Teaching prime factorisation is a core part of the GCSE Maths curriculum, but many students find it abstract at first. In this prime factorisation lesson, I’ll share how I introduce the topic, guide students through factor trees, and use exam-style questions to consolidate their learning.
I’ll also show you the starter, main teaching, and plenary activities I use, plus free interactive question generators that are perfect for quick-fire whiteboard practice.
At the start of the lesson we recall and recognise prime numbers.
This approach makes students think critically about which numbers are prime and how they combine to make other values. It naturally reinforces both the concept of primes and basic arithmetic operations.
Teacher Prompts:
The main phase of the prime factorisation lesson should focus on explicitly modelling how to decompose numbers into their prime factors. In the video tutorial, I demonstrate each example step by step so students can see not just what to do, but why each step works.
Depending on the ability of the class I may chose to omit the last exam style question involving the rules of indices.
Teacher Prompts:
To assess student progress throughout this prime factorisation lesson I display each equation one at a time for students to attempt using factor trees. I allow calculators for the divisions so they can focus on the decomposition. After each question, I gather feedback, and address misconceptions before moving to the next.
Teacher Prompts
To help teachers provide extra practice and rapid assessment on mini-whiteboards, I’ve included three interactive random question generators below. Each generator produces questions of increasing difficulty:
Writing integers as a product of prime factors
Decomposing products of two integers
Multiplying two expressions written in prime factor form
The full prime factorisation lesson includes:
You can read more research informed blogs on teaching maths on my blog page.
👉 Join Mr Mathematics for instant access, or if you’re already a member
A research-backed case exploring why over-reliance on automated math homework platforms and repetitive worksheets lowers student expectations, and how departments can build genuine mathematical thinking.
How to teach converting between fractions, decimals and percentages.
Four problem solving lessons to develop student’s mathematical reasoning and communication skills.
