Overview

You are 13. We will run a focused, high‑expectation program mapped to ACARA v9 using Beast Academy, AoPS Alcumus and Richard Rusczyk's Prealgebra and Introduction to Geometry. Expect clear goals, daily practice, and measuring progress. No fluff. Deep understanding is non‑negotiable.

ACARA v9 alignment (high level)

• Number and Algebra — integer arithmetic, fractions, ratios, algebraic manipulation, solving equations, patterns.
• Measurement and Geometry — properties of shapes, angles, area, perimeter, basic Euclidean reasoning.
• Statistics and Probability — data interpretation, basic probability.

Unit focus (first unit): Foundations of Prealgebra — Integers, Fractions, Factors, and Simple Equations

This unit builds the essential fluency for algebra and geometry. Duration: 3–4 weeks depending on mastery. Daily workload: 60–90 minutes (homework plus structured practice), plus weekly timed fluency checks.

Learning objectives (students must be able to):

1. Perform integer arithmetic quickly and accurately (add, subtract, multiply, divide).
2. Simplify fractions, convert between mixed numbers and improper fractions, perform operations with fractions.
3. Find greatest common factor (GCF) and least common multiple (LCM); prime factorisation.
4. Solve one‑step and two‑step linear equations; understand balancing and inverse operations.
5. Translate word problems into equations and solve them.

Weekly plan — sample Week 1 (Day‑by‑day)

Daily routine: 5–10 minute timed mental math warmup; 30–40 minutes taught task + guided practice; 20–30 minutes independent problem solving + Alcumus practice; 5 minute reflection.

Day 1 — Integers & Number Line

• Teach: integer addition/subtraction on number line; rules for signs (negative × positive, negative × negative).
• Guided problems: 10 varied integer problems; include contextual word problems (temperature, altitude, bank balance).
• Independent: Beast Academy practice set on integers (selected pages). AoPS Alcumus: 10 problems — set difficulty to practice mode.

Day 2 — Multiplication & Division of Integers; Order of Operations

• Teach: sign rules, distributive property examples, order of operations (PEMDAS) with negatives.
• Guided problems: mixed operations, three‑step expressions.
• Independent: Alcumus practice; timed 5‑minute drill (12 problems).

Day 3 — Fractions: Simplifying & Comparing

• Teach: simplifying fractions using GCF, converting improper fractions & mixed numbers.
• Guided problems: 10 conversions and reductions, compare fractions using common denominators.
• Independent: Beast Academy fractional practice; Alcumus fractional problems.

Day 4 — Operations with Fractions

• Teach: addition/subtraction with common and uncommon denominators, multiplication & division of fractions (invert and multiply).
• Guided problems: mixed operations including word problems (recipes, ratios).
• Independent: assigned Prealgebra chapter problems (Rusczyk) + Alcumus.

Day 5 — Prime Factorisation, GCF & LCM

• Teach: prime factor trees, compute GCF and LCM using prime factors.
• Guided problems: find GCF/LCM of several pairs and small sets; apply to fraction reduction and common denominators.
• Independent: timed fluency check; error review.

Practice & Homework (daily)

• Beast Academy: 3–5 problems that challenge reasoning (show full solution).
• AoPS Alcumus: 10 targeted problems; aim for mastery level progression (repeat incorrect problems until correct with correct reasoning recorded).
• Rusczyk (Prealgebra): 5 textbook problems, include at least one proof/explanatory question requiring sentences.

Assessment & Mastery Criteria

• Weekly timed fluency: 5 minutes, 20 problems. Target: 90%+ accuracy and speed improving week to week.
• Unit test at end of unit: mixed problem set (computational, multi‑step, two word problems). Mastery = 85%+ with clear written work.
• Incorrect work: student must rewrite solutions showing corrected method and explanation of the error.

Remediation & Enrichment

• If accuracy < 70%: do focused remediation for 2 sessions — diagnosis (identify error types), deliberate practice (targeted problems), reassess.
• If mastery > 95%: give enrichment — AoPS hard problems, Beast Academy challenge problems, introductory geometry proofs from Rusczyk's Introduction to Geometry.

Parent / Guardian Instructions (’Tiger’ cadence — firm expectations)

• Attendance: Student will do daily math at scheduled time. No exceptions except illness; makeup work required.
• Accountability: Review stamped weekly fluency. If performance drops, increase practice time immediately until regained.
• Homework review: Have student explain one problem aloud every day — insist on clear reasoning and complete written justification. If they cannot, rework it until they can.

How to use the resources

• Beast Academy — visual, puzzle‑based problems to build reasoning. Use as warmups and critical thinking tasks. Require complete written solutions, not just answers.
• AoPS Alcumus — set to appropriate topic modules (integers, fractions, equations). Use for adaptive practice and tracking weak areas. Require screenshot or record of incorrect problems and corrections.
• Rusczyk Prealgebra/Introduction to Geometry — core text for structured lessons and proofs. Assign readings and textbook problems; expect full, written, logical solutions.

Example worked problem (showing expected rigor)

Problem: Solve 3(2x - 5) = 4x + 1.

1. Expand left: 6x - 15 = 4x + 1.
2. Move variable terms to one side: 6x - 4x = 1 + 15.
3. Simplify: 2x = 16.
4. Divide: x = 8. Check by substitution: 3(2*8 - 5) = 3(16 - 5) = 3*11 = 33; RHS 4*8 + 1 = 32 + 1 = 33. Correct.

Progress tracking (weekly)

• Record: Alcumus mastery % per topic, timed fluency scores, unit test scores.
• Set targets: Improve fluency score by 5% each week until target achieved; reduce repeated mistakes type count each week.

Next steps after this unit

Proceed to two‑variable relationships, linear expressions, and an introduction to angle reasoning and triangle properties from Rusczyk's Introduction to Geometry. Continue alternating computational fluency with challenging reasoning problems.

Closing note

Discipline + deliberate practice = rapid improvement. Expect hard work. I will provide the next unit lesson when you confirm progress or request a specific topic to teach next.