KS3 Maths: Algebra & Geometry Foundations with Worked Examples
Deepen algebra and geometry fluency with step‑by‑step models, dual‑coded diagrams, and targeted retrieval practice.
Expressions, Equations, and Order of Operations
Clarify expressions vs equations; evaluate with order of operations (indices before multiply/divide before add/subtract). Worked: Simplify 3a + 2a − a = 4a. Solve 3x + 7 = 22 → x = 5 (subtract 7; divide 3; check).
Angles and Polygons
Angle facts: straight line 180°, around a point 360°, vertically opposite equal. Triangle sum 180°. Exterior angle of a polygon equals sum of remote interior angles. Worked: Find missing angles using supplementary and corresponding angles.
Area, Perimeter, and Transformations
Area rectangles/triangles/parallelograms; perimeter vs area distinction. Transformations: translations, rotations, reflections; describe fully (vector/centre/line). Worked: Translate (−3, 2) by ⟨4, −1⟩; reflect a shape in y‑axis; calculate area of triangle (b×h÷2).
How Cartisio Helps
- Worked examples with small steps + checks.
- Flipcards for rules (angle facts, area formulas).
- Quick quizzes mixing topics to prevent pattern guessing.
- Videos for alternative explanations when stuck.
Useful Videos
- Trusted explainer
Evidence
- Worked Example effect reduces cognitive load during acquisition.
- Retrieval Practice for formulas and rules.
- Spacing across weeks consolidates skills.
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