Mathematics • Year 7 • Unit 1 • Lesson 2
Integers in the Real World
Use integers to talk about temperatures, lift levels, golf scores, bank balances and altitudes. The number line is the same — only the units change.
1. Word problems
Each problem uses the integer ideas from Lesson 2: comparing negatives, finding distances on the number line, opposites, and absolute value. Show your working — a single answer with no working only earns half marks.
1.1 — Cold morning. One winter morning in Thredbo, the temperature was recorded as −6 °C at 6 am. By midday it had warmed to 3 °C.
(a) Which temperature is lower, and by how many degrees?
(b) Plot both temperatures on a number line (drawn below) and mark zero. 3 marks
1.2 — Apartment lift. An apartment building has 9 floors above ground (1 to 9) and 3 basement levels (−1, −2, −3). The lobby is on floor 0.
(a) Riley is on floor −2 and walks up to floor 5. How many floors did Riley climb?
(b) Which floor is the same number of floors below the lobby as floor 4 is above? 3 marks
1.3 — Bank account. Sam's bank balance was $40 on Monday. He spent $55 on Tuesday (the bank let him go overdrawn — into negative numbers).
(a) What is Sam's new balance, written as an integer?
(b) Sam's older sister has a balance of −$30. Who owes the bank more money, Sam or his sister? Explain how you compared the two negative balances. 3 marks
1.4 — Golf scores. In golf, par is 0. Scoring under par is written as a negative number ("3 under par" = −3) and scoring over par is positive. After one round, four friends have scores: Mia −2, Tia +1, Hugo 0, Ash −5.
(a) In golf, a smaller (more negative) score is better. List the four players from best to worst.
(b) Whose score has the largest absolute value, and what is it? 3 marks
1.5 — Altitudes. Mount Kosciuszko is 2,228 metres above sea level. The lowest point of the Dead Sea is 430 metres below sea level. Sea level is 0.
(a) Write each location's altitude as an integer (positive or negative).
(b) What is the difference in altitude between the two locations, in metres? 3 marks
2. Explain your thinking
This question is about communication, not just answers. Use full sentences. 4 marks
2.1 A classmate looks at the temperatures −10 °C and −2 °C and says "−10 is bigger than −2 because 10 is bigger than 2 — so −10 °C must be the warmer one." In your own words, explain (i) what mistake they have made, (ii) which idea from Lesson 2 they have forgotten, and (iii) what the correct comparison is. Use the temperature itself somewhere in your explanation.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Cold morning
(a) −6 °C is lower than 3 °C (further left on the number line). Difference: from −6 to 3 is 6 + 3 = 9 °C.
(b) Number line should have −6 to the left of 0 and 3 to the right, with zero clearly marked.
1.2 — Apartment lift
(a) From floor −2 to floor 5: distance = 2 + 5 = 7 floors.
(b) Floor 4 is 4 floors above the lobby. The same number below is floor −4 — the opposite of 4.
1.3 — Bank account
(a) Sam had $40, spent $55. New balance = 40 − 55 = −$15.
(b) Compare −$15 (Sam) and −$30 (sister). The sister is further into the negatives — more in debt. So Sam's sister owes more. The bigger the absolute value of the negative balance, the more money is owed: |−30| > |−15|.
1.4 — Golf scores
(a) Smallest score is best: Ash (−5), Mia (−2), Hugo (0), Tia (+1).
(b) Absolute values: |−5| = 5, |−2| = 2, |0| = 0, |+1| = 1. The largest is 5, belonging to Ash.
1.5 — Altitudes
(a) Kosciuszko: +2,228 m. Dead Sea: −430 m.
(b) Distance on the number line: 2,228 + 430 = 2,658 m. From −430 you climb 430 m to reach 0, then 2,228 m further to reach the summit.
2.1 — Explain your thinking (sample response)
My classmate has assumed that because 10 > 2, it follows that −10 > −2. That works for positive numbers, but it flips for negatives. The rule they forgot is the number line rule from Lesson 2: any number to the right is greater. On the number line, −10 is much further left than −2, so −10 is actually smaller. In temperature terms, −10 °C is colder than −2 °C — and the colder temperature is the smaller number. The correct comparison is −10 °C < −2 °C, so −2 °C is the warmer of the two.
Marking: 1 mark for naming the mistake (flipping the rule for negatives); 1 for the correct rule ("right is larger" on the number line); 1 for the correct comparison −10 < −2; 1 for connecting to temperature.