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
- 17 parts to scroll through
- 3 quick checks
- Marked quiz at the end
- Gentle pace: short sittings with pauses
Words to know
Scroll down — the lesson carries on below
Watch & discover
Part 1 of 17
Visual introductionPicture this
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.
In a nutshell
Use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals
Learning cycle
Part 2 of 17
Learning cycle 1 of 2
Part 1 · The order
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 3 of 17
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.
Reset break
Part 4 of 17
Pause
That's sitting 1 of 4 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.
Explore the idea
Part 5 of 17
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.
Quick check
Part 6 of 17
Quick check
Part 7 of 17
Reset break
Part 8 of 17
Pause
That's sitting 2 of 4 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.
Learning cycle
Part 9 of 17
Learning cycle 2 of 2
Part 2 · Roots and reciprocals
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 10 of 17
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.
Quick check
Part 11 of 17
Reset break
Part 12 of 17
Pause
That's sitting 3 of 4 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.
Challenge round
Part 13 of 17
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
Challenge round
Part 14 of 17
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).
Challenge round
Part 15 of 17
Game · Recall cards
Evaluate 18 − 2 × (3² − 5).
Card 1 of 4
Mastery quiz
Part 16 of 17
Marked quiz
End of lesson quiz: Order of operations with powers and roots
4 questions, marked with the reasoning shown. No timer.
1. Evaluate 18 − 2 × (3² − 5).
2. What is the reciprocal of 2/3?
3. Evaluate 5 + 3 × 4.
4. What is 3 + 2² × (5 - 1)?
Lesson round-up
Part 17 of 17
Lesson round-up
Ready when you are
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Ask LunaPart 1 of 17 · Watch & discover
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Use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals