Factorising – Year 10 maths lesson
Lesson 24 of 37 in the Year 10 maths course
UK version. UK school years, UK spelling and pounds (£). · US Math Department
A complete 45-minute lesson for Year 10 (ages 14–15) 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 10 (ages 14–15)
- 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 10 maths lessons
- Systematic listing and counting
- Standard form
- Laws of indices
- Surds
- Fractions, decimals and recurring decimals
- Circles: circumference, area, arcs and sectors
- Volume and surface area
- Pythagoras' theorem
- Trigonometry: SOH CAH TOA
- Transformations
- Similarity and congruence
- Vectors
- Circle theorems
- Bearings
- 3-D shapes, plans and elevations
- Quartiles, box plots and spread
- Histograms
- Pie charts and time series graphs
- Scatter graphs and correlation
- Sampling
- Combined events and tree diagrams
- Simplifying expressions
- Expanding brackets
- Solving linear equations
- Inequalities
- Sequences and the nth term
- Straight-line graphs
- Simultaneous equations
- Quadratic equations
- Functions
- Graphs of functions
- Algebraic proof and identities
- Growth and decay
- Direct and inverse proportion
- Scale drawings and maps
- Rates of change from graphs
Curriculum
National Curriculum for England, Year 10: “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”
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Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.