Mathematics • Year 7 • Unit 1 • Lesson 3
Adding and Subtracting Integers — Real World
Apply integer addition and subtraction to temperature changes, deposits and withdrawals, lift trips, video-game lives, and elevations above and below sea level.
1. Word problems
Each problem uses an addition or subtraction of integers. Show your working — a single answer with no working only earns half marks.
1.1 — Overnight temperature change. At 9 pm the temperature in Orange was 4 °C. Overnight it fell by 11 °C.
(a) Write the calculation as an integer subtraction (or addition of a negative).
(b) What was the temperature the next morning? 2 marks
1.2 — Bank account. Tilly's bank balance was −$12 (she was already overdrawn by $12). Her birthday money of $50 was deposited.
(a) Write the calculation as integer addition.
(b) What is her new balance? 2 marks
1.3 — Lift in an apartment block. The lift starts on floor −3 (the bottom car park). It goes up 6 floors, then down 4 floors, then up 2 more.
(a) Write a single integer expression for the lift's final floor.
(b) What floor does the lift end up on? 3 marks
1.4 — Video game lives. In a platformer, your character starts with 0 "extra lives". Collecting a heart adds 1 life; falling in lava costs 1 life (so your lives can go negative, which means a debt of lives until you collect hearts to clear it). In one run Ali collects 5 hearts and falls in lava 8 times.
(a) Write Ali's final lives total as an integer expression.
(b) Evaluate it.
(c) How many hearts does Ali need to collect to get back to 0 lives? 3 marks
1.5 — Sea level expedition. A scuba diver starts at sea level (0 m). They descend 18 m, then ascend 7 m, then descend another 11 m. (Descend = down = negative, ascend = up = positive.)
(a) Write the diver's final depth as a single integer expression.
(b) What is the diver's final depth below sea level? 3 marks
2. Explain your thinking
This question is about communication, not just answers. Use full sentences. 4 marks
2.1 A classmate sees the calculation 7 − (−4) and writes 7 − 4 = 3, "because two negatives just cancel out the minus signs and I subtract." In your own words, explain (i) which rule from Lesson 3 they have mixed up, (ii) what 7 − (−4) actually equals, and (iii) why "two negatives" actually turns the operation into addition, not subtraction. Use a real-world example (temperature, bank account or lift) to back up your explanation.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Overnight temperature
(a) 4 − 11 (or equivalently 4 + (−11)).
(b) 4 − 11 = −7 °C. The next morning was 7 degrees below zero.
1.2 — Bank account
(a) −12 + 50.
(b) Different signs: 50 − 12 = 38, sign of bigger magnitude is positive. New balance: +$38.
1.3 — Lift
(a) −3 + 6 − 4 + 2.
(b) Work left to right: −3 + 6 = 3; 3 − 4 = −1; −1 + 2 = 1. The lift ends on floor 1.
1.4 — Video game lives
(a) 0 + 5 − 8 (each heart is +1, each lava fall is −1).
(b) 5 − 8 = −3 lives.
(c) Ali needs to add 3 to get back to 0, so they need 3 hearts. The opposite of −3 is +3 — that's the amount you add to cancel the negative.
1.5 — Scuba diver
(a) 0 − 18 + 7 − 11.
(b) Left to right: 0 − 18 = −18; −18 + 7 = −11; −11 − 11 = −22 m. The diver is 22 m below sea level.
2.1 — Explain your thinking (sample response)
My classmate has confused "subtracting a negative" with "the two minus signs just disappear and leave a subtraction". The rule from Lesson 3 is actually subtracting a negative = adding the opposite, so 7 − (−4) becomes 7 + 4 = 11, not 3. A nice way to picture this is a bank account: if you owe me $4 and I cancel that debt (so I subtract the −$4), your balance goes up by $4. Subtracting something negative makes your total bigger, not smaller. Another way: on the number line, subtracting a positive jumps left, so subtracting a negative does the opposite — it jumps right. Starting at 7 and jumping 4 right lands on 11.
Marking: 1 for naming the rule "subtract a negative = add the opposite"; 1 for the correct answer 11; 1 for a real-world example; 1 for a clear explanation in full sentences.