Athletic Algebra (MATH 100: Elementary Algebra)
Undergraduate course, Southern Virginia University, 2026
MATH 100 is the lowest-level mathematics course we offer at SVU — essentially a first course in algebra, and for many students the course standing between them and everything else. A large share of the students are athletes, and a large share arrive having had genuinely bad experiences with mathematics.
I rebuilt the course around a single analogy: learning mathematics is mental conditioning, and it works the way athletic training works. Many students believe math ability is something you are born with, and that belief makes the subject far harder than it actually is. An athlete, though, already knows what it feels like to be bad at something and then get good at it through repetition. A quarterback reads a defense and chooses an action in a couple of seconds — not because of talent alone, but because that judgment has been conditioned. I argue that mathematical thinking develops the same way, and then I run the class like a practice instead of a lecture.
How a class period is structured
Students work from a PDF packet on their iPads. Every packet has the same five parts, in the same order, so the rhythm of the class becomes predictable:
- Warm-up — a timed, scored 3×3 grid of review problems drawn from topics I select. This is where fluency gets built. We start with the multiplication tables, which pays off in every later topic.
- Drills — short, focused work on atomic skills: adding and subtracting fractions, factoring integers, simplifying fractions, translating English into mathematical expressions, setting up an equation from context, solving by inverse operations. Drill stations go up around the room and students rotate between them, working on whiteboards and pasting screenshots of their work into the packet.
- Install — the whole-class segment where the day’s concept goes in. I present both the procedure and the reasoning underneath it, and work demonstrations.
- Small-group practice — students keep working at the boards together.
- Extra practice — additional problems to take away.
At the end of class students score their own work and submit the completed packet, which my TA audits.
Scrimmages are the assessment analogue: game-styled problem sets, issued in several parallel forms (Crimson, White, Gray). Games are the larger take-home rounds. The framing is deliberate — measured, frequent improvement is motivating in a way that a single midterm is not.
The packets are generated automatically by a Python script, which is what makes freshly randomized warm-ups and per-form scrimmages practical to run every class.
Course documents — Fall 2026
The course follows OpenStax Elementary Algebra 2e, which is free to students.
Installs
The concept notes for each section — the whole-class segment of the packet.
Chapter 1
- 1.5 — Visualize Fractions
- 1.6 — Add and Subtract Fractions
- 1.7 — Decimals
- 1.8 — The Real Numbers
- 1.9 — Properties of Real Numbers
- 1.10 — Systems of Measurement
Chapter 2
- 2.1 — Solve Equations Using the Subtraction and Addition Properties of Equality
- 2.2 — Solve Equations using the Division and Multiplication Properties of Equality
- 2.3 — Solve Equations with Variables and Constants on Both Sides
- 2.4 — Use a General Strategy to Solve Linear Equations
- 2.5 — Solve Equations with Fractions or Decimals
- 2.6 — Solve a Formula for a Specific Variable
- 2.7 — Solve Linear Inequalities
Chapter 3
- 3.1 — Use a Problem-Solving Strategy
- 3.2 — Solve Percent Applications
- 3.3 — Solve Mixture Applications
- 3.4 — Solve Geometry Applications
- 3.5 — Solve Uniform Motion Applications
- 3.6 — Solve Applications with Linear Inequalities
Chapter 4
- 4.1 — Use the Rectangular Coordinate System
- 4.2 — Graph Linear Equations in Two Variables
- 4.3 — Graph with Intercepts
- 4.4 — Understand Slope of a Line
- 4.5 — Use the Slope-Intercept Form of an Equation of a Line
- 4.6 — Find the Equation of a Line
- 4.7 — Graphs of Linear Inequalities
Chapter 6
- 6.1 — Add and Subtract Polynomials
- 6.2 — Use Multiplication Properties of Exponents
- 6.3 — Multiply Polynomials
- 6.4 — Special Products
- 6.5 — Divide Monomials
- 6.6 — Divide Polynomials
- 6.7 — Integer Exponents and Scientific Notation
Warm-ups
Sample timed warm-ups. Each is a randomly generated grid of review problems, so no two are alike.
- Warm-up 1.5 — Visualize Fractions
- Warm-up 1.6 — Add and Subtract Fractions
- Warm-up 1.7 — Decimals
- Warm-up 1.8 — The Real Numbers
Scrimmages
Parallel forms of the same scrimmage, so neighbors are not working identical problems.
Drill bank (Spring 2026)
The complete set of drill sheets from the previous run of the course. A variant is a second sheet covering the same skills with different problems.
- Drills 1.1 — Introduction to Whole Numbers
- Drills 1.1 — Introduction to Whole Numbers (variant)
- Drills 1.2 — Use the Language of Algebra
- Drills 1.2 — Use the Language of Algebra (variant)
- Drills 1.3 — Add and Subtract Integers
- Drills 1.3 — Add and Subtract Integers (variant)
- Drills 1.4 — Multiply and Divide Integers
- Drills 1.4 — Multiply and Divide Integers (variant)
- Drills 1.5 — Visualize Fractions
- Drills 1.6 — Add and Subtract Fractions
- Drills 1.7 — Decimals
- Drills 1.7 — Decimals (variant)
- Drills 1.8 — The Real Numbers
- Drills 1.9 — Properties of Real Numbers
- Drills 1.10 — Systems of Measurement
- Drills 2.1 — Solve Equations Using the Subtraction and Addition Properties of Equality
- Drills 2.2 — Solve Equations using the Division and Multiplication Properties of Equality
- Drills 2.3 — Solve Equations with Variables and Constants on Both Sides
- Drills 2.4 — Use a General Strategy to Solve Linear Equations
Atomic-skill drills
