Good Learning Co.
SavannahYear 8
← Maths
MathsNumber, algebra and geometry: connected foundations28 min★★ difficulty

Chapter 3: Substitution and formulae

A formula is a reusable machine: put values in carefully and it produces a result with meaning and units.

Part of your national curriculum
  • Algebra: Substitute numerical values into formulae and expressions, including scientific formulae

Lesson overview

What you'll learn in this lesson

Substitute numerical values into formulae and expressions, including scientific formulae

Key learning points

  • • Substitution
  • • Scientific formula
  • • Check the result

This lesson at a glance

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

Words to know

substitutenumericalvaluesformulaeexpressions

Scroll down — the lesson carries on below

Part 1 of 13 · Discover8%
1

Watch & discover

Part 1 of 13

Watch first

Chapter 3: Substitution and formulae

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

In a nutshell

Substitute numerical values into formulae and expressions, including scientific formulae

2

Learning cycle

Part 2 of 13

Learning cycle 1 of 2

Part 1 · Substitution

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

3

Explore the idea

Part 3 of 13

Learn

Substitution

Replace each letter with its given value, using brackets around negative numbers. If a = −3, then a² means (−3)² = 9.

4

Explore the idea

Part 4 of 13

Learn

Scientific formula

Speed v = d/t. If distance d = 150 m and time t = 12 s, v = 150/12 = 12.5 m/s.

5

Quick check

Part 5 of 13

Quick check

If x=4, find 3x+2.

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 v=d/t, find v when d=150 m and t=12 s.

8

Learning cycle

Part 8 of 13

Learning cycle 2 of 2

Part 2 · Check the result

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

9

Explore the idea

Part 9 of 13

Learn

Check the result

Estimate first, include units and ask whether the answer is sensible. Substitution errors often come from missing brackets or mismatched units.

10

Quick check

Part 10 of 13

Quick check

If a=−3, what is a²?

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 3: Substitution and formulae

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

  1. 1. If x=4, find 3x+2.

  2. 2. Using v=d/t, find v when d=150 m and t=12 s.

  3. 3. If a=−3, what is a²?

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

    Substitute numerical values into formulae and expressions, including scientific formulae

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