Math Literacy
There’s public shame if you walk out now
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Math Quiz
A baseball and bat together cost $1.10. The bat costs
$1.00 more than the ball. What does the ball cost?
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Did you pick 10¢?
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Did you pick 10¢?
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Word Problems
A baseball and bat together cost $1.10. The bat costs
$1.00 more than the ball. What does the ball cost?
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Word Problems
1 Ball
A baseball and bat together cost $1.10. The bat costs
$1.00 more than the ball. What does the ball cost?
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Word Problems
1 Ball + 1 Bat
A baseball and bat together cost $1.10. The bat costs
$1.00 more than the ball. What does the ball cost?
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Word Problems
= $1.10
1 Ball + 1 Bat
A baseball and bat together cost $1.10. The bat costs
$1.00 more than the ball. What does the ball cost?
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Word Problems
= $1.10
1 Ball + (1 Ball + $1.00)
A baseball and bat together cost $1.10. The bat costs
$1.00 more than the ball. What does the ball cost?
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Word Problems
= $1.10
1 Ball + (1 Ball + $1.00)
A baseball and bat together cost $1.10. The bat costs
$1.00 more than the ball. What does the ball cost?
1 Ball + 1 Ball + $1.00 = $1.10
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Word Problems
= $1.10
1 Ball + (1 Ball + $1.00)
A baseball and bat together cost $1.10. The bat costs
$1.00 more than the ball. What does the ball cost?
1 Ball + 1 Ball + $1.00 = $1.10
2 Balls + $1.00 = $1.10
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Word Problems
= $1.10
1 Ball + (1 Ball + $1.00)
A baseball and bat together cost $1.10. The bat costs
$1.00 more than the ball. What does the ball cost?
1 Ball + 1 Ball + $1.00 = $1.10
2 Balls + $1.00 = $1.10
2 Balls = 10¢
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Word Problems
= $1.10
1 Ball + (1 Ball + $1.00)
A baseball and bat together cost $1.10. The bat costs
$1.00 more than the ball. What does the ball cost?
1 Ball + 1 Ball + $1.00 = $1.10
2 Balls + $1.00 = $1.10
2 Balls = 10¢
1 Ball = 5¢
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Who the Heck am I
to Talk About Math?
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James Edward Gray II
• I’m a programmer
• We use at least a little math in our jobs
• I’m an atheist
• Good atheists use a little math too
• I’m not a math whiz
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Better Qualified
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Better Qualified
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Better Qualified
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Why Math?
Is this really Disbelief Discourse material?
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Skepticism
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Skepticism
Logic
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Skepticism
Logic Math
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Branches of Math
• Combinatorics: dealing with combinations
of objects
• Estimation: rough calculations of value,
quantity, or extent
• Probability: the extent to which an event is
likely to occur
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Math Quiz
How many people would you need to gather
to be absolutely certain (a 100% chance)
that two people in the group share a birthday
(month and day only)?
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Did you pick 365?
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Did you pick 365?
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366?
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366?
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It’s actually 367.
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Math Quiz: Round 2
How many people do we need to gather
if we are willing to accept half the odds (a 50% chance)
that two people in the group share a birthday?
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Did you pick 183?
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Did you pick 183?
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Would you believe 23?
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Would you believe 23?
Believe it
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Birthday Combinatorics
• Ignoring Leap Year to keep this simple…
• The possible combinations of five different
birthdays: 365 × 365 × 365 × 365 × 365
(or 3655)
• The ways you can select five birthdays
without repeats: 365 × 364 × 363 × 362 ×
361
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Birthday Probability
• The ratio (fraction) of events we’re
interested in to the total possible events
• Chance five people don’t share a
birthday: (365 × 364 × 363 × 362 × 361) /
(365 × 365 × 365 × 365 × 365)
• Subtract from one to get the chance of the
opposite occurrence (a birthday is shared)
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Chance Five People
Share a Birthday
365 × 364 × 363 × 362 × 361
365 × 365 × 365 × 365 × 365
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Chance Five People
Share a Birthday
365 × 364 × 363 × 362 × 361
365 × 365 × 365 × 365 × 365
= 0.972…
First Movie Second Movie
0
25
50
75
100
Why Second
Movies Suck
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First Movie Second Movie
0
25
50
75
100
Why Second
Movies Suck
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First Movie Second Movie
0
25
50
75
100
Why Second
Movies Suck
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“Plane crashes always
happen in threes!”
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“Plane crashes always
happen in threes!”
Over what time period?
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All Measurements are
some level of estimate
Image from http://iruler.net/
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All Measurements are
some level of estimate
Image from http://www.1234tools.com/caliper-measuring/
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All Measurements are
some level of estimate
Image from http://www.mitutoyo.com/producttyperesultform.aspx?type=1066
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Just Understanding
Scale can be Valuable
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Water Depth
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Water Depth
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Water Depth
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Water Depth
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Water Depth
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Money
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Money
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Money
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Money
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Money
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Money
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Radiation
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Radiation
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Radiation
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Radiation
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Radiation
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http://xkcd.com/
A webcomic of romance, sarcasm, math, and language.
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Is Math Cool?
This is where the war is being fought
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Heard Any of These?
• “I’m terrible at Math”
• “Math was always my worst subject”
• “A million dollars, a billion, a trillion,
whatever”
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xkcd: “Forgot Algebra”
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xkcd: “Forgot Algebra”
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Girls Suck at Math
Anyway, Right?
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Girls Suck at Math
Anyway, Right?
No: http://www.sciencedaily.com/releases/
2011/12/111212153123.htm
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Math Quiz: Girl’s Only!
A woman is about to give birth to her first child.
What are the odds that it’s a boy?
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Math Quiz: Girl’s Only!
A woman is about to give birth to her first child.
What are the odds that it’s a boy?
½
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Math Quiz: Round 2
A woman is about to give birth to her eighth child.
The first seven were all boys.
What are the odds that this child is a boy too?
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Math Quiz: Round 2
A woman is about to give birth to her eighth child.
The first seven were all boys.
What are the odds that this child is a boy too?
½
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Math Quiz: Round 3
You visit a friend, knowing she has two children
but not the gender of the children. A young girl
answers the door, so that’s one child. What are
the odds that the other child is a boy?
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Math Quiz: Round 3
You visit a friend, knowing she has two children
but not the gender of the children. A young girl
answers the door, so that’s one child. What are
the odds that the other child is a boy?
⅔
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Possible Combinations
of Two Children
• Boy boy
• Boy girl
• Girl boy
• Girl girl
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Possible Combinations
of Two Children
• Boy boy
• Boy girl
• Girl boy
• Girl girl
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Champions of Math
We hope
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Are They on Our Side?
Image from http://sharetv.org/shows/the_big_bang_theory
#1: http://tvbythenumbers.zap2it.com/2012/04/17/syndicated-tv-ratings-big-bang-theory-on-top-again-dr-phil-leads-talk-shows/129421/
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Is He on Our Side?
Image from http://www.boston.com/bigpicture/2008/11/the_next_president_of_the_unit.html
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Danica McKellar
is on Our Side
• Actress (Wendy on The
Wonder Years)
• Sex symbol
• Math degree (with
honors)
• Published author
• Chayes-McKellar-Winn
theorem
Image from http://allinone1-z.blogspot.com/2010/12/danica-mckellar-hotdanica-mckellar.html
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Danica’s Books
Images from http://www.amazon.com/
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It’s Very Important
to be Cool
Just ask Apple and Microsoft
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U.S. Math Literacy
• The U.S. is below a 34 country average
• 17 of those 34 countries score better than
we do while only 5 score below us (11 are
roughly even with us)
• Ranking math proficiency from level 1 to
level 6, only 27% of U.S. students score 4 or
higher
2009 statistics for 15-year-olds from http://nces.ed.gov/surveys/pisa/pisa2009highlights_3.asp
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Is Math Important?
The consequences of mathematical illiteracy
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Writing on This Subject
Images from http://www.amazon.com/
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My Book Club Pick
Image from http://www.amazon.com/
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A Biblical Flood
• “…all the high mountains under the entire
heavens were covered.”—Genesis 7:19 NIV
• 10,000 to 20,000 feet of water
• “And rain fell on the earth forty days and
forty nights.”—Genesis 7:12 NIV
• 960 hours of rainfall
• That’s water rising about 15 feet per hour
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Will it Sink?
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Will it Sink?
Image from http://www.naval-technology.com/projects/cvn-21/
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Will it Sink?
Image from http://www.naval-technology.com/projects/cvn-21/
Image from http://www.whybaptism.org/Creation-HTML/NoahArk.htm
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"The State Department is infested with
communists. I have here in my hand a list of 205—
a list of names that were made known to the
Secretary of State as being members of the
Communist Party and who nevertheless are still
working and shaping policy in the State
Department."—Joe McCarthy, U.S. Senator
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Are Exact Numbers
More True?
Internal Human Body Temperature: 98.6°F
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Are Exact Numbers
More True?
Internal Human Body Temperature: 98.6°F
37.0°C
Math Quiz
Judy is thirty-three, unmarried, and quite assertive.
A magna cum laude graduate, she majored in
political science in college and was deeply involved
in campus social affairs, especially in anti-discrimination
and anti-nuclear issues. Which statement is
more probable?
(a) Judy works as a bank teller.
(b) Judy works as a bank teller
and is active in the feminist movement.
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Occam’s Razor
(a) Judy works as a bank teller.
(b) Judy works as a bank teller
and is active in the feminist movement.
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Occam’s Razor
(a) Judy works as a bank teller.
(b) Judy works as a bank teller
and is active in the feminist movement.
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Occam’s Razor
(a) Judy works as a bank teller.
(b) Judy works as a bank teller
and is active in the feminist movement.
Bank Teller Odds * Feminist Odds < Bank Teller Odds
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Voting and Polls
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Polling
• Any kind of polling is subject to statistical
errors
• This is where our margin of error comes
from
• Even that can (rarely) be off
• You also have to worry about systemic
errors
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How Many People
Have You Slept With?
A famously problematic poll question
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Gerrymandering
• Nick had to move to even try to get
elected
• That’s because politicians use packing and
cracking to distribute votes
• Nick’s district looks like a dinosaur
• The Voting Rights Act made this illegal, but
only when racial (political is fine)
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The Census
• The constitution requires an “actual
enumeration” of the population every 10
years
• This process costs billions
• It contains known systemic errors
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Sampling
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Is Sampling Legal?
• In the past, the U.S. Census used both
approaches
• This has been fought out in the Supreme
Court:
• Sampling was declared unconstitutional
• Imputation is still allowed
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The Truth:
Humans Can’t Count
Well, not exactly
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Did Bush or Gore
win the popular vote
in 2000?
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Neither
It was a tie, mathematically speaking
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It Takes More Than
Just Math
• Two gamblers wager $100 on coin flips
• The first to win six flips takes the pot
• Their game is interrupted when the score
is five to three
• How do we fairly divide the pot?
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Payout Arguments
• Pay $100 to the gambler with five wins
since he’s leading and the prize is all or
nothing
• Payout ⅝ and ⅜ of the pot for their
respective wins
• Pay ⅞ and ⅛ for the odds each man will
win (½ × ½ × ½ = ⅛ and 1 - ⅛ = ⅞)
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How Do We Improve?
My recommendations for where we go from here
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A Traditional Approach
Images from http://www.amazon.com/
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For Puzzle Fans
Images from http://www.amazon.com/
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Math Quiz
You need to test the blood of 100 patients for a
disease. On average one in a 100 will have the
disease. Can you find those that have the disease by
doing less than 100 tests?
(Givens: you have enough of each patient’s blood to
test them several times and you can test multiple
patients at once by combining samples.)
A Good Rule of Thumb
• A lot of people choose to look up a new
word when they first encounter it
• It’s an equally good idea to look up new
math when you encounter it
• http://www.wolframalpha.com/
• Ask a math geek
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How Does a Home
Mortgage Loan Work?
What’s the formula?
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Wolfram|Alpha
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Wolfram|Alpha
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Wolfram|Alpha
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Wolfram|Alpha
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The Formulas
P = L(i(1 + i)m) / ((1 + i)m - 1)
B = L(1 + i)m - (1 + i)p) / ((1 + i)m - 1)
P = Monthly payment
L = Loan amout
i = Monthly interest (6% loan: 0.06 / 12 = 0.005)
m = Length of the loan in months
B = Balance remaining
p = Payments made
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Please, Help Bring Back
the Cool in Math
If we do nothing else