Good Learning Co.
SavannahYear 8
← Maths
MathsAlgebraic modelling27 min★★ difficulty

Turning real situations into algebra

A phone contract, a taxi fare, and a football league table can all be described by the same kind of formula — once you know how to spot the pattern.

Part of your national curriculum
  • Algebra: Model situations or procedures by translating them into algebraic expressions or formulae

Lesson overview

What you'll learn in this lesson

Model situations or procedures by translating them into algebraic expressions or formulae

Key learning points

  • • From words to expressions
  • • Worked example
  • • Building your own formula

This lesson at a glance

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

Words to know

situationsprocedurestranslatingalgebraicexpressions

Scroll down — the lesson carries on below

Part 1 of 13 · Discover8%
1

Watch & discover

Part 1 of 13

Watch first

Turning real situations into algebra

An English teaching video on this topic from Hakea Math & Science. Watch it, then scroll down for the lesson.

In a nutshell

Model situations or procedures by translating them into algebraic expressions or formulae

2

Learning cycle

Part 2 of 13

Learning cycle 1 of 2

Part 1 · From words to expressions

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

3

Explore the idea

Part 3 of 13

Learn

From words to expressions

A taxi charges £3 plus £2 per mile. If m is the number of miles, the cost formula is C = 3 + 2m. Each part of the sentence maps directly onto a term in the expression.

4

Explore the idea

Part 4 of 13

Learn

Worked example

Using C = 3 + 2m, find the cost of a 7-mile journey: C = 3 + 2 × 7 = 3 + 14 = £17. Substituting a number into the formula gives a real answer.

5

Quick check

Part 5 of 13

Quick check

A taxi costs £3 plus £2 per mile (m). Which formula matches?

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

Using C = 3 + 2m, what is the cost of a 7-mile journey?

8

Learning cycle

Part 8 of 13

Learning cycle 2 of 2

Part 2 · Building your own formula

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

9

Explore the idea

Part 9 of 13

Learn

Building your own formula

A gym charges a £15 joining fee plus £8 per month for n months. The total cost formula is T = 15 + 8n. Checking with n = 4: T = 15 + 32 = £47.

10

Quick check

Part 10 of 13

Quick check

A gym costs £15 joining fee plus £8 per month (n). What is the cost for 4 months?

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: Turning real situations into algebra

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

  1. 1. A taxi costs £3 plus £2 per mile (m). Which formula matches?

  2. 2. Using C = 3 + 2m, what is the cost of a 7-mile journey?

  3. 3. A gym costs £15 joining fee plus £8 per month (n). What is the cost for 4 months?

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

    Model situations or procedures by translating them into algebraic expressions or formulae

Good Learning Co. — personalised UK curriculum learning, built around what each learner loves.