
MULTIPLICATION & FACTORING
The distributive property is geometrically demonstrated
for products of all combinations of monomials, binomials, and trinomials.
The factored form of a^{2} – b^{2} is developed and proved.
Special emphasis is given to (x+h)^{2} ≠ x^{2}+h^{2}
and (x+h)^{3} ≠ x^{3}+h^{3}. "Completing
the square" is modeled physically. 

FOIL (a+a)(x+b)

(a+b)(c+d) = ac+ad+bc+bd

(a+b+c)(d+e+f)






a^{2}  b^{2} = (a+b)(ab)

(x+h)^{2} = x^{2} + 2xh + h^{2}

(x+h)^{3} = x^{3} + 3x^{2}h + 3xh^{2} +
h^{3}






completing
the square








GEOMETRY  added in 2016
ANGLES
definitions of all types of single angles and angle pairs,
including all transversal angles
TRIANGLES
all parts and definitions; the 180 degree sum; the Exterior Angle
Theorem; SSS, ASA, AAS, and SAS; the Isosceles Triangle Theorem;
visualizing overlapping triangles; altitudes, medians, and angle bisector
segments along with the centers they determine and the
characteristics of the loci of those centers including the Euler Line and
the 9point circle; the Triangle Inequality Theorem;
the Geometric Mean; 306090 degree triangles; and 454590 degree triangles
CIRCLES
all parts and definitions; the circle's equation in the coordinate plane;
major vs. minor arcs & semicircles; central angles; inscribed angles;
angles whose vertices are in the interior or exterior of the circle;
quadrilaterals inscribed in circles; chord, secant, tangent properties and
theorems;
rolling out pi; arc lengths and sector areas; plus a few extra explorations
for students who need a bit of a challenge
QUADRILATERALS, POLYGONS, SOLIDS
definitions and properties of each in the "family" of quadrilaterals
(trapezoid, parallelogram, rhombus, rectangle, square) plus a summary;
sums of interior and exterior angles in polygons; regular ngons; all area
formulas;
definitions, properties, volumes and surface areas of prisms, cylinders,
pyramids, cones, and spheres
For a quick view of these 40 new "geometryspecific" animations added to the
Algebra In Motion collection in 2016,
see them in action in the GEOMETRY video accessible from the home page (or
the online demo page).
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
xyzspace

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 &
THEIR 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

sine,
cosine, tangent, definitions

sin, cos, tan, sec, cec, cot on the unit circle






special angles of
the unit circle

unwrapping the unit circle

"morphing" trig graphs






Pythagorean Identities

Law of
Sines

Law of Sines ambiguous case






Law of
Coines

sin (a+b),
Q1

sin (a+b),
Q2 both acute






sin (a+b), Q2 acute+obtuse

cos (a+b),
Q1

sin
(a+b), cos (a+b)
geometric approach
