




"Related Rates.gsp"  the classics 
"Related Rates  MORE.gsp" 
"Volumes On
Base.gsp" 

As a
cone fills with water, analyze the change in the rate of increase of the
water's depth for various instants and various cones. Four other
classic animations are in this file as well. 
This file has 9 more related rates animations
exploring escalators (seen in the video), a clock, a pool, vehicles
approaching an intersection, baseball, a balloon, a kite, etc. 
This
classic problem is one of several that walk through the visualization of
these difficult shapes one step at a time. Afterwards, students
are able to transfer what they have learned to new bases and new
crosssections. 




"Slope
Fields.gsp" 
"Volumes by Revolution.gsp" 

First, develop the meaning of a slope
field by gliding a dynamic "slope column" across the graph of f '.
See one tangent segment "pilot" the field & create the graph of f.
Desired differential equations can be entered & many more features can
be explored (e.g. Euler's Method). 
Build this concept in 3 stages. First,
spin a single isolated rectangle. Second, revolve a discrete
number of rectangles determined by the curve which would approximate
the solid's volume. Third, revolve the entire region (infinitely
many, infinitely thin rectangles). Use any function, any
horizontal or vertical axis of revolution, any partitioning, any interval.
Then sweep a crosssection through the solid which would give the
exact volume via integration. This video demo shows the
disk/washer technique, but the same file also has pages presenting an
identical development of the shell method. 

Videos of Older Sample Free Response Animations
See the list near the top of this page for the
current year's Free Response Animations.
All Free Response animations from 2013  1997 AB & BC are contained in the
Calculus In Motion^{TM} set. 





2007 AB5/BC5 
2005
AB2 
2005
AB4 

More Videos of Sample Animations from the
Algebra In Motion^{TM} collection 





"Fractions.gsp" 
"Equation Balance.gsp" 
"Coordinate Plane Basics.gsp" 

Explore the meaning of the denominator and numerator individually with
interactive fractions. In addition, brief glimpses are seen of
other pages tabs addressing other aspects of fractions such as
comparing, adding, LCD, improper, etc..

Connect equation solving
with the concept of balance. Interact with the scales to discover
the value of x in each blue box. Use preset examples or create
your own. Also, reverse the process, if desired.

Demonstrate the basic
coordinate plane vocabulary and explore the connections between an
ordered pair and its point's location as points are dragged around the
plane.
.






"Linear Equations, Mdpt, Dist.gsp" 
"Function Vertical Line Test.gsp" 
"Multiply Polynomials.gsp" 

Create a visual rise/run on any line and interact with it learn the
critical concept of slope. Mention is also made of other pages of
this file that address other topics of linear equations.

Sweep a vertical line across
changeable relations to explore the definition of a function.
Other buttons demonstrate the meaning of domain and range.

Provide a concrete model for the factored
form of the difference of two squares.






"Conics.gsp" 
"Trigonometry.gsp" 
"Graph Classic Functions.gsp" 

Create the conic sections from their definitions. Explore their
graphs, equations, eccentricity, and how it is that they can all come from
the same general equation.

Here's a brief look at 4 of the many
trigonometry animations  basic rotation; definitions of the sine,
cosine, and tangent ratios; special angles on the unit circle with
reference triangles, and unwrapping the unit circle into the sine and
cosine graphs.

Interact with the graphs of
various functions (polynomial, trigonometric, exponential and
logarithmic) as well as parametric and polar graphs (plus anything you
wish to invent). Each can be morphed by dragging coefficient
values.






"Graph Transformation Discovery.gsp" 
"Vertical Team (open box).gsp" 


Discover how f(x) compares to
f(x)+a, af(x), f(xa), and f(ax) by interacting with "a" and choosing any 4
functions you desire.

Explore the characteristics
of an open box folded from a rectangular piece of material with squares
removed from its corners. Suitable for many different math
courses. 




