Negative Numbers
Negative numbers appear in Year 5 maths when pupils first encounter temperatures below zero, depths below sea level, and owing money. These concepts challenge students' understanding that numbers can exist below zero, requiring careful scaffolding to build conceptual understanding before procedural fluency.
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Why it matters
Negative numbers are essential for real-world problem solving across multiple contexts. Weather reports frequently show temperatures like −5°C during winter months, requiring students to compare and order these values. Bank statements display overdrawn accounts as negative balances, such as −£25, helping pupils understand debt and credit. In science, sea level measurements use negatives for depths below zero, like the Dead Sea at −430 metres. Geography lessons incorporate altitude changes, where locations can be 15 metres below sea level. Sports statistics track goal differences using negatives when teams concede more than they score. By Year 6 SATs, students must confidently work with negative numbers in various contexts, building towards GCSE topics like coordinate geometry and algebraic manipulation.
How to solve negative numbers
Negative Numbers
- Negative numbers are less than zero, written with a minus sign (−3).
- On a number line: negatives are to the left of zero.
- Adding a negative = subtracting: 5 + (−3) = 5 − 3 = 2.
- Subtracting a negative = adding: 5 − (−3) = 5 + 3 = 8.
Example: −4 + 7 = 3. −3 − 2 = −5. −2 × −3 = 6.
Worked examples
On a number line, where is -2? (left of zero, at zero, or right of zero)
Answer: left of zero
- Picture a number line → ... -3, -2, -1, 0, 1, 2, 3 ... — A number line goes left and right. Zero is in the middle. Negative numbers go to the LEFT. Positive numbers go to the RIGHT. Like a road: left goes to colder places, right goes to warmer places.
- Find -2 on the line → -2 is to the left of zero — -2 is 2 steps to the left of zero. Moving left on the number line means getting smaller.
What whole number is between -3 and -1 on the number line?
Answer: -2
- Picture the number line → ... -3, __, -1 ... — On a number line, negative numbers go in order: ... -4, -3, -2, -1 ... Moving right means getting bigger, even in the negatives.
- Find the number between -3 and -1 → -2 — The number between -3 and -1 is -2. It's one step right of -3 and one step left of -1.
What is 6 - 7?
Answer: -1
- Notice that we're subtracting a BIGGER number → 7 > 6 — We're taking away 7 from only 6. Since 7 is bigger than 6, we'll go past zero into the negatives. Think of having 6 cookies and eating 7 — you'd owe 1 cookies!
- Subtract step by step → 6 - 7 = -1 — From 6, we go down 6 to reach 0, then down 1 more to reach -1. On a number line: start at 6, move 7 steps to the left, land at -1.
Common mistakes
- Students often think −5 is greater than −2 because 5 > 2, writing −5 > −2 instead of −5 < −2 when comparing negative numbers.
- When subtracting past zero, pupils frequently write 3 − 7 = 4 instead of −4, forgetting that subtraction can produce negative results.
- Adding negative numbers confuses students who write 6 + (−3) = 9 instead of 3, treating the negative sign as positive.
- On number lines, students place −8 to the right of −3, reversing the correct order because they focus on the digit size rather than position.