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

Chapter 4: Expressions: expand, collect and factorise

Algebra becomes manageable when you recognise structure rather than treating every symbol separately.

Part of your national curriculum
  • Algebra: Use and interpret algebraic notation, including coefficients written as fractions and brackets
  • Algebra: Simplify and manipulate algebraic expressions by collecting like terms, multiplying a single term over a bracket and factorising into a single bracket

Lesson overview

What you'll learn in this lesson

Simplify and manipulate algebraic expressions by collecting like terms, multiplying a single term over a bracket and factorising into a single bracket

Key learning points

  • • Collect like terms
  • • Expand
  • • Factorise

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

simplifymanipulatealgebraicexpressionscollecting

Scroll down — the lesson carries on below

Part 1 of 13 · Discover8%
1

Watch & discover

Part 1 of 13

Watch first

Chapter 4: Expressions: expand, collect and factorise

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

In a nutshell

Simplify and manipulate algebraic expressions by collecting like terms, multiplying a single term over a bracket and factorising into a single bracket

2

Learning cycle

Part 2 of 13

Learning cycle 1 of 2

Part 1 · Collect like terms

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

3

Explore the idea

Part 3 of 13

Learn

Collect like terms

Terms can combine only when their variable parts match: 5x + 2x − 3 = 7x − 3, but x and x² are not like terms.

4

Explore the idea

Part 4 of 13

Learn

Expand

Multiply the term outside a bracket by every term inside: 3(2x − 5) = 6x − 15. A quick substitution can check equivalence.

5

Quick check

Part 5 of 13

Quick check

Simplify 5x+2x−3.

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

Expand 3(2x−5).

8

Learning cycle

Part 8 of 13

Learning cycle 2 of 2

Part 2 · Factorise

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

9

Explore the idea

Part 9 of 13

Learn

Factorise

Factorising reverses expansion. The highest common factor of 8x + 12 is 4, so 8x + 12 = 4(2x + 3).

10

Quick check

Part 10 of 13

Quick check

Factorise 8x+12.

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 4: Expressions: expand, collect and factorise

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

  1. 1. Simplify 5x+2x−3.

  2. 2. Expand 3(2x−5).

  3. 3. Factorise 8x+12.

13

Lesson round-up

Part 13 of 13

Lesson round-up

Ready when you are

Quiz score

Not sat

Games

Not played

Points this lesson

0

Best run

0 in a row

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

Ask Luna

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

How this is going

  • Not looked at yet

    Use and interpret algebraic notation, including coefficients written as fractions and brackets

  • Not looked at yet

    Simplify and manipulate algebraic expressions by collecting like terms, multiplying a single term over a bracket and factorising into a single bracket

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