Teachers should use every relevant subject to develop pupils’ mathematical fluency. Confidence in numeracy and other mathematical skills is a precondition of success across the national curriculum.

Teachers should develop pupils’ numeracy and mathematical reasoning in all subjects so that they understand and appreciate the importance of mathematics.

– National Curriculum in England Framework Document, September 2013, p10

Connections within Mathematics

Making connections to this topic in adjacent year groups

Year 2

Statutory requirements:

• solve problems with addition and subtraction:
  • using concrete objects and pictorial representations, including those involving numbers, quantities and measures
  • applying their increasing knowledge of mental and written methods
• recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100
• add and subtract numbers using concrete objects, pictorial representations, and mentally, including:
  • a two-digit number and ones
  • a two-digit number and tens
  • two two-digit numbers
  • adding three one-digit numbers
• show that addition of two numbers can be done in any order (commutative) and subtraction of one number from another cannot
• recognise and use the inverse relationship between addition and subtraction and use this to check calculations and missing number problems.

Non statutory guidance:

Pupils extend their understanding of the language of addition and subtraction to include sum and difference.

Pupils practise addition and subtraction to 20 to become increasingly fluent in deriving facts such as using 3 + 7 = 10, 10 - 7 = 3 and 7 = 10 - 3 to calculate 30 + 70 = 100, 100 - 70 = 30 and 70 = 100 - 30.

They check their calculations, including by adding to check subtraction and adding numbers in a different order to check addition (e.g. 5 + 2 + 1 = 1 + 5 + 2 = 1 + 2 + 5). This establishes commutativity and associativity of addition.

Recording addition and subtraction in columns supports place value and prepares for formal written methods with larger numbers.

Year 4

Statutory requirements:

• 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.

Non statutory guidance:

Pupils continue to practise both mental methods and column addition and subtraction with increasingly large numbers to aid fluency.

Cross-curricular and real life connections

Children need to be able to apply the concept of addition to real−life applications, for example the total cost of two items costing 48p and 36p. They may then need to be able to convert their answer into the appropriate units.

• To complement a garden centre/shop role-play area, or similar class theme, ask children to explore the cost of buying combinations of different items on paper or on a spreadsheet. The shop/market stall could link to a historical theme e.g. in Roman times.
• Give children a limited budget to buy items for a party. Often shops have free coloured leaflets with listed items for sale or on special offer , e.g. ‘buy one get one free’ or ‘three for two’.
• Make collections of biscuits/cakes/healthy snacks to sell and raise money for school fund or charity like Comic Relief or Children in Need.
• Visit a local shop or museum shop as part of a class trip. You have £2, £3 or £4, what can you buy with your money? What can’t you buy? How much more money might you need? How much change will you get? Have you got the correct change?