Mathematics 11–12 · Years 11–12
Walking pace as a linear model, and time against speed as a reciprocal one
Linear relationships: Linear modelling (Mathematics Standard, Year 11); Linear relationships: Direct variation (Mathematics Standard, Year 11); Algebraic relationships: Reciprocal relationships (Mathematics Standard 2, Year 12)
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The idea
Steady walking gives distance in direct variation with time, the gradient is the speed, and the time for a fixed distance varies inversely with that speed.
What you need
- A 25 m line with cones every 5 m
- A stopwatch with a lap-time function
- Graph paper or a spreadsheet
How to do it
- Walk the line at a steady pace; a partner records the lap time as you pass each cone.
- Plot distance (m) against time (s), draw the line of best fit through the origin and read the gradient.
- Convert the gradient to km/h.
- Repeat at a brisk pace and at a jog; plot all three on the same axes and compare gradients.
- Walk 15 m steadily, stop for 5 s, then continue; plot the run and describe the flat section.
- Plot the time for 25 m against the speed for your three runs and fit t = k / v.
What you should see
A steady walk passing cones every 3.6 s gives d = 1.39 t (1.39 m/s = 5.0 km/h) and takes 18.0 s for 25 m; a jog at 2.78 m/s takes 9.0 s. The time-speed points lie on t = 25 / v, a hyperbola, so doubling the speed halves the time. The stop appears as a horizontal segment of gradient 0. The learner knows it worked when the fitted line passes within 0.5 m of the origin and the reciprocal fit has k close to 25 m.
What changes
- What you change
- time (and, for the reciprocal model, speed)
- What you measure
- distance walked (and time for 25 m)
- What you keep the same
- cones at exactly 5 m
- same walker
- timing starts at the first cone
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- A steeper distance-time line means a longer walk; it means a faster walk.
- Twice the speed takes twice the time; time varies inversely with speed, so it halves.
Safety card
Hazards
- tripping over cones
Controls
- walk beside the cone line, not through it
Note
No chemicals and no heat are used, so the NSW Department of Education Chemical Safety in Schools package does not apply; outdoor work follows the school's grounds or excursion risk assessment (RiskAssess where the school uses it).
Curriculum references
The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.
- Mathematics Standard 11–12 Syllabus (2024), Year 11 focus area Linear relationships; Year 11 taught from Term 1 2026, Year 12 from Term 4 2026, first HSC examination 2027 (the 2017 syllabus is still taught to Year 12 until then); page read 2026-09-22MST-11-02
- Mathematics Standard 11–12 Syllabus (2024), Year 12 Standard 2 focus area Algebraic relationships; Year 11 taught from Term 1 2026, Year 12 from Term 4 2026, first HSC examination 2027 (the 2017 syllabus is still taught to Year 12 until then); page read 2026-09-22MST-12-S2-01
- Australian Curriculum v9No Australian Curriculum v9 code is listed.
Sources
The pages the author read to write this activity.