# Year 3 Mathematics

The long term plan below shows the order in which units are taught and approximately how many weeks are spent on each unit.

These are broken down further into the small steps for each unit of work. All small steps involve an element of reasoning and problem solving and link to the National Curriculum.

## Autumn

## Place Value

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

## Addition and Subtraction

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

## Multiplication and Division A

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

## Spring

## Multiplication and Division B

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

## Length and perimeter

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

## Fractions A

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

## Mass and capacity

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)

## Summer

## Fractions B

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

## Money

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

## Time

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]

## Shape

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

## Statistics

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