculum Links:

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 two-digit numbers times one-digit 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

Step 1 Multiples of 10

Step 2 Related calculations

Step 3 Reasoning about multiplication

Step 4 Multiply a 2-digit number by a 1-digit number – no exchange

Step 5 Multiply a 2-digit number by a 1-digit number – with exchange

Step 6 Link multiplication and division

Step 7 Divide a 2-digit number by a 1-digit number – no exchange

Step 8 Divide a 2-digit number by a 1-digit number – flexible partitioning

Step 9 Divide a 2-digit number by a 1-digit number – with remainders

Step 10 Scaling

Step 11 How many ways?

National Curriculum Links:

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 two-digit numbers times one-digit 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

Step 1 Measure in metres and centimetres

Step 2 Measure in millimetres

Step 3 Measure in centimetres and millimetres

Step 4 Metres, centimetres and millimetres

Step 5 Equivalent lengths (metres and centimetres)

Step 6 Equivalent lengths (centimetres and millimetres)

Step 7 Compare lengths

Step 8 Add lengths

Step 9 Subtract lengths

Step 10 What is perimeter?

Step 11 Measure perimeter

Step 12 Calculate perimeter

National Curriculum Links:

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 2-D shapes

Step 1 Understand the denominators of unit fractions

Step 2 Compare and order unit fractions

Step 3 Understand the numerators of non-unit fractions

Step 4 Understand the whole

Step 5 Compare and order non-unit fractions

Step 6 Fractions and scales

Step 7 Fractions on a number line

Step 8 Count in fractions on a number line

Step 9 Equivalent fractions on a number line

Step 10 Equivalent fractions as bar models

National Curriculum Links:

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 one-digit numbers or quantities by 10

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

• recognise and use fractions as numbers: unit fractions and non-unit 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, 5/7 + 1/7  = 6/7 ]

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

• solve problems that involve all of the above

Step 1 Use scales

Step 2 Measure mass in grams

Step 3 Measure mass in kilograms and grams

Step 4 Equivalent masses (kilograms and grams)

Step 5 Compare mass

Step 6 Add and subtract mass

Step 7 Measure capacity and volume in millilitres

Step 8 Measure capacity and volume in litres and millilitres

Step 9 Equivalent capacities and volumes (litres and millilitres)

Step 10 Compare capacity and volume

Step 11 Add and subtract capacity and volume

National Curriculum Links:

Pupils should be taught to:

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

Step 1 Add fractions

Step 2 Subtract fractions

Step 3 Partition the whole

Step 4 Unit fractions of a set of objects

Step 5 Non-unit fractions of a set of objects

Step 6 Reasoning with fractions of an amount

National Curriculum Links:

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 one-digit numbers or quantities by 10

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

• recognise and use fractions as numbers: unit fractions and non-unit 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, 5/7 + 1/7  = 6/7 ]

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

• solve problems that involve all of the above

Step 1 Pounds and pence

Step 2 Convert pounds and pence

Step 3 Add money

Step 4 Subtract money

Step 5 Find change

National Curriculum Links:

Pupils should be taught to:

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

Step 1 Roman numerals to 12

Step 2 Tell the time to 5 minutes

Step 3 Tell the time to the minute

Step 4 Read time on a digital clock

Step 5 Use am and pm

Step 6 Years, months and days

Step 7 Days and hours

Step 8 Hours and minutes – use start and end times

Step 9 Hours and minutes - use durations

Step 10 Minutes and seconds

Step 11 Units of time

Step 12 Solve problems with time

National Curriculum Links:

Pupils should be taught to:

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

Step 1 Turns and angles

Step 2 Right angles

Step 3 Compare angles

Step 4 Measure and draw accurately

Step 5 Horizontal and vertical

Step 6 Parallel and perpendicular

Step 7 Recognise and describe 2-D shapes

Step 8 Draw polygons

Step 9 Recognise and describe 3-D shapes

Step 10 Make 3-D shapes

National Curriculum Links

Pupils should be taught to:

• draw 2-D shapes and make 3-D shapes using modelling materials; recognise 3-D 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 half-turn, 3 make three-quarters 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

Step 1 Interpret pictograms

Step 2 Draw pictograms

Step 3 Interpret bar charts

Step 4 Draw bar charts

Step 5 Collect and represent data

Step 6 Two-way tables

National Curriculum Links

Pupils should be taught to:

• interpret and present data using bar charts, pictograms and tables

• solve one-step and two-step questions [for example ‘How many more?’ and ‘How many fewer?’] using information presented in scaled bar charts and pictograms and tables