Course contents document · Integrated Math · generated 2026-07-15

Integrated Math I (Honors)

31 core topics + 16 prerequisite topics taught as needed · approximately 12 hours of instruction including spaced review

How the course runs

An adaptive diagnostic (up to 40 questions) places the student on the course's knowledge graph — topics already known are credited, and instruction begins exactly at the learning frontier. Every topic is taught with a worked-example lesson and auto-graded practice; a topic is mastered at 75%+ and then maintained through spaced reviews on an expanding schedule. A cumulative quiz follows every 6 lessons. Prerequisite gaps below the course are detected and taught rather than skipped, so completion certifies the whole tower, not just the top.

Core curriculum

Expressions & Equations · 7 topics

Evaluating Expressions [M] Substituting a value for a variable.
Combining Like Terms [M] Adding the coefficients of matching variable parts.
The Distributive Property [M] Multiplying across a sum.
One-Step Equations [M] Undoing a single operation.
Two-Step Equations [M] Undo addition/subtraction first, then multiplication.
Multi-Step Equations [H] Equations needing distribution or variables on both sides.
Linear Inequalities [M] Solving with <, >, ≤, ≥.

Linear Functions · 10 topics

The Coordinate Plane [M] Locating points with (x, y) pairs.
Slope of a Line [M] Rise over run between two points.
Slope-Intercept Form [M] y = mx + b describes a whole line.
Finding a Line from Points [H] Reconstructing y = mx + b from data.
Systems of Equations (Substitution) [H] Two equations, two unknowns.
Elimination: A First Look [H] Add or subtract equations so one variable cancels.
Systems: Word Problems [H] Translating two facts into two equations.
Absolute Value Equations [H] Distance equations have two answers.
Arithmetic Sequences [H] Add the same amount each step.
Geometric Sequences [H] Multiply by the same ratio each step.

Geometry · 14 topics

Angle Relationships [E] Vertical, complementary, and supplementary angle pairs.
Parallel Lines & Transversals [E] Angle pairs formed when a transversal crosses parallel lines.
Triangle Angle Sum [E] The three angles of a triangle always add to 180°.
The Pythagorean Theorem [M] In a right triangle, a² + b² = c².
Distance & Midpoint [M] Measuring segments in the coordinate plane.
Similar Triangles [M] Same shape, different size: corresponding sides are proportional.
Perimeter & Area [E] Measuring around and inside basic shapes.
Circles: Area & Circumference [M] C = 2πr and A = πr².
Composite Areas [H] Adding and subtracting simple shapes to measure a complicated one.
Volume: Prisms & Cylinders [M] Volume = base area × height.
Volume: Cones, Pyramids & Spheres [M] Pointed solids hold one third of the matching prism; spheres use 4/3 πr³.
Surface Area [M] The total area of all the faces of a solid.
Special Right Triangles [H] The 45-45-90 and 30-60-90 side ratios.
Arc Length & Sector Area [H] A central angle takes the same fraction of the circumference and the area.

Prerequisite material — taught automatically when the diagnostic finds gaps

Arithmetic Foundations · 8 topics
Adding & Subtracting Whole Numbers Multi-digit addition and subtraction.
Multiplication Multiplying whole numbers.
Division Dividing whole numbers.
Order of Operations Parentheses first, then multiplication/division, then addition/subtraction.
Negative Numbers: Adding & Subtracting Working with numbers below zero on the number line.
Negative Numbers: Multiplying & Dividing Sign rules for products and quotients.
Exponents Repeated multiplication in shorthand.
Square Roots Undoing a square.
Fractions · 4 topics
Equivalent Fractions Different fractions can name the same amount.
Simplifying Fractions Reducing a fraction to lowest terms.
Multiplying Fractions Multiply straight across.
Dividing Fractions Multiply by the reciprocal.
Decimals, Percents & Ratios · 1 topics
Ratios & Proportions Two quantities that scale together.
Quadratics & Polynomials · 2 topics
Factoring Out the GCF Undoing the distributive property.
Solving x² = k Taking square roots of both sides — remembering ±.
Radicals & Exponentials · 1 topics
Simplifying Radicals Pulling perfect-square factors out of a square root.

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