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Why do this problem?
will help to improve learners' knowledge of factors, especially those in the usual multiplication tables, and encourages them to use trial and improvement. The competitive element can bring out the best in some pupils.
You could start by showing the group the 'training track' given in the problem, working on this so that they are able to see the rules in action. This sheet
has the 'training track' on, if you want it. Once they have had a go, you could spend a short time discussing the reasons for their choices and ultimately the minimum number of moves that
will take you round the track.
Next, introduce the trickier version of the track, giving pairs a copy of this sheet
. (The sheet gives the rules as well as the full track). This could be printed out in an enlarged version and could also be laminated for a longer life. Allow children to choose any other tools that they feel would be helpful. Some may want to mark their chosen
squares in pencil on the track, some may want to record the numbers or calculations on a separate sheet or whiteboard, some will have other ideas!
At the end of the lesson all the learners could come together to discuss the best and shortest route. Is there a consensus about the best moves to take?
Which tables will you find this number in?
What are the factors of that number?
Can you think of any more? How do you know you've thought of all the factors?
How are you keeping track of the route you're taking?
How do you know that you have found the best route?
Learners could make their own 'factor track' for others to try. Alternatively, the problem Factor-multiple Chains
offers another interesting way to explore factors.
You could suggest that learners record all factors of the number in green squares so they are able to keep track of the ones they have tried more easily. The problem Jumping Squares
has the same idea of getting round a track in as few moves as possible but focuses on counting, rather than factors.