Topic
High school
15 articles on high school: the maths or physics explained, ready-to-teach lesson plans, and how to build each slide in Tracé.
Why 45° Is the Best Launch Angle (and When It Isn’t)The proof that 45° gives the longest throw, why 30° and 60° land in the same place, and why real throws use less: launch height and air resistance.
The Unit Circle Lesson: Where Sine and Cosine Come FromA unit circle lesson plan: sine and cosine as coordinates, special angles, signs in each quadrant, the sine wave unrolled, common mistakes and checks.
Free-Body Diagrams and Newton’s Second Law: A Lesson PlanHow to teach free-body diagrams step by step, a worked example (30 N push, 10 N friction, 5 kg: a = 4 m/s²), the classic mistakes and check questions.
Solving Quadratic Equations by Factoring: Lesson PlanSolve quadratic equations by factoring: the zero-product rule, the product–sum method, a worked example, common mistakes and checks, with the graph alongside.
Graphing Quadratic Functions in Vertex Form: Lesson PlanTeach vertex form y = a(x − h)² + k: what a, h and k do to a parabola, completing the square, the sign trap with h, and live sliders to explore it.
The Derivative as the Slope of a Tangent: Lesson PlanIntroduce the derivative as the slope of the tangent line: secants that shrink, the limit (f(x+h) − f(x))/h, a worked example with x², mistakes and checks.
Riemann Sums: Teaching the Area Under a CurveA Riemann sums lesson: left, right and midpoint rectangles under y = x², exact numbers for 8 rectangles, how the error shrinks, mistakes and checks.
Exponential Growth and Decay: A Lesson PlanTeach exponential growth and decay with y = a·bˣ: doubling, half-life, compound interest, why exponential beats x², common mistakes and check questions.
Solving Systems of Equations by Graphing: Lesson PlanTeach systems of linear equations by graphing: the intersection as the solution, one, none or infinitely many solutions, substitution as a check, and mistakes.
Adding Vectors Head to Tail: A Lesson PlanTeach vector addition: head-to-tail drawings, adding components, the magnitude with Pythagoras, a river-crossing example, common mistakes and checks.
The Simple Pendulum Period: T = 2π√(L/g) Lesson PlanTeach the simple pendulum period formula T = 2π√(L/g): what changes the period and what does not, the small-angle limit, worked examples and checks.
Wave Speed, Frequency and Wavelength: v = fλ LessonTeach the wave equation v = fλ: wavelength, frequency, period and amplitude on one animated wave, examples with sound and light, mistakes and checks.
Circular Orbits and Gravity: Why Satellites Don’t FallA lesson on circular orbits: gravity as the centripetal force, orbital speed v = √(GM/r), the ISS at 7.7 km/s and 92 minutes, geostationary orbit, and mistakes.
Ohm’s Law and Simple Circuits: A Lesson PlanTeach Ohm’s law V = IR with a live circuit: current, voltage, resistance, series and parallel resistors, power, the classic misconceptions and checks.
Fractals in the Classroom: Koch, Sierpinski, MandelbrotThree fractals that hook a class: the Koch snowflake step by step, the Sierpinski triangle and the Mandelbrot set, with the maths behind each.