Introduction
Why Take Calculus?
Calculus prepares students with ideas, concepts, and notations which allow understanding of more advanced subjects in Medicine, engineering, biochemistry, biophysics, etc... Mathematicians, scientists, and engineers use concepts of calculus in all sorts of contexts and use jargon and notations that, without your learning about calculus, would be completely inscrutable to you. The study of calculus is normally aimed at giving you the "mathematical sophistication" to relate to such more advanced subjects.
CCGPS Standards for calculus AB
Calculus should be taught in High school with same level of rigor and depth as College or University courses. The syllabus made by College Board for Advanced Placement of Calculus AB/ BC is great tool to make the curriculum decision. Below are the standards of Common Core Georgia Performance Standards for Calculus AB.
ALGEBRA
Students will investigate properties of functions and use algebraic manipulations to evaluate limits and
differentiate functions.
MCA1. Students will demonstrate knowledge of both the definition and the graphical
interpretation of limit of values of functions.
a. Use theorems and algebraic concepts in evaluating the limits of sums, products, quotients,
and composition of functions.
b. Verify and estimate limits using graphical calculators.
MCA2. Students will demonstrate knowledge of both the definition and graphical interpretation
of continuity of a function.
a. Evaluate limits of functions and apply properties of limits, including one-sided limits.
b. Estimate limits from graphs or tables of data.
c. Describe asymptotic behavior in terms of limits involving infinity.
d. Apply the definition of continuity to a function at a point and determine if a function is
continuous over an interval.
MCA3. Students will demonstrate knowledge of differentiation using algebraic functions.
a. Use differentiation and algebraic manipulations to sketch, by hand, graphs of functions.
b. Identify maxima, minima, inflection points, and intervals where the function is increasing
and decreasing.
c. Use differentiation and algebraic manipulations to solve optimization (maximum - minimum
problems) in a variety of pure and applied contexts.
DERIVATIVES
Students will investigate limits, continuity, and differentiation of functions.
MCD1. Students will demonstrate an understanding of the definition of the derivative of a
function at a point, and the notion of differentiability.
a. Demonstrate an understanding of the derivative of a function as the slope of the tangent line
to the graph of the function.
b. Demonstrate an understanding of the interpretation of the derivative as instantaneous rate of
change.
c. Use derivatives to solve a variety of problems coming from physics, chemistry, economics,
etc. that involve the rate of change of a function.
d. Demonstrate an understanding of the relationship between differentiability and continuity.
e. Use derivative formulas to find the derivatives of algebraic, trigonometric, inverse
trigonometric, exponential, and logarithmic functions.
MCD2. Students will apply the rules of differentiation to functions.
a. Use the Chain Rule and applications to the calculation of the derivative of a variety of
composite functions.
b. Find the derivatives of relations and use implicit differentiation in a wide variety of problems
from physics, chemistry, economics, etc.
c. Demonstrate an understanding of and apply Rolle's Theorem, the Mean Value Theorem.
INTEGRATION
Students will explore the concept of integration and its relationship to differentiation.
MCI1. Students will apply the rules of integration to functions.
a. Apply the definition of the integral to model problems in physics, economics, etc, obtaining
results in terms of integrals.
b. Demonstrate knowledge of the Fundamental Theorem of Calculus, and use it to interpret
integrals as anti-derivatives.
c. Use definite integrals in problems involving area, velocity, acceleration, and the volume of a
solid.
d. Compute, by hand, the integrals of a wide variety of functions using substitution.
Task
You may work individually or in groups up to four people. The presentations must be a minimum of 7 minutes and a maximum of 12 minutes. This project will count as test grade
Summarize what you have learned in AP Calculus A. You can choose to focus on either on single topic, or entire first semester topics. You have several options for this project.
- You can create a video to summarize that will be useful for future next semester.
- You can create online presentation to summarize.
- You can write a song that would teach AP Calculus AB concept and make it easier to remember (this should be performed to music; the background song would be your choice.)
- You can create a game for learning some Calculus concepts.
Process
Here are the instruction in detail you need to follow to complete your project:
- Search the Internet for how to create a video. There are several ways to capture your media. You can use video camera, digital camera, or webcam.
- You can create a PowerPoint presentation on AP Calculus AB concept learned during the semester.
- You can search online on how to create a Jeopardy game and use it to make Jeopardy game in Calculus concepts
The following websites will help you to complete your project:
- http://www.math.lsa.umich.edu/~glarose/courseinfo/calc/calcprojects.html
- http://www3.wheatoncollege.edu/tratliff/writing/calculus_II.html
- http://www.math.unl.edu/~jorr/calculus/projects/spr95proj2.html
Evaluation
Student’s work will be evaluated using the following rubric
|
|
Excellent-4 |
Good-3 |
Satisfactory-2 |
Needs Improvement-1 |
|
Content - Accuracy |
Project covers sufficient calculus content and it is accurate. There are no factual errors |
Project covers most calculus content, but there is one piece of information that seems inaccurate. |
Project covers generally calculus content, but one piece of information is clearly inaccurate. |
Project content is confusing or contains more than one factual error. |
|
Sequencing of Information |
Information is organized in a clear, logical way. It is easy to anticipate the next slide. |
Most information is organized in a clear, logical way. One slide or piece of information seems out of place |
Some information is logically sequenced. An occasional slide or piece of information seems out of place. |
There is no clear plan for the organization of information. |
|
Effectiveness |
Project includes all material needed to give a good understanding of the topic. |
Project is lacking one or two key elements |
Project is missing more than two key elements. |
Project is lacking several key elements and has inaccuracies. |
|
Use of Graphics- Table-Formula |
All graphics, tables, and formulas are attractive (size and colors) and support the topic of the presentation. |
Few graphics, tables, and formulas are not attractive but all support the topic of the presentation |
All graphics, tables, and formulas are attractive but few do not support the topic of the presentation |
Several graphics, tables, and formulas are unattractive AND detract from the content of the presentation. |
|
Spelling and Grammar |
Presentation has no misspellings or grammatical errors. |
Presentation has 1-2 misspellings, but no grammatical errors. |
Presentation has 1-2 grammatical errors but no misspellings |
Presentation has more than 2 grammatical and/or spelling errors |
|
Text - Font Choice & Formatting |
Font formats (color, bold, italic) have been carefully planned to enhance readability and content. |
Font formats have been carefully planned to enhance readability. |
Font formatting has been carefully planned to complement the content. It may be a little hard to read |
Font formatting makes it very difficult to read the material. |
|
Creativity |
Project demonstrates a high level of creativity / originality and a wide variety of media (text, picture, photo, sound, video,..) |
Project demonstrates a good level of creativity / originality and a limited variety of media (text, picture, photo, sound, video,..) |
Project demonstrates a moderate level of creativity / originality and a lack in variety of media (text, picture, photo, sound, video,..) |
Project demonstrates a poor level of creativity or originality and a lack in variety of media (text, picture, photo, sound, video,..) |
Conclusion
Calculus is the highest level of math taught in K-12. By that point, students are prepared with ideas, concepts, jargon, and notations which allow understanding of more advanced subjects in Medicine, engineering, biochemistry, biophysics, etc...
Students should take every opportunity to learn Calculus concepts that will help them to better perform in advanced subjects and teachers should encourage students in that journey.
