Khaemenes Academy · Mathematics Hall · Placement-Based

Algebra I

Integrated Mathematics I · Structure, Functions, Evidence & Modelling

A complete 36-week Algebra I pathway with 87 instructional lessons, weekly mastery, strict 80% progression, cumulative assessment, applied laboratories, and a final modelling portfolio. The course is open by readiness, not age.

Begin Week 1 Readiness Open Lesson Directory Assessment Center Applied Labs Vocabulary Studio

36Weeks

87Lessons

13Units

80%Mastery Gate

Begin with evidence

Start Algebra I intentionally.

There are two readiness surfaces, and they have different jobs. The Week 1 diagnostic is the learner’s Algebra I starting assessment. The Readiness Bridge simply carries useful evidence forward from Pre-Algebra and toward later mathematics.

Step 1 · Algebra I starting assessment

Begin with the Week 1 diagnostic.

The 36-question Algebra I diagnostic is untimed, saves locally, and guides Foundation, Core, or Extended support. It is readiness evidence, not part of the official course grade.

1Take the diagnostic.
Work independently enough to make the evidence useful.
2Review the breakdown.
Use prerequisite skill evidence to choose support intentionally.
3Begin Unit 01.
From Unit 01 onward, normal 80% mastery progression controls advancement.

Open Diagnostic Open Unit 01

Continuity layer

Use the Readiness Bridge when prior evidence already exists.

Pre-Algebra evidence can help preselect support, while the Algebra I diagnostic confirms or adjusts that choice. The bridge also explains what Algebra I evidence will later travel into Geometry or Algebra II.

Open Readiness Bridge Read Transition Contract

Course architecture

A complete instructional cycle—not a list of topics.

Each phase has a different role. Readiness evidence guides support; lessons teach and check mastery; weekly checks preserve spaced retrieval; unit mastery validates synthesis; cumulative assessments require broader evidence.

Readiness

Week 1 diagnostic plus optional continuity evidence. Diagnostic results guide support but do not enter the course grade.

Daily Lessons

87 instructional lessons with worked reasoning, practice, error analysis, verification, and an 80% lesson gate.

Weekly Mastery

Weeks 02–36 use 10-question graded checks. Every required lesson and weekly check must reach 80% before normal progression.

Unit & Cumulative Evidence

13 unit mastery checks, a reviewed Midterm, and a reviewed Final preserve breadth, transfer, and human-reviewed reasoning.

Applied Modelling

Six laboratory experiences and the Unit 13 integrated portfolio/oral defence connect Algebra I to engineering, finance, systems, data, and decision making.

13-unit progression

The Algebra I pathway

Unit cards remain the canonical mastery-gated course sequence. The lesson directory below gives direct access only when the same evidence gates allow it.

01 · Real Numbers & Precision

Reasoning, notation, properties, units, estimation, and verification.

02 · Expressions & Polynomial Foundations

Structure, equivalence, distribution, polynomial language, and factoring foundations.

03 · Linear Equations & Models

Equality, equations, formulas, proportions, rates, and contextual models.

04 · Inequalities & Absolute Value

Solution sets, compound constraints, absolute value, tolerances, and feasible ranges.

05 · Functions & Representations

Function notation, domain/range, graphs, transformations, sequences, and piecewise rules.

06 · Linear Functions & Regression

Slope, line forms, parallel/perpendicular lines, regression, residuals, and modelling.

07 · Systems

Graphing, substitution, elimination, system classification, feasible regions, and optimization.

08 · Exponents & Exponential Functions

Exponent laws, scientific notation, sequences, growth/decay, and compound interest.

09 · Polynomial Operations & Factoring

Polynomial structure, operations, special products, factoring, zeros, and applications.

10 · Quadratic Functions & Equations

Parabolas, forms, factoring, completing the square, formula, systems, and optimization.

11 · Radical & Rational Relationships

Radicals, rational exponents, rational expressions/equations, variation, and restrictions.

12 · Statistics, Data & Evidence

Distributions, sampling, bivariate data, regression, probability, evidence, and data ethics.

13 · Integrated Modelling & Capstone

Integrated model design, sensitivity, communication, fairness, portfolio, and oral defence.

Direct instructional access

87 lessons · elegant unit drawers

Open a unit drawer to reach the exact canonical lesson files. Locks mirror the course’s existing 80% mastery authority; these buttons never create an alternate path around the progression rules.

Loading canonical lesson maps…

Find my next eligible lesson

Checking lesson access for the current learner…

Practice pathways: Foundation provides additional supports; Core develops course skills; Extended challenges deeper reasoning. Practice supports learning but does not replace required lesson, weekly, or unit mastery evidence.

Student support

Tools stay close without crowding the lesson.

Use these only when they support the mathematics. The learner should still show reasoning, units, verification, corrections, and model limitations where required.

Scientific Calculator

For numerical exploration, graphing support, and verification when the lesson permits calculator use.

Open Calculator

Archaemenes

Ask the mathematics mentor for a hint, an alternate explanation, or an error-analysis question without bypassing the required work.

Ask Archaemenes

Family & Student Records

Use the Academy profile and Family Hub for learner identity, family continuity, and supporting records outside the browser-local course evidence.

Student Profile Family Hub