Simplifying expressions – Year 9 maths lesson
Lesson 27 of 38 in the Year 9 maths course
UK version. UK school years, UK spelling and pounds (£). · US Math Department
A complete 45-minute lesson for Year 9 (ages 13–14) 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 9 (ages 13–14)
- 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: “Why can 3x + 2x be simplified but 3x + 2y cannot?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Combining unlike terms (3x + 2y = 5xy). Only like terms can be added: apples and bananas stay separate.
- Losing the minus sign of a term. Circle each term with the sign in front of it.
Tip for home: Make up expressions for shopping: 3 apples + 2 bananas + 1 apple.
What your child will learn
We are learning to simplify expressions by collecting like terms and using index laws.
Success looks like
- I can spot like terms.
- I can collect like terms.
- I can multiply and divide terms.
Key words
- like terms
- terms with the same letters and powers
- coefficient
- the number in front of a letter
- simplify
- write in the shortest form
- index
- a power
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Sort algebra cards into groups of like terms, then simplify each group.
The big ideas (for the adult)
Like terms have exactly the same letters and powers: 3x and 5x are like terms; 3x and 3x² are not.
Collect like terms by adding or subtracting their coefficients: 3x + 5y − x + 2y = 2x + 7y. The sign belongs to the term after it.
When multiplying terms, multiply the numbers and add the powers of the same letter: 2a³ × 4a² = 8a⁵.
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 9 maths lessons
- Prime factors, HCF and LCM
- Rounding and estimation
- Bounds and error intervals
- Standard form
- Laws of indices
- Powers and roots
- Units and measures
- Area of triangles, parallelograms and trapeziums
- Circles: circumference, area, arcs and sectors
- Volume and surface area
- Angle facts and parallel lines
- Angles in polygons
- Pythagoras' theorem
- Trigonometry: SOH CAH TOA
- Transformations
- Similarity and congruence
- Quadrilaterals and symmetry
- Coordinate geometry
- 3-D shapes, plans and elevations
- Quartiles, box plots and spread
- Pie charts and time series graphs
- Sampling
- Relative frequency and expected outcomes
- Venn diagrams and conditional probability
- Algebraic notation
- Substitution
- Expanding brackets
- Solving linear equations
- Inequalities
- Rearranging formulae
- Sequences and the nth term
- Straight-line graphs
- Graphs of functions
- Ratio
- Percentages
- Speed, density and pressure
- Scale drawings and maps
Curriculum
National Curriculum for England, Year 9: “[Fraction:a/b] in place of a ÷ b”
National Curriculum for England, Year 9: “collecting like terms”
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.