By the end of year 4, children will have been taught how to:

Number and Place Value

• Count in multiples of 6, 7, 9, 25 and 1000
• Find 1000 more or less than a given number
• Count backwards through zero to include negative numbers
• Recognise the place value of each digit in a four-digit number
• Order and compare numbers beyond 1000
• Identify, represent and estimate numbers using different representations
• Round any number to the nearest 10, 100 or 1000
• 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 zero and place value.

Addition and Subtraction

• 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.

Multiplication and Division

• Recall multiplication and division facts for multiplication tables up to 12 x 12
• Use place value, known and derived facts to multiply and divide mentally, including: multiplying by 0 and 1; dividing by 1; multiplying together three 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 one digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects.

Fractions

• Recognise and write decimal equivalents of any number of tenths or hundredths
• 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 one decimal place to the nearest whole number
• Compare numbers with the same number of decimal places up to two decimal places
• Solve simple measure and money problems involving fractions and decimals to two decimal places
• 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 one hundred and dividing tenths by ten.
• 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

Measurement

• 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
• Convert between different units of measure
• Measure and calculate the perimeter of a rectilinear figure 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

Geometry - Properties of Shape

• 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 two right angles by size
• Identify lines of symmetry in 2D shapes presented in different orientations
• Complete a simple symmetric figure with respect to a specific line of symmetry

Geometry - Position and Direction

• Describe positions on a 2D 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

Statistics

• 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.