Number - Addition and Subtraction
KS2MA-Y4-D002
Formal written methods of columnar addition and subtraction for numbers with up to four digits, estimation, inverse operations, and two-step problems including missing number problems.
National Curriculum context
In Year 4, pupils consolidate and extend the formal columnar methods introduced in Year 3 to four-digit numbers. The non-statutory guidance emphasises that pupils should practise adding and subtracting increasingly large numbers to aid fluency and develop their mental arithmetic, using jottings to support calculation where necessary. Pupils are expected to use efficient methods and to select the most appropriate approach for each calculation — mental, jottings or formal written. The extension to four-digit numbers means exchanges can occur in more columns simultaneously, making rigorous understanding of place value even more important. This consolidation prepares pupils for the multi-step addition and subtraction in contexts across all domains of Year 4 and the transition to larger numbers in Year 5.
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Concepts
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Clusters
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Prerequisites
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With difficulty levels
Lesson Clusters
Add and subtract four-digit numbers using formal columnar methods
practice CuratedOnly one concept in this domain. Four-digit columnar addition and subtraction (with exchange at multiple places) is the singular statutory focus and stands alone.
Teaching Suggestions (1)
Study units and activities that deliver concepts in this domain.
Addition and Subtraction: Efficient Methods and Problem Solving
Mathematics Worked Example SetPedagogical rationale
Y4 extends column methods to four-digit numbers and emphasises choosing the most efficient method. The phrase 'where appropriate' in the NC is deliberate — children should recognise when mental methods or adjustment strategies are more efficient than a written column. This requires confident place value understanding and number sense alongside procedural fluency. Estimation remains critical for checking reasonableness.
Prerequisites
Concepts from other domains that pupils should know before this domain.
Concepts (1)
Formal columnar addition and subtraction of four-digit numbers
skill AI DirectMA-Y4-C006
Columnar addition and subtraction are extended to four-digit numbers in Year 4, requiring exchanges (carries) to occur in up to three columns simultaneously. Pupils must apply the method reliably for any combination of four-digit numbers. Mastery means pupils can set out and solve any four-digit addition or subtraction using formal written methods, with correct alignment, carrying and borrowing, and can check answers using the inverse operation.
Teaching guidance
Revisit and consolidate three-digit columnar methods before extending to four digits. The structure of the method is identical — simply add a thousands column on the left. Emphasise alignment: use squared paper, printed column frames or turn plain paper landscape with hand-drawn columns. For subtraction with four digits, cascading exchanges (e.g. 3000 – 1 requires exchanging through three columns: 3000 = 2 thousands, 9 hundreds, 9 tens, 10 ones) need explicit practice. Check using the inverse.
Common misconceptions
The most common error remains forgetting the carry in addition. For subtraction, the cascading exchange through zeros (4000 – 1 = ?) is the most challenging case and requires step-by-step practice. Some pupils align the digits from the left rather than the right, corrupting the place value structure.
Difficulty levels
Completing columnar addition of two four-digit numbers with no exchanges (no carrying).
Example task
Use column addition: 3,214 + 2,563.
Model response: 3214 + 2563 ------ 5777 No carrying needed.
Completing columnar addition and subtraction with exchanges (carrying/borrowing) in one or two columns.
Example task
Use column subtraction: 5,432 – 2,876.
Model response: 5432 – 2876 = 2556. Borrowing needed in the ones (12 – 6 = 6), tens (2 – 7 requires borrow: 12 – 7 = 5), and hundreds (3 – 8 requires borrow: 13 – 8 = 5).
Reliably computing any four-digit addition or subtraction using formal columnar methods, with estimation to check.
Example task
Work out 6,003 – 2,458. Estimate first.
Model response: Estimate: 6,000 – 2,500 = 3,500. Formal: 6003 – 2458 = 3545. Cascading exchange through zeros: borrow from 6 thousands through the hundreds and tens.
Solving multi-step problems requiring addition and subtraction of four-digit numbers and explaining the method.
Example task
A school has 2,456 fiction books and 1,789 non-fiction books. They buy 325 more fiction books and donate 450 non-fiction books. How many books does the school have now?
Model response: Fiction: 2,456 + 325 = 2,781. Non-fiction: 1,789 – 450 = 1,339. Total: 2,781 + 1,339 = 4,120.
CPA Stages
concrete
Using Dienes blocks on a four-column place value mat to model addition and subtraction of four-digit numbers, physically exchanging between columns
Transition: Child explains each exchange verbally while performing columnar addition/subtraction on paper, no longer needing the blocks
pictorial
Recording columnar addition and subtraction using the expanded method alongside the compact method, drawing place value counters to show exchanges
Transition: Child sets up and completes four-digit columnar calculations independently on paper, handling cascading exchanges through zeros
abstract
Performing four-digit columnar addition and subtraction fluently, checking with estimation and inverse operations
Transition: Child completes any four-digit addition or subtraction with all exchange types, routinely estimating before and checking after
Delivery rationale
Upper primary maths (Y4) — most pupils at pictorial/abstract stage. AI can deliver with virtual representations.