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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?

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.

How Safe Are You?

Age 7 to 11
Challenge Level

We're going to look at opening safes!
Many have dials on them, and you turn the dials - as you see in these two pictures - to open them.

safe2 safe1
So I'll show you a simple dial first with just the numbers $0 - 5$ on it.

To open the safe, the dial has to have $2$ next to the arrow, like this;

The question for you is, how much turning of the dial did we have to do to get the $2$ at the top?
The next safe we get to has a different dial, it has the numbers $0 -7$.
How much turning to get the number $5$ at the top? [Shown in the second picture.]
The number that you have to get at the top is often called the "combination" of the safe. These three different safes all start with $0$ [zero] at the top. You have to find the amount of turning to get to the combination, shown in each second picture:


Now have a go at these different safes. Remember they would all start with $0$ [zero] at the top, so, how much turning to get the required combinations shown below?