Two-Way Tables and Frequency Trees

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.

Two-Way Tables and Frequency Trees Tutorials

Two-Way Tables and Frequency Trees

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.

Frequency Trees

Two-Way Tables and Frequency Trees

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.

Two-Way Tables

Two-Way Tables and Frequency Trees

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.

Teach this lesson


Share this article…


About Mr Mathematics

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.


If you liked this you may like …

Drawing Frequency Trees

A scaffolded approach to teaching frequency trees.

Mr Mathematics Blog

Teaching Reciprocals of Numbers and Terms

How to teach working out the reciprocal of integers, fractions, decimals and mixed numbers.

Proving Geometrical Relationships using Algebra

How to teach proving geometrical properties using algebra.

Solving 3D Problems using Trigonometry

How to teach solving 3D problems using trigonometry.