Sketchpad Activities for Introducing Calculus TopicsScott Steketee
KCP Technologies, Inc.
The five activities here are suitable for introducing the main topics of a calculus course. You can either use all of the activities at the beginning of the course to give students an overview of the topics they will be covering, or you can use each activity as you introduce the particular topic covered in the activity. These activities are also useful at the end of a pre-calculus course. Pursuing these activities with The Geometer's Sketchpad will give students a hands-on introduction to the major concepts to be studied in detail during the calculus course. By actually manipulating sketches that introduce these concepts, students are more involved and find the concepts more vivid and more accessible than is possible by means of textbook or classroom explanations.
The activities are designed to be short and easy to use. Each activity includes a two-page handout containing directions for the student, a GSP sketch for students to manipulate and investigate, and notes for the teacher (including answers to the questions asked in the handout). No prior experience with Sketchpad is required for these investigations.
The first activity provides an introduction to the concept of instantaneous rate and derivative. The second and third introduce one type of integral, the definite integral. The fourth and fifth provide two different approaches to the concept of limits.
You can use the links below to download the handouts and sketches for all five activities. The handouts are available either in Adobe Acrobat Reader (.pdf) format for printing, or in Microsoft Word (.doc) format in case you want to make any modifications.
My sincere thanks to Paul Foerster for the inspiration for these activities. The first chapter of his book Calculus: Concepts and Applications provides an introduction to the big ideas that students will study throughout the year in calculus, and these Sketchpad activities are adapted from the lessons in that chapter.
I'd also like to thank the participants in the Key Curriculum Press 2003 Summer Institutes on Exploring Calculus with The Geometer’s Sketchpad and on The Geometer’s Sketchpad: Advanced Tools and Topics. Participants in both these institutes used the activities and made valuable suggestions for improving and clarifying the handouts and sketches.
Click one of the two links below to download the handouts and teacher notes for all five activities:
Click the links below to download the sketches used in the five activities:
1. Instantaneous Rate Sketch
2. One Type of Integral Sketch
3. Trapezoidal Accumulation Sketch
4. Limits with Tables Sketch
5. Limits with Delta and Epsilon Sketch
Or download all five sketches in a single archive: