Drawing frequency trees for GCSE maths is a new topic and appears on both the higher and foundation curriculum. I’ve taught this lesson a couple of times, once to Year 10 and once to Year 11 and I have to say the kids really enjoy it.
Frequency trees can be confused with probability trees. Frequency trees show the actual frequency of different events They can show the same data as a two-way table but frequency trees are clearer because it shows the hierarchy of the frequencies. Probability trees show the probability of a combination of events. Click here to watch the video.
I teach frequency trees after a lesson on two-way tables. By the end of the lesson I want all the students to create a frequency tree from a written description. Recapping two-way tables in the starter both consolidates student’s previous learning and helps them to understand the need to organise data in a clear and efficient way.
As we begin the main activity I provide the frequency tree template for the question. This helps students with poor literacy to break down the problem by highlighting a particular phrase and matching it to its position on the diagram. Each time I taught this lesson I found students had no difficulty with the numerical calculations but some did struggle to understand what part of the frequency tree they were calculating. By having the template already drawn students could use the built in hierarchy of the tree to read the text.
Once we had completed the frequency we discussed how to check our answers using the numbers at the end of the branches. If our tree was correct the frequencies would add up to the number at the start of the branch.
At this point we’re about 25 minutes into the lesson and students are ready to work independently through the worksheet. I let the students decide for themselves which question to start at. Those who had difficulties with the written description all decide to start with the two-way tables as they were already familiar with two-way tables from the starter and previous lesson.
The plenary challenges the students to create a frequency tree with 6 combinations. Initially I hid the frequency tree to see who could create it on their own. Some students found this quite difficult because the text only gives the total number of boys in the sample and they had to calculate the number of girls. Once they understood to include boys and girls in the tree the majority of students completed the problem fairly easily.
In the next lesson we go on to designing questionnaires and identifying bias.
Problem solving lesson on two-way tables and frequency trees.
Three typical exam questions to revise on plotting quadratic, cubic and reciprocal graphs.
Linking cumulative frequency graphs to ratio, percentages and financial mathematics.