This course uses a standards ­based approach to the study of calculus. The course surveys the main topics of calculus dealing with differential calculus, some integral calculus, and analytical geometry in the plane. It leans heavily on the intuitive approach with an emphasis on physical applications. Use of a graphing calculator is required. Connections to real world and cross­-curricular applications will be made

Unit 0

Pre-Calculus Review

Essential Question(s)

Standard(s) to be addressed in the Unit

  • CR2b-connect concepts and processes. 

  • CR2c-implement algebraic/computational processes. 

  • CR2d-engage with graphical, numerical, analytical, and verbal representations and demonstrate connections among them. 

  • CR2e-build notational fluency. 

  • CR2f-communicate mathematical ideas in words, both orally and in writing.

Primary Indicators

 (How will the student be able to demonstrate proficiency in their learning? These will be formally assessed.)

Transferable Skills

(What are the big picture understandings that are transferable across contexts, places, and times?)

Unit 1

Limits and Continuity

Essential Question(s)

(These are related to the enduring 

In this unit we will define limits of functions. We will evaluate limits using substitution, graphical investigation, numerical approximation,  and algebra. We will also differentiate between continuous and discontinuous graphs. 

Standard(s) to be addressed in the Unit

  • CR1a- Big Idea 1: Limits.

  • CR2a- reason with definitions and theorems. 

  • CR2b-connect concepts and processes. 

  • CR2c-implement algebraic/computational processes. 

  • CR2d-engage with graphical, numerical, analytical, and verbal representations and demonstrate connections among them. 

  • CR2e-build notational fluency. 

  • CR2f-communicate mathematical ideas in words, both orally and in writing. 

Unit 2

Differentiation

Essential Question(s)

(These are related to the enduring 

In this unit we will explore the concept of the derivative or instantaneous rate of change. We will learn different techniques of finding the derivative which include using the Power Rule, Product Rule, Quotient Rule, Chain Rule, and Implicit Differentiation.

Standard(s) to be addressed in the Unit

  • CR1b-Big Idea 2: Derivatives.

  • CR2a- reason with definitions and theorems. 

  • CR2b-connect concepts and processes. 

  • CR2c-implement algebraic/computational processes. 

  • CR2d-engage with graphical, numerical, analytical, and verbal representations and demonstrate connections among them. 

  • CR2e-build notational fluency. 

Unit 3

Applications of the Derivative

Essential Question(s)

(These are related to the enduring 

In this unit we will draw conclusions from the derivative. With the help of the derivative, we will investigate functions and sketching their graphs, We will optimize various systems and modes of operations, simplify algebraic expressions, and approximate calculations in real world situations

Standard(s) to be addressed in the Unit

  • CR1b-Big Idea 2: Derivatives.

  • CR2a- reason with definitions and theorems. 

  • CR2b-connect concepts and processes. 

  • CR2c-implement algebraic/computational processes. 

  • CR2d-engage with graphical, numerical, analytical, and verbal representations and demonstrate connections among them. 

  • CR2e-build notational fluency. 

Unit 4

Integration of Algebraic Functions*(given enough time)

Essential Question(s)

(These are related to the enduring

In this unit we explore the basic concepts of Integral Calculus.  We will utilize the necessary tools to find the area under a curve and the length of a curve. We will explore the idea of adding infinitely many infinitely small things.