Problem
Adam bought a watch for 50c. Unfortunately it gains 30 minutes every day! If Adam set his watch at noon one day, how long would it be before it next correctly shows 12 o’clock again?

What is this problem about?
This problem uses analogue time and logic. It can be solved by using a series of diagrams, by being systematic or by using arithmetic carefully.

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

Mathematical Processes
- devise and use problem solving strategies to explore situations mathematically (use a diagram, be systematic).

Resources
Analogue watch (or clock) to introduce the problem
Blackline master of the problem (English)
Blackline master of the problem (Maaori)

Specific learning outcomes
The children will be able to:
- use an analogue clock to tell the time
- apply logic to a problem involving time

1. Ask the children to use their watches to tell you the time. List their responses on the board and the reasons for them (set incorrectly, gain/lose time). It is important the children feel "inclined" or motivated to solve problems which is why you should introduce them in ways that work for the children in your class.
2. Give the problem to the children to solve in pairs.
3. As the children work ask questions that focus their thinking on the reasoning behind the strategies they are using.
   What are you doing? Why did you decide to do it that way?
   Are you convinced that your answer is correct? How do you know?
4. Encourage the children to record their solution in a way that would convince someone else that they were correct.
5. Display and share written records.

Extension to the problem
Adam has another watch that loses a minute a day. How long will it take to show 12 o'clock at midday?

Solution to the problem
After the first 24 hours Adam’s watch will show 12:30 at midday. After the second day it will show 1:00 at that time. After 24 days Adam’s watch will show 12:00 at 12 o’clock.