MATHEMATICIAN OR

MAGICIAN?

Mabra Karpie and Jamie RossSUNY Fredonia

AMTNYSOctober 27-29, 2011

Great hooks, ice breakers, Friday Fun activities, or great ideas to have in your back pocket!

…Using

Lets beginour

First Magic Trick….

PICK A NUMBER

DON’T TELL ME!

17 24 29 2816 22 31 1921 18 20 2325 30 26 27

Is your number on this page?

27 14 15 1031 24 30 2811 8 12 2529 26 13 9

Is your number on this page?

20 23 12 225 28 13 7

15 29 30 621 14 31 4

Is your number on this page?

14 10 18 619 7 31 2327 11 30 215 3 26 22

Is your number on this page?

23 5 17 119 21 1 133 27 7 25

29 31 15 19

Is your number on this page?

Your number is...

PICK A NUMBER

DON’T TELL ME!

17 24 29 2816 22 31 1921 18 20 2325 30 26 27

Is your number on this page?

27 14 15 1031 24 30 2811 8 12 2529 26 13 9

Is your number on this page?

20 23 12 225 28 13 7

15 29 30 621 14 31 4

Is your number on this page?

14 10 18 619 7 31 2327 11 30 215 3 26 22

Is your number on this page?

23 5 17 119 21 1 133 27 7 25

29 31 15 19

Is your number on this page?

Your number is...

Binary Representation How does this work?

Every positive integer has a unique binary representation. In layman’s terms, every positive integer can be written as a sum of powers of 2.

You can add more cards to guess numbers up to one less than a power of two. For example, you can add one more card to guess numbers up to 63.

Where in the curriculum can you use this? Introduction to binary numbers Exponents & powers Place Value

On to the NextMagic Trick..

Functional Card Trick How did Mabra know your card!!??

Stacked Deck “CHaSeD” Composite Functions

Functional Card TrickA 2 3 4 5 6 7 8 9 10 J Q K

A 2 3 4 5 6 7 8 9 10 J Q K

C H S D

C H S D

Functional Card Trick Where in the curriculum?

Functions Composition of functions Modular arithmetic

The Finale…

Step 1: Pick your favorite three-digit number _ _ _ (all different digits).

Step 2: Reverse the three-digit number.

Step 3: Take the smaller three-digit number and subtract it from the larger. Make sure you have a 3-digit number.

Step 4: Take that answer and reverse it again.

Step 5: Add the numbers from Step 3 & 4.

1089! What just happened??!!!!

, which is Steps 1, 2, & 3 result in

Steps 4 & 5 always give

Where in curriculum? Addition, Subtraction Number sense

Tricks cover: Algebra Binary numbers Composition of functions Digital root Exponents, powers Functions Modulo arithmetic Number sense Parity Place value

Questions?

Mabra Karpie: mkarpie@fredonia.edu

Jamie Ross: jross@fredonia.edu

SUNY Fredonia

We have one more trick for you!

Every good magician can pull a bunny out of his hat

right?

Want to see it happen live?!