Unit 1
Number Systems & Algebraic Structure
- Real and rational numbers
- Properties of operations and order of operations
- Absolute value and interval language
- Integer and rational exponents
- Radicals and numerical estimation
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School Mathematics · Grades 6–12
Algebra 1
A structured first high-school algebra pathway built around expressions, equations, linear functions, systems, quadratics, exponentials, statistics, and mathematical modeling.
Course overview
This roadmap builds the algebraic fluency and function sense students need for Geometry, Algebra 2, AP-level mathematics, and later precalculus. It emphasizes multiple representations—symbolic, graphical, tabular, verbal—and uses modeling throughout.
Math Aficionado uses this structure as a tutoring roadmap rather than a fixed school syllabus. Lessons can be reordered around the student's current unit, teacher materials, placement level, assignments, and assessment goals.
Units & topics
Unit 2
Expressions, Equations & Inequalities
- Simplifying and evaluating algebraic expressions
- Distributive property and combining like terms
- One- and multi-step equations
- Literal equations and formulas
- One-variable inequalities and compound inequalities
Unit 3
Ratios, Proportions & Linear Relationships
- Rates, unit rates and proportional reasoning
- Percent, scale and dimensional reasoning
- Proportional relationships as linear functions
- Tables, graphs, equations and verbal descriptions
- Slope as constant rate of change
Unit 4
Linear Functions & Graphs
- Function notation and input/output thinking
- Domain, range and representations
- Slope-intercept, point-slope and standard form
- Graphing and interpreting linear functions
- Piecewise and absolute-value situations
Unit 5
Systems of Linear Equations
- Graphing systems
- Substitution and elimination
- Interpreting intersections and no-solution/infinite-solution cases
- Systems of inequalities
- Applications and modeling with constraints
Unit 6
Exponents, Polynomials & Scientific Notation
- Exponent laws
- Scientific notation
- Polynomial vocabulary and degree
- Adding, subtracting and multiplying polynomials
- Special products and algebraic identities
Unit 7
Factoring & Quadratic Equations
- Greatest common factor
- Factoring trinomials and special products
- Zero-product property
- Solving quadratics by factoring
- Choosing an efficient solution method
Unit 8
Quadratic Functions
- Parabolas and key features
- Vertex and axis of symmetry
- Transformations of quadratic functions
- Completing the square
- Quadratic formula and discriminant
Unit 9
Quadratic Modeling & Complex Numbers
- Quadratic applications and projectile models
- Interpreting zeros and maximum/minimum values
- Complex-number basics and operations
- Real versus non-real solutions
- Choosing representations to solve problems
Unit 10
Exponential Functions & Growth
- Exponential growth and decay
- Geometric growth factors
- Graphs and transformations
- Compound interest and real-world growth
- Comparing linear and exponential models
Unit 11
Data, Statistics & Regression
- Univariate data and distributions
- Scatterplots and association
- Two-way tables and conditional reasoning
- Linear regression and residuals
- Interpreting model fit and limitations
Unit 12
Integrated Mathematical Modeling
- Building and validating models
- Checking assumptions and units
- Communicating solutions with evidence
- Technology-assisted exploration
- Cumulative algebra review and readiness for Algebra 2
How the roadmap is aligned
Wisconsin Standards for Mathematics (2021), especially the Grade 8 bridge and high-school Algebra/Functions/Statistics strands.
This is an independent tutoring roadmap, not an official UW–Madison or Wisconsin Department of Public Instruction course. Wisconsin standards are used as the K–12 framework; current UW–Madison course descriptions are used where the pathway overlaps with college-level precalculus and calculus preparation.
Wisconsin Standards for Mathematics (2021) · UW–Madison Mathematics Course Guide
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