Chapter 1: Operations, powers and roots
Mathematical notation is a set of traffic rules: it ensures everyone evaluates the same expression in the same order.
Part of your national curriculum
- Number: Use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals
- Number: Use integer powers and associated real roots, recognise powers of 2, 3, 4 and 5, and distinguish between exact representations and truncated or rounded decimals
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 priority
- • Worked example
- • Reciprocals
This lesson at a glance
- 28 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
Watch first
Chapter 1: Operations, powers and roots
Connect number structure, algebraic balance and geometric reasoning.
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 priority
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 3 of 17
Learn
The priority
Evaluate brackets first, then indices such as powers and roots, then multiplication and division from left to right, then addition and subtraction from left to right.
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
For 18 − 2 × (3² − 5): brackets contain 9 − 5 = 4; multiplication gives 2 × 4 = 8; subtraction gives 10.
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 · Reciprocals
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 10 of 17
Learn
Reciprocals
The reciprocal of a non-zero number is 1 divided by that number. Multiplying a number by its reciprocal gives 1: the reciprocal of 4 is 1/4, and of 2/3 is 3/2.
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.
Evaluate ____ first, then indices such as powers and roots, then multiplication and division from left to right, then addition and subtraction from 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: Chapter 1: Operations, 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
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 LunaPart 1 of 17 · Watch & discover
How this is going
- Not looked at yet
Use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals
- Not looked at yet
Use integer powers and associated real roots, recognise powers of 2, 3, 4 and 5, and distinguish between exact representations and truncated or rounded decimals