Probability Session: Lessons Learnt

Timetable
5 mins intro
10 mins Head/Tails game
10 mins card game
20 mins probability scale
5 plenary, wrap-up and summary
Rushed too fast through the first part of the session and then had to pad during the probability scale section. Suggest taking more time on the introduction in particular  but generally slowing down and adding an extra task. Could talk about what they think a statistician/mathematician does as a job and what subjects its necessary to know maths for. Maybe make some more links with probabilty in their daily lives, TV programmes.
Introduction
Welcome. Introduce who I am & what I do.
Garbled explanation of what my job is which needs preparing better. Need to make it clear to the kids what the role is and why its imporant.
Going to talk about probability. This is like a ruler for random things.
Maybe ask about how different things are measured: height, length, time, weight...
Lottery video of the ball jumping around. Why can’t we predict what the winning numbers will be? Why do they do this mixing? What is the pattern of winning numbers?
Ask them to multiply all the lottery numbers together!
Tell them that at the end I will tell them what the best strategy for playing the lottery is.
The lottery video was a little bit too long. remove some of the chat before hand.
ipod shuffle picture: How does ipod shuffle decide what song to play next? What is the chance of getting your favourite song?
They didn't come up with the fact that it was a shuffle.
Head/Tails Game
Don’t explain the motivation to the game at first. “Let’s see how much they know about randomness”
Everyone stands-up and chooses either ‘head’ or ‘tails’ from a toss of a coin by either touching their head or bum. When someone is incorrect they sit down. Repeat the process until everyone is sat down. If there is a play-off at the end then bring the pupils to the front.
Prize for last person standing.
What was their strategy? Why?
Explanation: each toss of the coin is independent. The history of the tosses is irrelevant for a fair coin. E.g. lottery numbers are independent of past results.
Needed to keep the kids who had sat down engaged a bit better. It might be worth recording how many are sat down in each go and discuss what we see. Could mark these on the board. We should expect to see about half each time but they are not independent selections!
Could use a video on the computer to show the coin toss better.
Card Game
‘Play you cards right’ format. Several large ‘cards’ are turned over in sequence at the front. The pupils are told that the cards are between 1 and 10. Between each turn the pupils choose higher (H) or lower (L) than the previous card by holding up a card with the appropriate letter on it. Consensus determines the group decision.
This demonstrates a type of probability scale (between 1 and 10). If the number is high then there is more chance of the next number being lower because there are more possible cards.
Again, a slightly uncelar explanation of the outcome of the game. This needs improving. The kids did not use the `H', `L' cards very well, e.g. waving the `H' when they thought it was lower. Seemed to be more engaged when they were asked to shout out what they thought.
Could go back and get them to work out the number of possible card higher and lower. Think that should consider with replacement to make the probabilities more straightforward.
Could then give them something related to work on individually/in groups. ??
Probability Scale
Introduce the modification of the card game scale to the probability scale.
a) Individually have a worksheet. Put the listed events on the scale in the right place. Aim is to think about other locations to 1, 0.5 and 0.
b) Each pupil is given a probability event card, e.g. lottery win, rain tomorrow, eat tea today. They come up one-at-a-time and put these on a line of probability. Can do the selection is steps so first decide which half of the line, then which part of that half and so on.
Quick discussion amongst themselves about the relative probabilities.
Reassess whether their classmates have put the cards in the right place.
They really didn't get the idea of 1,0 probabilities never happening. They thought that everything was either 0,0.5 or 1. I think when the first kids puts their paper at 0.5 then all of the others follow. I think that is important to stress the relative probability of events.I think that the paper should have an arrow on it or something to mark exactly where on the line they mean to put it. I think it would have helped to have fraction markers on the line.IDEA: to get the pupils to think about what 0 and 1 probability events actually mean could get them to come up with reasons why things are not 0 or 1 i.e. something really unlikely but with a non-zero probability e.g. martians landing or the laws of physics change.
An idea is to not use a line at all but rather subdivide something else, like for example a cake. Pupils can then imagine slicing the cake into two pieces.
Plenary
Learnt about:
Independent events (H/T game)
Relative probability (card game)
Probability scale between 0 and 1.
What is my job? How do I use probability in my job?
I think that I need a hard example which connects more directly with what they've been doing. Something to do with the probability line?
What other probability course and jobs are there?
I think that it needs to be a lot clearer why probability, stats and maths is important and useful. Maybe go back to the examples from the beginning.
Could list lots of jobs that need maths and stats including law, physics, ...
Benefit of university? Benefit of doing mathematics?
Consider in their lives where probability occurs. What is random from day-to-day? What is unlikely and likely?
Best strategy for playing the lottery is DON’T PLAY!