Assignments Page




Tech Enhanced Activity

Trapezoid and Triangle Area Play with the area of the triangle until it matches the trapezoid
Trapezoid Exploration Showing how the area of a trapezoid and triangle relate



Polar Coordinates Video




Applet 1: Sine Function Transformation

Move the a and b sliders and notice how f(x)=a*sin(b*x) changes.



1. What occurs when you move the b slider but keep a=1?

2. What occurs when you move the a slider and keep b=1?

3. Applying what you learned, how does this now relate to the function g(x)=a*cos(b*x)?



Applet 2: Lemniscate of Bernoulli

Move the α slider to watch the figure appear!



α is the degree at which circle A rotates

d is the size at which the figure grows




Applet 3: 3D Conics




1. Uncheck the sphere. Move the height (h) and radius (r) sliders. What do you notice about the relationship between the cone and cylinder?

2. Using ratios, what do you nice about the relationship between the volumes of the cone and cylinder? Show your work.

3. Recheck the sphere and uncheck the cone. Set the radius(r) = height(h). Now what do you notice about the relationship between the sphere and cylinder geometrically and mathematically?

4. What happens when you add the ratios of the sphere and cone together?

5. How would this relationship change if the height of the sphere, cone and cylinder were the same?



Original Applet


Click the "New Equation" button and move the f, g, h sliders until you get the spiral that corresponds with the equation. The spiral will turn green when you are right.



1. When moving f, how does the spiral change?

2. When moving g, how does the spiral change?

3. When moving h, how does the spiral change?

4. What part does each slider play in the equation above?

5. Do this until you get all 4 spirals. What are they and how do they differ?



Applet Libraries

Math Cats Library of math links with categories like: Applets, logic puzzles, math games, websites with specific targets like algebra or prime numbers , real life connections, etc.
Physics and Math Over 11 topics demonstrating math and physics relationships through adjustable applets such as oscillations, electrodynamics, quantum mechanics and linear algebra and more.
National Library of Virtual Manipulatives Organized by grade level and math topic, this site offers simple applicable applets that allow students of all ages to understand and visualize what they are learning.
Applet Maths 5 applets created by students/professors to support their research projects including the nature of roots and circles.
Applet Directory Simple use Geogebra math applets organized alphabetically to aide in teaching but not to replace it.


Spirals

Euler Spiral Draws a Euler spiral and allows you to change the distance and speed. Also allows a secondary graph to be drawn next to it .
Fibonacci Spiral Construction An applet with instructions on how to create a fibonacci spiral.
Fermat Spiral A website that teaches about the fermat spiral and provides an applet that you can manipulate as you follow along.
3D Spiral of DNA Shows a 3D model of DNA that can be moved around to display spirals not only in real life but also in 3-dimensional.
2D to 3D Shows a 2D plane and allows you to move a dot which in turn moves the corresponding dot on the 3D curved plane.


Project Resources

Spiral Tilings Using shapes to make spirals.
Archimedean Spiral Learning how to draw an archimedean spiral through a video representation.
Statistics of Nature Showing examples of spirals in the real world.
Spirals Informative page on different kinds of spirals and the math behind them.
Kiddle History of spirals, the types, pictures and examples in simple terms for kids.