Running Speed
Task Description
Students explore how fast they can run and calculate their speed in kilometres per hour
based on data collected through experimenting with various running trials. How do they
compare to the fastest man on earth?
Length of Task
100 minutes
Materials

Stopwatches, trundle wheels, cones, calculators.
Using the Activity
Introduction
The teacher probes the students’ understanding of the meaning of ratio and creates a
mind map to record responses.
The teacher poses the following problem and suggests different problem-solving strategies
to assist the students, e.g. using drawings or diagrams.
Stompie escaped from his tank last week as I was
cleaning it. Surprisingly, he moves quickly for a
turtle. He managed to run 10 metres in
approximately 30 seconds.
How fast in kilometres per hour did Stompie move?
Before the students commence the problem the teacher clarifies the meaning of
kilometres per hour with the class. The students work individually on the problem for 3–5
minutes and afterwards share their thoughts with a partner.
A whole class discussion provides an opportunity for students to reflect on the
effectiveness of their strategy for answering the question.
Main Activity
The teacher poses the next problem to the students.
This activity is intended for use by teachers for research purposes only, as part of the Task Types and Mathematics Learning (TTML) project at
Monash University. No authority is granted for persons to use these activities beyond the scope of this project, without express permission of the
TTML Project Leader.
Running Speed
Usain Bolt is the fastest man on earth. He can run
100m in 9.58 seconds.
How fast can you run over 100m?
The students form small groups and are invited to use the equipment available to solve
the problem, e.g. stopwatches, trundle wheels, cones, calculators. Before moving outside
to the oval, the students are directed to write a plan describing how they will collect the
data for this problem. The teacher confirms with the students the two important pieces of
information they need to gather outside - time and distance.
The students are given 30 minutes to explore ways to calculate their speed. Allow
students to explore different approaches, such as: measuring out 100m and timing how
long it takes to run the distance; or students running for 10 seconds and measuring how
far they travelled.
The class return to the classroom and calculate their speed based on the data collected.
The teacher asks, “If someone wanted to find out their own speed, what rule would help
them work it out?” During this time the teacher roves the room and questions the students
about the different strategies they employ for the task. The teacher may choose to stop
the class during this time to ask selected students to share their strategies if it seems
helpful for the remaining students. The teacher may encourage the students to round
their answers to assist in easy of calculation.
Reflection: The whole class share their responses and approaches to the task. The teacher
asks the students to consider how this task relates to ratio and comparisons.
Key Mathematical Concepts

Comparison of ratios to calculate speed.
Prerequisite Knowledge

Understanding simple ratios and conversion of metric measurements.
Links to VELS
Dimension
Number (Level 5)
Working mathematically
(Level 4)
Measurement, chance and
data (Level 6)
Standard
Students understand ratio as both set:set comparison and
set:subset and find integer proportions of these, including
percentages.
Students use the mathematical structure of problems to
choose strategies for solutions. They explain their reasoning
and procedures and interpret solutions.
Students calculate constant rates such as average speed.
This activity is intended for use by teachers for research purposes only, as part of the Task Types and Mathematics Learning (TTML) project at
Monash University. No authority is granted for persons to use these activities beyond the scope of this project, without express permission of the
TTML Project Leader.
Running Speed
Assessment
To be working at Level 4, students should be able to:
 Use ratio to compare the relationship between measurements.
 Develop a plan to collect suitable data to response to the task.
Extension Suggestions
For students who would benefit from additional challenges:
 Usain Bolt is the fastest man in the world. His world record time for the 100m is 9.58
seconds. Calculate this time into km/h? Predict how fast you think Bolt will run in
200m. What might this be in km/h? Justify your response.
Note: The speed of Bolt’s 100m run is 37.6 km/h. His world record time for the 200m
is 19.19 seconds.
 Below is a graph of the 100m record breaking times from the 1920s to now. Based on
this data, students predict what the speed of the fastest man might be in 2020, 2050
and 2100. The following blog website maintained by a theoretical astrophysicist
provides a discussion of “The math of the fastest human alive”. The graph is sourced
from this blog.
http://scienceblogs.com/startswithabang/2009/08/the_math_of_the_fastest_human.php
This activity is intended for use by teachers for research purposes only, as part of the Task Types and Mathematics Learning (TTML) project at
Monash University. No authority is granted for persons to use these activities beyond the scope of this project, without express permission of the
TTML Project Leader.
Running Speed
Teacher Advice and Feedback
This was a challenging task for many of the students; however, all groups were able to
calculate their speeds by the end of the session. Some students realised that their
calculations were incorrect when comparing their speed to a realistic setting such as cars
driving past the school.
It was interesting to note that many of the students chose to fix the distance and not the
time. If the time is fixed (e.g., one minute), then it is much easier to find the speed.
This task gives great autonomy to the students as they are choosing the method, the
distance, the time, the mode of calculation.
Potential Student Difficulties
Some students were having difficulty accessing the initial problem. The problem could be
simplified to become more accessible, e.g.:
Last week as I was cleaning Stompie the turtle’s tank he escaped. Surprisingly, he moves
quickly for a turtle. He managed to run 10 metres in approximately 1 minute. How many
metres did Stompie move in one hour? How many kilometres did Stompie move in one
hour?
For students having difficulties during the main task, the teacher may suggest they run for
10 seconds and measure the distance covered and measure how long it would take them
to run 10m. The students will now have two forms of data to select from when calculating
their speed. With some encouragement the students may find that the initial data will be
easier to calculate.
References / Acknowledgements
Thank you to the teachers and students from Lloyd Street PS, for providing valuable
feedback on the use of this activity.
This activity is intended for use by teachers for research purposes only, as part of the Task Types and Mathematics Learning (TTML) project at
Monash University. No authority is granted for persons to use these activities beyond the scope of this project, without express permission of the
TTML Project Leader.
Running Speed
Students working through problems together
Example 1: The example below illustrates the students sharing their understanding of
kilometres per hour and how fast Stompie moves.
Example 2: The students shared strategies that were successful and difficult when
answering the problem about their speed.
This activity is intended for use by teachers for research purposes only, as part of the Task Types and Mathematics Learning (TTML) project at
Monash University. No authority is granted for persons to use these activities beyond the scope of this project, without express permission of the
TTML Project Leader.
Running Speed
Student work samples
Example 3: Working at Level 4
These students were using a diagram to assist their understanding of the task.
This activity is intended for use by teachers for research purposes only, as part of the Task Types and Mathematics Learning (TTML) project at
Monash University. No authority is granted for persons to use these activities beyond the scope of this project, without express permission of the
TTML Project Leader.
Running Speed
Example 4: Working at Level 4
These students devised an appropriate rule for calculating an individual’s speed.
Example 5: Working at Level 4
These students compared different distances runs over the same period of time then
multiplied each time by 6 to calculate the distance per minute. This distance is multiplied
by 60 to calculate kilometres per hour. This process matches the rule in example 4.
This activity is intended for use by teachers for research purposes only, as part of the Task Types and Mathematics Learning (TTML) project at
Monash University. No authority is granted for persons to use these activities beyond the scope of this project, without express permission of the
TTML Project Leader.
Running Speed
This activity is intended for use by teachers for research purposes only, as part of the Task Types and Mathematics Learning (TTML) project at
Monash University. No authority is granted for persons to use these activities beyond the scope of this project, without express permission of the
TTML Project Leader.