Progression in addition and subtraction - new curriculum



Progression: Addition and subtraction

Programme of study (statutory requirements)

|Y1 |Y2 |Y3 |Y4 |Y5 |Y6 |

|Addition and subtraction |Addition and subtraction |Addition and subtraction |Addition and subtraction |Addition and subtraction |Addition and subtraction |

| | | | | | |

|Pupils should be taught to: |Pupils should be taught to: |Pupils should be taught to: |Pupils should be taught to: |Pupils should be taught to: |Pupils should be taught to: |

| | | | | | |

|read, write and interpret | |add and subtract numbers mentally, |add and subtract numbers with up |add and subtract whole numbers with |perform mental calculations, |

|mathematical statements |solve problems with addition and subtraction: |including: |to 4 digits using the formal |more than 4 digits, including using |including with mixed operations and |

|involving addition (+), |- using concrete objects and pictorial |- a three-digit number and ones |written methods of columnar |formal written methods (columnar |large numbers |

|subtraction (-) and equals (=) |representations, including those involving |- a three-digit number and tens |addition and subtraction where |addition and subtraction) | |

|signs |numbers, quantities and measures |- a three-digit number and hundreds |appropriate | |use their knowledge of the order of |

| |- applying their increasing knowledge of mental| | |add and subtract numbers mentally |operations to carry out calculations |

|represent and use number bonds |and written methods |add and subtract numbers with up to |estimate and use inverse |with increasingly large numbers |involving the four operations |

|and related subtraction facts | |three digits, using formal written |operations to check answers to a | | |

|within 20 |recall and use addition and subtraction facts |methods of columnar addition and |calculation |use rounding to check answers to |solve addition and subtraction |

| |to 20 fluently, and derive and use related |subtraction | |calculations and determine, in the |multi-step problems in contexts, |

|add and subtract one-digit and |facts up to 100 | |solve addition and subtraction |context of a problem, levels of |deciding which operations and methods|

|two-digit numbers to 20, | |estimate the answer to a calculation |two-step problems in contexts, |accuracy |to use and why |

|including zero |add and subtract numbers using concrete |and use inverse operations to check |deciding which operations and | | |

| |objects, pictorial representations, and |answers |methods to use and why |solve addition and subtraction |solve problems involving addition and|

|solve one-step problems that |mentally, including: | | |multi-step problems in contexts, |subtraction, use estimation to check|

|involve addition and |- a two-digit number and ones |solve problems, including missing | |deciding which operations and methods|answers to calculations and |

|subtraction, using concrete |- a two-digit number and tens |number problems, using number facts, | |to use and why |determine, in the context of a |

|objects and pictorial |- two two-digit numbers |place value, and more complex addition | | |problem, an appropriate degree of |

|representations, and missing |- adding three one-digit numbers |and subtraction | | |accuracy |

|number problems such as 7 = □ -| | | | | |

|9 |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 | | | | |

Notes and guidance (non-statutory)

|Y1 |Y2 |Y3 |Y4 |Y5 |Y6 |

|Addition and subtraction |Addition and subtraction |Addition and subtraction |Addition and subtraction |Addition and subtraction |Addition and subtraction |

| | | | | | |

|Pupils memorise and reason with |Pupils extend their understanding of the |Pupils practise solving varied addition|Pupils continue to practise both |Pupils practise using the |Pupils practise addition and |

|number bonds to 10 and 20 in |language of addition and subtraction to include|and subtraction questions. For mental |mental methods and columnar |formal written methods of |subtraction for larger numbers, using |

|several forms (for example, 9 + 7|sum and difference. |calculations with two-digit numbers, |addition and subtraction with |columnar addition and |the formal written methods of columnar |

|= 16; 16 - 7 = 9; 7 = 16 - 9). | |the answers could exceed 100. |increasingly large numbers to aid |subtraction with increasingly |addition and subtraction (see |

|They should realise the effect of|Pupils practise addition and subtraction to 20 | |fluency (see Mathematics Appendix |large numbers to aid fluency |Mathematics Appendix 1). |

|adding or subtracting zero. This |to become increasingly fluent in deriving facts|Pupils use their understanding of place|1). |(see Mathematics Appendix 1). | |

|establishes addition and |such as using 3 + 7 = 10, 10 - 7 = 3 and 7 = 10|value and partitioning, and practise | | |They undertake mental calculations with|

|subtraction as related |- 3 to calculate 30 + 70 = 100, 100 - 70 = 30 |using columnar addition and subtraction| |They practise mental |increasingly large numbers and more |

|operations. |and 70 = 100 - 30. They check their |with increasingly large numbers up to | |calculations with increasingly|complex calculations. |

| |calculations, including by adding to check |three digits to become fluent (see | |large numbers to aid fluency | |

|Pupils combine and increase |subtraction and adding numbers in a different |Appendix 1). | |(for example, 12 462 – 2 300 =|Pupils round answers to a specified |

|numbers, counting forwards and |order to check addition (for example, 5 + 2 + 1| | |10 162). |degree of accuracy, for example, to the|

|backwards. |= 1 + 5 + 2 = 1 + 2 + 5). This establishes | | | |nearest 10, 20, 50 etc, but not to a |

| |commutativity and associativity of addition. | | | |specified number of significant |

|They discuss and solve problems | | | | |figures. |

|in familiar practical contexts, |Recording addition and subtraction in columns | | | | |

|including using quantities. |supports place value and prepares for formal | | | |Pupils explore the order of operations |

|Problems should include the |written methods with larger numbers. | | | |using brackets; for example, 2 + 1 x 3 |

|terms: put together, add, | | | | |= 5 and (2 + 1) x 3 = 9. |

|altogether, total, take away, | | | | | |

|distance between, difference | | | | | |

|between, more than and less than,| | | | | |

|so that pupils develop the | | | | | |

|concept of addition and | | | | | |

|subtraction and are enabled to | | | | | |

|use these operations flexibly. | | | | | |

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Herts for Learning – Teaching and Learning

Herts for Learning – Teaching and Learning

Herts for Learning – Teaching and Learning

Herts for Learning – Teaching and Learning

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