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.