Unit Plan
Richland Community College

Richland Community College: Parametric Equations

For Students 11th - 12th
This is a discussion of how to graph parametric equations, how to enter them into your calculator, and how to eliminate the parameter. The site has examples to help clarify the concept of eliminating the parameter.
Handout
Wolfram Research

Wolfram Math World: Parametric Equations

For Students 9th - 10th
Read a short explanation of parametric equations and how they differ from other kinds. Also provides a diagram and a bibliography.
Whiteboard
ClassFlow

Class Flow: Parametric Equations and Further Graphing

For Teachers 9th - 10th Standards
[Free Registration/Login Required] Excellent diagrams, including the Ferris wheel, depict parametric equations and their related graphs.
Activity
Varsity Tutors

Varsity Tutors: Hotmath: Practice Problems: Parametric Equations and Projectile Motion

For Students 9th - 10th
Six problems offer practice working with parametric equations and projectile motion. They are given with each step to the solution cleverly revealed one at a time. You can work each step of the problem then click the "View Solution"...
Lesson Plan
Alabama Learning Exchange

Alex: Jump!!! An Exploration Into Parametric Equations

For Teachers 9th - 10th
Young scholars will use vectors and parametric equations to determine the velocity that they should jump out of the window of a burning building in order to land safely into the rescue net. They will work in small groups and utilize...
Interactive
Shodor Education Foundation

Shodor Interactivate: Parametric Graph It

For Students 9th - 10th Standards
This activity allows the user to plot ordered pairs and parametric equations on the same coordinate plane.
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Math Graphs

Houghton Mifflin: Math Graphs: Parametric Equations 1 [Pdf]

For Students 9th - 10th Standards
Learners explore the graph of a line given by a parametric equation. Topics explored are the orientation and coordinates of the equation. The exercise consists of an enlarged printable version of a graph available in PDF format.
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Math Graphs

Houghton Mifflin: Math Graphs: Parametric Equations 2 [Pdf]

For Students 9th - 10th Standards
Students explore the graph of a line given by a parametric equation. Topics explored are the orientation and coordinates of the equation. The exercise consists of an enlarged printable version of a graph available in PDF format.
Activity
Mathematics Archives

Math Archives: Visual Calculus: Families of Parametric Equations

For Students 9th - 10th
This site gives an example of parametric equations. The site also gives an animation of how the curve is drawn. Requires the use of Live-Math plug-in, which is free.
Graphic
Other

Lake Tahoe Community College: Parmetric Equations

For Students 9th - 10th
Parmametric equations are explained by finding the parametric equation of a line giving two points on a line.
Unit Plan
Duke University

Duke University: Parametric Surface Area and Vector Product

For Students 9th - 10th
This site walks through how to find the surface area of a torus given its parametric equation. The site gives wonderful visual aids to help the reader understand the steps. Follow the link to the following page for a summary.
Activity
Texas Instruments

Texas Instruments: Numb3 Rs: Fresh Air and Parabolas

For Teachers 9th - 10th
Based off of the hit television show NUMB3RS, this lesson examines a plane crash, and gets students to try to find the location of various pieces of wreckage. This is done using parametric equations which form a parabolic trajectory....
Website
National Council of Teachers of Mathematics

The Math Forum: Ask Dr. Math: Ellipse or Circle? Parametric Equation

For Students 9th - 10th Standards
Dr. Math, in reply to a student question, shows how a specific pair of parametric equations produces a circle as opposed to an ellipse.
Activity
Texas Instruments

Texas Instruments: Parametric and Polar Graphing

For Teachers 9th - 10th
Here's an activity to use to teach students how to use the TI-86 graphing calculator to graph functions in parametric or polar modes. Calculator keystroke instructions and calculator screenprints are given in this student activity.
Whiteboard
ClassFlow

Class Flow: Pre Calculus Parametric Equations

For Teachers 9th - 10th
[Free Registration/Login Required] Students interactively explore parametric equations.
Activity
Khan Academy

Khan Academy: Bonus: Equations From De Casteljau's Algorithm

For Students 9th - 10th
Challenge question: can you work out the equations for n-degree curves generated by de Casteljau's algorithm?
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Khan Academy

Khan Academy: Parametric Ray Intuition

For Students 9th - 10th
This is a seven-question quiz/practice review the parametric representation of a ray.
Handout
Johan Claeys

Math Abundance: The Circle: Basic Concepts

For Students 9th - 10th Standards
Goes over the equation of a circle, parametric equations of a circle, intersection of circle and line, tangent line in a point of a circle, etc.
Activity
Texas Instruments

Texas Instruments: Numb3 Rs: The Great Escape

For Teachers 9th - 10th
Based off of the hit television show NUMB3RS, this activity introduces students to the concept of parametric equations. Using such equations, students model (on their graphing calculator) a scenario which questions whether a vehicle...
Activity
Texas Instruments

Texas Instruments: Numb3 Rs: Trawling for an Intersection

For Teachers 9th - 10th
Based off of the hit television show NUMB3RS, this lesson is designed to draw a connection between polar and parametric equations, as well as to expose students to the Trawler Problem (involving a fast boat chasing a slower boat which...
Activity
Texas Instruments

Texas Instruments: Crawling Around: Parametric Plots

For Teachers 9th - 10th
In this activity, students' will record the x- and y-coordinates of a rod moving in a figure-eight pattern. They will then use the recorded motion information to separately model the x- and y-motion as a function of time. They will plot...
Activity
Texas Instruments

Texas Instruments: Vectors and Projectile Motion on the Ti 89

For Teachers 9th - 10th Standards
Students will study various properties of projectile motion by showing how the calculator manipulates three dimensional vectors, deriving the standard equations of motion for projectile motion, and applying these equations to 1st and 2nd...
Activity
Richland Community College

Richland Community College: Math 116 Lecture Notes

For Students 9th - 10th Standards
This site from the Richland Community College provides the detailed lecture notes to a college algebra course, complete with equations and definitions. Content ranges from "functions and their graphs" to "conics and parametric equations."
Handout
Wolfram Research

Wolfram Math World: Ellipsoid

For Students 9th - 10th
This site from Math World begins with a picture of an ellipsoid and then gives cartesian and parametric equations for the surface. The site gives much more information for the ellipsoid, including special ellipsoids, a surface area...

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