Unit Overview
This five lesson Unit plan teaches the basics of integration. It spans from teaching students the relationship between integration to differentiation, to solving indefinite integrals, to using the fundamental theorem of Calculus. The students are assessed by taking a pretest on differentiation, doing a group project where they solve an intense definite integral, and taking a conclusive unit test. By the end of this unit, students will have the tools to tackle most integration problems. This Unit is heavy in content and the concepts build off each other, so it is essential that the students do their homework to practice the techniques the integration.
Unit Timeline
Monday:
Lesson Title: Introduction to Integration; Indefinite Integrals
Type of Lesson: Direct Instruction
Tuesday:
Lesson Title: The Fundamental Theorem of Calculus and Definite Integrals
Type of Lesson: Concept Lesson
Wednesday:
Lesson Title: The Disk Method
Type of Lesson: Multimedia Inquiry Lesson
Thursday:
Lesson Title: Finding the Area Under a Curve
Type of Lesson: Cooperative Learning Lesson
Friday:
Lesson Title: Integration by Parts
Type of Lesson: Integrative Model Lesson
Lesson Title: Introduction to Integration; Indefinite Integrals
Type of Lesson: Direct Instruction
Tuesday:
Lesson Title: The Fundamental Theorem of Calculus and Definite Integrals
Type of Lesson: Concept Lesson
Wednesday:
Lesson Title: The Disk Method
Type of Lesson: Multimedia Inquiry Lesson
Thursday:
Lesson Title: Finding the Area Under a Curve
Type of Lesson: Cooperative Learning Lesson
Friday:
Lesson Title: Integration by Parts
Type of Lesson: Integrative Model Lesson
Standards
This Unit covers the first three objectives of the third competency goal of the AP Calculus Standards.
Competency Goal 3
The learner will use integrals to solve problems.
Objectives
3.01 Explore and interpret the concept of the definite integral.
a. Compute Riemann sums using left, right, and midpoint evaluation points.
b. Find the definite integral as a limit of Riemann sums over equal subdivisions.
c. Find the definite integral of the rate of change of a quantity over an interval interpreted as the change of the quantity over the interval:
d. Identify basic properties of definite integrals.
3.02 Apply standard techniques of anti-differentiation.
- Find anti-derivatives following directly from derivatives of basic functions.
- Find anti-derivatives by substitution of variables. (including change of limits for definite integrals).
- Use the Fundamental Theorem to evaluate definite integrals.
- Use the Fundamental Theorem to represent a particular anti-derivative, and the analytical and graphical analysis of functions so defined.
Technology
Technology is a main component of this lesson plan. Here are three examples:
1) There is a Prezi I made that lists the steps of U-Substitution that would be shown during class. Click here for link to Prezi.
2) The third lesson of the five lesson unit plan will be shown on a SmartBoard using SmartBoard technology. Click here for link to Lesson Plans.
3) Calculus web applets will be used often during class to show integration graphically. Click for link to web site.
1) There is a Prezi I made that lists the steps of U-Substitution that would be shown during class. Click here for link to Prezi.
2) The third lesson of the five lesson unit plan will be shown on a SmartBoard using SmartBoard technology. Click here for link to Lesson Plans.
3) Calculus web applets will be used often during class to show integration graphically. Click for link to web site.
Differentiation
For differentiation in my lesson plans I will use multiple levels of questions, learning contracts, compacting, and flexible grouping. In the file below I will show which differentiation strategy is used in each lesson.
differentiation.docx | |
File Size: | 15 kb |
File Type: | docx |