Unit Objectives: Upon completion of this unit, students will demonstrate an understanding of the following topics and/or be able to do the following: identify when to use implicit differentiation apply implicit differentiation simplify differentiated implicit relations and express these derivatives strictly in terms of x and y find 2nd order derivatives of implicit relations accurately translate English to appropriate calculus variables within the context of related rates problems solve problems involving related rates Focus Standards Addressed in this Unit: EK 2.2A2 Key features of functions and their derivatives can be identified and related to their graphical, numerical, and analytical – representations EK 2.1C5 The chain rule is the basis for implicit differentiation – EK 2.3C2 The derivative can be used to solve related rates problems, that is, finding a rate at which one quantity is changing by – relating it to other quantities whose rates of change are known EK 2.3D1 The derivative can be used to express information about rates of change in applied contexts – Important Standards Addressed in this Unit: EK 2.1A4 - For , notations for the derivative include and EK 2.3A1 The unit for is the unit for f divided by the unit of x – Misconceptions: Related problems tend be one of the toughest areas for students. Many students report that they simplify have difficulty determining what the problem is asking. Teaching a slow, methodical approach to solving problems helps. Concepts/Content: Competencies/Skills: Description of Activities: implicit differentiation differentiate implicit relations teacher led direct instruction related rates identify given rates question & answer translation identify unknown check/review HW problems warm-up / exit ticket questions quiz problem set end-of-unit test specific example of activity water “blue leaking from funnel demonstration” goes – along with the classic related rates problem involving water leaking from a cone-shaped container Assessments: informal questioning quiz
Unit Objectives: Upon completion of this unit, students will demonstrate an understanding of the following topics and/or be able to do the following: identify when to use implicit differentiation apply implicit differentiation simplify differentiated implicit relations and express these derivatives strictly in terms of x and y find 2nd order derivatives of implicit relations accurately translate English to appropriate calculus variables within the context of related rates problems solve problems involving related rates Focus Standards Addressed in this Unit: EK 2.2A2 – Key features of functions and their derivatives can be identified and related to their graphical, numerical, and analytical representations EK 2.1C5 – The chain rule is the basis for implicit differentiation EK 2.3C2 – The derivative can be used to solve related rates problems, that is, finding a rate at which one quantity is changing by relating it to other quantities whose rates of change are known EK 2.3D1 – The derivative can be used to express information about rates of change in applied contexts Important Standards Addressed in this Unit: EK 2.1A4 - For , notations for the derivative include and EK 2.3A1 – The unit for is the unit for f divided by the unit of x Misconceptions: Related problems tend be one of the toughest areas for students. Many students report that they simplify have difficulty determining what the problem is asking. Teaching a slow, methodical approach to solving problems helps. Concepts/Content: implicit differentiation related rates translation problems Competencies/Skills: differentiate implicit relations identify given rates identify unknown Description of Activities: teacher led direct instruction question & answer check/review HW warm-up / exit ticket questions quiz problem set end-of-unit test specific example of activity “blue water leaking from funnel demonstration” – goes along with the classic related rates problem involving water leaking from a cone-shaped container Assessments: informal questioning quiz
2017-AP-Calculus-AB-BHASD-Math-Curriculum.docx