Whether teaching remedial, mainstream, or honors classes, in a segregated or integrated program, these 168 dynamic animations bring to life algebraic topics from pre-algebra through pre-calculus. Packaged on a CD-ROM (with a basic license for 4 on-site computers to use at a variety of levels), Algebra In Motion™ animations perform equally well on either the Windows or Macintosh platform. They must be run by The Geometer’s Sketchpad v4 (no prior version), owned and sold by Key Curriculum Press (www.keypress.com). Although a detailed instruction manual is included on the CD-ROM (PDF format), most of the animations can be run successfully using only the on-screen information.

Algebra In Motion LITE™ is a subset of the full Algebra In Motion package. It contains 62 animations exploring topics from upper elementary math (such as fractions, signed number operations, equation balance) through early algebra (basics of the coordinate plane, graphing linear equations, multiplying polynomials, Pythagorean Theorem with visual proofs and applications, etc.). Its basic license is for 1 computer.

In the pictures below, those with a * are included in Algebra In Motion™ Lite.

THE BASICS
INTRODUCING THE COORDINATE PLANE
MULTIPLICATION & FACTORING
CONNECTING SOLUTIONS TO GRAPHS
ADVANCED GRAPHING
CONICS & APPLICATIONS
TRIGONOMETRY
THEOREMS
MORE APPLICATIONS & VERTICAL TEAMING
   
  



















 

 

 

  

  
 

 

  THE BASICS
Visually explore or review fractions (meanings, comparisons, improper, LCD, adding, decimals, percents), signed number operations, absolute value, and introduce the concept of an equation as a balance of values and use that balance to solve preset equations or create your own.
 
  absolute value*
 adding signed integers*
 adding signed numbers*
 subtracting signed numbers*
         
  fractions of 1 whole unit* comparing
fractions(1)*		 comparing
fractions(2)*		 fractions of a group*
         
  improper fractions* finding LCDs* adding fractions* decimal fractions*
         
    percent fractions* common uses of fractions*  
         
  equation balance*
(+ 3 different preset examples,
1 adapts to your own examples)
 		equation balance – “backwards”*
(+ 2 different preset examples,
1 adapts to your own examples
)
     
  the Real Number System - define*
 		the Real Number System - practice*
     
  geometric transformations - reflect*, rotate*, translate*, dilate*, and a summary*

 

 

INTRODUCING THE COORDINATE PLANE & GRAPHING
Introduce students to the basic vocabulary and characteristics of the coordinate plane (+ history). Dynamically display the definition of slope. Practice graphing lines from y = mx+b, Ax+By = C, and y-y1 = m(x-x1) forms. Explore the relationship of parallel and perpendicular lines to slope. Develop the formulas for midpoint and distance. Test relations using an animated vertical line test
Present 4 different graphing grids on the same screen.
 

axes~quadrants~coordinates*
 		vertical line test, domain/range*
 		exploring domain/range
with any function*
       
  visualizing slope*
 		graph y = mx + b*
 		graph Ax + By = C*
       
 
graph y-y1 = m(x-x1)*
parallel and perpendicular*
 		developing the midpoint formula*
       
  developing the distance formula*
4 grids on 1 screen
evolution of a polynomial
       
  transform f(x) to f(x) + a
 		transform f(x) to af(x)
 		transform f(x) to f(x-a)
       
 
transform f(x) to f(ax)*
 transformation practice
(line)
 transformation practice
(absolute value)
       
  transformation example
(parabola)
 transformation practice
(sine)
 transformation practice
(exponential)

 

 

MULTIPLICATION & FACTORING
The distributive property is geometrically demonstrated for products of all combinations of monomials, binomials, and trinomials. The factored form of a2 – b2 is developed and proved. Special emphasis is given to (x+h)2 ≠ x2+h2 and (x+h)3 ≠ x3+h3.  "Completing the square" is modeled physically.
  FOIL (x+a)(x+b)*
 (a+b)(c+d) = ac+ad+bc+bd*
 		 (a+b+c)(d+e+f)*
       
   a2 - b2 = (a+b)(a-b)*
 		(x+h)2 = x2 + 2xh + h2*
 		(x+h)3 = x3 + 3x2h + 3xh2 + h3*
   completing the square
 		    
       
  CONNECTING SOLUTIONS TO GRAPHS
Reinforce meaningful understanding of solutions to sentences with absolute value, systems of 2 linear equalities or inequalities, and finding the roots of a quadratic equation (including complex roots) using its related parabola.
  |ax+b| ≥ c
 		system of linear equalities*
 		system of linear inequalities*
       
  complex roots of quadratic equations
 		polynomial root dragging
(set of 7 animations)
 		 
       
  ADVANCED GRAPHING
Dynamically graph points in 3D space or on the complex number plane (history included). Control coefficients of a polynomial to “morph” it from a constant function up through a 5th degree polynomial. Similarly “morph” graphs of logarithmic & exponential functions, parametric & polar graphs, greatest integer functions, and inverses. Explore how composites of functions are created, and create linear programming examples.
 
  points in xyz-space
 		points in complex plane
 		"morphing polynomials"
       
  "morph" exponential functions
 		"morph" logarithmic functions
 		parametric graphs
       
  polar graphs
 your choice
 		greatest integer functions
       
 
more greatest integer
inverses
 creating composites
(adapts to any example)
       
  composite ex. 1
 composite ex. 2
 composite ex. 3
       
  linear programming
(create your own example)
 		linear programming
(preset example 1) 		linear programming
(preset example 2)
 
       
  CONICS & APPLICATIONS
Dynamically create each conic section from its definition. Graph and “morph” all features of each. Alter coefficients of the general equation or eccentricity to “morph” one conic into another. Explore applications to satellite dishes, elliptical pool tables, whisper chambers, & falling objects.
 
  overview
 		construct circle by def. & graph
 		construct parabola by def.
       
 
construct ellipse by definition
 construct hyperbola by definition
graphing parabolas
       
 
graphing ellipses
graphing hyperbolas
 "morphing" from general equation
       
  parabaloid, ellipsoid, hyperboloid
family of hyperbolas & ellipses
mutually orthogonal
       
  reflections & collections
 falling projectile
 		altering eccentricity
       
  TRIGONOMETRY
In an environment where rotation is real, not merely imagined, thoroughly investigate the unit circle’s angles, coordinates, and ratios. Literally unwrap the unit circle to form sine and cosine waves. Dilate and translate trigonometric graphs to explore amplitude, period, and shift. Explore and prove Pythagorean identities, the Law of Sines, and the Law of Cosines. Convincingly demonstrate that sin (a+b) can’t be (sin a + sin b).
 
 
unit circle angles
 aim62.gif (81293 bytes)		 sine, cosine, tangent, definitions
special angles of the unit circle
 aim22.gif (81293 bytes)
       
  unwrapping the unit circle
 "morphing" trig. graphs
 Pythagorean Identities
       
  Law of Sines
 		Law of Cosines
 		sin (a+b), Q1
       
  sin (a+b), Q2 both acute
 sin (a+b), Q2 acute+obtuse
 cos (a+b), Q1

 

 

THEOREMS
Dynamically explore conventional theorems such as the Pythagorean Theorem (+ history) along with 7 different visual proofs of it. In addition, discover a large selection of unusual and unexpected theorems concerning tangents to parabolas, cubics, and quartics that will amaze and fascinate your students while laying an excellent foundation for more advanced mathematical study.
 
Pythagorean Theorem*
More Pythagorean Theorem*		 any 3 tangents to any parabola
3 tangent proof (part 1)
         
  3 tangent proof (part 2)
 		parallel tangent at midpoint
 		inflection point at midpoint
 		use 2 roots to find 3rd (+ extend to imag. rts)
         
  ratio of areas in cubic
 		more ratios of areas in cubic
 		ratios of areas in quartic
 		PT – shearing proof*
         
  PT – Chinese proof* PT – Pythagoras proof* PT – Bhaskara proof* PT – DaVinci proof* 
         
 
PT – Garfield proof*
PT – Generalized*		 any 2 tangents to any parabola
2 tangent proof (part 1)
         
  2 tangent proof (part 2)
      
         
  MORE APPLICATIONS & VERTICAL TEAMING
Build basic graphing sense using intriguing questions about real-world situations that animate at the click of a button. Thoroughly explore classic problems such as the “open box” (vary the size of squares removed from the corners of the original rectangle), the sliding ladder, flying kite, etc. As the level of the class increases, more and more features can be explored at the click of a button. Finally, even calculus students will benefit by experiencing the varying rates of change in familiar favorites – perfect for vertical teaming!
 
 
truck with square wheels*		 path of pebble caught in wheel*
mapping a Ferris wheel*
escalators
         
  4 bugs*
 		logarithmic spirals
 		dog & marching band*
 		 
         
  distance = (rate)(time)*
 distance = (rate)(time)*
 midpoints
 		more midpoints
         
 
Aristotle’s Wheel paradox
linear vs. angular velocity		 linear vs. angular velocity in gears
 		 
         
 
vertical team-open box
 		vertical team - clock
(convert time)*
 		vertical team - clock
(geometry)
 		vertical team - clock
(trig. & adv. graphing)
         
  vertical team – ladder*
basic PT application
 vertical team – ladder
trig. application
 vertical team – ladder
rag & graph application
 vertical team – ladder
calculus application
         
  vertical team – kite*
basic PT application
 vertical team – kite
trig. application
 vertical team – kite
function graphs application
 vertical team – kite
calculus application
         
  vertical team – balloon*
basic formulas (approx. pi)
 vertical team – balloon*
basic formulas (pi exact)
 vertical team – balloon
dimensional analysis
 vertical team – balloon
angle elevation/depression
         
  vertical team – balloon
trig. application
 vertical team – balloon
function graphs application
 vertical team – balloon
calculus application