Running Rates


The purpose of this activity is to engage students in solving a problem involving fractions (time in hours, minutes and seconds) and decimals (distance in km) to find a rate.

Achievement Objectives
NA4-4: Apply simple linear proportions, including ordering fractions.
NA4-5: Know the equivalent decimal and percentage forms for everyday fractions.
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. With the values involved, tools such as a calculator could be provided, so that ability in numeracy might not become a barrier to the problem solving skills being developed through this activity. The approach should be chosen in sympathy with students' skills and depth of understanding.



In the 2014 Auckland marathon, the average time was 4:27:15 for the full and 2:22:53 for the half.

A full marathon is 42.195 km in length. How much faster (in minutes or seconds per km) was the average full marathon pace than the half?


The procedural approach  (show more)

  • The student is able to make the appropriate calculations, with guidance, in order to solve the problem.

The conceptual approach  (show more)

  • The student is able to make the appropriate calculations in order to solve the problem.

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