Inspiration for this connection was taken was taken from a series of interesting articles on the Nrich website about transitioning from frequency trees to probability trees (available here). While the frequency tree looks at observed data for many people playing the games, the probability tree looks at the theoretical probabilities for each individual person playing the games. The numbers above were modelled roughly on the probability tree from the question below. For example, students may work with frequency trees in younger years to solve problems like the one below. Students can start to be familiarised with some ideas relating to probability trees long before they get to the ‘probability tree’ section of the scheme of work. I’ve also discussed some of these things in conversion with Craig Barton on his podcast (available here). I don’t always use them all every year it usually depends on how much support of extension I feel is appropriate. Some of them support the introduction of probability trees by helping students think about their structure and meaning some help extend and challenge students further within the topic. This blog post shares a selection of things that have gradually been added to my lessons on this topic over the years. This meant that more time was spent discussing the aspects of the problems that students were already familiar with (how to probabilities and calculate with fraction) than the aspects that were most novel to them. Instead, I jumped too quickly to calculations and solving complete problems. In hindsight, I suspect that some of the students’ uncertainties and mistakes with this topic were because I tended to skim over explanations about how to set out probability trees and their meaning. …the way they arranged the information on trees… I think the biggest issue was that some of my students didn’t seem to understand what was going on when they were drawing probability trees and what the diagrams really meant.Įvidence of such misconceptions would occasionally present themselves in the way students set out their branches… So even though students knew how to perform all the calculations they needed to solve a probability tree question, they made mistakes before getting to the point of calculatuon. The biggest issue tended to be drawing the tree! Knowing how to set them out, how many branches to use, how many sets of branches, how to arrange the labels, etc. I’d then always be surprised with how difficult they found solving probability tree questions by themselves, how many marks would be dropped in exams on them and how it would often be a common request for revision. The students would answer these questions so confidently that I’d think, “They’ve got this!” and set them off with independent practice. While solving a problem on the board, I would call on students to give me the fractions that go on each line, multiply together each pair of fractions and add up the fractions that I needed to solve the problem. Thinking back to those old lessons, a lot of my explanations would centre around solving whole probability tree problems from the get-go. This means that when students are introduced to probability trees, the most unfamiliar aspects of the topic are the last two bullet points. The first three bullet points are things that students (hopefully) already know before getting to this section of their programme of study.
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