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| IMSA Math Home | Workshop Information |
We want to share a collection of short activity sheets that we have written for use in our own classes. These are designed to introduce concepts, and most may be used easily within the context of your own course and your own textbook. They lead students through various steps to develop the ideas. Most activities will benefit from help from the teacher - some activities more than others - but the goal is to get the students to do the math themselves. We firmly believe that's how students learn best.
Each of the activities below may be downloaded in Adobe Acrobat PDF format so they may be printed clearly from any platform. All include a page of notes for teachers, including purposes, prerequisites, and a few other thoughts. Technology is assumed, so it is rarely mentioned specifically.
For Algebra, Pre-Calculus, and Calculus Activities, see below on this page.
 For Mathematica notebooks and activities, click here to go to another page.
Questions, comments, and suggestions are welcome! Please send them to Ruth Dover.
| Algebra and Precalculus | Calculus |
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| Definition of Logs: | A first introduction and definition.
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Polynomial: Power Functions: | A quick exploration of functions of the form y = xn.
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Polynomial: Quadratic Parameters: | Look at y = ax2 + bx + c. Of the parameters a, b, and c, keep two constant while changing the third. What happens to the vertices of the resulting parabolas? Some interesting patterns!
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Polynomials: Definition: | A statement of definition plus some beginning ideas on roots and how the degree relates to the graph of a polynomial. (Got Mathematica? Check out the notebook below.)
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Polynomials: "Pass Through" and "Bounce" Points: | What happens to the graph of y = (x - 2)(x + 1)(x - 4) when it becomes
y = (x - 2)2 (x + 1)3 (x - 4)4 ?
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 Polynomial: Bounce Points: | A Mathematica notebook which allows students to explore the graphs in the previous two activities. No previous experience with Mathematica is necessary.
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Reciprocals of Power Functions - 1/xn: | A quick exploration of functions of the form y = 1/xn. (Did you notice the activity above on Power Functions?)
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Reciprocals of Parabolas: | What does the graph of the reciprocal of a parabola look like?
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Slopes and Tangents: | An introduction to the tangent function along with a connection to the angle of inclination of a line.
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Trigonometric Reciprocals: | An introduction to secants, cosecants, and cotangents as reciprocal functions. (Did you notice the activity above on rational functions - the reciprocal of a parabolic function?)
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Law of Cosines: | Lead students through a derivation and then do some problems.
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Law of Sines: | A little measurement, a proof, and a few problems.
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| Derivatives - Exponential Functions | Introduce derivatives of exponential functions early. Let your students see that the rule for differentiation is reasonable. |
| Derivatives of y = f(kx) | This is a very simple introduction to the chain rule. It considers the special cases of functions of the form y = b(kx) and y = sin(kx), where k is a constant. |
| Newton's Method | An introduction to Newton's Method, having students go through the steps once, then leading them through the formula and a quick calculator program. |
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