Clocks
1 out of 3
These clocks have been reflected in a mirror. What times do they say?
Problem
Getting Started
Where is the hour hand pointing?
Where is the minute hand pointing?
If you draw your solutions on a clock face, you could check them in a mirror! You could print off this sheet which has the problem clocks and some blank clock faces. You may prefer this sheet which is just blank clocks.
Student Solutions
We had a lot of emails about this problem. You had to think very carefully in order to work out the times on the clock faces. Well done to Ben from St Michael's School who who sent in a completely correct solution. He said:
Red clock: 10.45
Blue clock: 7.15
Yellow clock: 5.35
Green clock: 7.49
The last one was particularly difficult and Ben explained that he looked upsidedown to find the answer!
Teachers' Resources
Using NRICH Tasks Richly describes ways in which teachers and learners can work with NRICH tasks in the classroom.
Why do this problem?
This problem is one where careful thinking is needed to work out the times on the clocks. Not only is it necessary to understand times on an analogue clock but also to work out what effect a mirror has on the clock faces.
Possible approach
You could start this problem by looking at some clock times that lie between the five minute intervals. It would be helpful to have a demonstration analogue clock handy during the lesson. Two Clocks would be a good problem to have tried with the class beforehand.
After this, the group could work in pairs so that they are able to talk through their ideas with a partner. It would help if they had copies of this sheet which pictures the problem clocks and also has four normal clocks that can be used for rough work or the solution. This sheet of eight blank clock faces might also prove useful.
When you gather together to talk about the solutions, encourage learners to explain how they have worked out the times. This is likely to involve looking at each hand separately, thinking in turn about what their position tells us. In fact, when broken down like this, the tricky part is making sure the numbers on the clock are identified correctly! You might like to test the solutions by holding up a demonstration clock to a large mirror.
Key questions
Where is the hour hand pointing?
Where is the minute hand pointing?
Possible extension
Those who worked quickly on this problem could use a small mirror to make up some similar problems for a friend to do.
Possible support
A small mirror would help a child who is experiencing difficulty with this tricky problem. This sheet should also help even if others are not using it.