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.