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 paper
- Solve Algebraically & Graphically
- *Slope in sound and pictures
- compute distances w/ web page
- Model for Distance
- Solving Equations
- calculator to solve
- solving equations and inequalities: algebraically, graphically
- solving equations and inequalities: technologically
- linear equation solver
- *linear inequality notation and "proofs"
- Who Has? ----- Lines
- Lines Library
- Lines Classes
*Exploring Functions Through the Use of Manipulatives, the entire book
- 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=
- 2. y= -
- 3. y=
( - x)
- 4. y= -
- 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
- 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
- animation on hundreds board and coordinate plane
- Quadratic Functions
- "Why = a(x - h)² + 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
- Complex Numbers
- off site: Elizabeth Stapel on Complex Computation I
- Polynomial Functions
- increasing/decreasing, end behavior definition
- Functions Home Page
- 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
- 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.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
- *maytrix computation, inverse, solve systems
- *tiles.xls all stuff & hot
- Writing To Learn Assignments
- · Writing Assignments
- · Writing Project Questions
- · Possible Projects
- · Coversheet
- * graph paper
- high school and college stuff
- *Who Has Games
- *Math Exercises
It's time for "Math Exercises."
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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