Programs Calculus Project-based Learning Resources
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AP Calculus BC Polar Design Project (Taylor and Maclaurin series also included)
Polar Design Project – AP Calculus BC End-of-Year Project (Includes Series, Derivatives & Integrals)Bring creativity into your AP Calculus BC classroom with this engaging Polar Design Project that combines art, calculus, and real understanding! Students create a unique design using polar equations and analyze it using key BC concepts such as: Area between polar curves (definite integrals) Slope of tangent lines in polar form (derivatives) Taylor/Maclaurin series (local approximation) This
11th - 12th, Higher Education
Calculus, Math Test Prep, Other (Math)
Threads & Trends: Build a T-Shirt Company with Calculus
Turn your classroom into a business lab with this engaging end-of-year AP Calculus AB project! In Threads & Trends, students create their own T-shirt company and use calculus to make real business decisions. They’ll build cost, revenue, and profit functions, use derivatives to maximize profit, graph their models, and make data-driven recommendations like real entrepreneurs. This project blends optimization, derivatives, modeling, and business applications into a creative, real-world challenge
11th - 12th
Calculus, Engineering, Math Test Prep
Optimization Volume Project for Calculus
This project is for Calculus after students have mastered Optimization using derivatives. It is a hands-on activity in which students will find the minimum surface area of different geometric objects given a specific volume and then build the object. It includes worked out solutions for multiple geometric objects so that every student can do a different object. It culminates with a day to fill the objects with candies to see how close their object is to the set volume. Great project!
12th, Higher Education
Calculus
Investigate Newton's Law of Cooling
This calculus activity on Newton's Law of Cooling is fun, hands-on, and effective in reinforcing knowledge and practice of differential equations. The activity ties into multicultural themes of food and drink from around the world. Included is the activity and answer key.
12th
Calculus
AP Calculus Project: Roller Coaster with Piecewise Functions & Derivatives
Engage your AP Calculus students after the exam with this hands-on and creative project! Students design a mathematically valid roller coaster using piecewise functions that are continuous and differentiable at each transition point. They must graph the coaster, build a 3D model, and provide formal mathematical proofs of continuity and differentiability. Perfect for: AP Exam wrap-up weeks Summative assessments Honors Calculus projects Includes: Full student instructions Grading rubric Proof
10th - 12th
Calculus
AP Calculus BC “Tough Stuff” Project | Review & Concept Mastery Activity
Looking for a meaningful way to help your AP Calculus BC students review challenging concepts while building confidence before the exam? This FREE “Tough Stuff” Project is a student-centered activity that encourages deeper understanding, ownership of learning, and peer teaching—all essential for success in AP Calculus BC. Students identify a concept they find difficult, learn it more deeply, and then teach it in a clear and engaging way. This project is perfect for pre-exam review, post-unit r
9th - 12th
Calculus, Math Test Prep, PreCalculus
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.
9th - 12th, Higher Education
Calculus, Graphing, PreCalculus
Investigate Derivative Applications: Multicultural and Global Connections
These exciting, multicultural math activities provide learners the opportunity to to apply their knowledge of the derivative to diverse and relevant global issues. This bundle includes student worksheets, reflection questions, extension activities, and answer key.
12th
Calculus
CCSS
HSA-APR.B.3
, HSF-IF.B.4
, HSF-IF.B.6
+1
Investigate Related Rates Through Polynesian Ocean Navigation
This exciting, multicultural math activity expands students' knowledge and application of related rates in calculus through real-world exploration . Includes student worksheet, reflection questions, and answer key.
12th
AAPI History, Calculus
CCSS
HSF-IF.B.6
, HSG-SRT.C.6
, HSG-SRT.C.8
Investigate Optimization: The Granary of Bamileke
This exciting, multicultural math activity expands students' knowledge and application of optimization methods in calculus. Includes student worksheet, optional extension activity, and answer key.
12th
Calculus
CCSS, NGSS
HSA-APR.A.1
, HSA-APR.B.3
, HS-ETS1-2
+3
Investigate Second Derivative Test and Concavity Through Navajo Weaving
This exciting, multicultural math activity expands students' knowledge and application of the second derivative test and concavity in calculus. Includes student worksheet, reflection questions, and answer key.
12th
Calculus, Native Americans
CCSS
HSA-APR.B.3
, HSF-IF.B.6
, HSF-IF.C.7
+1
Investigate Curves: The Spread of Disease in Marginalized Communities
This relevant, multicultural math activity expands students' knowledge and application of curve analysis in calculus by exploring the spread of disease in marginalized communities. Includes student worksheet, reflection questions, and answer key.
12th
Calculus, Health
CCSS, NGSS
HSA-APR.B.3
, HSF-IF.B.6
, HSF-IF.C.7c
+6
Investigate The First Derivative Test: Environmental Justice Among the Adivasi
This relevant, multicultural math activity expands students' knowledge and application of the first derivative test in calculus by exploring issues of environmental justice among India's Adivasi. Includes student worksheet, reflection questions, and answer key.
12th
Asian Studies, Calculus, Environment
CCSS
HSF-IF.B.6
, HSF-IF.C.7c
, HSF-IF.C.9
Investigate Newton's Method Through Nubian Architecture
This exciting, multicultural math activity expands students' knowledge and application of Newton's method for finding derivatives in calculus. Includes student worksheet, reflection questions, and answer key.
12th
African History, Calculus
CCSS
HSA-APR.B.3
, HSF-IF.B.4
, HSF-IF.B.6
+2
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