Mathematics • Year 7 • Unit 4 • Lesson 6
Line Graphs — Real World
Apply line graph thinking to real situations: a fitness tracker, a weather station, the petrol price, a Sydney commute, and a global climate dataset. Reading a trend correctly tells a story; reading it wrong loses information that matters.
1. Word problems
Each scenario uses real-world data. Show short working and write your answer in a full sentence where asked.
1.1 — Fitness tracker. Aisha records her daily step count over five days: Mon 6,000, Tue 8,500, Wed 9,000, Thu 4,500, Fri 11,000.
(a) Identify the peak day and the trough day. (b) Calculate Aisha's average daily steps (mean). (c) On which day(s) did her steps INCREASE compared to the day before? 4 marks
1.2 — Weather station. A Sydney rain gauge records monthly rainfall (mm) for the first half of the year: Jan 90, Feb 120, Mar 130, Apr 95, May 110, Jun 130.
(a) Why is a line graph (rather than a bar chart) appropriate here? (b) Describe the trend in two short sentences. (c) Use the data to predict the rainfall expected in July if the trend continued — and state whether this is interpolation or extrapolation. 4 marks
1.3 — Petrol price tracker. The average price per litre (cents) of unleaded petrol over 6 weeks: W1 180, W2 192, W3 205, W4 198, W5 188, W6 175.
(a) State the peak week and trough week. (b) Use interpolation to estimate the price halfway through Week 3 to Week 4. (c) Describe the overall trend across the 6 weeks in one sentence. 4 marks
1.4 — Sydney commute time. Jordan times their morning train trip each day: Mon 32 min, Tue 35, Wed 60, Thu 33, Fri 36.
(a) Identify the day with the unusually long commute. What might have caused it? (b) Excluding the unusual day, what is the typical commute time (mean of the other 4 days)? (c) Why would extrapolating to "next Monday's commute" be risky here? 4 marks
1.5 — Global climate. Global average surface temperature anomaly (°C above the 1951–1980 mean): 1980 +0.27, 1990 +0.45, 2000 +0.42, 2010 +0.72, 2020 +1.02.
(a) Describe the overall trend in one sentence. (b) Calculate the change from 1980 to 2020. (c) Extrapolate the 2030 value if the 2010→2020 rate continues, and explain in one sentence why we should be cautious about predicting decades ahead. 4 marks
2. Explain your thinking
Communication matters. Use full sentences. 4 marks
2.1 A news article shows a line graph of house prices in a suburb from 2015 to 2024 (steady increase). The journalist writes: "If this trend continues, prices in 2050 will be triple today's." Identify (i) whether the journalist is interpolating or extrapolating, (ii) why a 26-year prediction is risky, and (iii) what kind of evidence would make you trust the prediction more.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Fitness tracker
(a) Peak = Fri (11,000 steps); Trough = Thu (4,500 steps).
(b) Mean = (6000 + 8500 + 9000 + 4500 + 11000) ÷ 5 = 39,000 ÷ 5 = 7,800 steps/day.
(c) Increases: Mon→Tue (6000→8500), Tue→Wed (8500→9000), Thu→Fri (4500→11000). Decreased: Wed→Thu.
1.2 — Weather station
(a) Months are an ordered TIME variable, so the x-axis is continuous and a line graph correctly suggests "monthly change". A bar chart would imply separate, unrelated categories.
(b) Rainfall rose Jan→Mar (peak 130 mm), dipped in April, then climbed back to 130 mm by June. Overall the rainfall is variable but high (90–130 mm/month).
(c) July prediction is extrapolation (beyond the data). Following the recent May→Jun rise (+20), one might guess ~130–150 mm, but the trend may not continue.
1.3 — Petrol price
(a) Peak = Week 3 (205c); Trough = Week 6 (175c).
(b) Halfway between W3 (205) and W4 (198) = (205 + 198) ÷ 2 = 201.5 cents (interpolation).
(c) The price rose from W1 to a peak in W3, then fell steadily through W6 — an inverted V shape, with W6 the cheapest week of the six.
1.4 — Sydney commute
(a) Wednesday (60 min). Possible causes: signal failure, track work, an accident, or a major weather event delaying trains.
(b) Mean of Mon, Tue, Thu, Fri = (32 + 35 + 33 + 36) ÷ 4 = 136 ÷ 4 = 34 minutes.
(c) Train delays depend on the weather, infrastructure problems and one-off incidents that are hard to predict. Five days of data is a tiny sample, so any extrapolation to next week is unreliable.
1.5 — Global climate
(a) The temperature anomaly has increased overall from 1980 to 2020 (with a small dip in 2000), showing clear long-term warming.
(b) Change = 1.02 − 0.27 = +0.75 °C from 1980 to 2020.
(c) Rate 2010→2020 = 0.30 ÷ 10 = 0.03 °C/year. Extrapolated 2030 ≈ 1.02 + 0.30 = 1.32 °C. Caution: climate depends on many factors (emissions policy, ocean cycles, volcanic events) — assuming the recent rate is unsafe over decades.
2.1 — Explain your thinking (sample response)
(i) The journalist is extrapolating — predicting a value (2050) beyond the data range (2015–2024). (ii) A 26-year prediction is risky because property prices depend on interest rates, government policy, immigration, recessions and many other factors that can reverse a trend at any time. The history of the last 9 years is no guarantee for the next 26. (iii) Trust would grow if there were longer historical data (50+ years) showing the same steady trend, expert modelling that accounts for the major drivers of price, AND a clear statement of the uncertainty (e.g. a confidence range, not a single number).
Marking: 1 mark each for (i) extrapolation, (ii) two valid reasons it's risky, (iii) two ideas for stronger evidence (longer data, expert modelling, uncertainty bands).