Good Learning Co.
SavannahYear 8
← Maths
MathsNumber sense24 min★★ difficulty

Order of operations with powers and roots

BIDMAS is the referee's rulebook for a calculation — without it, the same expression could give three different 'right' answers.

Part of your national curriculum
  • Number: Use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals

Lesson overview

What you'll learn in this lesson

Use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals

Key learning points

  • • The order
  • • Worked example
  • • Roots and reciprocals

This lesson at a glance

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

Words to know

conventionalnotationpriorityoperationsbrackets

Scroll down — the lesson carries on below

Part 1 of 14 · Discover7%
1

Watch & discover

Part 1 of 14

Watch first

Order of operations with powers and roots

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

In a nutshell

Use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals

2

Learning cycle

Part 2 of 14

Learning cycle 1 of 2

Part 1 · The order

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

3

Explore the idea

Part 3 of 14

Learn

The order

Work through Brackets, Indices (powers and roots), Division and Multiplication (left to right), then Addition and Subtraction (left to right). Reciprocals are treated like a power of -1.

4

Explore the idea

Part 4 of 14

Learn

Worked example

Evaluate 3 + 2² × (5 - 1). Brackets first: 5 - 1 = 4. Then the power: 2² = 4. Then multiplication: 4 × 4 = 16. Finally addition: 3 + 16 = 19.

5

Quick check

Part 5 of 14

Quick check

What is 3 + 2² × (5 - 1)?

6

Reset break

Part 6 of 14

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 14

Quick check

What comes first in BIDMAS?

8

Learning cycle

Part 8 of 14

Learning cycle 2 of 2

Part 2 · Roots and reciprocals

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

9

Explore the idea

Part 9 of 14

Learn

Roots and reciprocals

Evaluate √16 + 4⁻¹. The root gives √16 = 4. The reciprocal gives 4⁻¹ = 1/4. Adding: 4 + 1/4 = 4 1/4.

10

Quick check

Part 10 of 14

Quick check

What is √16 + 4⁻¹?

11

Challenge round

Part 11 of 14

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

Challenge round

Part 12 of 14

Game · Fill the gaps

Finish the sentences

Choose the word that belongs in each gap.

Work through ____, Indices (powers and roots), Division and Multiplication (left to right), then Addition and Subtraction (left to right).

13

Mastery quiz

Part 13 of 14

Marked quiz

End of lesson quiz: Order of operations with powers and roots

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

  1. 1. What is 3 + 2² × (5 - 1)?

  2. 2. What comes first in BIDMAS?

  3. 3. What is √16 + 4⁻¹?

14

Lesson round-up

Part 14 of 14

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 14 · Watch & discover

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    Use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals

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