# Year 4 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. ## Place Value

Step 1 Represent numbers to 1,000

Step 2 Partition numbers to 1,000

Step 3 Number line to 1,000

Step 4 Thousands

Step 5 Represent numbers to 10,000

Step 6 Partition numbers to 10,000

Step 7 Flexible partitioning of numbers to 10,000

Step 8 Find 1, 10, 100, 1,000 more or less

Step 9 Number line to 10,000

Step 10 Estimate on a number line to 10,000

Step 11 Compare numbers to 10,000

Step 12 Order numbers to 10,000

Step 13 Roman numerals

Step 14 Round to the nearest 10

Step 15 Round to the nearest 100

Step 16 Round to the nearest 1,000

Step 17 Round to the nearest 10, 100 or 1,000

Pupils should be taught to:

• count in multiples of 6, 7, 9, 25 and 1,000

• find 1,000 more or less than a given number

• count backwards through 0 to include negative numbers

• recognise the place value of each digit in a four-digit number (1,000s, 100s, 10s, and 1s)

• order and compare numbers beyond 1,000

• identify, represent and estimate numbers using different representations

• round any number to the nearest 10, 100 or 1,000

• solve number and practical problems that involve all of the above and with increasingly large positive numbers

• read Roman numerals to 100 (I to C) and know that over time, the numeral system changed to include the concept of 0 and place value

## Addition and Subtraction

Step 1 Add and subtract 1s, 10s, 100s and 1,000s

Step 2 Add up to two 4-digit numbers – no exchange

Step 3 Add two 4-digit numbers – one exchange

Step 4 Add two 4-digit numbers – more than one exchange

Step 5 Subtract two 4-digit numbers – no exchange

Step 6 Subtract two 4-digit numbers – one exchange

Step 7 Subtract two 4-digit numbers – more than one exchange

Step 8 Efficient subtraction

Step 9 Estimate answers

Step 10 Checking strategies

Pupils should be taught to:

• add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate

• estimate and use inverse operations to check answers to a calculation

• solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why

## Area

Step 1 What is area?

Step 2 Count squares

Step 3 Make shapes

Step 4 Compare areas

Pupils should be taught to:

• convert between different units of measure [for example, kilometre to metre; hour to minute]

• measure and calculate the perimeter of a rectilinear figure (including squares) in centimetres and metres

• find the area of rectilinear shapes by counting squares

• estimate, compare and calculate different measures, including money in pounds and pence

## Multiplication and Division A

Step 1 Multiples of 3

Step 2 Multiply and divide by 6

Step 3 6 times-table and division facts

Step 4 Multiply and divide by 9

Step 5 9 times-table and division facts

Step 6 The 3, 6 and 9 times-tables

Step 7 Multiply and divide by 7

Step 8 7 times-table and division facts

Step 9 11 times-table and division facts

Step 10 12 times-table and division facts

Step 11 Multiply by 1 and 0

Step 12 Divide a number by 1 and itself

Step 13 Multiply three numbers

Pupils should be taught to:

• recall multiplication and division facts for multiplication tables up to 12 × 12

• use place value, known and derived facts to multiply and divide mentally, including: multiplying by 0 and 1; dividing by 1; multiplying together 3 numbers

• recognise and use factor pairs and commutativity in mental calculations

• multiply two-digit and three-digit numbers by a one-digit number using formal written layout

• solve problems involving multiplying and adding, including using the distributive law to multiply two-digit numbers by 1 digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects

## Multiplication and Division B

Pupils should be taught to:

• recall multiplication and division facts for multiplication tables up to 12 × 12

• use place value, known and derived facts to multiply and divide mentally, including: multiplying by 0 and 1; dividing by 1; multiplying together 3 numbers

• recognise and use factor pairs and commutativity in mental calculations

• multiply two-digit and three-digit numbers by a one-digit number using formal written layout

• solve problems involving multiplying and adding, including using the distributive law to multiply two-digit numbers by 1 digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects

## Length and perimeter

Pupils should be taught to:

• convert between different units of measure [for example, kilometre to metre; hour to minute]

• measure and calculate the perimeter of a rectilinear figure (including squares) in centimetres and metres

• find the area of rectilinear shapes by counting squares

• estimate, compare and calculate different measures, including money in pounds and pence

## Fractions

Pupils should be taught to:

• recognise and show, using diagrams, families of common equivalent fractions

• count up and down in hundredths; recognise that hundredths arise when dividing an object by 100 and dividing tenths by 10

• solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number

• add and subtract fractions with the same denominator

• recognise and write decimal equivalents to 1/4, 1/2, 3/4

• find the effect of dividing a one- or two-digit number by 10 and 100, identifying the value of the digits in the answer as ones, tenths and hundredths

• round decimals with 1 decimal place to the nearest whole number

• compare numbers with the same number of decimal places up to 2 decimal places

• solve simple measure and money problems involving fractions and decimals to 2 decimal places

## Decimals A

Pupils should be taught to:

• recognise and show, using diagrams, families of common equivalent fractions

• count up and down in hundredths; recognise that hundredths arise when dividing an object by 100 and dividing tenths by 10

• solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number

• add and subtract fractions with the same denominator

• recognise and write decimal equivalents of any number of tenths or hundreds

• recognise and write decimal equivalents to 1/4, 1/2, 3/4

• find the effect of dividing a one- or two-digit number by 10 and 100, identifying the value of the digits in the answer as ones, tenths and hundredths

• round decimals with 1 decimal place to the nearest whole number

• compare numbers with the same number of decimal places up to 2 decimal places

• solve simple measure and money problems involving fractions and decimals to 2 decimal places

## Decimals B

Pupils should be taught to:

• recognise and show, using diagrams, families of common equivalent fractions

• count up and down in hundredths; recognise that hundredths arise when dividing an object by 100 and dividing tenths by 10

• solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number

• add and subtract fractions with the same denominator

• recognise and write decimal equivalents of any number of tenths or hundreds

• recognise and write decimal equivalents to 1/4, 1/2, 3/4

• find the effect of dividing a one- or two-digit number by 10 and 100, identifying the value of the digits in the answer as ones, tenths and hundredths

• round decimals with 1 decimal place to the nearest whole number

• compare numbers with the same number of decimal places up to 2 decimal places

• solve simple measure and money problems involving fractions and decimals to 2 decimal places

## Money

Pupils should be taught to:

• estimate, compare and calculate different measures, including money in pounds and pence

## Time

Pupils should be taught to:

• convert between different units of measure [for example, kilometre to metre; hour to minute]

• read, write and convert time between analogue and digital 12- and 24-hour clocks

• solve problems involving converting from hours to minutes, minutes to seconds, years to months, weeks to days

## Shape

Pupils should be taught to:

• compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes

• identify acute and obtuse angles and compare and order angles up to 2 right angles by size

• identify lines of symmetry in 2-D shapes presented in different orientations

• complete a simple symmetric figure with respect to a specific line of symmetry

## Statistics

Pupils should be taught to:

• interpret and present discrete and continuous data using appropriate graphical methods, including bar charts and time graphs

• solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs