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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?

Estimating Angles

How good are you at estimating angles?

Take the Right Angle

Age 7 to 11 Challenge Level:

Take the Right Angle


How many times in twelve hours do the hands of a clock form a right angle?

What are these times to the nearest minute?


Why do this problem?

This problem is one which could be done as an introduction when extending or revising work on time and clocks. It will encourage the use of digital times.


Key questions

At what time is the first right angle after 12 o'clock?
Why is it not just 15 minutes later?
Can you write down these times using digital notation
Why is the number of times not divisible by 4?


Possible extension

Learners could find out the times for 24 hours and record using 24 hour digital notation.


Possible support

Using a geared clock would be helpful. (Some 'play' clocks allow you to move the minute and hour hands separately, which can lead to the hands being placed in an impossible way!)