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Parallel Lines Project

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Preview of AP Precalculus Unit 1 Modeling Project | The Clepsydra Challenge

AP Precalculus Unit 1 Modeling Project | The Clepsydra Challenge

Bring AP Precalculus Unit 1 to life with The Clepsydra Challenge, a hands-on modeling project where students investigate how the shape of a vessel affects the rise of water.In this real-world investigation, students collect volume-height data, create a graph, analyze changing rates of change, compare wide and narrow sections of a vessel, and connect their results to concavity, domain, range, and mathematical modeling. This project is designed to support conceptual understanding of Unit 1 topics
Preview of Combinatorics I Set Partitions I Bell Numbers I Counting Principles HS (9-12)

Combinatorics I Set Partitions I Bell Numbers I Counting Principles HS (9-12)

This advanced combinatorics project introduces Bell Numbers, set partitions, and the Fundamental Counting Principle. It balances theory, structure, and real-world problem solving. Designed for AP-style reasoning and Grade 9+ accelerated learners, it strengthens discrete math thinking. The resource is classroom-ready, accessible, and engaging. Students explore how counting extends beyond simple multiplication rules. They model and analyze set partitions using structured reasoning. Students
Preview of Calculus Part 2 Notes (Derivative, Motion, Slope Fields, Euler's, Antideriv)

Calculus Part 2 Notes (Derivative, Motion, Slope Fields, Euler's, Antideriv)

These notes cover introductions to the following topics: Derivative (basic trig and power rule)Motion (graphically and analytically)Slope FieldsTangent Lines and Euler's MethodAntiderivates/Indefinite IntegralsAntiderivatives and Initial ConditionsThese note sheets are formatted to be on 1/2 sheets of paper. They are intended to be handed out to the students so that they do not have to write everything down - not for them to cram everything on the note page. They can use them as part of their in
Preview of Instantaneous Rate of Change | Answer Key

Instantaneous Rate of Change | Answer Key

This worksheet focuses on estimating and calculating the instantaneous rate of change of functions at specific points. Students practice finding slopes of tangent lines using limits, difference quotients, and interpreting graphs or tables to approximate instantaneous rates. Problems include polynomial and quadratic functions. Ideal for deepening understanding of derivatives and preparing for calculus concepts.
Preview of Lesson Plan: Parallax and Trigonometry

Lesson Plan: Parallax and Trigonometry

Created by
Yang Li
This lesson engages high school students in understanding how trigonometry is applied to measure distances using the principle of parallax, a key method in astronomy. Students investigate how a shift in viewpoint creates a measurable angle that, combined with a known baseline, forms a triangle. By applying trigonometric functions and small-angle approximations, students calculate distances to objects, simulating the method astronomers use to determine the distance to nearby stars. Through intera
Preview of Polar Coordinates Mystery Picture

Polar Coordinates Mystery Picture

Students will practice plotting polar coordinates to create a mystery picture. Coordinates include radians, degrees, negative angles and radii, and coterminal angles. When points are plotted and connected in order, the resulting picture is a sea turtle. A link to an editable Google Doc is included.
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