Task 83 ... Years 2 - 10


This task is a challenge for anyone and one that seems also to intrigue just about everyone. All you have to do is run a pen around a racetrack - while looking at the track in a mirror! The task engages the body's kinaesthetic sense in an unexpected way. There are many levels of difficulty within the task and you will find students will want to return to the challenge.



  • development of spatial perception
  • mirror symmetry
  • identifying left and right
  • measuring and recording time
  • problem solving strategies


A task is the tip of a learning iceberg. There is always more to a task than is recorded on the card.

There isn't much you can do to help a student through this task, but then you don't really need to anyway. It is one that can be 'on the table' to be tackled when the students wish. However, as the students tackle the task try to encourage them to talk to each other about how they have to think to send messages to their hands. Have they discovered that their left hand is the right hand of the person in the mirror?

To follow up the task, students might like to make their own racetracks with which to challenge others. Of course, they have to be first to show that their challenge track can be successfully negotiated.

It is also important to connect the task to places in life where this mirror skill is needed. For example, the truck driver's challenge of reversing into a space using mirrors only. Students can come close to experiencing this by holding a mirror in each hand as if they were the side mirrors of a vehicle, then, starting at the classroom doorway, trying to navigate themselves safely to the far back corner of the room by looking in the mirrors only.

Another opportunity for developing the task relates to the time measurements the students are recording. As they are working on the task you have the opportunity to assess in context their ability to use a stop watch or other timing device and discuss relationships between units of time (seconds, minutes, hours etc.) and the representation of time with both digital and analogue clocks.

Whole Class Investigation

Tasks are an invitation for two students to work like a mathematician. Tasks can also be modified to become whole class investigations which model how a mathematician works.

The time data collected in this task can be the beginning of a lesson or two on displaying and measuring data. If the task is left 'on the table' for a few days, each student will have recorded three results on each track. Consider Track 1 for example and ask who thought they did better with practice. Describe the 'hands up' response as a feeling or suggestion that the class improved as a whole, even though individual results may been different. Explain that mathematicians use graphs and statistics such as range, mean, median and mode to try to measure that feeling.

Let's explore how much better we did as a class between the first and third tries at Track 1.
When the graphing and statistics appropriate for your students has been explored, the results from Tracks 2 or 3 can be used as a group challenge, or personal assignment, to assess whether the learning transfers to a different set of data.

You can also create a physically involving form of the task by chalking a racetrack on the playground and using the reversing with mirrors idea above as a challenge from which class data can be collected. Best not to take the whole class outside at the same time for this activity. There will be too much time waiting around for others to finish. Rather send the students outside in groups to collect their data.

At this stage, Racetrack does not have a matching lesson on Maths300, however, Lesson 123, Mirror Bounce, is based around reflecting sunlight from outside the room to a target on the board and would therefore be a complementary lesson to this task. For more ideas and discussion about Mirror Bounce, open a new browser tab (or page) and visit Maths300.

Is it in Maths With Attitude?

Maths With Attitude is a set of hands-on learning kits available from Years 3-10 which structure the use of tasks and whole class investigations into a week by week planner.

The Racetrack task is an integral part of:

  • MWA Space & Logic Years 3 & 4
  • MWA Space & Logic Years 7 & 8
This task is also included in the Primary Library Kit. Solutions for tasks in the this kit can be found here.

Green Line
Follow this link to Task Centre Home page.