Probability Scales - worth spending time on.

For many years now I have viewed probability scales as something a little beneath the brighter pupils; a Level 4 (in olde English money) skill that bore little practicality for those pupils who would eventually go on to take higher GCSE where such trivial skills would not be tested. Something always nagged at me though - kids would get these questions wrong. Good kids, bright kids, who could use sample spaces and calculate with relative frequency got tripped up when having to describe a situation in words or place it in even broadly the right place on a number line.

So this year I decided to teach it, properly, to my top set Year 7. We looked at describing events in words and looked at where probabilities of events would go on a scale. Boy am I glad I did! Now I am not going to stand here and say every kid made 'rapid progress' nor am I going to stand here and say that every kid benefitted greatly from every activity or every pupil needed to recap every part, but as a whole the lesson was worth doing. Some tips then for making this a success with upper sets:

1) Enforce correct notation [P(...)] alongside correct language.

2) Use alternative language freely and force pupils to describe in different ways.

3) Ensure you hold them to reasonable accuracy when placing values on the number line (I had a lad who told me that a probability that numerically was 1/7 mark an arrow too close to 0 and we challenged this as a class by looking at 1/7 as 14.29% and whether we thought that his arrow was nearly 15% of the way up the line).

4) Use a number line broken into segments (I was nice and went for 10ths) to ensure they have to think about at which point or between which points does it go (and apply point 3 here as well, I was penalising for probabilities of 1/3 being closer to the 4th mark then the 3rd mark)

5) Teach this as a follow on from writing probabilities as fractions, rather than before it (as is often the case), so that you can tie fractional ideas to scales.

I used some really nice stuff from CIMT as well here (in their Maths Enhancement Program, Year 9 book 6) which challenged their thinking a little more and pulled some of the better questions into a nice worksheet.

The link to the full lesson is here, and the link to the worksheet is here, but however you decide to teach it I would heartily recommend making the effort to challenge your upper set pupils on probability scales.