# 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.

## Autumn

## 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

**National Curriculum Links:**

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

**National Curriculum Links:**

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

**National Curriculum Links:**

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

**National Curriculum Links:**

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

## Spring

## Multiplication and Division B

Step 1 Factor pairs

Step 2 Use factor pairs

Step 3 Multiply by 10

Step 4 Multiply by 100

Step 5 Divide by 10

Step 6 Divide by 100

Step 7 Related facts – multiplication and division

Step 8 Informal written methods for multiplication

Step 9 Multiply a 2-digit number by a 1-digit number

Step 10 Multiply a 3-digit number by a 1-digit number

Step 11 Divide a 2-digit number by a 1-digit number (1)

Step 12 Divide a 2-digit number by a 1-digit number (2)

Step 13 Divide a 3-digit number by a 1-digit number

Step 14 Correspondence problems

Step 15 Efficient multiplication

**National Curriculum Links:**

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

Step 1 Measure in kilometres and metres

Step 2 Equivalent lengths (kilometres and metres)

Step 3 Perimeter on a grid

Step 4 Perimeter of a rectangle

Step 5 Perimeter of rectilinear shapes

Step 6 Find missing lengths in rectilinear shapes

Step 7 Calculate perimeter of rectilinear shapes

Step 8 Perimeter of regular polygons

Step 9 Perimeter of polygons

**National Curriculum Links:**

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

Step 1 Understand the whole

Step 2 Count beyond 1

Step 3 Partition a mixed number

Step 4 Number lines with mixed numbers

Step 5 Compare and order mixed numbers

Step 6 Understand improper fractions

Step 7 Convert mixed numbers to improper fractions

Step 8 Convert improper fractions to mixed numbers

Step 9 Equivalent fractions on a number line

Step 10 Equivalent fraction families

Step 11 Add two or more fractions

Step 12 Add fractions and mixed numbers

Step 13 Subtract two fractions

Step 14 Subtract from whole amounts

Step 15 Subtract from mixed numbers

**National Curriculum Links:**

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

Step 1 Tenths as fractions

Step 2 Tenths as decimals

Step 3 Tenths on a place value chart

Step 4 Tenths on a number line

Step 5 Divide a 1-digit number by 10

Step 6 Divide a 2-digit number by 10

Step 7 Hundredths as fractions

Step 8 Hundredths as decimals

Step 9 Hundredths on a place value chart

Step 10 Divide a 1- or 2-digit number by 100

**National Curriculum Links:**

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

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

## Summer

## Decimals B

**National Curriculum Links:**

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

**National Curriculum Links:**

Pupils should be taught to:

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

## Time

**National Curriculum Links:**

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

**National Curriculum Links:**

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

**National Curriculum Links:**

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

## Position and direction

**National Curriculum Links:**

Pupils should be taught to:

describe positions on a 2-D grid as coordinates in the first quadrant

describe movements between positions as translations of a given unit to the left/right and up/down

plot specified points and draw sides to complete a given polygon