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'A Mixed-up Clock' printed from http://nrich.maths.org/
Why do this problem?
is one that needs logical thinking. At first it might look impossible but if the clues are followed in a suitable order then it only requires simple arithmetic to solve.
You could begin with a few oral challenges to remind the class of number properties such as odd, even and consecutive. For example, could they suggest three consecutive odd numbers greater than 50 but less than 70? How many different sets of consecutive odd numbers are there between 50 and 70?
Share the problem with learners and describe briefly what it entails without reading all the information at first. Invite pupils to talk in pairs about how they would start the problem. You could read through the clues in turn, stopping after each to give children chance to discuss what exactly could be learned from it. Give them time to look through each clue in pairs and
decide what can be filled in immediately. You could draw everyone together to share ideas before giving more time to complete the challenge.
A plenary could give learners the opportunity to explain the steps they took to solve the problem. Making it clear that the ordering of the information constitutes a systematic approach will help them begin to understand the meaning of being systematic and therefore apply it to future problems.
Can you find a statement that gives you a definite number that you know is right?
Can you now find some more that follow from this one?
Learners could use the clock-face given to work out some clues for themselves.
Some children may need help reading the clues so this may influence your choice of pairs.