Mathematics • Year 7 • Unit 1 • Lesson 3
Adding and Subtracting Integers
Build the two big rules: same sign — add the magnitudes, keep the sign; different signs — subtract, keep the sign of the bigger one. And the subtraction trick: subtracting a negative is the same as adding a positive.
1. I do — fully worked example
Read every line. Each step has a short reason on the right so you can see why, not just what.
Problem. Calculate 5 − (−3) using the number line.
Step 1 — Spot the trap.
There are two negative signs side by side: − (−3).
Reason: "subtract a negative" is one of the four sign combinations to remember. Two minuses next to each other turn into a plus.
Step 2 — Rewrite using the rule "two minuses make a plus".
5 − (−3) = 5 + 3
Reason: subtracting a negative is the same as adding the opposite. Adding the opposite of −3 means adding +3.
Step 3 — Add.
5 + 3 = 8
Reason: both positive — just add the magnitudes.
Step 4 — Check on the number line.
Start at 5. Subtracting a negative = jump RIGHT (the opposite direction to subtracting a positive). 5 → 6 → 7 → 8.
Reason: the answer is LARGER than 5 because we effectively added 3.
Answer: 5 − (−3) = 8.
2. We do — fill in the missing steps
Same structure as Section 1, but with the working faded. Fill in each blank line. 4 marks
Problem. Calculate −7 + (−4) using the number line.
Step 1 — Spot the signs: both numbers are __________ (same / different) signs.
Step 2 — Apply the rule "same sign: add magnitudes, keep the sign":
Magnitudes: 7 + 4 = _______
Step 3 — Apply the sign: both negative, so the answer is _________ (positive / negative).
−7 + (−4) = _______
Step 4 — Number line check: start at −7. Adding a negative = jump _______ (left / right). Land on _______.
3. You do — independent practice
Show your working in the space under each problem. The first four are foundation, the middle two are standard, and the last two are extension.
Foundation — single step
3.1 Calculate −6 + (−5). 1 mark
3.2 Calculate 8 + (−3). 1 mark
3.3 Calculate −4 + 9. 1 mark
3.4 Calculate 2 − (−6). 1 mark
Standard — combine two ideas
3.5 Calculate −10 − (−4). 2 marks
3.6 Calculate 3 − 11. 2 marks
Extension — push your thinking
3.7 Calculate −8 + 12 − (−5) − 7 by first rewriting all subtractions as "add the opposite", then working left to right. 3 marks
3.8 Fill in the missing integer to make each statement true:
(a) −3 + ____ = 0 (b) ____ − (−5) = 2 (c) 6 + ____ = −1. 3 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — We do (−7 + (−4))
Step 1: both numbers are same sign (both negative).
Step 2: 7 + 4 = 11.
Step 3: both negative, so answer is negative: −7 + (−4) = −11.
Step 4: start at −7, adding a negative means jump left. Land on −11.
3.1 — −6 + (−5)
Same signs (both negative): add magnitudes 6 + 5 = 11, keep the negative sign. Answer: −11.
3.2 — 8 + (−3)
Different signs: subtract the smaller magnitude from the larger: 8 − 3 = 5. Keep the sign of the bigger magnitude (+8), so answer is +5.
3.3 — −4 + 9
Different signs: 9 − 4 = 5. Keep the sign of the bigger magnitude (+9). Answer: +5. (Same as Q3.2 — the order doesn't change the result.)
3.4 — 2 − (−6)
Two minuses make a plus: 2 − (−6) = 2 + 6 = 8.
3.5 — −10 − (−4)
Two minuses make a plus: −10 − (−4) = −10 + 4. Different signs: 10 − 4 = 6, sign of bigger magnitude is negative. Answer: −6.
3.6 — 3 − 11
3 − 11 = 3 + (−11). Different signs: 11 − 3 = 8, sign of bigger magnitude is negative. Answer: −8. (Number line check: start at 3, jump 11 left, land on −8.)
3.7 — −8 + 12 − (−5) − 7
Rewrite: −8 + 12 + 5 + (−7).
Left to right: −8 + 12 = 4; 4 + 5 = 9; 9 + (−7) = 2.
Alternative: group positives (12 + 5 = 17) and negatives (−8 + (−7) = −15), then 17 + (−15) = 2.
3.8 — Missing integers
(a) −3 + ▢ = 0 → ▢ = +3 (opposite of −3).
(b) ▢ − (−5) = 2 → ▢ + 5 = 2 → ▢ = −3.
(c) 6 + ▢ = −1 → ▢ = −1 − 6 = −7.