Drawing Frequency Trees for GCSE Maths

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.

What is a frequency tree?

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.

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.

Drawing Frequency Trees for GCSE Maths

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.

Drawing Frequency Trees for GCSE Maths

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.

Differentiation with frequency trees

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.

Wrapping up

Drawing Frequency Trees for GCSE Maths

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.

Leave a Reply

Your email address will not be published. Required fields are marked *

You may use these HTML tags and attributes:

<a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <s> <strike> <strong>

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Mr Mathematics Blog

Solving Inequalities using a Number Line

Students should be able to represent the solutions to an inequality on a number line, using set notation or as a list of integer values.  Here’s how I teach using the balance method for solving inequalities using a number line. Matching inequalities, Number sets and Number Lines At the start of the lesson students recap […]

Practical Tips for Using Mini-Whiteboards in a Mathematics Lesson

In this blog I will share some practical tips for using mini-whiteboards in a mathematics lesson.  I use mini-whiteboards nearly every lesson because they help the students show me the progress they are making.  When I understand what the misconceptions are I am able to address them in subsequent examples as part of my feedback.  […]

Showing Progress during a Mathematics Lesson

Demonstrating student progression during a mathematics lesson is about understanding the learning objective and breaking that down into explicit success criteria. Using Success Criteria Take, for example, a lesson on calculating the area of compound rectilinear shapes. The intended learning objective was written on the main whiteboard. Success criteria were used to break down the individual […]