A Review of the Basic Concepts of Calculus
by
Kari Meyering
Resources Needed:
Computer with Internet access for each individual or, if computer access is limited, for groups of three students, Power Point presentation or overheads outlining the basic concepts of calculus, crossword puzzle reviewing definitions, class set of Graphing Calculators, handout of limit, differentiation, and integration problems.
Exposition:
1. Using a Power Point presentation or overheads, review limits, derivatives and integrals. The students will have already learned and been tested over the material and the material should be reviewed before taking a final examination.
2. In explaining the limit, redefine and explain how students will later explore this concept more on the Internet.
3. For derivatives, reiterate the original definition and then proceed to reviewing the differentiation rules.
4. For integrals, briefly review what is an integral and the integration techniques of substitution and by parts.
5. Assign students to groups, with no more than three students to a group, and assign them to a computer. Each group should have members with the following roles: Recorder, Reporter, and Reader/Computer Controller. In these groups the students will calculate a few of the sample problems on the handout, one from each integration technique, and check their answers on the Internet.
Experience:
6. The students will begin by looking at the limit of an n-sided polygon in a circle at http://www.coolmath.com/limit1.htm
7. To continue with limits the students will explore the section on limits at http://www.netsrq.com/~hahn/calculus.html#toc. Make sure to bookmark this page as it will be revisited during the latter part of the lesson.
8. While students are working in groups on the Internet, handout the problems for limits, differentiation, and integration.
9. Assign each group a limit to compute by hand by using the definition. Then, allow them to check their answers at http://www.geocities.com/Area51/Shire/7474/calculus.html
10. Each group will then review integration techniques at http://iq.orst.edu/mathsg/integration.html
Critical Thinking:
11. Each group will read and examine one of the five examples for limits at the website in step 7.
12. Have the groups examine one of the first four examples of derivatives at the same website.
13. Each group presents their problems and solutions or findings to the class about limits and derivatives.
Interactive Learning:
14. In the cooperative groups assigned, the students will calculate the integrals of a few of the sample problems on the handout; one problem with each integration technique.
15. Then, the groups will check their answers on the Internet using The Integrator at http://integrals.wolfram.com/
Assignment:
16. Each group is responsible for finding another Internet site that relates to calculus and writing a brief description (1 paragraph) about what they learned from that site.
17. Each student will be responsible for completing the problems on the handout and the crossword puzzle.
Resources:
http://www.netsrq.com/~hahn/calculus.html
http://iq.orst.edu/mathsg/integration.html