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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.
Age 7 to 11
Challenge Level
It seems that everyone found this a bit tough! It certainly is very hard to picture the shapes moving around. You really need to find some clear plastic to draw the shapes on, so you can turn them around and see what happens. Or, you could just cut some out of cardboard. You might try drawing them on thin paper and holding them up on a window to let the light shine through.
Try one of these ways of making the clock hands and have another go at the investigation. We would be thrilled to get some solutions on this one.
NRICH is part of the family of activities in the Millennium Mathematics Project.