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SavannahYear 8
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MathsNumber, algebra and geometry: connected foundations32 min★★ difficulty

Chapter 5: Solving linear equations

An equation is a balance: every operation must preserve equality on both sides.

Part of your national curriculum
  • Algebra: Use algebraic methods to solve linear equations in one variable, including all forms that require rearrangement

Lesson overview

What you'll learn in this lesson

Use algebraic methods to solve linear equations in one variable, including all forms that require rearrangement

Key learning points

  • • Inverse operations
  • • Unknowns on both sides
  • • Check

This lesson at a glance

  • 32 minutes
  • 13 parts to scroll through
  • 3 quick checks
  • Marked quiz at the end
  • Gentle pace: short sittings with pauses

Words to know

algebraicmethodslinearequationsvariable

Scroll down — the lesson carries on below

Part 1 of 13 · Discover8%
1

Watch & discover

Part 1 of 13

Watch first

Chapter 5: Solving linear equations

An English teaching video on this topic from mathantics. Watch it, then scroll down for the lesson.

In a nutshell

Use algebraic methods to solve linear equations in one variable, including all forms that require rearrangement

2

Learning cycle

Part 2 of 13

Learning cycle 1 of 2

Part 1 · Inverse operations

A short piece of teaching, then a check to make sure it has landed.

3

Explore the idea

Part 3 of 13

Learn

Inverse operations

Solve 4x − 7 = 21 by adding 7 to both sides, then dividing both sides by 4. This gives x = 7.

4

Explore the idea

Part 4 of 13

Learn

Unknowns on both sides

For 5x + 2 = 2x + 20, subtract 2x from both sides, then subtract 2: 3x = 18, so x = 6.

5

Quick check

Part 5 of 13

Quick check

Solve 4x−7=21.

6

Reset break

Part 6 of 13

Pause

That's sitting 1 of 2 done

Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.

Stop here for now
7

Quick check

Part 7 of 13

Quick check

Solve 5x+2=2x+20.

8

Learning cycle

Part 8 of 13

Learning cycle 2 of 2

Part 2 · Check

A short piece of teaching, then a check to make sure it has landed.

9

Explore the idea

Part 9 of 13

Learn

Check

Substitute the solution into the original equation. Both sides must produce the same number; if not, revisit each transformation.

10

Quick check

Part 10 of 13

Quick check

Why substitute the solution back?

11

Challenge round

Part 11 of 13

Game · Sort it

Which of these are true?

Drag each card into the right column. Tap a card first if dragging is fiddly.

True

Not true

12

Mastery quiz

Part 12 of 13

Marked quiz

End of lesson quiz: Chapter 5: Solving linear equations

3 questions, marked with the reasoning shown. No timer.

  1. 1. Solve 4x−7=21.

  2. 2. Solve 5x+2=2x+20.

  3. 3. Why substitute the solution back?

13

Lesson round-up

Part 13 of 13

Lesson round-up

Ready when you are

Quiz score

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Games

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Points this lesson

0

Best run

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Luna: 0 out of 3 on the practice checks. Only if you feel up to it — one more?

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Do the work

Your written work for this lesson

This is the part you'd do in your book at school. Pick the pieces below, write here or on paper, and photograph anything you draw or work out.

Article

The cost of a school trip

A school is planning a trip to a wildlife park. The coach costs £480 however many people go. Entry costs £9.50 for each pupil and each adult goes free. The school says every pupil must pay the same amount, and the trip must not lose money.

If 60 pupils go, the coach works out at £8 each, so the total for each pupil is £17.50. If only 40 pupils go, the coach works out at £12 each, so the price rises to £21.50. The teacher explains that the coach is a fixed cost and the entry is a cost per person — which is why the price per pupil changes when the number changes.

The school decides to charge £20 and to use anything left over for a second trip later in the year.

Written for Good Learning Co.

Reading questions

  1. Work out the total cost of the trip if 50 pupils go.
  2. Show why the price per pupil falls when more pupils go, using numbers.
  3. At £20 each, how many pupils must go before the trip makes money? Show your working.

  • Working out

    Working out

    Do the practice questions on paper, showing every step — not just the answer. Mark them yourself and circle anything you got wrong.

    10–15 questions

  • Worked example, explained

    Writing

    Copy one question out and write underneath, in words, why each step works.

    1 question, 4–5 sentences

  • Problem in words

    Working out

    Write your own real-life problem that uses today's method, then solve it.

    1 problem + solution

Saved as you type.

Part 1 of 13 · Watch & discover

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    Use algebraic methods to solve linear equations in one variable, including all forms that require rearrangement

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