putting the fun in function since 2002 corey cogswell
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The Function DogPutting the “Fun” in Function Since 2002
Corey Cogswell
The Function DogPutting the “Funk” in Function Since 2002
Wrong Funk
Right Funk
Gross-out math is intended for grossing out students, not teachers. If at any point during this presentation, you are offended, then it’s 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…
Disclaimers
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 master’s program through Lamar Academic Partnerships in Educational Technology Leadership.
Brief Biography
I understand the irony in a 2-page “brief” biography.
I am the math / speech / interview coach for Pearland’s 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.
Brief Biography (cont.)
The Evolution of the Function Dog
2002 - 20052005 - 20062006 - Present
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
When to use the Function Dog
Pre-Algebra
Please Excuse My Dear Aunt Sally
Order of Operations
Parentheses Exponents Multiplication Division Addition Subtraction
Order of Operations
GroupingsExponentsMultiplicationAddition
New Order of Operations
Grandmothers
ExpoundMultipleAnecdotes
GirlsExpectMemorizedAnniversaries
GorillasEatMimesAddictively
The simplest operation one can do with two numbers is add or subtract them.
Order of Operations
35 8
+
The simplest operation one can do with two numbers is add or subtract them.
Order of Operations
35 2-
The next simplest operation one can do with two numbers is multiply or divide them.
Order of Operations
35 15
×
The next simplest operation one can do with two numbers is multiply or divide them.
Order of Operations
35 53
÷
The most complex operation one can do with numbers (in Pre-Algebra) is applying an exponent or radical to them.
Order of Operations
5 25^2
The most complex operation one can do with numbers (in Pre-Algebra) is applying an exponent or radical to them.
Order of Operations
25 5
√
The most complex dogs eat first.
Order of Operations
^2 √
The next most complex dogs eat second.
Order of Operations
× ÷
The least complex dogs eat last.
Order of Operations
+ -
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.
Order of Operations
Example 1
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 -.
5
210
×
Example 1
10
52
÷
Example 1
2
4
6+
Example 1
6
3
3
-
Example 2
18
2
36××
Example 2
36 6×√
Example 2
2
6
12
×÷
Example 2
2
-1
4
5
×-
Example 2
2
-1
1×+
Algebra 1
Relations
Functions
Example
x4x+5
3 17
y
If all functions are named y, then we run into a slight problems when there are multiple functions…
Function Notation
yy
y
y
y
yy
y
y y
y
Which y were you looking for?
Function Notation
x
f
f(x)
g
g(x)
Example
x
f
f(x)4 f(4)
=3(4)2+5=
Input Output
Coordinate: (4,53)
53
Geometry
Commutative Property
Properties
3 +85
Associative Property
Properties
× ×
Distributive Property
Properties
+3
5
2
8
× 16
2×
6
10
Trigonometry
sin
sin(θ)θ
ANGLERATIO
cos
cos(θ)
tan
tan(θ)
Algebra 2
Composite Functions
xf(g(h(x)))g(h(x))h(x)
ghf
Example and
2g
6f
26
x g f
External TransformationsFunction Transformations
xf
f(x)
Internal TransformationsFunction Transformations
x f(x)x+c
b(x+c)f(b(x+c))
×b+cf
Example 1
f(2(x+5))x fx
Function Inverses
x f(x)
f-1f
Example 1
5 10f-1
2 4f
Example 2
5 25f-1
-5f
Example 3
f3 27
f-1
Logarithmic Aside
3x = 27
log
Logarithmic Aside
Logarithmic Aside
Example 3
f3 27
f-1
Reciprocal Functions
x 1xf
Precalculus
Inverse Trig Functions
θ sin(θ)sin-1sin
Reciprocal Trig Functions
θ 1 sin θ
csc
Comparison
x sin(x)sin-1
x 1 sin x
csc
This x is an angle.
This x is a ratio.
Calculus
Differentiation
ff’x
f(x)f’(x)
Chain Rule
ff(g(h(x)))
xh’(x)
g’h’ f’f’(g(h(x)))g’(h(x))
gh(x) g(h(x))h
Example
sin usin(e3x2)
x6x
eu6u cos u
cos(e3x2)e3x2eu
3x2 e3x23u2
Closing Thoughts
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.
Benefits of Using the Function Dog
Contact Information
Pearland High Schoolcogswellc@pearlandisd.org
This presentation and other materials can be found at:
http://www.pearlandisd.org/webpages/ccogswell/
Corey Cogswell
GOZER THE DESTRUCTOR COGSWELL
THIS SESSION WAS SPONSERED BY
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