### Clock Hands

This investigation explores using different shapes as the hands of the clock. What things occur as the the hands move.

### Watch the Clock

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

### Take the Right Angle

How many times in twelve hours do the hands of a clock form a right angle? Use the interactivity to check your answers.

# Sweeping Hands

## Sweeping Hands

In $10$ minutes, through how many degrees does the minute hand of the clock sweep?

In $3$ hours, how many degrees does the hour hand of the clock sweep through?
If the minute hand goes through $180^{\circ}$, how many degrees does the hour hand sweep?

### Why do this problem?

This problem is a great context in which to apply knowledge of angles based on a full turn and it helps to consolidate analogue clock features too.

Having a large geared demonstration clock available would be a good idea to discuss this problem with the group.

### Key questions

Which is the minute hand and which is the hour hand?
How long does it take the hour hand do go a full circle ($360$ $^\circ$) round the clock?
How long does it take the minute hand do go a full circle round the clock?
How many degrees does the minute hand go through in one hour?
So many degrees does it go through in $15$ minutes? In $10$ minutes?
So, how many degrees does it go through in $5$ minutes?

### Possible extension

Learners could go on to either of these two problems - Watch the Clock or Two Clocks .

### Possible support

Suggest doing this problem, Two Clocks or possibly just exploring the interactivity to see how clocks move.