This is an activity that could be used to introduce the ideas of probability compared to likelihood.
The lesson before:
For a homework I asked students to take six cards (size A6 seems to work well) and to write on each of these an event that might or might not happen the following week – some of them will be fairly outlandish but that does not matter. I ask them to include one which they think
• will definitely not happen
• will definitely happen
• has an even chance of happening
The following lesson their cards are all gathered in. I add these cards to those that my other classes have produced before and so build up a stock – The more the merrier.
If I have not primed a few students to do this already for their homework, I include in the pack a few with the common events with a calculable probability such as
• I will throw a six on the first roll of my dice (I know it should be die but you choose)
• I will throw an even number on the first roll of my dice
• I will get a head when I flip a coin
In the lesson:
Students work in small groups (I usually prefer threes as they seem to be more engaged).
I shuffle the, now fairly large, pack of cards and split them all between the groups (It does not matter if they do not have exactly the same number).
They need to
• draw a long likelihood scale with points for certain, evens and impossible marked clearly.
(In good weather (no rain and no wind) I do this outside in the playground)
• In a fixed amount of time they need to position as many of their cards in an appropriate place along this scale as they can. They hand in to you any that they were not able to position (isolate any with a predictable outcome to discuss at the end)
After the allotted time the groups move round to look at the work of the next group. They now remove any cards for which they disagree with the positioning along the scale, and hand them in to you. Repeat this until the groups have visited all the others.
Now go round and look at the cards that are still on the scale. These will usually be those that
• are impossible (although these are often removed as they come up with outlandish reasons why these things could happen)
• are certain
• events with a predictable outcome
I use the position of these cards as an introduction to probability.