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?

Students will need to know and be able to work with standard units of time including minutes, hours, days and days in one year.

The problem uses analogue time and logic. It can be solved by using a series of diagrams, by being systematic or by using arithmetic carefully.

Analogue watch (or clock) to introduce the problem

### 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?

### Teaching sequence

- Engage your students in the problem by having them use their watches to tell you the time. List their responses on the board and the reasons for any variation in given times (set incorrectly, gain/lose time).
- Give the problem to the students to solve in pairs.
- As the students 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? - Encourage the students to record their solution in a way that would convince someone else that they were correct.
- 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.

#### Extension:

After 60 days it will show 11 o'clock at midday. Therefore it will take 12 x 60 = 720 days to show the correct time. 720 days = 1 year and 355 days (using 365 days in a year).