I am going to start the probability unit with my year 9 middle set class this week and have decided to start with listing outcomes. I have the lesson planned and then i started thinking about all the approaches we teach when teaching probability; using a probability tree, sample space diagrams, listing outcomes, venn diagrams, two way tables. I started to wonder how many of my class know why some are useful in some situations for example for 2 events where you want to know all the outcomes or if its just to know P(flipping 4 tails in a row)
I thought a good discussion point could be this question I have created. It also recaps a previous topic on types of number and a previous discussion on what happens when odd/even numbers are added.
Students could list the outcomes, discussions could be had on how many there would be first. Students could use a probability tree and discuss why other types of diagrams aren’t helpful.
The next lesson we looked at expected and theoretical probability and i wanted to do a little experiment. I showed them a bag of 12 counters and 6 were red, 3 blue, 2 green and 1 yellow. Students would choose where to place 4 tally marks in their grid (like the one below) if i pulled out a counter and they had a tally in the matching box they got those points per tally mark. The person with the highest score after 12 tries won. We also talked about how many of each colour we would expect after 12 attempts.
I asked students to minus 48 from their score and see if it was a negative or positive. Can you think why?
They really enjoyed the task and we then had some great discussions about theory and practical and why how some students chose to place their tallies. Students used language such as ‘i put 2 in red because theres a 50:50 chance it will be red but i also placed one in yellow because although its a 1 in 12 chance if it does ill get 12 points.’
Multiple ways to look at a problem