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KS3 Mathematics · National Curriculum · Number
Mini-Lesson

Number

This mini-lesson walks you through the whole KS3 Number strand: place value, ordering, primes, factors & multiples, HCF & LCM, the four operations, order of operations, powers, roots & standard form, fractions ↔ decimals ↔ percentages, and rounding & estimation.

-2 -1 0 1 2 numbers get bigger →
Everything in this lesson lives on the number line — the further right, the bigger the number.

Work through each screen, answer the questions as you go (some are calculations, some are true/false ideas) and collect ⭐ stars. Press Start when you're ready.

Place value

Every digit has a value

A digit's value depends on its column. Reading left to right, each column is worth ten times the one to its right — and to the right of the decimal point the columns get ten times smaller.

hundreds3 tens0 ones6 . tenths4 306.4 the 3 means 300, the 6 means 6, the 4 means four tenths (0.4)
The columns: hundreds, tens, ones · tenths, hundredths, thousandths.

Watch out: the 0 in 306 is a place-holder — it keeps the 3 in the hundreds column. Drop it and 306 becomes 36, a totally different number.

Quick check

What's it worth?

?In the number 4.702, what is the value of the digit 7?
Ordering & inequalities

Which is bigger?

To order numbers, compare them column by column, starting from the left. We write comparisons with inequality symbols:

3 < 8   8 > 3< means "less than", > means "greater than" — the arrow always points at the smaller number

Watch out with decimals: more digits does not mean bigger! 0.7 is greater than 0.65, because 7 tenths beats 6 tenths — compare the tenths column first.

Negatives: the further left on the number line, the smaller. So -5 < -2 (−5 is colder / lower than −2).

Sort it

Pick the bigger number

Tap the greater number in each pair. Compare column by column!

Factors, multiples & primes

Building blocks of number

  • A factor divides into a number with no remainder. Factors of 12: 1, 2, 3, 4, 6, 12.
  • A multiple is in a number's times-table. Multiples of 4: 4, 8, 12, 16, …
  • A prime has exactly two factors — 1 and itself (2, 3, 5, 7, 11, …).

Watch out: 1 is not prime (it has only one factor). 2 is the only even prime — every other even number is divisible by 2.

Quick check

Spot the prime

?Which of these numbers is prime?
Sort it

Prime or not prime?

Tap a number, then tap the box it belongs in.

✅ Prime

➗ Not prime

Prime factorisation

Splitting into primes

Every whole number can be written as a product of primes. A factor tree breaks it down step by step until every branch ends on a prime:

60 6 10 2 3 2 5
60 = 2 × 2 × 3 × 5 = 2² × 3 × 5. The blue circles are the primes.

Tip: circle each prime as you reach it so you don't forget it. The order you split doesn't matter — you always get the same primes.

HCF & LCM

Highest common factor & lowest common multiple

The HCF is the biggest number that divides into both. The LCM is the smallest number that is a multiple of both. A Venn diagram of prime factors makes it easy:

12 = 2×2×3 18 = 2×3×3 2 2 3 3 overlap (shared)
Shared primes 2 × 3 → HCF = 6. All primes 2 × (2×3) × 3 → LCM = 36.
Worked example — HCF & LCM of 12 and 18

12 = 2 × 2 × 3   18 = 2 × 3 × 3

HCF = product of the shared primes = 2 × 3 = 6

LCM = every prime, using the most it appears = 2 × 2 × 3 × 3 = 36

Calculate

Your turn — HCF

1Find the highest common factor of 24 and 36.
HCF
Hint: 24 = 2×2×2×3, 36 = 2×2×3×3. Shared primes: 2×2×3.
Calculate

Your turn — LCM

2Find the lowest common multiple of 4 and 6.
LCM
Hint: multiples of 4: 4, 8, 12… multiples of 6: 6, 12… What's the first one in both lists?
Four operations & negatives

Adding, subtracting & the sign rules

Add, subtract, multiply and divide work with integers, decimals and fractions. The trickiest part at KS3 is negative numbers:

  • Subtracting a negative adds: 5 − (−3) = 5 + 3 = 8.
  • Two same signs multiply/divide to a +: (−4) × (−2) = +8.
  • Two different signs multiply/divide to a : (−6) ÷ 2 = −3.
-2 -1 0 1 2 -2 + 5 = 3 (jump 5 to the right)
Adding moves right, subtracting moves left along the number line.
Calculate

Your turn — negatives

3Work out −7 − (−10).
=
Hint: subtracting a negative is the same as adding: −7 + 10.
Order of operations

BIDMAS — do things in the right order

When a calculation has several operations, do them in this order:

B I D M A SBrackets · Indices (powers) · Division & Multiplication · Addition & Subtraction
Worked example

3 + 4 × 2²  →  do the index first: 2² = 4

3 + 4 × 4  →  then multiply: 4 × 4 = 16

3 + 16 = 19  (not 3+4=7, then ×… that would be wrong!)

Watch out: reading strictly left to right gives the wrong answer. 3 + 4 × 2 = 11, not 14, because you multiply before you add.

Calculate

Your turn — BIDMAS

4Work out 2 + 3 × 4.
=
Hint: multiply before you add. Do 3 × 4 first.
Powers & roots

Squares, cubes & roots

A power (or index) tells you how many times to multiply a number by itself. A root undoes a power — they are inverse operations.

5² = 5 × 5 = 25   √25 = 5"5 squared" is 25; the square root of 25 is 5
  • ("2 cubed") = 2 × 2 × 2 = 8, and the cube root ∛8 = 2.
  • Square numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100…

Watch out: 5² is not 5 × 2 = 10. The little 2 means "multiply by itself", so 5 × 5 = 25.

Calculate

Your turn — powers

5Work out (4 cubed).
=
Hint: 4 × 4 × 4.
Standard form

Writing huge (and tiny) numbers

Standard form writes a number as A × 10ⁿ, where A is between 1 and 10. It's a neat way to handle very big or very small numbers.

3200 = 3.2 × 10³the power of 10 counts how many places the decimal point moves
  • Big numbers → positive power: 50 000 = 5 × 10⁴.
  • Small numbers → negative power: 0.004 = 4 × 10⁻³.

Watch out: the first part must be at least 1 but under 10. So 32 × 10² is not standard form — it should be written 3.2 × 10³.

Quick check

Into standard form

?Which of these is 4500 written correctly in standard form?
Fractions, decimals & percentages

Three ways to write a part

Fractions, decimals and percentages are the same idea written differently. You should be able to swap between them:

½ = 0.5 decimal = 50% percentage
½ = 0.5 = 50%. To go fraction → decimal, divide top by bottom; × 100 for a percentage.

Terminating decimals (like 0.5, 0.75, 0.2) stop after a few digits and always come from a simple fraction: 0.75 = ¾, 0.2 = ⅕.

Percentages as operators

Finding a percentage of an amount

"Percent" means "out of 100". To find a percentage of an amount, turn it into a fraction or decimal and multiply:

Worked example — 20% of £45

10% of £45 = £45 ÷ 10 = £4.50

20% = double 10% = £9.00

(Or: 0.2 × 45 = £9.00.)

Handy building blocks: 50% = ÷2, 25% = ÷4, 10% = ÷10, 1% = ÷100. Build any percentage from these.

Calculate

Your turn — percentages

6Work out 15% of £80.
£
Hint: 10% of 80 = 8, and 5% is half of that (4). Add them.
Rounding & estimation

Rounding, estimating & error bounds

To round, look at the next digit: 5 or more rounds up, 4 or less rounds down.

  • 47 to the nearest 10 → 50 (the 7 rounds up).
  • 3.14159 to 2 decimal places → 3.14 (the next digit, 1, rounds down).
  • To 1 significant figure, 68 → 70.

Estimate by rounding every number to 1 significant figure first: 19 × 31 ≈ 20 × 30 = 600.

Error bounds: a length given as 12 cm to the nearest cm could really be anywhere from 11.5 cm up to 12.5 cm — half a unit either side.

Quick check

Rounding check

?Round 3.867 to 2 decimal places.
Recap

The big ideas to remember

Place value: a digit's worth depends on its column.

Ordering: compare left to right; < and > point at the smaller number.

Primes/factors: HCF = shared primes, LCM = all primes (most of each).

BIDMAS: Brackets, Indices, ÷×, +−.

Powers & roots: inverse operations; 5² = 25, √25 = 5.

Standard form: A × 10ⁿ with 1 ≤ A < 10.

FDP: ½ = 0.5 = 50%; percentages are just operators.

Rounding: 5-or-more rounds up; estimate with 1 s.f.

You've covered the whole KS3 Number strand. Press Finish to see your score.

🏆

Mini-lesson complete!

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You've worked through Number for KS3 Mathematics. 🎉

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