Accelerated Prealgebra–Geometry Plan for a 15-year-old — ACARA v9-aligned 2-Semester Outline

Rigorous 2-semester accelerated Prealgebra and Introductory Geometry course plan for a 15-year-old, aligned to ACARA v9 strands (Number & Algebra, Measurement & Geometry, Statistics & Probability). Includes topics, pacing, Alcumus & video supports, and high-expectation objectives.

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Listen and do. A clear, relentless 2-semester plan for a 15-year-old

You will complete a demanding Prealgebra sequence (Semesters 1–2) plus a full Introduction to Geometry. No excuses. Every week has focus, every day has purpose. Use the Alcumus system and the free aligned video library. Attempt the starter problems before reading solutions. Review every error.

Semester 1 — Prealgebra 1 (Foundations)

  • Weeks 1–2: Arithmetic rules, integer operations, order of operations.
  • Weeks 3–4: Exponent laws, squares, zero and negative exponents.
  • Week 5: Multiples, divisibility tests; prime identification and prime factorisation.
  • Week 6: LCM and GCD applications.
  • Weeks 7–8: Fractions intensive (operations, simplification, mixed numbers).
  • Weeks 9–10: Linear equations; advanced word problems and algebraic manipulation.
  • Week 11: Inequalities and interval notation.
  • Weeks 12–13: Decimals ↔ fractions; arithmetic with decimals.
  • Weeks 14–16: Ratios, proportions, unit conversions, speed and rates.

Semester 2 — Prealgebra 2 (Extensions + Discrete Math)

  • Weeks 1–2: Percents, percent change, applied problems.
  • Weeks 3–4: Square roots, arithmetic with radicals.
  • Weeks 5–11: Geometry essentials — angles, polygons, perimeter, area, special triangles, Pythagoras, quadrilaterals.
  • Weeks 12–13: Basic statistics — mean/median/mode, graphs, interpretation.
  • Weeks 14–15: Counting techniques, permutations, combinations, elementary probability.
  • Week 16: Consolidation — problem-solving strategies and timed practice.

Full Intro Geometry (parallel or following)

Follow the 24-lesson Introduction to Geometry sequence: similarity, congruence, circles, power of a point, 3D geometry, transformations, basic trig, analytic geometry. Over 900 challenging problems; full solutions provided.

ACARA v9 mapping & resources

Mapped to ACARA v9 strands: Number & Algebra (number sense, algebraic techniques), Measurement & Geometry (shapes, Pythagoras, area, transformations), Statistics & Probability (data interpretation, probability). Use Alcumus for adaptive practice and the aligned video collection for flipped instruction.

Expectation: daily practice, error log, weekly timed problem sets. You will be precise, persistent, and proud of measurable improvement.

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