☀️ Summer 2026 · Maths Pre-IGCSE · Week 1 · Algebra
Algebra
By the end of this lesson, your teenager can actually do these 4 things:
Simplify and expand algebraic expressions with full confidence
Solve linear equations and inequalities — showing every step
Recognise and extend sequences; find the nth-term rule
Substitute into formulae and rearrange them fluently
The Lesson Plan
⏱ Week 1 · Algebra — 90-Minute Lesson Plan One topic, covered properly. Every minute is active — no passive note-taking, no theory without practice.
0:00
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0:10
🚀 Introduction — Diagnostic Starter
A few targeted questions show the tutor exactly where your teenager's algebra stands — and where the session needs to focus most.
Sets the pace · adapts in real time · no downtime
- A few rapid diagnostic questions spanning key Algebra skills
- Identify misconceptions early — before they cost marks at IGCSE
- Every question is mapped to learning objectives — no wasted time
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0:35
✏️ Part 1 — Expressions & Expanding Brackets
The language of algebra. Get this right and every topic — equations, sequences, graphs — becomes accessible.
Focus: like terms · expanding brackets · factorisation · HCF
- Simplify expressions by collecting like terms
- Expand single and double brackets — including perfect squares
- Factorise expressions by extracting the highest common factor
- Recognise and apply the difference of two squares
0:35
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1:00
⚖️ Part 2 — Linear Equations & Inequalities
The most exam-tested strand of Pre-IGCSE Algebra. Students who can solve equations quickly gain confidence across every maths topic.
Focus: solving equations · word problems · inequalities
- Solve one-step and two-step linear equations
- Solve equations with unknowns on both sides
- Form and solve equations from word problems
- Represent and solve linear inequalities on a number line
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1:20
🔗 Part 3 — Sequences & Formulae
Sequences and formulae bridge arithmetic and algebra — and appear in almost every IGCSE paper.
Focus: nth term · arithmetic sequences · substitution · rearranging
- Find the next terms of arithmetic and geometric sequences
- Write the nth-term rule for a linear sequence
- Substitute values into and evaluate algebraic formulae
- Rearrange formulae to change the subject
1:20
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1:30
🎯 Outro — Exam Question & Target
The session ends with a real GCSE-style Algebra question under timed conditions, then a focused reflection.
What they take home: a completed GCSE-style algebra solution with a personalised target
- Solve one unseen algebra exam question independently
- Review the solution together — spot where marks are won and lost
- Leave with one written target for the week ahead
Build the algebra foundations that make Year 10 & 11 manageable — every session builds on the last.
Ready to Start?
Summer 2026 spots are limited
Build the algebra foundations that make Year 10 & 11 manageable — small groups, expert guidance.