Page 1 · Introduction
Numbers below zero
Until now, most maths has used numbers from zero up. High school introduces negative numbers — numbers below zero, like −3. They’re everywhere: temperatures, money owed, floors below ground. The number line makes them simple.
The big ideaPicture a number line: positives to the right of zero, negatives to the left. Adding moves right, subtracting moves left. That one picture handles almost everything.
💡Negative numbers feel strange at first, then click quickly with the number-line picture. We build up gently.
On the real testWhere this appearsIntegers and negatives are introduced early in Year 7 maths and used in every later topic — algebra, coordinates, and more.
Page 2 · The number line
Left and right of zero
On a number line, numbers get smaller as you go left. So −5 is smaller than −2, and both are smaller than 0.
Which is smaller: −3 or −7?
−7 is further left on the number line, so it is smaller.
−7
Put in order, smallest first: 2, −4, 0, −1
Left to right on the line: −4, −1, 0, 2.
−4, −1, 0, 2
Page 3 · Adding
Moving along the line
Adding a positive moves right; adding a negative moves left.
Work out: −3 + 5
Start at −3, move 5 right: −3→−2→−1→0→1→2. Answer 2.
2
Work out: 4 + (−6)
Start at 4, move 6 left: lands on −2.
−2
Page 4 · Subtracting
The two-minus trick
Subtracting moves left. And subtracting a negative (two minuses together) becomes adding: 5 − (−3) = 5 + 3.
Work out: 2 − 5
Start at 2, move 5 left: lands on −3.
−3
Work out: 3 − (−4)
Two minuses make a plus: 3 + 4 = 7.
7
Page 5 · In real life
Temperature & change
Negatives often appear as temperature or as a rise/fall. Find the difference by counting along the line.
The temperature is −2°C and rises by 5°. What is it now?
−2 + 5 = 3°C.
3°C
From 4°C the temperature falls by 9°. What is it now?
4 − 9 = −5°C.
−5°C
Level 1 · Easy
Warm up
Ordering and comparing. Tap to check.
1. Which is smaller: −2 or 3?
−2 is left of 3 on the number line, so it is smaller.
2. Which is largest: −5, −1, −8?
−1 is furthest right, so it is the largest.
3. What comes next going down: 2, 1, 0, ?
Counting down past zero gives −1.
Level 2 · Medium
Building up
Adding with negatives.
1. Work out: −4 + 6
Start at −4, move 6 right: 2.
2. Work out: 3 + (−5)
Start at 3, move 5 left: −2.
3. Work out: −2 + (−3)
Both negative: move left twice, −2 − 3 = −5.
Level 3 · Hard
Getting tougher
Subtracting, including two minuses.
1. Work out: 1 − 4
Start at 1, move 4 left: −3.
2. Work out: 5 − (−2)
Two minuses make plus: 5 + 2 = 7.
3. Work out: −3 − 4
Start at −3, move 4 left: −7.
Level 4 · Challenge
Challenge
Real-life and multi-step.
1. The temperature is −6°C and rises 10°. What is it now?
−6 + 10 = 4°C.
2. Work out: −5 − (−8)
Two minuses make plus: −5 + 8 = 3.
3. A diver at −12 m rises 7 m, then falls 3 m. What depth now?
−12 + 7 = −5, then −5 − 3 = −8 m.
Page 10 · Well done
You’ve finished Integers & Negative Numbers
You can now order, add and subtract positive and negative numbers, handle the two-minus trick, and use them in real situations like temperature. The number line is your reliable guide.
RememberPicture the number line. Adding moves right, subtracting moves left, and two minuses together make a plus.
🎉Great work getting through all four tiers. Try another module next — every one builds a different skill.
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