The 50 Day Challenge


The purpose of this activity is to engage students in solving a problem using measurement and arithmetic techniques.

Achievement Objectives
GM4-2: Convert between metric units, using whole numbers and commonly used decimals.
GM4-4: Interpret and use scales, timetables, and charts.
NA4-7: Form and solve simple linear equations.
Description of Mathematics

The background knowledge and skills that need to be established before and/or during this activity are outlined in the diagram below:

Click to show example questions for each heading

This activity may be carried out with step by step guidance, or by allowing the student to follow their own method of solution. The approach should be chosen in sympathy with students' skills and depth of understanding.


A teacher has set her class the task of ‘walking the length’ of State Highway 1 in 50 school days. They are allowed to count each step that each student takes if they walk to and from school and if they walk laps of the 400 m track on the school field at fitness time.

Use the data the class have collected below, to work out how many laps of the track each student will need to walk on each of the 50 challenge days.

How do we get to school?


How many metres do each of the walkers take? (Each walker used a gps app on a smartphone to measure their walk to school)

250, 186, 373, 1256, 812, 280

How many metres do each of the bus pupils walk to get to the stop? (Each pupil used a gps app on a smartphone to measure their walk to school)

140, 203, 95, 413, 77

The class ‘googled’ the length of State Highway 1 and got 2 047 km.

The arithmetic approach  (show more)

  • The student is able to explore, with appropriate calculations, to solve a measurement problem involving proportional reasoning.

The conceptual approach  (show more)

  • The student is able to find the solution to a proportional reasoning problem in a measurement context.

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