- On the board I have drawn a model of a horse race, where the numbers 1 to 12 are the horses and the boxes to the right is the track. You are going to roll two dice and add the scores. Whatever total you get means that horse will move one space. The winner is the horse that touches the end first. I will give odds of 1/12 on each horse, so if you bet £1 (which we are only going to imagine!) and your horse won, I would have to give you £12. In your books you need to write down which horse you want to bet on.
I then pass the two dice to a student and specify the direction in which the dice are to be passed around the room. Each time a student calls out the total I shade in the appropriate box.
- Hands up who won? Looks like I would/would not have won money on that game.
The students will almost inevitably want to play a second game. A discussion of what took place in the first game is useful - why are some numbers coming up more often than others? Ask how many students are changing their horse.
The issue may arise from a student that the odds I offer should be different for each horse - this can motivate the question I want to get to of finding the correct odds.
After a second game, the discussion can turn more fully to why some numbers occur more often than others and what the correct odds should be. Students will usually suggest listing the ways of making each total.
Another issue that is bound to arise is whether 6,5 is the same as 5,6. And if it is different, then why isn't 6,6 counted twice? The game is an ideal opportunity to tackle this important misconception. If necessary playing a '2 dice horse race' with horses ' 2 heads', '2 tails' and '1 head 1 tail', can provoke an awareness that HT is different from TH.
Students should complete the task of getting probabilities for the 2 dice (and 2 coins) game. A homework can be to repeat the race at home (at least … times) and write up their results.
WHERE ARE WE GOING?
There are several probability experiments in the 'Carousel' box that you can choose from (select 4 to 6). The students ideally will be in three lines of 4 or 5 pairs. They need to know that they start filling in the sheets from the bottom (without leaving gaps).
Hand out sheets and equipment to each pair. Their first task is to write the title of the experiment and write down a prediction of what they think will happen. They then play the game, recording their results on one sheet. After a few minutes they then pass their equipment forward - I have to take the front desk's to the back! The process then repeats - they write the title and make a prediction for their new game and then start to play. Each round should take approx. 5 minutes.
At the end, if there are equal numbers in each row, the students should end up with their original sheets, now filled out with lots of trials.
Their first task is to write down whether their predictions were correct and then work out the relative frequencies for each column. These results (there will probably be three groups who played each game) can be collected together on a common board.