Amatyc Ignite 2015 Second Half

Pat Riley – Hopkinsville
Community College (KY)
Vs. Math

Students like seeing how math
applies ... and eating … students like
eating!!

Two pounds
14 Inch Diameter
Enough dough for a
dozen

Six pounds
¾ each
Adam finished in Top
10%

42 Inch Pizza
What is the area?
How many regular
Papa John’s Pizzas

10″ 12″ 14″ 16″ 20″ 37″ 42″
CHEESE $8.09 $9.49 $12.49 $14.09 $18.09 $41.09 $51.09
1
TOPPING
$8.89 $10.49 $14.09 $16.09 $20.09 $46.09 $56.09
2
TOPPING
$9.49 $11.49 $15.09 $17.39 $22.09 $51.09 $61.09
3
TOPPING
$10.39 $12.49 $16.39 $19.09 $24.09 $56.09 $66.09
4
TOPPING
$11.49 $13.49 $17.49 $20.39 $26.09 $61.09 $71.09
SUPER
TOPPING
$12.09 $14.49 $19.09 $22.09 $27.29 $71.09 $81.09
VEGGIE $12.09 $14.49 $19.09 $22.09 $27.29 $71.09 $81.09
WHITE
PIZZA $9.89 $11.69 $14.69 $15.89 $19.89 $46.09 $56.09
BBQ
PIZZA $9.49 $11.49 $15.09 $17.89 $22.09 $66.09 $71.09

50 Wings in 30 minutes
Eating speed per wing?
How many wings per minute
to eat?

4 burger options
6 cheeses
9 toppings
12 condiments

“As calculated by a
University of
Michigan Student”

As also calculated by dozens
of Hopkinsville Community
College Students

Math League Problem
Pre-Algebra Students
Can Do!
(Or I Make Them Try!)
Sophia Georgiakaki
Tompkins Cortland CC, New York

NYSMATYC Math-League
๏ Coordinator: Abe Mantell, Nassau CC
๏ 20 Questions, 60 Minutes
๏ No Calculator, no Tables, no Aids
๏ Topics up to Pre-Calculus
๏ TC3 Campus Coordinator:

TC3 Pre-Algebra Course
๏ No Calculator
๏ Whole Numbers, Integers, Decimals,
Fractions, Algebra Intro, Proportions,
Geometry, Percents, Probability/Statistics
๏ Reinforce Multiplication Facts
๏ Pre-Algebra Coordinator:

Fall 2014
I have a 5x5x5 solid cube that I paint on all
six sides. I then cut it up into 125 1x1x1
cubes. How many of the 1x1x1 cubes have
no paint?
Pre-Algebra Textbook Images
Chapter 1: Whole Numbers
Chapter 7: Geometry

Fall 2014
The magic square shown uses each integer
from 1 through 9, exactly once, so that the
sum along any row, column, and both
diagonals is 15. What is the value of x?
9 4
x
Pre-Algebra Homework 2, Problem 1: Fill in
the magic square with the integers -1 thru -9.

Fall 2014
When the fraction 1/7 is expressed in
decimal form, what is the digit in the 2014th
decimal place? (Note: the 2014th decimal
place is the digit that is 2014 places to the
right of the decimal place.)
1/7 = 0.142857 142857 142857 …
Pre-Algebra Textbook, Chapter 4: Divide to
find the exact value of 1/7;
Chapter 1: State the quotient and remainder
of the division 2014 ÷ 6 (= 335 R 4)

Fall 2014
A cylindrical storage unit has a diameter of
12ft and a height of 25ft. A red stripe with a
horizontal width of 2ft is painted on it, as
shown, making a complete revolution around
it. What is the area of the stripe in square
feet?
12’
2’
2’
25’ 25’

Fall 2014
Suppose a fly lands on one of the seven
circles and then moves, exactly one position,
along a path to a neighboring circle. What is
the probability it will end up on a shaded
circle? Assume all moves by the fly are
random.

Spring 2015
In how many ways can we obtain $20.15
using ONLY quarters and dimes?
Odd number of quarters: 2 possibilities per
dollar  20 x 2 = 40 ways

Spring 2015
The accompanying diagram shows three
different triangles with a common base drawn
between two parallel lines. Let T1 represent
the triangle with the dotted lines, T2
represent the triangle with solid lines, and T3
represent the triangle with the dashed lines.
Which triangle has the SMALLEST area?

Spring 2015
The mathematician Augustus De Morgan
lived his entire life in the 1800’s. As a young
man, when asked his age, he responded, “I
will be x years old in year x2. How old was
he when that occurred?
x > 40; 43 x 43 = 1849  43 years old

Fall 2015
How many DIFFERENT pairs of prime
numbers have a sum of 2015?
NONE: one has to be even  2
the other one has to be 2013 (not prime)

Spring 2014
If n is an integer greater than 21, and 21n is
a perfect square, what is the MINIMUM value
of n?
n = 3*7*2*2 so that 21n = 3*3*7*7*2*2

Spring 2014
In a galaxy far, far away, there is a planet
whose inhabitants have either 6, 7, or 8 legs.
Those with 6 and 8 legs always tell the truth,
while the 7-legged creatures always lie. One
day four of them gathered and one of the
exclaimed, “Altogether, we have 25 legs!”
Another said, “Altogether, we have 26 legs!”
The third one stated, “Altogether, we have 27
legs!” Finally, the last one claimed,
“Altogether, we have 28 legs!” How many
legs are there in total?

Galaxy far, far away…
3 liars:
Total legs: 7 + 7 + 7 = 21
Fourth inhabitant must have 6 legs for a total
of 27.

Fall 2013
The diagram shows a dartboard with points
awarded for hitting each region,
but two digits are missing. 48
I threw darts, hit three ?4
different regions, and 1?
scored 132. My friend 60
also threw three darts,
hit three different regions,
and scored only 90. What is
the sum of the missing digits?

Dartboard…
48
?4 48+60+1? < 132
1? So, 48+60+2? = 132
60 24
60+24+1? > 90
So, 48+24+1? = 90
4+8 = 12 18
Pre-Algebra Homework 3: Find missing digits
in addition, subtraction and multiplication

Fall 2013
Suppose we have 5 bags that each contain
10 gold coins. One bag, which remains to be
identified, contains all counterfeit coins. All
the coins look and feel identical. However,
genuine coins weigh 10 each, while
counterfeit coins weigh 10.1 grams each.
What is the FEWEST number of weighings,
using a standard digital scale, needed to
GUARANTEE the bag of counterfeit coins is
identified? Note: We can open each bag and
remove as many coins as we need.

Counterfeit Coins…
1 weighing attempt is enough
B1 B2 B3 B4 B5
+ + + +
The decimal part of the answer will indicate
which bag the counterfeit coins came from

It’s Never Too Early
To Get Them Hooked!
Old NYSMATYC Math League Exams:
www.nysmatyc.org
Sophia Georgiakaki
Tompkins Cortland Community College

WORDS TO PLAY
WITH FIRE, BY
THE STONES
BY STEVE KREVISKY

๏ WELL YOU’VE GOT YOUR FRACTIONS,
AND YOUR SQUARE ROOTS BY THE
SCORE
๏ BUT YOU’D BETTER DO YOUR
HOMEWORK, OR ELSE YOU’LL BE OUT
THE DOOR!

๏ CHORUS: BUT DON’T MESS WITH
MATH, ‘CAUSE YOU’RE PLAYING
WITH FIRE!!!

๏ WELL YOU’VE GOT YOUR CONICS,
AND QUADRATICS , THAT’S FOR SURE
๏ AND YOUR PRIME #’S ARE ENDLESS:
YOU JUST CANNOT COUNT THEM
ALL!

๏ YOUR SQUARE ROOTS ARE NOT
PRETTY, WHEN YOU DON’T HAVE
PERFECT SQUARES,
๏ AND YOUR SMART PHONE CANNOT
HELP YOU, WHICH IS NOT REALLY
FAIR!

๏ YOUR HISTOGRAMS LOOK NORMAL,
AND YOUR VARIANCE IS GOOD
๏ BUT, BE SURE THERE ARE NO
OUTLIERS
๏ AS YOU ONLY SHOULD

๏ NOW YOU HAVE SOME FUNCTIONS,
AND YOU WILL HAVE SOME OTHERS
๏ BUT YOU’D BETTER WATCH YOUR
STEP THERE, OR START LIVING WITH
YOUR MOTHER!

WITH FIRE!!!
WITH FIRE!!!

A Roller Coaster
of Puzzles and
Games
Dr. Mike Long
Howard Community College

That Leads To Another
Calculus Problem
f (17) =17, f (19) =18, f (22) =10, f (26) = 3, f (31) = 9, f (36) =15
f (41) = 9, f (45) =1, f (49) = 4, f (52) = 7, f (55) = 4,(58) =1, f (61) = 4
f '(x) = constant, 0 < x <17,f '(x) = 0 when x = 19, 26, 36, 45, 52, 58
f '(x) > 0: 17 < x <19, 26 < x < 36, 45< x < 52, 58 < x < 61
f '(x) < 0: 19 < x < 26, 36 < x < 45, 52 < x < 58
f ''(x) = 0 when x = 22, 31, 41, 49, 55, 61
f ''(x) > 0: 22 < x < 31, 41< x < 49, 55< x < 61
f ''(x) < 0: 0 < x < 22, 31< x < 41, 49 < x < 55

And Speaking Of Graphs
-20
0
20
40
60
80
100
1
57
113
169
225
281
337
393
449
505
561
617
673
729
785
841
897
953
1009
1065
1121
1177
1233
1289
1345
1401
1457
1513
1569
1625
1681
1737
1793
1849
1905
1961
2017
2073
2129
2185
2241
2297
2353
2409
2465
2521
2577
2633
2689
2745
2801
2857
2913
2969
3025
3081
3137
3193
3249
3305
3361
3417
3473
3529
3585

What’s The Story Here
-5
0
5
10
15
20
25
0 20 40 60 80 100 120 140 160
HeightinMeters
Time in Seconds
Rockin'

And Back To Algebra
Coaster Train Size
Great Bear 32 seats
Fahrenheit 12 seats
Sooper Dooper Looper 24 seats
Storm Runner 20 seats
Log Flume 4 seats

For A Shocking Reveal
y = 0.18x + 2.0531
y = 0.1092x + 1.7609
y = 0.2883x + 1.1926
y = 0.2909x + 21.073
0
50
100
150
200
250
0 200 400 600 800 1000 1200 1400 1600 1800 2000
R
i
d
e
r
s
Time in Seconds
Riders versus Time
Skyrush
Fahrenheit
Great Bear
SooperDooperLooper
Coal Cracker

And My Own Personal Math
Disney
World 9
Magic
Kingdom 5
Space
Mountain
Alpha 1
Space
Mountain
Omega 1
Goofy's
Barnstorme
r 1
Thunder
Mountain
Railroad 1
Seven
Dwarfs
Mine Train 1
Animal
Kingdom 3
Everest 1
Primeval
Whirl Left 1
Primeval
Whirl Right 1
Studios 1
Rockin'
Roller
Coaster 1
Busch
Gardens 7
Apollo's
Chariot 1
Big Bad
Wolf 1
Aplengeist 1
Griffon 1
Loch Ness
Monster 1
Verbolten 1
Air Grover 1

Let’s Talk
Why common Algebra mistakes
are more than just mistakes

Adding Fractions Straight Across

๏ We cannot add unless the denominators are
the same.

the same.
๏ So why do students do it?

the same.
๏ So why do students do it?
๏ How can one un-programmed this mistake?

Simplifying Fractions
๏ How many of us here have seen this mistake?

๏ What do you do to help the students?

๏ What do you do to help the students?
๏ How many ways can you say “no” only to have
a student take it as a yes?

Multiplying Polynomials
Multiply.

๏ Johnny, be careful. You cannot do that.
Multiply.

Multiply.
๏ Johnny, please listen to me. You must not do
that!

๏ Johnny, please listen to me. You must not do
that!
๏ Exam time – Johnny did exactly that!
Multiply.

Why study Algebra?
๏ Our goal is to get our students to not make
those algebra mistakes, pass our exams, and
move ahead.

Why study Algebra?
move ahead.
๏ But maybe, just maybe, they need to make
those mistakes.

Why study Algebra?
move ahead.
those mistakes.
๏ If that is the case, perhaps we want them to
make those mistakes and learn from their
mistakes.

Why study Algebra?
move ahead.
those mistakes.
๏ If that is the case, perhaps we want them to
make those mistakes and learn from their
mistakes.
๏ We just don’t want them to be so quick at
erasing their mistakes as if nothing had ever
happened.

Why do I want Johnny to learn
Algebra?
๏ So that Johnny can learn that it is okay to
make mistakes.

Algebra?
make mistakes.
๏ It is just not okay to keep making them.

Algebra?
make mistakes.
๏ It is just not okay to keep making them.
The End

Pat Riley
Hopkinsville
Community College
MY FAVORITE
MATH TOY

Started with a class
activity I heard at
AMATYC called
“Bears In Space”

Students built a small
catapult used to
launch Gummi Bears
They measured the
launch angle to use
for predictions

I tried to
replicate the
activity…
…EPIC FAIL 

I still liked the concept so
looked for other ways to
do it when I saw the
Nerf guns at Wal-Mart
and bought some

Turned out to be one
of the better ideas
I’ve ever had…
…ended up having
benefits in many other
ways I hadn’t
expected!

Developmental Math
Students shot across
room and timed
Used to introduce
speed via d=v*t

Intermediate Algebra
Using the falling
object formula,
students shot straight
into air in order to
calculate initial
velocity

College Algebra
Building on the initial
velocity example,
students could then
calculate the highest
points (vertex)

College Algebra
“But they got a
different answer than
we did!”

Trigonometry
-Modeling projectile
motion given launch
angles
-Calculate angles to
hit targets

Statistics
Collecting data
(distance from target,
time in air, distance
vs launch angle)

Statistics
Standard Deviations
-Enforces the concept
of consistency

Statistics
Hypothesis Testing
-different shooting
styles

Statistics
Regression Analysis
-launch angle vs
distance flown

Statistics
Final Project
Hit The Target
(offspring of Bears In
Space)

Has been used in
other college-events
for school children on
campus.
Other faculty have
started using them
too!

TV is Funnier When
You Know Your Math
Sophia Georgiakaki
Tompkins Cortland CC, New York

Inspired By…
Julie Miller, Daytona State College
NYSMATYC 2015 - Keynote Address
“Marrying Mathematics and Media
for Humor and Relevance”
(Video snapshots from YouTube)

Scare Crow Gets a Brain
The sum of the square roots of any two sides
of an isosceles triangle is equal to the square
root of the remaining side.
√(x) + √(x) = √(b) ??
x x
“Oh Joy!!! I’ve got a brain!”
b

Star Trek
… It has an auditory sensor. It can, in effect,
hear sounds. By installing a booster, we can
increase this capability by the order of one to
the fourth power.
The Multiplier: 14 = … Too Big!

A Serious Man
Also the answer to the equation “D-in-P” is
equal to the square root of bracket-p squared
minus bracket-p squared, which is also equal
to the square root of h-over-a squared…
∆P = √ <P>2 - <P>2 = √ (h/a)2
Seriously ??

Fox News
Know Your Percents
When it comes to landing the nomination,
Palin is at 70% (With 193% certainty!)

Know Your Money
๏ ABC’s sitcom star plays for charity at the
Millionaire’s 10th anniversary celebration.
๏ “You know I went to Ohio State, right? I
don’t know that much.” (!!!)

Know Your Multiplication…
Nikki from New Orleans, LA

Big Bang Theory
Sheldon Tries Rock Climbing

Big Bang Theory
- This is not bad. It’s like vertical swimming
- You are half way there.
< Sheldon panics>
- Are you alright there?
- Not really. I feel like an inverse tangent
function approaching an asymptote.

Big Bang Theory
- Are you saying you are stuck?
- What part of inverse tangent function
approaching an asymptote do you not
understand?
- I understand all of it. I am not a moron.
To inverse or not to inverse?

YouTube Videos:
๏ Math Mistakes in Movies and TV -
dbaum1987
๏ The Big Bang Theory – Sheldon Tries
Rock Climbing – JL18
๏ Who Wants to Be a Millionaire –
imna2007, mathclips, Chad Mosher,
causeofb
Sophia Georgiakaki – NY

How Open Licensing Brings on
Innovation
Barbara Illowsky, PhD
Professor, Mathematics & Statistics
Dean, Basic Skills & OER for CCC Online Ed Initiative
Foothill – De Anza College CCD
Co-author, Introductory Statistics, by OpenStax College
OEConsortium 2014 Educator ACE Award
Teaching Excellence Award, AMATYC, 2012
@DrBSI illowskybarbara@fhda.edu

The bottom line:
savings over 8 years
One course, one OER text, one college:
Estimated student savings of
$3,000,000+
• Elementary Statistics using Collaborative Statistics at De Anza
College Fall 2008 – December 2013
• Elementary Statistics using Introductory Statistics at De Anza College
since January 2014

Two needs:
๏ Innovation…. for increased
student learning
๏ Sustainability of non-
profits….for continuation
of OER

*OER is free
the way
a puppy is
free!
*Jason Pickavance, Salt Lake City CC

• Distribute
• Remix
• Tweak
• Build upon
• Commercial use allowed
• Only attribution required
Partnership benefits to non-profits
Why partner?

The big question:
Are we “selling
out” by partnering
with for-profit
companies?

VERY BIG NOTE!!!!
๏ I am NOT promoting any particular
company!!
๏ I am here to demonstrate why various
corporate partnerships are important.
๏ I include the three corporate partnerships
with one non-profit as EXAMPLES of how
such partnerships can work.
๏GOT THAT???

What is WebAssign?
๏ Flexible, customizable online instructional
system
๏ Powerful online tools enable teachers to
deploy assignments, assess student
performance, and enrich the teaching and
learning experience
๏ Reaches 1.5M students at 2,300 institutions
each year

Corresponding
Textbook problem

Linear Regression
graphing
“Red” values are different
from textbook’s values

Student benefits
๏ Features that an author cannot
easily contribute
๏ Increased support
๏ More flexibility
๏ Options to participate or not
๏ Still a low cost
๏ and …..

The biggie:
Increased
student
learning
and success!

Contributions to Sustainability
Reinvested
into new
OER
materials
Reinvested
into:
• Additional
High-Quality
Supplemental
Content
• New
Application
Functionality
• Support of
new OER
materials

Bottom line
๏ Innovation…. leads to:
Increased student learning
๏ Sustainability of non-profits …
leads to:
Greater services for students

Using Google Hangouts
to Enhance
Online Teaching

With Google Hangouts, you can
 Make video calls with your students and
share each other’s computer screens

 Make video calls with more than one
students to discuss a group assignment

 Broadcast your lectures and invite your
online students to watch in real time

Step 1: Create a Gmail account

Step 2: Sign in to Google+ and
find the Hangout frame

Step 3: Click “Start a Video Hangout”

Step 4: Click “Video Call”

You can broadcast live lectures to your
online students:

Sign in to Google + and
click “Create a Hangout On Air”

Google Effects: Stickers, Emoji…

Enliven
classroom
doldrums
with quick
and
easy
games!
Kathleen Offenholley
Borough of Manhattan
Community College
Z
Z
Z

Game it up!
A game will get your students to
๏ Focus
๏ Make some noise
๏ Have fun!
You can prepare a game in advance
or make one up on the spot!

Some games take prep
time…
Envelopes with coins in them
make coin word problems
much more fun!
Do NOT open the envelope until
your whole team has done the
problem!! This envelope contains
nickels and dimes. The number of
dimes is…

Play in teams…
๏ If your team thinks it has the
correct solution using
algebra, open the envelope!
๏ If the answer is right, keep
the money.
๏ In the end, the team with
the most money wins!

PowerPoint Jeopardy
๏ Templates are available online for free
๏ Just add your own problems

But what if you need a
game…Right Now?
๏ Add an element of randomness and you
have a game!

Here’s an instant game…
๏ Write a polynomial
multiplication problem on
the board, like (x + 5)(x -
2)
๏ Each group of students
gets 10 random cards
from a deck.
๏ If the group simplifies this
correctly, they can discard
any cards that equal or
add up to the last number.

Instant card game,
continued
Example: (x + 5)(x - 2) = x2 + 3x –
10
Each group that gets this correct can
either discard a royal card, a ten card,
or cards adding up to 10.
Bonus round: If students do a special
difficult problem correctly, they can
discard one card of any kind.

Instant card game,
continued
Consider modifying this for other
topics, like integer arithmetic -- make
red negative!

What if you don’t have
cards or dice handy?
๏ Virtual dice:
http://www.bgfl.org/bgfl/custom/resources_
ftp/client_ftp/ks1/maths/dice/index.htm

Great for working on
review sheets
๏ Students can work in pairs
๏ When the pair gets 4 problems correct,
they can come up to the class computer to
roll the die, then advance along a game
board you have drawn on the board.

When class is fun, we’re all
winners!
Start
Finish
!

Amatyc Ignite 2015 Second Half

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