Equality & Inequality
Equality and inequality form the cornerstone of mathematical reasoning that Year 1 pupils encounter when learning to read, write and interpret +, − and = signs. Understanding when expressions are equal, greater than, or less than builds the foundation for algebraic thinking throughout primary and secondary maths.
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Why it matters
Equality and inequality concepts appear constantly in real-world situations. When Amelia compares prices at the tuck shop (£1.20 for crisps versus £0.85 for a biscuit), she's using inequality to determine which costs more. Football league tables rely on inequality comparisons when Manchester United has 67 points and Liverpool has 72 points. In cooking, recipes demand precise equality — 250g flour plus 125g butter must equal exactly 375g of mixture. Shop workers use these concepts when calculating change: if Harry buys a £3.50 sandwich with a £5 note, the equation becomes £3.50 + change = £5.00, so change = £1.50. GCSE Foundation pupils extend these skills to solve linear equations, whilst advanced students tackle complex inequalities in A-level Further Maths. Even basic budgeting requires understanding that monthly income must be greater than or equal to monthly expenses to avoid debt.
How to solve equality & inequality
Equality & Equations
- The equals sign means both sides have the same value.
- A balanced equation stays balanced if you do the same to both sides.
- Use + , − , × , ÷ on both sides to keep equality.
- Check by substituting your answer back in.
Example: 7 + ? = 12 → ? = 12 − 7 = 5. Check: 7 + 5 = 12. ✓
Worked examples
Is 3 + 9 = 12 true or false?
Answer: true
- Look at each side separately → 3 + 9 = ? — Before we can compare, we need to figure out what 3 + 9 actually equals. Think of it like counting: start at 3 and count up 9 more.
- Add up the left side: 3 + 9 → 12 — If you have 3 apples and get 9 more, you have 12 apples total. So 3 + 9 = 12.
- Look at the other side: 12 → 12 — The other side of the equals sign shows 12. We just need to compare this with our answer.
- Compare — are they the same? → true — 12 is the same as 12. The equals sign works like a balance scale — both sides weigh the same!
Which sign goes in the box? 3 + 4 __ 10 (< = >)
Answer: <
- First, add up the left side: 3 + 4 → 7 — 3 + 4 = 7. Now we know what the left side is worth.
- Compare 7 with 10 → 7 < 10 — Think of a number line: 7 is to the left of 10. Less than means the first number is smaller.
Make both sides equal: 2 + __ = __ + 3 (the total is 8)
Answer: 6 and 5
- The left side must equal 8 → 2 + __ = 8, so __ = 8 - 2 = 6 — We need 2 + something = 8. Subtract: 8 - 2 = 6.
- The right side must also equal 8 → __ + 3 = 8, so __ = 8 - 3 = 5 — We need something + 3 = 8. Subtract: 8 - 3 = 5.
- Verify both sides → 2 + 6 = 8 = 5 + 3 ✓ — Left: 2 + 6 = 8. Right: 5 + 3 = 8. Both sides are balanced!
Common mistakes
- Students often confuse the equals sign with 'the answer goes here', writing 3 + 4 = 7 + 2 = 9 instead of recognising that 3 + 4 ≠ 7 + 2 because 7 ≠ 9.
- Pupils frequently mix up < and > symbols, writing 8 > 3 when they mean 8 < 3, especially when comparing results like 2 + 1 versus 4 + 1.
- Children struggle with inequality comparisons involving subtraction, incorrectly stating that 10 − 3 < 6 − 2 when actually 7 > 4.
- Year 1 students often believe addition always makes numbers bigger, writing 5 + 0 > 5 instead of understanding that 5 + 0 = 5.