Solving linear equations – Year 9 maths lesson
Lesson 29 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: “How can you check your solution is right?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Doing an operation to one side only. Write the operation on both sides each time.
- Subtracting when the term is negative (−2x = 8 gives x = 10). Divide both sides by −2: x = −4.
Tip for home: Make up "think of a number" puzzles and solve them with equations.
What your child will learn
We are learning to solve linear equations, including with brackets and unknowns on both sides.
Success looks like
- I can solve one-step and two-step equations.
- I can solve equations with brackets.
- I can solve equations with unknowns on both sides.
Key words
- equation
- two expressions that are equal
- solve
- find the value that makes it true
- inverse operation
- the operation that undoes another
- solution
- the value of the unknown
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Model equations with a balance: cups with hidden counters and loose counters.
The big ideas (for the adult)
An equation is like a balance: whatever you do to one side, do to the other.
Undo operations in reverse order: for 3x + 5 = 20, subtract 5, then divide by 3, so x = 5.
With unknowns on both sides, first collect the x terms on one side. Expand any brackets first. Check by substituting.
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
- Simplifying expressions
- Expanding brackets
- 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: “use algebraic methods to solve linear equations in 1 variable (including all forms that require rearrangement)”
GCSE subject content A17: “solve linear equations in one unknown algebraically (including those with the unknown on both sides of the equation); find approximate solutions using a graph”
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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.