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Under exam conditions, students normally achieve most, if not all the marks, when asked to complete a two-way table or frequency tree. Because of this, I wanted to link two-way tables and frequency trees to topics that students who are aiming for a grade 4 often struggle with.

These topics include: fractions, percentages, ratio and simplifying expressions. My intention is that by embedding these skills within a context students are confident with they are more likely to have greater resilience if they find the calculations difficult.

In this problem solving lesson there are five problems, each with fully worked solutions and a student handout. Below are two sample questions, a non-calculator problem with frequency trees and a calculator question with two-way tables.

To work out the number of girls and boys in the first branch of the frequency tree students need to share the sample by a ratio.

To work out the second branches students calculate a fraction of an amount.

Finally, when the tree is completed students can work out the probability.

This is a calculator question with links to:

- proportional reasoning
- sharing an amount to a ratio
- fractions of an amount
- percentages of an amount
- writing one number as a percentage of another.

My name is Jonathan Robinson and I am passionate about teaching mathematics. I am currently Head of Maths in the South East of England and have been teaching for over 15 years. I am proud to have helped teachers all over the world to continue to engage and inspire their students with my lessons.

A scaffolded approach to teaching frequency trees.

January 1, 2021

Problem solving lesson on two-way tables and frequency trees.

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Linking cumulative frequency graphs to ratio, percentages and financial mathematics.