This mini-lesson walks you through the whole KS3 Algebra strand: using letters for numbers, simplifying and expanding, formulae, solving equations, coordinates & straight-line graphs, and sequences.
Work through each screen, answer the questions as you go (some are calculations, some are ideas) and collect ⭐ stars. Press Start when you're ready.
In algebra a letter (a variable) stands for a number we don't know yet. There are shorthand rules for writing it:
Watch out: 3a is not the same as 3 + a. 3a means three lots of a. If a = 5, then 3a = 15 but 3 + a = 8.
Substitution means swapping a letter for its value and working out the answer. Remember to keep to the order of operations (BIDMAS).
Find the value of 3a + 2 when a = 4.
Step 1: replace a with 4 → 3 × 4 + 2
Step 2: multiply first → 12 + 2
Step 3: add → 14
Watch out: do the multiplying before the adding. 3 × 4 + 2 = 14, not 3 × 6 = 18.
To simplify an expression we collect like terms — terms with exactly the same letter part. You add or subtract their number parts (coefficients):
Unlike terms cannot be joined. 4a + 3b stays as 4a + 3b, because a and b are different.
Simplify 5x + 2y + 3x − y.
x terms: 5x + 3x = 8x. y terms: 2y − y = y.
Answer: 8x + y
Watch out: a and a² are not like terms — a² means a × a. So a + a² cannot be simplified.
Tap the correct simplified form for each expression.
To expand a bracket, multiply everything inside by the term outside:
Expand 5(2a − 3).
5 × 2a = 10a and 5 × (−3) = −15.
Answer: 10a − 15
Watch out: the outside number multiplies every term. 3(x + 2) = 3x + 6, not 3x + 2.
Factorising is the reverse of expanding. You take out the highest common factor and put a bracket back:
Factorise 10a + 15.
Step 1: highest common factor of 10 and 15 is 5.
Step 2: divide each term by 5 → 2a and 3.
Step 3: write it as 5(2a + 3). Check: expand it back to 10a + 15. ✓
Tip: always check by expanding your answer — it should give the original expression.
A formula is a rule connecting quantities, e.g. the area of a rectangle: A = l × w. You can substitute values in, or change the subject to make a different letter the star of the show.
A rectangle has area A = 24 and length l = 6. Find the width w.
w = A ÷ l = 24 ÷ 6 = 4
Golden rule: whatever you do to one side, do to the other — that keeps it balanced (more on that next).
An equation says two things are equal, like a balance scale. To find the unknown, keep the scale balanced: do the same to both sides until the letter is alone.
Solve 2x + 3 = 11.
Step 1: subtract 3 from both sides → 2x = 8.
Step 2: divide both sides by 2 → x = 4.
Step 3: check by substituting: 2 × 4 + 3 = 11. ✓
Watch out: undo operations in reverse order — undo the "+3" before the "×2".
A point is written as (x, y) — go along the x-axis first, then up the y-axis. A function like y = x + 1 gives a y-value for every x, and plotting the points makes a graph.
Every straight line can be written y = mx + c:
So for y = 3x + 2: gradient = 3, and it crosses the y-axis at 2. A simultaneous equations pair (two lines) is solved by the point where the lines cross.
A sequence is an ordered list of numbers following a rule. In a linear sequence the step (common difference) is the same each time:
Step 1: the common difference is 3, so the rule starts with 3n.
Step 2: 3 × 1 = 3, but the first term is 2, so subtract 1.
Rule: nth term = 3n − 1. Check: n = 4 → 3 × 4 − 1 = 11. ✓
Tap a term, then tap the box it belongs in. "Like 3x" means it can be added to 3x.
Notation: 3a = 3 × a; a² = a × a; 3a ≠ 3 + a
Substitution: swap the letter for its value, use BIDMAS
Simplify: collect like terms (4a + 3a = 7a)
Expand: 3(x + 2) = 3x + 6 · Factorise: 6x + 9 = 3(2x + 3)
Equations: keep both sides balanced to find the unknown
Straight line: y = mx + c (m = gradient, c = y-intercept)
Sequences: nth term rule from the common difference
You've covered the whole KS3 Algebra strand — notation, manipulation, formulae, equations, graphs and sequences. Press Finish to see your score.
You've worked through Algebra for KS3 Mathematics. 🎉
Your stars: 0 / 0
Next: test yourself in the Evaluate stage Confidence Quiz, then lock it in with Verify.