GCSE Maths - Year 1 Week 7
Formulae & Algebraic Fractions
This week extends what you already know about brackets and factorising into two new directions: expanding two brackets at once, and rearranging a formula to make a different letter the subject. We finish with algebraic fractions, treating expressions with letters in exactly the way you already treat ordinary fractions.
Same shape as previous weeks: warm-up, teach, practice (Foundation, Intermediate or Higher — pick one), mark, exit ticket.
Monday — Expanding Two Brackets
What you're learning: How to expand an expression like (x + 3)(x + 5), multiplying every term in the first bracket by every term in the second, then collecting like terms.
Warm-up (5 min): Corbett Maths — Factorising Practice Questions, first few questions — recall of last week's factorising, the reverse process of what you're learning today.
Teach (10 min):
A reliable method: multiply the first term in the first bracket by both terms in the second bracket, then the second term in the first bracket by both terms in the second bracket — four multiplications in total — then collect like terms.
Practice (20 min): Pick one path:
Foundation: Transum — Brackets, Levels 3–5, applied to two-bracket questions where they appear.
Intermediate: Corbett Maths — Expanding Two Brackets Practice Questions, one page.
Higher: Corbett Maths — Textbook Exercise (the longer piece) plus Transum — Brackets, Levels 9–10.
Mark & fix: Check, correct, and note why for anything you got wrong — a very common mistake is forgetting one of the four multiplications, so if your answer is short a term, that's the first thing to check.
Exit ticket: Expand and simplify (x + 4)(x + 2). Show all four multiplications before collecting like terms.
Tuesday — Changing the Subject of a Formula
What you're learning: How to rearrange a formula so that a different letter becomes the subject, using exactly the same balancing principle as solving an equation, just applied to a formula with several letters instead of one.
Warm-up (5 min): Corbett Maths 5-a-day (GCSE) — general mixed recall.
Teach (10 min):
The subject of a formula is whichever letter is on its own. To make a different letter the subject, use inverse operations to peel away everything else, one step at a time, exactly as you would to solve an equation.
Practice (20 min): Pick one path:
Foundation: Transum — Changing the Subject, Level 1.
Intermediate: Corbett Maths — Changing the Subject Practice Questions, one page.
Higher: Corbett Maths — Textbook Exercise (the longer piece) plus Transum — Changing the Subject, Level 3.
Mark & fix: As before.
Exit ticket: Make x the subject of y = 3x + 7. Show each step, explaining which inverse operation you used.
Wednesday — Algebraic Fractions: Simplifying
What you're learning: How to simplify a fraction that contains algebraic terms, by finding common factors in the numerator and denominator, exactly the same idea as simplifying an ordinary fraction, just with letters involved.
Now I understand that some of you may not have worked with fractions before. So I recommend that if that is you, stop now. Go to Khan Academy Algebra Basics - Fractions. Work through the unit, take your time, and when you are ready, come back and finish this week's work.
Warm-up (5 min): Transum — Changing the Subject, Level 1 — recall of yesterday.
Teach (10 min): Watch:
Practice (20 min): Pick one path:
Foundation: Transum — Algebraic Fractions, Level 1.
Intermediate: Corbett Maths — Algebraic Fractions Practice Questions, one page.
Higher: Corbett Maths — Textbook Exercise (the longer piece) plus Transum — Algebraic Fractions, Level 2.
Mark & fix: As before — a fraction is only fully simplified once there's no common factor left in the numerator and denominator, so double check yours can't be simplified further.
Exit ticket: Simplify fully. Show the common factor you took out.
Thursday — Algebraic Fractions: Addition & Subtraction
What you're learning: How to add and subtract algebraic fractions with different denominators, finding a common denominator exactly as you would with ordinary fractions.
Warm-up (5 min): Transum — Algebraic Fractions, Level 1 — recall of yesterday.
Teach (10 min):
Practice (20 min): Pick one path:
Foundation: Transum — Algebraic Fractions, Level 2, focusing on the addition-style questions.
Intermediate: Corbett Maths — Algebraic Fractions Practice Questions, later questions on the page.
Higher: Corbett Maths — Adding Algebraic Fractions Textbook Exercise (the longer piece) plus Transum — Algebraic Fractions, Level 4.
Mark & fix: As before.
Exit ticket: Work out as a single fraction. Show how you found the common denominator.
Friday — Consolidation
Today's not about new content — it's about locking in this week's ideas.
Quiz (10–15 min): Transum — Algebra hub, which lists Brackets, Changing the Subject and Algebraic Fractions activities together in one place — a good mixed recap of the whole week.
Weekend printable: MEP GCSE Pupil Text 2 — Unit 2: Formulae (PDF), 2.6 and 2.11, have a look and complete what you think is good practice for you, you might complete all the questions or just a few in each section — good pen-and-paper reinforcement of this week'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: expanding two brackets, changing the subject, simplifying algebraic fractions, adding algebraic fractions.
Keep this reflection — we'll circle back to anything you flagged as shaky during next week's mixed review, before the Unit 2 assessment.
Next week: The final week of Unit 2, algebraic fractions with multiplication and division, mixed algebra problem solving, forming equations from real-life contexts, a mixed review, and the Unit 2 assessment.
