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'A Bag of Marbles' printed from http://nrich.maths.org/
Why do this problem?
builds on simple sorting skills and gives children the experience of using logical reasoning.
It would be helpful if pupils had a sheet of marbles to cut out so that they could physically move or group them. (You might find it useful to print off this sheet which depicts four sets of the marbles.) In addition, some children might benefit from having coloured
pens to use so that they can record different marbles easily.
The first part of the problem, describing each marble, could be done as a whole group so that everyone become more familiar with the different attributes. You could then ask pairs of pupils to work on the second and third parts of the problem, emphasising that you will be interested in how they arrived at their solutions. You may like to draw attention to efficient ways of approaching the
problem that you see, or to clear ways of recording their solutions. It might be appropriate to stop them briefly after five minutes or so, once they have had a chance to look at the first question in the third part "What colour(s) could be on a marble that is cold?". The idea here is for the children to appreciate that there is not just one right answer - there are in fact several possibilities.
You could challenge the class to find all the possible marbles which fit the criteria, perhaps by having a section of a display board devoted to collecting examples over the week to come.
How do you know that the marbles you've chosen are correct?
What other colours could be on a marble which is cold/sparkles when rolling?
Children could be challenged to look at how marbles could be coloured if they have exactly two attributes, or three attributes or all attributes, and to record the number of possibilties each time. Do they have a system for making sure they don't leave out any possibilities each time?
Having circles of paper cut out to represent marbles, and coloured pens to mark each with, may help children access this problem.