Course Overview
We cover everything in the Calculus AB topic outline as it appears in the AP Calculus Course Description, including integration by parts.
The primary textbook is Calculus of a Single Variable, 6th ed. by Larson Hostetler Edwards. The two stated objectives of this course are that the students do well on the AP Exam and in subsequent courses. Consequently, there is an attempt to balance understanding, skills, and the use of technology.
Course Planner
Below is the sequence of our AP Calculus AB course.
First Semester AP Calculus AB
Section Numbers Topics Timeline
Chapter P
P1 Graphs and Models (1day)
P2 Linear Models and Rates of Change (1 day)
P3 Functions and Their Graphs (2 days)
Chapter 1
1.1 Limits and Their Properties (1day)
1.2 Finding Limits graphically and numerically (2 days)
1.3 Evaluating Limits analytically (2 days)
1.4 Continuity and One-Sided Limits (1.5 days)
Chapter 2
The Idea of the Derivative (1.5 days)
2.1 The Derivative and the Tangent Line Problem (1day)
2.2 Basic Differentiation Rules and Rates of Change (2 days)
2.3 The Product and Quotient Rules and Higher-Order Derivatives (3 days)
2.4 The Chain Rule (2.5 days)
2.5 Implicit Differentiation (4 days)
2.6 Related Rates (3 days)
Chapter 3
3.1 Extrema on an Interval (2 days)
3.2 Rolles Theorem and the Mean Value Theorem (2 days)
3.3 Increasing and Decreasing Functions and the First Derivative Test (2 days)
3.4 Concavity and Second Derivative Test (2.5 days)
3.5 Limits at Infinity (2 days)
3.6 A summary of Curve Sketching (1.5 days)
3.7 Optimization Problems (3 days)
3.8 Newtons Method (2 days)
3.9 Differentials (2.5 days)
Chapter 4
4.1 Antiderivative and Indefinite Integration (4 days)
4.2 Area (2 days)
4.3 Riemann Sums and Definite Integrals (3 days)
4.4 The Fundamental Theorem of Calculus (2 days)
4.5 Integration by Substitution (3 days)
4.6 Numerical Integration (2 days)
Second Semester AP Calculus AB
Chapter 5
5.1 The Natural Logarithmic Function and Differentiation (1.5 days)
5.2 The Natural Logarithmic Function and Integration (1.5 days)
5.3 Inverse Functions (2.5 days)
5.4 Exponential Functions: Differentiation and Integration (2 days)
5.5 Bases Other than e and Applications (2 days)
5.6 Differential Equations: Growth and Decay (1.5 days)
5.7 Differential Equations: Separation of Variables (3 days)
6.1 Slope Fields and Eulers Method (2.5 days) (Larson Hostetler, 8th ed. Pg 404)
Chapter 6
6.1 Area of a Region Between Two Curves (3 days)
6.2 Volume: The Disc Method (3 days)
6.3 Volume: The Shell Method (3 days)
6.4 Arc Length and Surfaces of Revolution (3 days)
After the AP Exam
Section Numbers Topics Timeline
7.1 Basic Integration Rules 2 days
7.2 Integration by Parts 2 days
7.3 Trigonometric Antiderivatives 2 days
7.4 Trigonometric Substitutions 2 days
Teaching Strategies
Concept presentation consists of the following pedagogical features.
Glossary (key terms to learn)
Topic overview or explanation
Context of the topic is set with other subtopics
Worked problems, examples
Text
Graphics
Problems to work
Reading assignments: textbook, articles, web links
Group or team projects
For about 50 percent of our students, Calculus AB is the first course that they take from our honors track. For these students, the expectations are considerably higher than they had been up to this point. A complete tentative schedule, clearly showing the target day of the AP Exam, is given to students on day one. The teacher tries to be seen as a coach, with the student and coach working together toward a common goal of doing well on the AP Exam. The following assessment methods are provided:
Post-assessments for each unit of study.
Pre-assessments for larger or cumulative units of study.
Post-assessments for larger or cumulative units of study.
Continuous assessments throughout the content presentation.
Mid-term and final assessments.
Group or collaborative projects.
Technology and Computer Software
Teachers use TI-83 and TI-84 graphing calculators for presentations. Almost all students use one of these two calculators.
Student Evaluation
Tests represent 60 percent of the 9 weeks grade. Quizzes, projects, writings, and other activities represent the remaining 40 percent of the 9 weeks average. The final exam represents 40 percent of the semester grade. Homework is awarded a score based on each individual teachers preference. Quizzes vary depending on the teacher, but tests tend to be the same for everyone who teaches a particular course. On about half of the tests, students are allowed to use a calculator. As early as possible in the course, teachers try to incorporate multiple-choice practice problems. The semester final and mock AP Exams use multiple-choice questions that follow the format of the AP Exam. Questions from previous AP Exams strongly influence assessment during the year. This course includes multiple high-quality tools for learners to track their progress: a traditional online grade book, a pace chart, and a study plan. The pace chart provides both traditional and accelerated timelines for completing the course. Students are instructed to print out the pace chart and fill in the target and actual completion dates for each chapter. The study plan is displayed as a table that lists specific assignments and suggested timelines for completing each lesson.
Teacher Resources
Larson, Hostetler, Edwards. Calculus of a Single Variable. 6th ed. Boston: Houghton Mifflin, 1998.
Larson, Hostetler, Edwards. Calculus of a Single Variable. 8th ed. Boston: Houghton Mifflin, 2006.
http://www.clcmn.edu/kschulte/mathworksheets.html#Geometry
http://www.pen.k12.va.us/Div/Winchester/jhhs/math/lessons/calculus/workderv.html
http://www.mathematicshelpcentral.com/lecture_notes/calculus_2_folder/differential_equations_and_notation.htm
Technology Resources
http://education.ti.com/educationportal/activityexchange/Activity.do
In all of our calculus sections, graphing calculators play a major role in both teaching and learning. Students are required to have a graphing calculator. The TI-83 Plus is strongly recommended for Calculus AB.
Student Activities
Exercises, projects, and activities provide effective, additional learning experiences that are related to the primary course content. Each instructional unit is built around lessons, activities, explorations, worksheets, and assessments. The explorations and activities relate directly to the lesson ideas being covered. The worksheets are also aligned with the lesson topics. Each chapter requires students to work a free-response question from previous AP Exams. These problems are selected to match with the lessons of the chapter. The course does a very good job of reviewing both content and test preparation for the AP Exam. Students are told all the necessary information they need to understand how the test is constructed and what form their responses must take. Students are given multiple choice and free-response questions in an AP format. This is an excellent preparation for the actual exam and should increase student confidence. There are an appropriate number of interactive exercises, activities and projects available to students. These include self-testing activities, as well as activities that students are required to complete and submit for instructor review, comment, or grading. The course includes excellent applets that allow students to manipulate graphs to see how changing a parameter can change the problem.
AP Calculus (Week of January 22 - 25)
Test over Sections 4.5/4.6(Numerical Integration/Integration by Substitution)
Chapter 5
5.1 The Natural Logarithmic Function and Differentiation
5.2 The Natural Logarithmic Function and Integration
5.3 Inverse Functions
5.4 Exponential Functions: Differentiation and Integration
Kendrick High School
Informal Geometry
Lesson Plans
Please respond to each question by writing your plans next to each bullet. Keep in mind the new thrust of multiple assessments vs. grading should be used to determine mastery.
1. What do you want students to know and be able to do? ( the objective)
Identify segments and lines related to circles.
Use properties of arcs, tangents, and chords of circles
Use inscribed angles to solve problems
Use angles formed by tangents and chords to solve problems
Find the lengths of segments of chords
Write equations of circles
2. How will you know when students have achieved question number one? ( the assessment/evaluation)
Homework discussions/whiteboard explanations
Homework quizzes
Student feedback
Group activities
Chapter reviews
Chapter tests
3. What are your best strategies for the learner to achieve question number one? (the activities)
Check homework daily
Quiz students on the topics discussed the previous day
Get the students involved in the lesson through student feedback/classroom activities
Mandatory study hall for those students who fall below 70%
4. How do you plan to incorporate writing across the curriculum in this lesson?
Students will write a reflective essay. In this essay, students will reflect on what they have learned and some of their strengths and weaknesses.
5. What standard(s) or QCCs did you target this week?
QCC # 30, 31, 33
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