Introduction to Accumulation of Change
Overview
To Interpret the meaning of areas associated with the graph of a rate of change in context.
Brian-Based Lesson
| Lesson Objectives:To Interpret the meaning of areas associated with the graph of a rate of change in context. | |||
| Grade: 11/12 AP CalculusTime frame: | Lesson Title: Introduction to Accumulations of Change | ||
| Brain-based Strategies Used in the Lesson: 1) Productive Struggle2) Social Interaction3) Authentic Application of Learning4) Visual Learning | Formative or Summative Assessments:Google Form with Short Answer:Using the last slide on the “Vroom” Desmos activity, how would you describe the area approximation as the limit of the width of the rectangles used approaches 0? | ||
| Prior to this lesson: What understanding and/or knowledge was taught prior? Where does this lesson fit in your unit?This lesson would serve as in introduction to the first lesson in Unit 6. From the AP Calculus AB Course Guide:“In this unit, students establish the relationship between differentiation and integration using theFundamental Theorem of Calculus. Students begin by exploring the contextual meaning of areasof certain regions bounded by rate functions. Integration determines accumulation of changeover an interval, just as differentiation determines instantaneous rate of change at a point.Students should understand that integration is a limiting case of a sum of products (areas) in thesame way that differentiation is a limiting case of a quotient of differences (slopes). Future units will apply the idea of accumulation of change to a variety of realistic and geometric applications.”Accordingly, students have extensive experience from the course with derivatives and calculating rates of change. This is the first time students begin to contend with the idea of accumulating rates of change. Students do not have any experience with summation notation prior to this unit, so a mini lesson on the notation used would occur prior to this introduction. | |||
| Materials: Include a copy of everything required to teach. Use hyperlinks when possible. You may add additional pages to the bottom of this lesson plan also. Include the assignment that students will be completing.Technology materials: (hardware, websites, video links,etc.)Student LaptopsDesmos Activity - “Vroom” - Introduction to Accumulations of ChangeCheck for Understanding Google Form | |||
| Content Core Standard: (List the standard(s) and then hyperlink it to the standards website.CHA.4.A: Interpret the meaning of areas associated with the graph of a rate of change in context.AP Calculus AB/BC Course and Exam Description | |||
| Technology used: Desmos Activity | |||
| Time | Materials | Lesson Procedures(Include the materials & technology.) | |
| 5Mins | Introduction - Sketch a Graph | IntroductionStudents complete a sketch in their notes and then share with their group. If needed, we can complete a sketch together on the board. Pose the question, “Would it be possible to figure out how far the car traveled?” | |
| 5 Mins. | Introduce New Information: (Teaching)Using the introduction activity, share out strategies for calculating how far the car traveled in the introduction question. Discuss how we will continue using rates of change to answer questions, but we will start to use rates of change in a whole new way. Discuss how in this unit, we will explore contextual meaning of areas of certain regions bounded by rate functions, and see how that leads into what is called “Integration”, which determines accumulation of change over an interval. Note that this is different than differentiation, which determines instantaneous rate of change at a point.To start to explore this, we will complete the Desmos Activity “Vroom”. | ||
| 10 Mins | Desmos Activity - “Vroom” | Hands-on Activity Steps: (Prepare ways for students to practice the new information.)Have students complete the Desmos activity in pairs. Make sure students take turns controlling the computer and discuss together as they complete the activity. | |
| 5 Mins | Feedback: (How will the students provide feedback?) Group activity? Instructor feedback?As students submit answers, review responses. Particularly, slides 6-8. Discuss as a class if necessary. | ||
| Assessment: | Assessment(s): (assignments and/or activities)Check for Understanding Google FormThis helps serve as a springboard to the next lessons, where accumulations of change are investigated further, eventually leading to the definition of a definite integral. |