Solving linear equations – Year 7 maths lesson

Lesson 14 of 18 in the Year 7 maths course

UK version. UK school years, UK spelling and pounds (£). · US Math Department

A complete 45-minute lesson for Year 7 (ages 11–12) 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 7 (ages 11–12)
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

45 minutes in 5 parts
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

All Year 7 maths lessons and tests · Maths Department

More Year 7 maths lessons

Curriculum

National Curriculum for England, Year 7: “use algebraic methods to solve linear equations in 1 variable (including all forms that require rearrangement)”

National Curriculum for England, Year 7: “understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors”

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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.