Assessments: informal questioning quiz problem set end-of-unit test Interdisciplinary Connections: Additional Resources: Optimization problems can be applied to many practical Foerster textbook (Kendall Hunt) sections: 8-2, 8-3, 5-5 – examples (for example, finding the minimum textbook supplemental materials (explorations) amount of material needed to manufacture a can that can TI-89 graphing calculator, desmos.com hold a specific volume). selected MC/FR items from released AP exams College Board’s AP Calculus AB course description Subject: AP Calculus AB Grade: 10/11/12 Suggested Timeline: 14 42 minute periods – Unit Title: Unit 7 Integral I – Unit Overview/Essential Understanding: In this unit, students are introduced to the reverse process of differentiation finding the antiderivative (indefinite integral). Students – learn and practice several anti-differentiation rules. The definite integral is introduced as a limit of Riemann sums. Riemann sums are used as a way to not only define the definite integral, but approximate the definite integral. The unit culminates with an introduction to the first part of the Fundamental Theorem of Calculus (FTC) as a way to exactly evaluate definite integrals. Unit Objectives: Upon completion of this unit, students will demonstrate an understanding of the following topics and/or be able to do the following: find indefinite integrals using anti-differentiation rules calculate left, right, midpoint, upper, and lower Riemann sums to approximate definite integrals use the first part of the Fundamental Theorem of Calculus to evaluate definite integrals use properties of indefinite and definite integrals to evaluate integrals use algebraic manipulation and u-substitution to evaluate indefinite and definite integrals Focus Standards Addressed in this Unit: EK 3.1A1 An anti-derivative of a function f is a function g whose derivative is f – EK 3.1A2 Differentiation rules provide the foundation for finding anti-derivatives – EK 3.2A1 A Riemann sum, requires a partition of an interval I, is the sum of products, each of which is a value of the function – at a point in a subinterval multiplied by the length of that subinterval of the partition
Assessments: informal questioning quiz problem set end-of-unit test Interdisciplinary Connections: Optimization problems can be applied to many practical examples (for example, finding the minimum amount of material needed to manufacture a can that can hold a specific volume). Additional Resources: Foerster textbook (Kendall Hunt) – sections: 8-2, 8-3, 5-5 textbook supplemental materials (explorations) TI-89 graphing calculator, desmos.com selected MC/FR items from released AP exams College Board’s AP Calculus AB course description Subject: AP Calculus AB Grade: 10/11/12 Suggested Timeline: 14 – 42 minute periods Unit Title: Unit 7 – Integral I Unit Overview/Essential Understanding: In this unit, students are introduced to the reverse process of differentiation – finding the antiderivative (indefinite integral). Students learn and practice several anti-differentiation rules. The definite integral is introduced as a limit of Riemann sums. Riemann sums are used as a way to not only define the definite integral, but approximate the definite integral. The unit culminates with an introduction to the first part of the Fundamental Theorem of Calculus (FTC) as a way to exactly evaluate definite integrals. Unit Objectives: Upon completion of this unit, students will demonstrate an understanding of the following topics and/or be able to do the following: find indefinite integrals using anti-differentiation rules calculate left, right, midpoint, upper, and lower Riemann sums to approximate definite integrals use the first part of the Fundamental Theorem of Calculus to evaluate definite integrals use properties of indefinite and definite integrals to evaluate integrals use algebraic manipulation and u-substitution to evaluate indefinite and definite integrals Focus Standards Addressed in this Unit: EK 3.1A1 – An anti-derivative of a function f is a function g whose derivative is f EK 3.1A2 – Differentiation rules provide the foundation for finding anti-derivatives EK 3.2A1 – A Riemann sum, requires a partition of an interval I, is the sum of products, each of which is a value of the function at a point in a subinterval multiplied by the length of that subinterval of the partition
2017-AP-Calculus-AB-BHASD-Math-Curriculum.docx