Unmuddling Maths – Viking Rune Stones and Probability Part One

On our family holiday this year, the children came face to face with amusement arcades.  Never having seen anything like it before, they were enamoured and very enthusiastic to spend our money in order to win more back.  Needless to say we did not allow them.  Until, that is, the last day.  It was pouring with rain and we thought we might be able to teach them a lesson by allowing them the experience.  We gave them each a pound, changed it into 2 penny pieces and let them at it.  At the end of approximately half an hour, whilst some money had been won along the way, all three older children ended up with not a penny to their name.  They did, however, end up with a lot of tat in terms of cheap plastic rings – they thought it was great and not wanting to ruin their fun of the moment I left them to enjoy it.

I was always going to return to the subject, which today I did.  We had made it clear that this was not the best way to spend their money.  Now I was asking them why.  They were genuinely surprised.  They felt they had got a bargain.  Six rings for three pounds.  I then started probing them about the rings.  Were they of good quality and therefore would they last?  How much did they think they would pay for them in a shop and what type of shop and/or aisle did they think they would find rings like that?

It was, as always, fascinating to see them think through what I was asking.  They had seen similar rings, sold in a pack of 20, in a discount store down the party favour aisle, selling for £1.  Light bulbs began glowing!  They could buy 20 for £1 or lose three pounds and gain 6 rings.  This was a good starting point for a statistics lesson.

I asked them to think about who ran the arcades and why.  T10 immediately answered to make money.  All the children suddenly started looking at the whole experience from a different perspective.  I asked whether they thought the owners of the arcade knew they would make money or was it just luck.  Nudging them in the right direction I asked what the costs would be of running a place – they came up with rental of the premises, electricity, staff.  I added rental of the machines.  T10 realised that in order to run it as a business they needed to turn a profit.  They were horrified when I told them that the machines were fixed so that, although there would be some winners, there were more losers – that the probability of winning was smaller than the probability of losing.

Together we looked into what the actual word probability meant.  C10 thought it might mean that something was probable, T10 went one further asking if the probability of something was a measurement of how probable it was.  Bingo, we had our starting point!

As you know, I want to be teaching their maths using things they have made or are using in their history studies (the mainstay of our home school).  Whilst we were making the Viking Runes I had thought how perfect they were for a probability lesson.  First I wanted them to just play with them, sorting them into their letter groups and then separating them into marked and unmarked (I had kept some unmarked for the purpose):

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Separating them into letters, some were more numerous than others
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Separating them into marked and unmarked. It is not obvious here, but there were far fewer unmarked stones than marked.

I asked if a stone would be more likely to be marked or unmarked.  They answered correctly marked because there were more marked than unmarked.  I reiterated what they had just said inserting the word ‘probable’ in the place of ‘likely’.  L10 jumped up and said it was probability! Eureka!  We played around asking each other whether it was more probable that so and so letter was chosen until I was sure each understood that the higher the number present, the higher the probability of it being chosen.  This ended our first lesson.

I did a total of three lessons on probability, because the girls had never encountered it before.  I’ll do the second post tomorrow on the remaining two lessons.

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