## Stop the Clock

This is a game for two players. You can use the interactivity below, or you could print off a page of blank clock faces in

Word or as a

pdf.

Set the time on the clock to $6$ o'clock to start the game.

Decide who will go first (player $1$) and who will go second (player $2$).

Take it in turns to choose to move the hands of the clock on by $\frac{1}{2}$ hour or by $1$ hour. For example, player $1$ could choose $\frac{1}{2}$ hour, so the clock hands move to 6.30, then player $2$ might choose $1$ hour, moving the clock hands to 7.30 ... etc.

The winner is the player who moves the hands exactly onto $12$ o'clock.

Can you work out a winning strategy so that you can always beat your opponent?

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### Why play this game?

Stop the Clock is a motivating context in which children can develop their fluency with telling the time and calculating time intervals. However, the real challenge here is to find a winning strategy and, at the highest level, to be able to beat an opponent whatever the start time and whatever the time
intervals.

### Possible approach

Introduce the game to the class by playing as a whole group, perhaps one half against the other, several times. Then suggest that children play in pairs, either at computers, or by using sheets of blank clocks (

Word document or pdf) to record their game. Challenge them to find a strategy for beating their partner.
As they play, circulate around the classroom and ask them what they think is important so far. Some might suggest that in order to win, they must make the clock show 10.30. Others may have thought further back and have ideas about how they can make sure they get to 10.30, and therefore 12.00. After a suitable length of time bring the whole class together and invite one pair to demonstrate
their strategy, explaining their decisions as they go along. Use other ideas from the group to refine the strategy.

You could then choose some extension ideas (see below) for pairs to work on - perhaps different pairs working on a different set-up. Investigating this game fully could become a long-term challenge for the class which you come back to at various stages throughout a term, for example.

### Key questions

What happens if your opponent gets to 10.30? Why?

How can you make sure you get exactly on $12$ o'clock? What time would you leave on the clock so that you can get to 12.00 on your next go, after your opponent has been?

So, what time would you want the clock to say on the go before that?

How can you work out these "key times" that you must "land on" on your way to the target?

### Possible extension

Invite children to investigate how their strategy would change if they could choose a different starting time.

What about if they were only allowed to choose quarter of an hour, half an hour or three quarters of an hour?

How would their strategy change if the could choose quarter of an hour or half an hour only?

### Possible support

The length of the game can be reduced by choosing $9$ o'clock as the start time. A game starting at 9.00 involves the same thinking, which is the important point, but might be more manageable for some children. If pupils are encouraged to record the times that are made and the intervals chosen, then it will help them to notice patterns.