Mathematics 7–10 · Years 7–8

Rates from timed walking: a distance-time graph from real data

Number and algebra

Practical, model not builtLow risk

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The idea

Speed is a rate, distance per unit time, and it appears as the gradient of a distance-time graph drawn from stopwatch readings taken at measured marks.

Safety card

Low riskAn adult supervises

Hazards

  • collisions on the course
  • uneven ground
  • sun exposure

Controls

  • one walker on the course at a time
  • flat clear surface
  • hats

Note

No chemicals or heat are used, so the NSW Department of Education Chemical Safety in Schools package does not apply; outdoor work follows the school's excursion and playground supervision rules.

What you need

  • 20 m tape measure and 5 cones or chalk marks at 0, 5, 10, 15 and 20 m
  • 5 stopwatches (or phones): 4 timers standing at the 5, 10, 15 and 20 m marks, and a second watch for the 10 m timer in the stop-and-go trial
  • Recording table with columns distance (m) and time (s)
  • Grid paper

How to do it

  1. Mark a straight 20 m course on flat ground with marks every 5 m.
  2. One walker starts on go; every timer stops their watch as the walker passes their mark. Record the four times.
  3. Repeat for a slow walk, a brisk walk and a jog, and once for a walk that stops for 5 s at the 10 m mark; in that trial the 10 m timer stops one watch as the walker arrives and the second as the walker leaves, giving two points at 10 m.
  4. Plot distance against time for each trial on the same axes and join the points.
  5. Compute the gradient of each line in m/s (rise over run) and convert to km/h by multiplying by 3.6.
  6. Describe the stop-and-go trial from the shape of its graph and compute the average speed over the whole 20 m.

What you should see

Steady walking gives points close to a straight line through the origin; a walker covering 20 m in 14.3 s has a gradient of 1.40 m/s, which is 5.04 km/h (1.40 × 3.6). A jog gives a steeper line, and the trial with a 5 s stop shows a flat segment at 10 m between the arrival and departure times (7.1 s and 12.1 s at 1.40 m/s) and a lower average speed than its moving gradient. Timers at successive marks give times that increase; small kinks come from each timer's reaction time in stopping the watch. The learner knows it worked when the gradient from the graph matches 20 m divided by the final time within 5 per cent.

What changes

What you change
time
What you measure
distance from the start
What you keep the same
  • same course
  • same walker within a trial
  • timers start on the same signal

Common misconceptions

Each of these ideas is wrong, and the activity is a chance to test it.

  • A steeper distance-time line means the walker is further away rather than faster.
  • A flat segment means the walker is moving at a steady speed.
  • km/h and m/s can be compared without conversion.

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 K–10 Syllabus (2022), Stage 4 Ratios and rates; page read 2026-09-22MA4-RAT-C-01
  • Australian Curriculum v9AC9M8M05AC9M7A04AC9M8A03

Sources

The pages the author read to write this activity.

  1. curriculum.nsw.edu.au/learning-areas/mathematics/mathematics-k-10-2022/content/stage-4/faf41ae0d9
  2. www.amsi.org.au/ESA_middle_years/Year8/Year8_md/Year8_1a.html

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