Factorising – Year 11 maths lesson
Lesson 8 of 17 in the Year 11 maths course
UK version. UK school years, UK spelling and pounds (£). · US Math Department
A complete 45-minute lesson for Year 11 (ages 15–16) that runs on this page – at school or at home. Every answer is marked straight away, with a worked explanation.
- Time
- 45 minutes + 20 min homework
- Year
- Year 11 (ages 15–16)
- You need
- Paper, a pencil and this page
- Marked
- Instantly, with explanations
For parents: how to use this lesson
You don't need to know this topic yourself. The lesson explains each step on screen, one tidy step at a time. Every answer is marked straight away with a worked explanation, so you never have to mark anything.
- Read what your child will learn and the big ideas together.
- Press Start the lesson below and sit with your child for the teaching and the worked examples (about 19 minutes).
- Let them do the practice on their own. They choose Getting started, On track or Challenge – start on On track and move up after a few right in a row.
- Finish with the exit ticket and the talk question: “How can you check a factorisation is right?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Not taking out the highest common factor (6x + 9 = 2(3x + 4.5)). Use the biggest whole number and letter that divide every term.
- Choosing numbers with the right product but the wrong sum. Check both: multiply to c and add to b.
Tip for home: Make factorising puzzles: give a number pair and find the quadratic.
What your child will learn
We are learning to factorise expressions, including quadratics.
Success looks like
- I can take out a common factor.
- I can factorise a quadratic.
- I can use the difference of two squares.
Key words
- factorise
- write as a product of factors
- common factor
- a factor of every term
- quadratic
- an expression with x² as the highest power
- difference of two squares
- a² − b² = (a + b)(a − b)
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Expand some brackets, then cover up the question and work backwards to the brackets.
The big ideas (for the adult)
Factorising is the reverse of expanding: find the highest common factor and put it outside a bracket: 6x + 9 = 3(2x + 3).
To factorise x² + 5x + 6, find two numbers that multiply to 6 and add to 5: (x + 2)(x + 3).
The difference of two squares: x² − 25 = (x + 5)(x − 5). Always check by expanding.
The lesson, step by step
| Part | Time | How it is checked |
|---|---|---|
| Starter: quick recall | 5 min | Marked by Classfern |
| Teaching input | 10 min | Not assessed, self-checked |
| Worked examples and guided practice | 9 min | Not assessed, marked by Classfern |
| Independent practice | 15 min | Marked by Classfern |
| Plenary and exit ticket | 6 min | Marked by Classfern, self-checked |
Starter, "your turn", practice and exit ticket are marked by Classfern. Worked examples and teaching are not assessed. The hands-on task and the reflection are self-assessed. Explanations in talk are judged by the parent and not recorded.
The lesson
It runs here on the page. No sign-up and no names – progress is kept only in this browser.
Homework and practice at home
20 minutes: 10 practice questions, 3 multiple-choice questions and 2 to remember from earlier work, then a short reflection. New questions every time, all marked instantly.
More practice
More Year 11 maths lessons
- Volume and surface area
- Trigonometry: SOH CAH TOA
- Sine rule, cosine rule and area of a triangle
- Transformations
- Similarity and congruence
- Vectors
- Circle theorems
- Inequalities
- Sequences and the nth term
- Quadratic equations
- Iteration
- Functions
- Algebraic fractions
- Graphs of functions
- Algebraic proof and identities
- Growth and decay
Curriculum
National Curriculum for England, Year 11: “factorising quadratic expressions of the form x^{2} + bx + c, including the difference of 2 squares; {factorising quadratic expressions of the form ax^{2} + bx + c}”
GCSE subject content A4: “simplify and manipulate algebraic expressions (including those involving surds and algebraic fractions) by: collecting like terms; multiplying a single term over a bracket; taking out common factors; expanding products of two or more binomials; factorising quadratic expressions of the form x² + bx + c, including the difference of two squares; factorising quadratic expressions of the form ax² + bx + c; simplifying expressions involving sums, products and powers, including the laws of indices”
Contains public sector information licensed under the Open Government Licence v3.0.
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.