Mathematics • Year 7 • Unit 4 • Lesson 6
Line Graphs — Mixed Challenge
Combine every line-graph skill: axes and scales, plotting, trend description, peaks and troughs, interpolation and extrapolation. Then spot one plausible student error, and design your own data-collection project.
1. Mixed problems — apply every skill
Each question uses a different idea from the lesson. Show short working. 2 marks each
1.1 Daily temperatures (°C) over a week: Mon 18, Tue 22, Wed 28, Thu 25, Fri 20, Sat 17, Sun 19. State the peak and trough, and the difference between them.
1.2 A bushfire fuel-load reading (tonnes/hectare) was 12 at Year 0 and 22 at Year 4. Interpolate the reading at Year 2 and state in one short sentence why interpolation is more reliable than extrapolation.
1.3 A line graph shows a baby's weight (kg): Birth 3.2, 3 mo 6.0, 6 mo 7.6, 9 mo 8.6, 12 mo 9.4. Describe the trend in one sentence — be specific about HOW the rate of growth changes over the year.
1.4 The maximum value of a dataset is 187. The minimum is 23. What is the smallest sensible y-axis upper bound you would use, in steps of 10? Explain in one line.
1.5 Why must lines on a line graph connect consecutive points only — never skip a time period? Answer in one or two sentences using an example.
1.6 A plant's height in cm is recorded: Day 1: 5, Day 3: 9, Day 5: 13, Day 7: 17. (a) Calculate the rate of change (cm/day). (b) Extrapolate the height at Day 10. (c) State one reason your Day 10 estimate could be wrong.
2. Find the mistake
Another Year 7 student answered this question: "A plant was 10 cm at Week 2 and 20 cm at Week 6. Estimate the height at Week 4." Their working has exactly one error. Spot it, explain why it's wrong, then write the correct solution. 3 marks
Student's working:
Line 1: Change in height = 20 − 10 = 10 cm.
Line 2: Change in time = 6 − 2 = 4 weeks.
Line 3: Rate = 10 ÷ 4 = 2.5 cm per week.
Line 4: Week 4 is 2 weeks after Week 2, so add 2 × 2.5 = 5 cm.
Line 5: Height at Week 4 = 5 cm. [Answer: 5 cm]
(a) Which line contains the mistake?
(b) Explain in one or two sentences why the answer is wrong.
(c) Write the correct calculation and the correct Week 4 height.
Stuck? The rate (2.5 cm/wk) is correct. Check what the student does with the 5 cm — do they add it to anything, or just call it the answer?3. Open-ended challenge — design a personal data project
This question has many correct answers. Show your work clearly. 4 marks
3.1 Choose ONE thing you could measure about yourself or your household over at least 6 time points (e.g. daily screen time, weekly grocery spend, daily glasses of water, time spent on homework each day). For your chosen variable:
- (i) State what you would measure and how often;
- (ii) Write the axis labels for your line graph, with units;
- (iii) Invent six realistic data values for six time points;
- (iv) Describe the trend you would expect to see in your data (e.g. weekday vs weekend pattern);
- (v) Identify one question you could answer using interpolation, and one you could answer using extrapolation.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Weekly temperatures
Peak = 28 °C (Wednesday). Trough = 17 °C (Saturday). Difference (range) = 28 − 17 = 11 °C.
1.2 — Fuel load interpolation
Change = 22 − 12 = 10 t/ha over 4 years → 2.5 t/ha per year. Year 2 ≈ 12 + (2 × 2.5) = 17 t/ha. Interpolation is more reliable because Year 2 sits BETWEEN the two known measurements, so we are not assuming the rate continues into unknown territory.
1.3 — Baby weight trend
The baby's weight increases throughout the year, but at a slowing rate: gains of about 2.8 kg in the first 3 months, 1.6 kg in the next 3, and only 0.8 kg in the last 3 — growth is fastest in early infancy and decelerates.
1.4 — Axis scale
Smallest sensible upper bound = 190 (in steps of 10): 190 is the smallest multiple of 10 that is ≥ 187.
1.5 — Why join consecutive only
Joining non-consecutive points creates X-shaped crossings that imply the variable jumped backwards in time. Example: if Mon = 10 and Wed = 20, draw Mon→Tue→Wed in order; if you connect Mon directly to Wed and ignore Tue, you erase Tuesday's data from the visual.
1.6 — Plant growth
(a) From Day 1 to Day 7: change = 17 − 5 = 12 cm over 6 days → rate = 2 cm/day.
(b) Extrapolated Day 10 ≈ 17 + (3 × 2) = 23 cm.
(c) Day 10 estimate could be wrong because the plant may slow its growth as it matures, or unexpected events (drought, pest, lack of light) could change the rate.
2 — Find the mistake
(a) The mistake is on Line 5 (final answer).
(b) The student calculated the extra height grown between Week 2 and Week 4 (5 cm), but forgot to add that gain to the starting height of 10 cm. The 5 cm is the change in height, not the height itself.
(c) Correct: rate = 2.5 cm/wk, so Week 4 height = 10 + (2 × 2.5) = 15 cm. (Quick check: 15 sits halfway between 10 cm and 20 cm — exactly what you'd expect for the midpoint week.)
3 — Personal data project (sample answer)
(i) Daily screen time, measured every evening for one week.
(ii) x-axis: "Day (Mon–Sun)". y-axis: "Screen time (minutes)".
(iii) Mon 80, Tue 75, Wed 90, Thu 70, Fri 110, Sat 180, Sun 160.
(iv) Expected trend: roughly steady on weekdays (~75–90 min) with a clear weekend spike (Sat–Sun). Friday already starts to climb because school finishes.
(v) Interpolation question: "What was my screen time on Wednesday afternoon (between morning and evening)?" — within data. Extrapolation question: "How much screen time will I likely use next Monday?" — beyond data, less reliable.
Marking: 1 mark for variable + axes; 1 mark for plausible data; 1 mark for trend description; 1 mark for sensible interpolation AND extrapolation questions.