## Sunday, March 21, 2010

### A Smart Eleven Plus Child

Helping a child to learn how to cope with reasonably complex probability questions is sometimes a little stressful for the even the most able eleven plus child. Here is a simple suggestion. Gather all the family together. You need five members. The experiment will still work of you `borrow’ next door’s child.

Purchase 30 packets of smarties. Sort the smarties into colours within ten bags. Make sure that the red smarties predominate in the majority of the bags. Blue smarties should be the major colour in the rest of the bags.

Empty the rest of the smarties into a bowl – and invite all concerned to share the plunder.

Place the bags under a towel – and mix them up. Ask one person to take one bag from under the towel. You have now established that the bag was chosen by chance.

Hold the bag up and ask each person to estimate how many smarties are likely to be in the bag. Keep it simple. Are there likely to be more smarties or less?

Now ask each person to select a bag and repeat the question. Are there more or fewer red smarties?

By now the more mathematically able readers will have worked out that if there were more smarties in one particular bag it is possible that there will be fewer smarties in the other bags that were chosen.

The ratios will keep changing as each of the bags is selected and then used.

Now comes the fun part. Each person has to empty out their bag and count the number of smarties. They must keep their proportion of red smarties – if that was the predominant colour. Each person then rounds up the proportions to arrive at simple ratios like 70 : 60 or 60 : 40. They then eat the residue.

The whole sequence has to be repeated with the remaining five bags. This gives us a range of reasonably exotic questions on probability. We are now entering the realms of binomial probability which is to do with the outcome of several successive decisions, each of which has two possible outcomes.

If your eleven plus child can cope with binomial probability (you will have used the example of repeated heads and tails) and with the after effects of eating hundreds of smarties then you know you are a true eleven plus parent. You are genuinely a person to be revered and looked up by all concerned. As you prepare the breakfast tomorrow morning you will hum a little probability song.

I am a member of a binomial probability family.
I know the coin will be heads or tails.
If my child gets a question on one in the exam,
I know my child will be a real little smartie.