Applet Links:
Use the following applet to explore how a, b, and c change the graph of f(x).
Click here for the Geogebra Parabola Transformation Applet Assignments ListThe following applet will help students explore conic sections.
Directions: Move the planes and cone around by clicking and dragging the planes, cones, and axis. To move the plane,
click and drag the points titled A, B, and C and move along their respective axis. Observe the different shapes created
by changing the plane and reorienting the cone. Consider the following questions as you explore:
#1. How many different types of shapes can you create by moving the plane and reorienting the cone?
#2. How do these new shapes relate to shapes you already know about?
#3. How would you describe or predict a type of shape based on how you move the plane?
Click here for the Conic Sections Applet
Assignments List
This applet will help you discover relationships between the volumes of cones, cylinders, and spheres. To use the applet,
you can use the slider (n) to change the radius and height of each polyhedron. Also, use the checkboxes to view the polyhedrons
either one at a time, or all at once. Consider the following prompts as you explore:
1. Is there any relationship between the volume of the cylinder (a) and the volume of the cone (b) with the same radius?
2. Is there any relationship between the volume of the cylinder (a) and the volume of the sphere (c) with the same radius?
3. Is there any relationship between the volume of the cone (b) and the volume of the sphere (c) with the same radius?
4. Is there any relationship between the volume of all three shapes?
Click here for the Geogebra Volumes of Solids Applet
Assignments List
The following applet is used to discover relationships between polar and rectangular coordinates.
To explore, you can check/uncheck the boxes to show the poloar and rectangular coordinates. You can also drag the point 'A'
around to change the coordinates.
Click here for the Geogebra Polar and Rectangular Coordinates Applet
Assignments List
Directions: Use the applet below to explore the relationships between the upper and lower sums methods of finding the area under the curve.
Also, compare to integration.
* Type in a function (in terms of x) into the opening.
*Drag points A and B along the x axis to change the starting and stopping points.
*Use the slider to change n, the number of rectangles.
*Check/Un-check boxes to show the upper sum, lower sum, and integral.
Consider the following questions as you explore:
1. Does the Upper Sum method over or under-estimate?
2. Does the Lower Sum method over or under-estimate?
3. Are there any relationships between the Upper and Lower Sum estimations and the actual area under the curve (integral?)
Click here for the Geogebra Upper and Lower Sums Applet
Assignments List
Directions:
Use the following applet to explore how a, b, c, and d can change the features of the three trigonometric graphs f(x)=sin(x),
g(x)=cos(x), and h(x)=tan(x). Use the check-boxes to show and hide the different graphs. Also, use the four sliders to change the
values for a, b, c, and d. You may also use the check-boxes to show and hide the parent graphs for the three main trigonometric functions.
Consider the following questions as you explore:
#1. How does a change the attributes of the graph of each function? Does it change each function in the same way?
#2. How does b change the attributes of the graph of each function? Does it change each function in the same way?
#3. How does c change the attributes of the graph of each function? Does it change each function in the same way?
#4. How does d change the attributes of the graph of each function? Does it change each function in the same way?
#5. Is there a generalized rule for how each attribute (a, b, c, and d) change the graphs of trigonometric functions?
Click here for the Geogebra Trigonometric Graph Transformations Applet
Assignments Lists
Directions:
Use the following applet to explore the Normal Approximation to the Binomial. Use the sliders to adjust the sample size (n) and the
probability (p). Examine how it changes the histogram. Also, use the checkboxes to show the comparisons of the Binomial distribution to the
Normal distribution and to show the areas on the histogram.
Consider the following questions as you explore:
#1. How similar are the Normal and Binomial distributions in shape?
#2. Do the shape similarities change as you change n and p?
#3. How similar are the areas under the curves for the Normal and Binomial Distributions? What differences can you find here?
Click here for the Normal Approximation to the Binomial Applet
Assignments Lists
Directions:
Use the applet below to explore the relationships between asymptotes and as x → ∞, discover what f(x) goes towards.
Begin by inputting a function in the input box (where it says f(x)=). Slide the point A on the graph left or right along the x-axis to
make the x values grow larger and smaller, and observe how the y-values react. Use the check-box to show the equations for the asymptotes and
graph them on the graph.
Consider the following questions as you explore:
#1. As x → ∞ (this means the x-values get larger and larger- big enough to the point we don't want to count them anymore),
what does f(x) or the y-values approach?
#2. As x → -∞ (this means the x-values get larger and larger- big enough to the point we don't want to count them anymore),
what does f(x) or the y-values approach?
#3. How do the asymptotes (specifically the horizontal asymptotes) relate to parts #1 and #2?
Click here for the Asymptotes and Limits of Functions Applet
Assignments Lists
To explore similar triangles and learn more about them, use the Desmos activity below. You can use this activity as a 'teacher' and generate
an access code for each of your students so that you can monitor their achievement.
Click here for the Similar Triangles Desmos Activity
Assignments Lists