GCSE Maths Year 1 Week 5
Algebraic Notation, Simplifying & Substitution
Welcome to Unit 2, Algebra. This is the point where maths starts using letters instead of just numbers, and it can feel like a different subject at first. It isn't; it's the same rules of arithmetic you've spent the last four weeks getting solid on, just written in a more general way. This week covers the notation itself, how to simplify expressions by collecting like terms, and how to substitute numbers into an expression.
Same shape as previous weeks: warm-up, teach, practice (Foundation, Intermediate or Higher — pick one), mark, exit ticket.
Monday — Algebraic Notation
What you're learning: The conventions of algebra, why we write 2a instead of a2, why ab means a × b, and how powers like a² are written and read.
Warm-up (5 min): Transum — Bidmaze — recall of order of operations from Unit 1, which matters just as much when the numbers are replaced by letters.
Teach (10 min):
A few conventions worth fixing in your head now:
3 × a is written 3a (the number always comes first);
a × b is written ab;
a × a is written a²;
a ÷ b is written as a fraction, a/b.
Practice (20 min): Pick one path:
Foundation: Transum — Algebraic Notation, Level 1.
Intermediate: Corbett Maths — Algebraic Notation Practice Questions, one page.
Higher: Corbett Maths — Textbook Exercise (the longer piece) plus Transum — Algebraic Notation, Level 2.
Mark & fix: Check, correct, and note why for anything you got wrong.
Exit ticket: Write "5 lots of x, plus 3 lots of y, minus 2" using correct algebraic notation.
Tuesday — Collecting Like Terms
What you're learning: How to simplify an algebraic expression by combining terms that involve the same letter (or the same combination of letters) raised to the same power.
Warm-up (5 min): Transum — Algebraic Notation, Level 1 — quick recall of yesterday.
Teach (10 min):
Only terms with exactly the same letters and powers can be combined — 3x and 5x combine to 8x, but 3x and 5x² cannot be combined, and neither can 3x and 3y. Think of trying to combine apples with bananas; it just doesn't work!
Practice (20 min): Pick one path:
Foundation: Transum — Collecting Like Terms, Level 1.
Intermediate: Corbett Maths — Collecting Like Terms Practice Questions, one page.
Higher: Corbett Maths — Textbook Exercise (the longer piece) plus Transum — Collecting Like Terms, Level 2, which mixes in more letters and negative terms.
Mark & fix: As before, a common mistake is combining terms that only look similar (like x and x²), so double-check the powers match before combining.
Exit ticket: Simplify 4a + 3b − a + 5b. Show which terms you combined and why.
Wednesday — Substitution into Expressions
What you're learning: How to substitute given numbers into an algebraic expression to find its value — using BIDMAS exactly as you would with pure numbers.
Warm-up (5 min): Transum — Collecting Like Terms, Level 1 — recall of yesterday.
Teach (10 min):
Practice (20 min): Pick one path:
Foundation: Transum — Algebraic Notation, Level 1, applied to substitution-style questions, or the first page of questions from the Corbett practice link below using only positive whole numbers.
Intermediate: Corbett Maths — Substitution Practice Questions, one page.
Higher: Corbett Maths — Textbook Exercise (the longer piece, includes negative numbers and powers) plus Transum — Algebra hub, the Substitution activity.
Mark & fix: As before — substitution mistakes usually come from BIDMAS errors (forgetting that a power applies before a multiplication) or sign errors with negative values, so check both carefully.
Exit ticket: If a = 3 and b = −2, work out the value of 2a² + b. Show every step.
Thursday — Multiplying & Dividing Terms
What you're learning: How to multiply and divide algebraic terms, including terms with powers. This is an early, gentle introduction to the index laws you saw in Unit 1, now applied to letters instead of numbers.
Warm-up (5 min): Corbett Maths — Substitution Practice, first few questions — quick recall of yesterday.
Teach (10 min):
Practice (20 min): Pick one path:
Foundation: Transum — Algebra hub — the introductory multiplying/dividing terms activities.
Intermediate: Corbett Maths — Multiplying Terms Practice Questions, one page.
Higher: Corbett Maths — Dividing Terms Textbook Exercise (the longer piece, the harder of today's two sub-skills) plus Transum — Algebra hub, the multiplying/dividing terms activities at a harder level.
Mark & fix: As before.
Exit ticket: Simplify 3a × 4a and 12a³ ÷ 3a. What happens to the powers in each case?
Friday — Consolidation
Today's not about new content; it's about locking in this week's ideas.
Weekend printable: MEP GCSE Pupil Text 2 — Unit 2: Formulae (PDF), section 2.1 (Using Formulae) — this covers substitution into formulae and is good pen-and-paper reinforcement of Wednesday's work.
End-of-week reflection (5 min): In your notebook, answer:
Which topic this week felt most solid?
Which topic do you want to see again before we move on?
Rate your confidence 1–5 on: algebraic notation, collecting like terms, substitution, multiplying/dividing terms.
Keep this reflection. Algebra builds very directly on itself, so anything shaky this week is worth catching now rather than later.
Next week: Expanding brackets and factorising, the next building block in algebra, using everything from this week.
