Only a FEW animations from each collection are demonstrated here - MANY MANY more are on the CDs.

Algebra In MotionTM - 224 animations
Calculus In MotionTM - 240 animations

  • Each video has been restricted to be under 2 minutes, so to reveal as much information as possible, features are displayed very rapidly - MUCH faster than "classroom pace".

  • These videos provide just a glimpse of the actual power and capabilities of the animations.

  • Screen capture software to create videos noticeably affects the running of the animations.  The actual animations run smoother and sharper on their own.

  • In the actual animations, a Motion Controller can be accessed to control the speed of any animation as desired.

Simply click on any overview titles below OR on the pictures that follow

and be sure your volume is up. 

     CALCULUS IN MOTION (video overviews)
   (def, graphs, rel rates, MVT, slope fields, etc)
   (definition, Riemann, area, MVT, arc length)
          Volumes by Revolution
          Volumes on a Base
          2017 AB/BC Free Response
          2016 AB/BC Free Response
          2015 AB/BC Free Response
          2014 AB/BC Free Response
          2013 AB/BC Free Response
                Click on photos below for more calculus videos.

(video overviews)
          Algebra 1
          Algebra 2
               Click on photos below for more algebra videos.




Click to jump past the additional calculus videos below and on to more for
...  Algebra In MotionTM


More Videos of Sample Animations from the Calculus In MotionTM collection



"Graph f tan der int.gsp"



Interact with graphs including sliding tangents, 1st and 2nd derivatives, and the integral as an accumulation of heights.  Pages cover polynomials, trig, exp, ln, parametric, polar, and any curve of your own choosing. Morph the original curve to see the effects on the other components.

Choose 1 to 80 subdivisions of interval [A,B] and approximate the integral using rectangles for left sums, right sums, or midpoints; or use trapezoids for the Trapezoidal Rule.  Change the domain, morph the function, or use the examples on the other pages of the file.


  "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 cross-sections.


  "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 cross-section 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 MotionTM 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.




"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(x-a), 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.