# Year 4 Maths Online practice for lower Key Stage 2 , age 8–9

Unit 1. Addition & subtraction in Year 4

• 1s,_10s_100s_1,000
• Add two 4-digit numbers – more than one exchange
• Add two 4-digit numbers – no exchange
• Add two 4-digit numbers – one exchange
• Adding amounts of money
• Adding three 3-digit numbers
• Checking strategies
• column addition to add pairs of 4-digit numbers
• Efficient subtraction
• Expanded column subtraction 2
• Expanded column subtraction
• Subtract two 4-digit numbers – more than one exchange
• Subtract two 4-digit numbers – no exchange
• Subtract two 4-digit numbers – one exchange
• Subtraction 1

Unit 2. Place values

• Place value models up to thousands
• Place value names up to thousands
• Place value names up to hundred thousands
• Value of a digit
• Convert to/from a number
• Convert between standard and expanded form
• Place value word problems

Unit 4. Subtraction

• Subtract numbers with up to three digits
• Subtraction input/output tables – up to three digits
• Subtract numbers with up to three digits – word problems
• Complete the subtraction sentence – up to three digits
• Balance subtraction equations – up to three digits
• Subtraction patterns over increasing place values
• Subtract numbers with up to four digits
• Subtraction input/output tables – up to four digits
• Subtract numbers with up to four digits – word problems
• Subtraction: fill in the missing digits

Unit 5. Understand multiplication

• Count equal groups
• Identify multiplication expressions for equal groups
• Write multiplication sentences for equal groups
• Relate addition and multiplication for equal groups
• Identify multiplication expressions for arrays
• Write multiplication sentences for arrays
• Write multiplication sentences for number lines

Unit 6. Multiplication fluency

• Multiplication fluency – Multiplication facts up to 12: find the missing factor
• Multiplication fluency – Multiplication facts up to 12: sorting
• Multiplication fluency – Multiplication facts up to 12: true or false?
• Multiplication fluency – Multiplication sentences up to 12: true or false?

Unit 7. Multiplication

• Multiply by a multiple of ten
• Multiply numbers ending in zeroes
• Multiplication patterns over increasing place values
• Multiplication input/output tables
• Multiplication word problems
• Multiply a one-digit number by a two-digit number: word problems
• Multiply a one-digit number by a three-digit number
• Multiply three or more numbers
• Multiply three or more numbers: word problems
• Box multiplication

Unit 8. Understand division

• Understand division – Write division sentences for arrays
• Understand division – Write division sentences for equal groups

Unit 10. Division

• Complete the division table
• Divide numbers ending in zeroes
• Division patterns over increasing place values
• Division input/output tables
• Division word problems
• Divide larger numbers
• Divide larger numbers: word problems
• Divisibility rules for 2, 5 and 10
• Interpret remainders

Unit 11. Mixed operations

• Complete the addition, subtraction, multiplication or division sentence
• Multiplication and division facts up to 5: true or false?
• Multiplication and division sentences up to 12: true or false?
• Add, subtract, multiply and divide
• Write numerical expressions
• Addition, subtraction, multiplication and division word problems
• Add and subtract data from tables
• Multi-step word problems
• Missing operators

Unit 12. Properties

• Addition, subtraction, multiplication and division terms
• Understanding parentheses
• Properties of addition
• Solve using properties of addition
• Properties of multiplication
• Solve using properties of multiplication
• Distributive property: find the missing factor
• Multiply using the distributive property
• Relate addition and multiplication
• Relate multiplication and division

Unit 13. Equations and variables

• Identify equations
• Solve for the variable: addition and subtraction
• Solve for the variable: multiplication and division
• Solve for the variable: addition, subtraction, multiplication and division
• Write variable expressions
• Write variable expressions from word problems
• Write variable equations to represent word problems

Unit 14. Estimation and rounding

• Rounding
• Round money amounts
• Rounding puzzles
• Solve inequalities using estimation
• Estimate sums
• Estimate sums: word problems
• Estimate differences
• Estimate differences: word problems
• Estimate products
• Estimate products: word problems
• Estimate quotients
• Estimate quotients: word problems
• Estimate sums, differences, products and quotients: word problems

Unit 15. Logical reasoning

• Guess the number
• Largest/smallest number possible
• Find the order
• Age puzzles
• Find two numbers based on sum and difference
• Find two numbers based on sum, difference, product and quotient

### The curriculum for maths in Year 4

Years 3 and 4 (lower Key Stage 2) share similar curriculum targets.

In lower Key Stage 2, the principal focus of maths teaching is to ensure that pupils become increasingly fluent with whole numbers and the four operations, including number facts and the concept of place value. This should ensure that pupils develop efficient written and mental methods and perform calculations accurately with increasingly large whole numbers.

At this stage, pupils should develop their ability to solve a range of problems, including with simple fractions and decimal place value. Pupils will also draw with increasing accuracy and develop mathematical reasoning so they can analyse shapes and their properties, and confidently describe the relationships between them. It should ensure that they can accurately use measuring instruments and make connections between measure and number.

By the end of Year 4, pupils should have memorised their times tables up to and including the 12 times table, and they will show precision and fluency in their work. Pupils should read and spell mathematical vocabulary correctly and confidently, using their growing word reading knowledge and their knowledge of spelling.

We’ve outlined England’s curriculum for maths in Year 4 below. Follow the links for help and activities:

### Number & place value in Year 4

• 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 (thousands, hundreds, tens, and ones)
• 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 & subtraction in Year 4

• 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 & division in Year 4

• 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 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 (including decimals) in Year 4

• 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
• recognise and write decimal equivalents of any number of tenths or hundredths
• recognise and write decimal equivalents to $\huge&space;\frac{1}{4}$$\huge&space;\frac{1}{2}$$\huge&space;\frac{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.

### Geometry (properties of shapes) in Year 4

• compare and classify geometric shapes, including quadrilaterals and trianglesbased 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 2-D shapes presented in different orientations
• complete a simple symmetric figure with respect to a specific line of symmetry.

### Geometry (position and direction) in Year 4

• 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.

### Measurement in Year 4

• 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

### Statistics in Year 4

• 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.