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Putting the Fun in Function Since 2002 Corey Cogswell

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Putting the Funk in Function Since 2002

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Gross-out math is intended for grossing out students, not teachers. If at any point during this presentation, you are offended, then its totally on you and your sensibilities. This presentation is meant for purely instructional purposes and not for personal use. What that use might be, no one knows… but no judgments… Finally, this is not intended to change your life, and if it does so, your life probably needed changing any way…

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I graduated with a degree in mathematics from Rice University in 2002. I have taught 8 years in Pearland ISD. I have taught Algebra 1, Geometry, Algebra 2, SAT Prep, AMDM, PAP Precalculus, and AP Caclulus AB, and I will be adding AP Stats to that list this year. I am currently writing a textbook for a fourth year math class, Pre-College Math, to satisfy the four by four rule. I just began my masters program through Lamar Academic Partnerships in Educational Technology Leadership.

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I understand the irony in a 2-page brief biography. I am the math / speech / interview coach for Pearlands Two-Time State Champion Academic Decathlon team. I am a playwright in my spare time. I dislike guacamole. I have a Welsh corgi named Gozer the Destructor.

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2002 - 20052005 - 2006 2006 - Present

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Order of Operations Functions Conceptually Function Notation Properties Composite Functions Function Transformation (New for 2010) Function Inverses (Updated for 2010) Trigonometry Chain Rule for Differentiation

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Please Excuse My Dear Aunt Sally Parentheses Exponents Multiplication Division Addition Subtraction

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Groupings Exponents Multiplication Addition Grandmothers Expound Multiple Anecdotes Girls Expect Memorized Anniversaries Gorillas Eat Mimes Addictively

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The simplest operation one can do with two numbers is add or subtract them. 35 8 +

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35 2 -

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The next simplest operation one can do with two numbers is multiply or divide them. 35 15 ×

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The next simplest operation one can do with two numbers is multiply or divide them. 35 5353 ÷

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The most complex operation one can do with numbers (in Pre-Algebra) is applying an exponent or radical to them. 5 25 ^2

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The most complex operation one can do with numbers (in Pre-Algebra) is applying an exponent or radical to them. 25 5

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The most complex dogs eat first. ^2

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The next most complex dogs eat second. ×÷

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The least complex dogs eat last. +-

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Groups of dogs, or packs, can be found inside parentheses, numerators, denominators, or radicals. Packs eat before everyone else, maintaining internal pecking order. Dogs of equal complexity eat in the order they line up.

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There are four symbols in this expression and thus four dogs have lined up for dinner. Based on our rules, × will eat first followed by ÷, then +, and finally -. 52 10 ×

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5 2 ÷

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2 4 6 +

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63 3 -

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182 36 × ×

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6 ×

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26 12 × ÷

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2 45 × -

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2 1 × +

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x 4x+5 3 17 y

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If all functions are named y, then we run into a slight problems when there are multiple functions… yyyyyyyyyyy Which y were you looking for?

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x f f(x) g g(x)

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x f f(x) 4 f(4) =3(4) 2 +5= Input Output Coordinate: (4,53) 53

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Commutative Property 3 + 8 5

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Associative Property ××

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Distributive Property + 3 5 2 8 × 16 2 × 610

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sin sin(θ) θ ANGLE RATIO cos cos(θ) tan tan(θ)

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x f(g(h(x)))g(h(x))h(x) ghf

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and 2 g 6 f 26 x g f

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x f f(x)

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x x+c b(x+c) f(b(x+c)) ×b +c f

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f(2(x+5)) x f x

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x f(x) f -1 f

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5 10 f -1 24 f

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5 25 f -1 -5 f

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f 327 f -1

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3 x = 27 log

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f 327 f -1

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x 1x1x f

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θ sin(θ) sin -1 sin

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θ 1 sin θ csc

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x sin(x) sin -1 x 1 sin x csc This x is an angle. This x is a ratio.

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f f x f(x)

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f f(g(h(x))) x h(x) g h f f(g(h(x)))g(h(x)) g h(x) g(h(x)) h

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sin u sin(e 3x 2 ) x 6x eueu 6u cos u cos(e 3x 2 )e 3x 2 eueu 3x 2 e 3x 2 3u 2

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Everyone likes puppies… even when they have accidents… Visual representations of abstract concepts help students of all grades and abilities learn, regardless of maturity level. Vertically aligning the presentation of concepts ties the different mathematical subjects together. For many high school students, the range of a dog, and in fact most biological entities, is funny.

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Pearland High School cogswellc@pearlandisd.org This presentation and other materials can be found at: http://www.pearlandisd.org/webpages/ccogswell/

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GOZER THE DESTRUCTOR COGSWELL

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