Addition
Addition forms the bedrock of every maths lesson from Reception through GCSE, yet many pupils struggle with place value alignment and carrying. Year 1 pupils must confidently add numbers to 20, whilst Year 2 students tackle two-digit addition with regrouping.
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Why it matters
Addition appears in every real-world scenario pupils encounter daily. When Oliver buys a £3.50 sandwich and £1.25 drink at the tuck shop, he's using two-digit addition with decimals. Emma calculating her weekly pocket money of £4 plus £2 birthday money demonstrates single-digit addition. At GCSE level, students apply addition within algebra, geometry, and statistics. Year 6 SATs questions frequently embed addition within multi-step problems involving measurements, money, and time. Construction workers add measurements, shop assistants calculate totals, and families budget household expenses. Mastering column addition with carrying prepares students for decimal addition, fraction operations, and algebraic manipulation. Without solid addition foundations established in KS1, pupils struggle with advanced mathematical concepts throughout secondary school.
How to solve addition
Addition — how to
- Line up digits by place value (ones under ones, tens under tens).
- Add each column starting from the right.
- If a column sum is 10+, carry the tens digit to the next column.
Example: 27 + 38: 7+8=15, write 5 carry 1. 2+3+1=6. Answer: 65.
Worked examples
You find 4 cards and then 1 more. How many cards do you have?
Answer: 5
- Understand the story → 4 + 1 — You started with 4 cards and found 1 more. We need to combine them.
- Count on from the bigger number → 4 + 1 = 5 — Start at 4 and count 1 more to reach 5.
- Answer the question → 5 cards — You now have 5 cards in total!
A bus has 4 passengers. 14 more get on. How many passengers now?
Answer: 18
- Find the starting amount → 4 passengers — The bus started with 4 people on it.
- Add the new passengers → 4 + 14 = 18 — Then 14 more people got on. We add them to the 4 already there.
- Answer → 18 passengers — The bus now has 18 passengers.
_______ + 55 = 129
Answer: 74
- Read the problem → ? + 55 = 129 — We know one number (55) and the total (129). We need the missing one.
- Use subtraction to find the missing number → 129 - 55 = 74 — Since addition and subtraction are opposites, take the total and subtract 55.
- Check our answer → 74 + 55 = 129 ✓ — Put 74 back in: 74 + 55 = 129. Correct!
Common mistakes
- Pupils often misalign place values, writing 27 + 8 as 27 + 80 = 107 instead of 35, placing the 8 in the tens column rather than the ones.
- Students forget to carry the tens digit, calculating 47 + 36 as 713 instead of 83, writing both the 1 and 3 from 7+6=13 in the answer.
- Children add from left to right instead of right to left, computing 29 + 14 as 311 instead of 43, processing 2+1=3 then 9+4=13.