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In Key Stage 2 you build on your earlier addition and subtraction skills to work with numbers in the thousands and beyond. You will use written column methods, mental strategies, and estimation — and learn how to check your answers.
Column addition lines up digits by place value and works from right to left, carrying when a column totals 10 or more.
Example: 4,763 + 2,584
Th H T O
4 7 6 3
(carry 1 to next column as needed)
Step by step:
Example: 156,428 + 73,695 (6-digit column addition)
HTh TTh Th H T O
1 5 6 4 2 8
+ 7 3 6 9 5
----------------------------
Step by step:
Whenever a column adds to 10 or more, write the ones digit and carry the tens to the next column. The flow always runs right to left:
flowchart LR
A["Start at<br/>ones column"] --> B["Add the digits<br/>+ any carry"]
B --> C{Total >= 10?}
C -->|Yes| D["Write the ones digit<br/>Carry 1 to next column"]
C -->|No| E[Write the total]
D --> F{"More columns<br/>to the left?"}
E --> F
F -->|Yes| G[Move one column left] --> B
F -->|No| H[Final answer]
Column subtraction also works from right to left. When a digit on top is too small to subtract from, you exchange (borrow) from the column to the left.
Example: 6,421 - 2,748
Check: 3,673 + 2,748 = 6,421. Correct!
For some calculations, a mental method is faster than written column work.
Counting on: For subtraction, count up from the smaller number to the larger.
Adjusting: Round one number to the nearest easy number, then compensate.
Partitioning: Split numbers into parts.
Empty number line (for subtraction): Jump forwards from the smaller number to the larger.
Example: 503 − 276
276 ---+4---> 280 ---+20---> 300 ---+200---> 500 ---+3---> 503
Jumps: 4 + 20 + 200 + 3 = **227**
This "counting on" approach avoids difficult exchanges with zeros and is especially useful when the bigger number ends in 00 or has many zeros.
Before calculating, round each number to make a quick estimate. This helps you check whether your answer is sensible.
Example: 3,872 + 1,456
Example: 7,203 - 2,891
Addition and subtraction are inverse operations — they undo each other.
Always check your answer — it is a habit that catches errors quickly.
Real-life problems often need more than one calculation.
Problem: A school raises £4,856 in the autumn term and £3,204 in the spring term. They spend £2,975 on new books. How much do they have left?
Problem: A factory produces 12,450 items on Monday and 9,875 on Tuesday. A delivery of 6,300 items is sent out. How many items remain?
A school holds a charity fundraiser over three days. On Friday they raise £4,856. On Saturday they raise £3,489 more than Friday. On Sunday they raise £2,750 less than Saturday. The school then spends £6,378 on supplies for the local food bank and donates the remainder to charity. How much is donated?
Step 1 — Calculate Saturday's takings using column addition.
Th H T O
4 8 5 6
+ 3 4 8 9
--------------------
8 3 4 5
Working column by column, right to left:
Saturday: £8,345.
Step 2 — Calculate Sunday's takings using column subtraction.
Th H T O
8 3 4 5
- 2 7 5 0
--------------------
Sunday: £5,595.
Step 3 — Total raised over the three days. Add £4,856 + £8,345 + £5,595.
4 8 5 6
8 3 4 5
+ 5 5 9 5
--------------------
Total: £18,796.
Step 4 — Subtract supplies cost.
£18,796 - £6,378 = ?
1 8 7 9 6
- 6 3 7 8
-------------------------
Donation: £12,418.
Step 5 — Estimate to check. Round to the nearest thousand:
£5,000 + £8,000 + £6,000 = £19,000
£19,000 - £6,000 = £13,000
The actual answer £12,418 is close to £13,000, so it is sensible.
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