Problem
It’s 7km from Tim’s house to where his grandma lives. It’s uphill on the way there so he can only cycle at 14kph but he can do 21kph on the way back.

Tim leaves his house at 6pm. How long can he stop at his grandma’s house if he wants to be back home for his favourite TV programme at 7pm?

What is this problem about?
Children first have to know how long it takes Tim to do 7km given the speed that he can make on his bike. They have to combine two times (the time to grandma’s house and back) to see how long he takes travelling. This time will then need to be taken from 1hr. The numbers used in this problem will give some children the opportunity to work it out mentally. Encouraging children to work out problems mentally develops their understanding of numbers and number operations.

Achievement Objectives
Measurement (Level 3)
- read and interpret everyday statements involving time.

Mathematical Processes
- devise and use problem solving strategies to explore situations mathematically (guess and check, draw a diagram)

Resources
Blackline master of the problem (English)
Blackline master of the problem (Maaori)

Specific learning outcomes
The children will be able to:
- calculate accurately using units of time and speed.
- explain their methods and reasoning using correct mathematical terms

Teaching sequence

1. Discuss reasonable cycling speeds as an introduction to this problem. Ask the children to justify their estimates (eg followed a cyclist in the car, know the speeds of professional cyclists).
2. Pose the problem.
3. Brainstorm for strategies that will help solve the problem (eg. a picture of the trip.)
4. As the children work on the problem with a partner ask questions that focus their thinking on the use of units of time and speed?
   What does 14 kmph mean?
   How far would Tim travel in 2 hours?
   How far would Tim travel in 30 minutes? How did you know that?
5. Share solutions.

Extension to the problem
At what time should Tim leave home if he wants to spend 45 minutes at his grandma's?

Solution
The trip to grandma’s takes 30 minutes. (If he were travelling at 7kph he would take an hour. Travelling at twice that speed halves the time.) This means that the home trip takes a third of an hour or 20 minutes. Tim’s total travelling time is therefore 50 minutes. If he spends 10 minutes with grandma he can still get home to watch his favourite programme.