math ed stuff

    Precalc Stuff

      Last year I presented "Teaching with Trig Tricks." This year look at much of the rest of my precalculus resources. Examine a spreadsheet for writing tests, quizzes, doing computation. Kinesthetically explore functions in 3 ways. Take an inverse in the visual, auditory, symbolic, and kinesthetic modalities. Examine a library of precalc resources in topics like quadratics, logs/exponents, trig, polynomial and rational functions.

Pre Precalculus
 
Syntax, numbers, expressions, computation
number systems
how to use calculator to express or simplify
*use compute.xls to complete arithmetic from proportions to solving trig equations
basic precalc functions from an order of operations standpoint
Heronian Triangles and Pythagorean Triples
 
Graph
*graph paper
Solve Algebraically & Graphically
 
Formulas
distance
midpoint
*Slope in sound and pictures
compute distances w/ web page
Model for Distance     model info
 
Solving Equations
calculator to solve
solving equations and inequalities: algebraically, graphically
solving equations and inequalities: technologically
linear equation solver
*linear inequality notation and "proofs"
 
Lines
Who Has? ----- Lines
Lines Library
Lines Classes
 
Non-Functions
 *Conics
 
Functions
  *Exploring Functions Through the Use of Manipulatives, the entire book
 
 
 
  library     *Function Library
most important functions -- IDENTITY, OPPOSITE, RECIPROCAL
smile odd/even/neither
definition odd/even graphics and questionbook
symmetry definition
 
*curve shifting -- translations, dilations, reflections: algebraically and graphically

Place the wax paper on top of the coordinate plane to graph:
 
1. y= (x)
 
2. y= - (x)
 
3. y= ( - x)
 
4. y= - (- x)
 
5. y= (x - 3)
 
6. y= (x + 2) - 1
 
7. y= - (x + 2) - 1
 
8. y= (x - 6) + 2
 
9. the inverse of y= (x - 6) + 2

* more graphing
* solving
* raw masters
*absolute value dilator in hand
*absolute value dilator w/movement
Math Exercises (later)
notes: joer16b.gif , joer16c.gif
 
Inverse Functions
*Inverse Notes
*Inverse Problems
Take An Inverse In 4 Language Families
 
 
More on composition of functions
 
Dilation -- multiplication of functions
dilation of a function
*(Line)(line)=(quadratic)
animation on hundreds board and coordinate plane
 
Quadratic Functions
"Why = a(x - h) + k?" -- EVERYTHING
Function Library -- Quadratics
quadratic dictionary definition
quadratic formula
standard and general forms
solve quadratic by calculator
completing the square summary sheet
solve a quadratic equation vs. simplify a radical expression
quadratic equation
discriminant
 
Complex Numbers
[tutorials & resource material arranged by topic
*00
off site: Elizabeth Stapel on Complex Computation I & II
 
 
Polynomial Functions
increasing/decreasing, end behavior definition
Functions Home Page
polynomials
more polynomials
poly.xls by degree & coeff or in factored, synthetic division, solves
roots of polynomial functions
*Pass or Touch
*Who Has? Polynomial F(x)
 
Rational Functions
*(Line)/(line)=(rational function) another kind of dilation
*asymptote definition
rational functions , harder problem, factors
*ratl.xls top vs bottom, graph, endbehavior, A(x)/B(x) + C(x), asymptotes
Notes on Rational and Polynomial Graphing Individual Graphics
Log & Exponential Functions
*e by area
Log use
log-log paper
semi log paper
log laws
*slide rule
exp.xls pay, 2 curves
Who Has? Exoponential
Logs
Logs without Feeling Out on A Limb
Log Papers
 
Trig Functions
Lessons 330 - Trig Functions
Last year's "Trig Tricks"
Sine Law Ambiguous Case
  · web page & text
  · just the master
  · *sinelaw.xls -- sine law digital manipulative
Six Trig Functions and the Unit Circle
  · The Animated Unit Circle. - Words w/text.
  · *jig1.xls -- UNIT CIRCLE JIG SAW PUZZLE
  · *unit circle jig saw puzzle master
*sine.xls -- Asin(Bx-C)+D, sine, cosine, tangent, or sine & cosine
  · sine & cosine animation only
Inverse Trig Functions Graphic
*solvtrig.xls all sorts of triangles
 
Vector
Addition
vector.xls -- completes scalar addition, multiplication, and vector addition
polrect.xls -- A DIGITAL MANIPULATIVE for drawing and addition of vectors.
*cramers.xls 2x2, 3x3, systems, minors, augmented columns
 
Matrices
*maytrix computation, inverse, solve systems
 
Other
tiles.xls all stuff & hot
Writing To Learn Assignments
      · Writing Assignments
      · Writing Project Questions
      · Possible Projects
      · Coversheet
Precalc Notes
 
Algebra Notes
[tutorials & resource material arranged by topic Lessons
graph paper
high school and college stuff
Connect-the-Dots
Who Has Games
 
*Math Exercises

It's time for "Math Exercises."

Please stand.

Use your body particularly your hands and arms to represent:

The line y = 0, the x-axis.

Represent the y-axis: x = 0

Represent: y = x, the identity.

Represent: y = -x, the opposite.

Represent: y = x², the squaring function.

Represent: y = |x|, the absolute value.

Represent: y = -2x².

Represent: y = 1/x, the reciprocal.

Represent: x = y².

Represent: y - |x-1|, the distance between a number and 1.

Represent: y = |x| - 1, the absolute value, less 1.

Represent: y = |x| + 1, the absolute value, plus 1.

Please take your seat.


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