Powers, roots and rounded decimals
√2 goes on forever without repeating — so when we write 1.41, we are always making a choice about how much accuracy we actually need.
Part of your national curriculum
- 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 integer powers and associated real roots, recognise powers of 2, 3, 4 and 5, and distinguish between exact representations and truncated or rounded decimals
Key learning points
- • Recognising powers
- • Worked example
- • Exact vs rounded
This lesson at a glance
- 25 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
Powers, roots and rounded decimals
√2 goes on forever without repeating — so when we write 1.41, we are always making a choice about how much accuracy we actually need.
In a nutshell
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
Learning cycle
Part 2 of 17
Learning cycle 1 of 2
Part 1 · Recognising powers
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 3 of 17
Learn
Recognising powers
Powers of 2: 2, 4, 8, 16, 32. Powers of 3: 3, 9, 27, 81. Learning these patterns helps you spot roots quickly, since √81 = 9 and cube root of 27 = 3.
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 2⁵. That is 2×2×2×2×2 = 32. Now find √32 to 1 decimal place: √32 ≈ 5.656..., which rounds to 5.7.
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 · Exact vs rounded
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 10 of 17
Learn
Exact vs rounded
√2 is an exact value that never terminates. Writing √2 keeps it exact; writing 1.41 is a rounded approximation, useful for measuring but not for further exact working.
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.
____ of 2: 2, 4, 8, 16, 32.
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: Powers, roots and rounded decimals
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 2⁵?
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 integer powers and associated real roots, recognise powers of 2, 3, 4 and 5, and distinguish between exact representations and truncated or rounded decimals