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.