MA 3177: Advanced Placement Calculus AB

Subject Area

Credits 1

Years

Level

High School

This course is a study of differentiation and integration techniques with an emphasis on applications. It is equivalent to first-year calculus courses offered by many colleges and is designed for students who have completed four years of mathematics in the advanced studies program. Topics meet the requirements set forth in the syllabus of the College Board.

Parent Docs

Advanced Placement Calculus AB Parent Doc 2021-2022

Storyboard

AB Calculus AB Essential Questions: How do I become a mathematical problem solver to better understand the world around me? In what ways can I communicate and represent my mathematical thinking?
Title	Limits: Foundation of Calculus	Differentiation: Solving the Tangent Line Problem	Integration: Solving the Area Problem
Focus of the Story	Have you ever wondered exactly how fast you are traveling through a tunnel such as the HRBT? We begin our story investigating if change can happen at an instant. Through application of limits, the foundation of calculus, we are able to determine how fast we travel through the tunnel and apply the concept to solve a variety of real-world problems. !	Now that you have arrived at your destination, how did your speed in the tunnel relate to the time it takes? The distance traveled? Through the mean value theorem, we will discover the relationship between average and instantaneous rates of change leading to the discovery of differentiation and how every point contributes to the behavior of the function.	Have you ever left your house only to realize that you left something and had to turn around? As we approach the end of our story, we will consider where objects begin and end their journey and wonder about the story in between. Through integration, we find the area under any curve and how it connects to where you are and where you have been. We end our journey by applying integration to generate models of solids.
Transfer Goals	Explore: Make sense of the world mathematically by asking questions and making connections through inquiry.	Apply: Utilize effective strategies, processes, and tools to model new situations and/or real-world experiences.	Explain: Communicate mathematical thinking by justifying solutions using multiple representations while attending to precision.
Learning Targets	I can express and investigate limits in multiple ways, including graphically, numerically, and analytically. I can explore how limits will allow me to solve problems involving change and to better understand mathematical reasoning about functions.	I can apply limits to define the derivative, become skillful at determining derivatives, and continue to develop mathematical reasoning skills. I can master using the chain rule, develop new differentiation techniques, and be introduced to higher-order derivatives. I can apply derivatives to set up and solve real-world problems involving instantaneous rates of change and use mathematical reasoning to determine limits of certain indeterminate forms. I can explore relationships among the graphs of a function and its derivatives and learn to apply calculus to solve optimization problems.	I can apply limits to define definite integrals and determine how the Fundamental Theorem connects integration and differentiation. I can apply properties of integrals and practice useful integration techniques. I can solve certain differential equations and apply that knowledge to deepen my understanding of exponential growth and decay. I will make mathematical connections that will allow me to solve a wide range of problems involving net change over an interval of time and to find areas of regions or volumes of solids defined using functions.

AP Calculus AB: Assessment Matrix
Title	Unit	Rich Tasks:	Learning Target
	Unit 1: Limits and Continuity	Personal Progress Check 1 Can You Shoot Free Throws	I can express and investigate limits in multiple ways, including graphically, numerically, and analytically.
	Unit 1: Limits and Continuity	Many Coffee Beans 5-Star Uber Driver	I can explore how limits will allow me to solve problems involving change and to better understand mathematical reasoning about functions.
	Unit 2: Differentiation: Definition and Basic Derivative Rules	Personal Progress Check 2 Breaking the Sound Barrier Divide and Conquer	I can apply limits to define the derivative, become skillful at determining derivatives, and continue to develop mathematical reasoning skills.
	Unit 3: Differentiation: Composite, Implicit, and Inverse Functions	Personal Progress Check 3 How is Lindt Chocolate Made The Tangent Line Problem Calculus Round Table	I can master using the chain rule, develop new differentiation techniques, and be introduced to higher-order derivatives.
	Unit 4: Contextual Applications of Differentiation	Personal Progress Check 4 The Lovely Ladybug Birthday Balloons Close Enough is Good Enough	I can apply derivatives to set up and solve real-world problems involving instantaneous rates of change and use mathematical reasoning to determine limits of certain indeterminate forms.
	Unit 5: Analytical Applications of Differentiation	Personal Progress Check 5 Can Calculus Get You Fined? Canalysis	I can explore relationships among the graphs of a function and its derivatives and learn to apply calculus to solve optimization problems.
	Unit 6: Integration and Accumulation of Change	Personal Progress Check 6 How Much Snow Under Cover	I can apply limits to define definite integrals and determine how the Fundamental Theorem connects integration and differentiation. I can apply properties of integrals and practice useful integration techniques.
	Unit 7: Differential Equations	Personal Progress Check 7 Seeing is Believing Are you a Solution Seeker Coronavirus Spreading?	I can solve certain differential equations and apply that knowledge to deepen my understanding of exponential growth and decay.
	Unit 8: Applications of Integration	Personal Progress Check 8 Whitney’s Bike Ride Volume of a Pear Volume of a Bagel	I will make mathematical connections that will allow me to solve a wide range of problems involving net change over an interval of time and to find areas of regions or volumes of solids defined using functions.