Magic Menu

Engineers' tools: Math, science, and computers.

Actors' tools: Dress, play script, and stage props.

Chefs' tools: Food, spices, oven, and kitchen utensils

Singers' tools: Song and music.

Magicians' tools:

Pick a card

Central Michigan University, Mt. Pleasant, Michigan

Materials Required: Paper and pencil

Activity Time: 5 - 10 minutes

Concepts Taught: Subtraction/regrouping

"Math Magic" is a wonderful activity to use with students when you find

that you have some time to fill!

Ask students to select a three-digit number. However, stress to students

that the first and last digits of the number CANNOT be the same (ex.

121, 474, etc.). Once the students have selected their numbers, have

them invert the number. For instance, 123 would become 321. Have

students subtract the smaller number from the larger of the two, keeping

their answer a "secret" from you.

Next, ask a student to give you either the first or the last digit of

their answer. You then "guess" their whole answer! How does it work? The

center digit will ALWAYS be "9". The sum of the first and last digits

will ALWAYS be "9". So, if a student gives you his first number as "2",

you instantly know that the answer is 297!! If, however, a student gives

you the last number of their answer and it is "9", then you know that

their answer is only 99.

ENJOY! The students love this one, and marvel that their teacher is

"psychic"! Once they learn the secret, they love to try it out on all of

their family and friends!!

Performance: Predicting a Number

1.Write down the year of your birth.

2.Write down the year when something interesting happened and add the two

years together.

3.Add to this sum your age this year.

4.Add to this sum the number of years since the interesting event

happened.

5.Sum will always be twice the current year.

Performance: The Missing Eight

1.Write down 12345679

2.Ask someone which of the digits in the number s/he likes the least and

have the person put an "x" over the digit selected.

3.Ask the person to multiply 12345679 by a number you select.

4.All of the digits in this product will match the number marked with the

"x."

Performance: Predicting the Remainder

1.Write a 3-digit number

2.Add the 3 digits until you get a single digit.

3.Have volunteer divide the 3-digit number by 9

4.Remainder should be number (unless the single digit is 9, remainder is

0)

Performance: Secret Number

1.Write a 3-digit number with all different digits

2.Reverse the digits and subtract the smaller from the larger

3.Reverse the result and add them up

4.Answer should be secret number

Balloons

1.Probability

2.Angles

3.Air Pressure - How many bubbles can be twisted ... maximum? Estimate!

4.Create Shapes

Performance: The Lightning Calculator 1.Choose a volunteer and ask her/him

to write down a 5-digit number. 2.You write down a number under her/his

number. 3.Continue in this manner, alternating numbers, until the column

is at least 8 figures long. 4.Have the volunteer find the sum of these

numbers.

5.While s/he is summing the column of figures, you write down the sum as

fast as you can write the digits.

Performance: Foretelling a Sum

1.Choose a volunteer and have her/him write down any two numbers and

announce what they are.

2.Have the volunteer find the sum of these two numbers, write it down, and

announce the sum.

3.Have the volunteer find the sum of the second and third numbers, write

that down, and announce the sum.

4.Give the same instructions for the third and fourth numbers.

5.Instruct the volunteer to continue the pattern until ten numbers are

listed.

6.After the seventh number is listed, announce: I predict that the sum of

these numbers will be ___.

7.Have the volunteer compute the sum of the ten numbers.

Performance: Foretelling a Sum

1.Write down any 2 numbers.

2.Find the sum of these numbers and write it down.

3.Find the sum of the last two numbers (the second number and the sum) and write it down.

4.Continue adding the last two numbers written until ten numbers are

listed.

5.The sum of the ten numbers can be predicted from the seventh number in

the list.

Performance: Unveiling Even and Odd

1.The first person chooses either 9 or 10 and multiplies it by 2.

2.The second person takes the other number and multiplies it by 3.

3.They compute the sum of the two products.

4.From this sum, you can determine which person chose 9 and which person

chose 10.

Performance: Predicting the Hour

1.Have your subject think of any number on the dial of a clock.

2.Tell the person to silently add one to the number s/he selected each

time you point to a number on the clock dial, until s/he gets to 20. Have

the person announce aloud when s/he reaches 20.

3.Point to 7 randomly selected numbers on the dial, then point to the 12

and continue pointing counterclockwise until 20 is announced.

4.When 20 is announced, you will be pointing to the number the person

selected.

Performance: Amazing Prognostication

1.Write a prediction (any number between 1 and 50) on a piece of paper and

fold it.

2.Give the paper to someone to hold during the trick.

3.Ask a different person to choose any whole number between 50 and 100 and

say it aloud.

4.Ask the person who chose the number to perform the calculations below.

a.Add the 2-digit number __ to the number chosen.

b.Delete the leftmost digit from the sum.

c.Add the deleted digit to the remaining number.

d.Subtract this result from the number originally chosen and

announce the answer.

5.Ask the person holding the folded paper to read your prediction. The

two numbers will match.

Performance: Predictable Dice

1.Roll a pair of six-sided dice.

2.Find the following products:

(top of DIE #1) X (top of DIE #2)

(bottom of DIE #1) x (bottom of DIE #2)

(top of DIE # 1) x (bottom of DIE #2)

(top of DIE #2) x (bottom of DIE #1)

3.Find the sum of the products.

4.The sum of these four products can be predicted before the dice are

rolled.

Performance: Who Is Hiding the Coin?

1.Select a group of 2-9 people and assign an identification number to each

person.

2.When your back is turned, one person in the group hides a coin in

her/his left or right hand. Each person in the group should know where

the coin is.

3.Randomly choose someone in the group to perform the following

calculations:

a.Multiply the identify number of the person concealing the coin by 2.

b.Add 5 to this number.

c.Multiply the result by 5.

d.Add 10 to the result.

e.Now add 1 if the coin is in the person's right hand or 2 if the coin

is in her/his left hand and announce the result.

4.From this result, you identify who is holding the coin and which hand it

is in.

Performance: The Marble Transfer

1.Person A takes a handful of marbles from a bowl and counts them.

2.Person B takes 3 times as many marbles as A took.

3.Person A gives 5 marbles to person B.

4.Person B gives back to person A 3 times as many marbles as A is now

holding.

5.At this point, you can predict the number of marbles Person B is

holding.

6.When you know how many marbles person A has now, you can determine how

many marbles both A and B originally took.

Performance: The Money Mystery

1.Imagine a sum of money less than ten dollars.

2.Transpose the digits.

3.Take the difference between these two amounts.

4.Transpose the digits in the difference.

5.Add this transposition to the difference.

6.You can predict the final answer.

Performance: Permutation Prediction

1.Choose any number consisting of three consecutive ascending digits.

2.Determine all permutations (possible arrangements) of these digits and

list these six three-digit numbers.

3.Compute the sum of these numbers and divide the sum by 6.

4.From the quotient, the original number can be predicted.

Performance: Magical Number Nine

Variation 1

1.Select a three-digit number in which none of the three digits is the

same.

2.Form another three-digit number by rearranging the original digits.

3.Now subtract the two three-digit numbers and add the digits in this

difference.

4.From the first (or last) digit in the sum, you can tell the other digit.

Variation 2

1.Select a three-digit number in which none of the three digits is the

same.

2.Form another three-digit number by rearranging the original digits.

3.Now subtract the two three-digit numbers and add the digits in this

difference.

4.If the sum is not one digit, continue adding the digits in the result

until you reach a one digit number. You can predict this digit.

Performance: The Missing Digit

1.Choose a four-digit number and compute the sum of its digits.

2.Cross out any one of the digits in the original number, and write the

remaining three digits as a three-digit number.

3.From this three-digit number, subtract the sum of the digits previously

computed.

4.Sum the digits in this difference.

5.From this result, you can tell the digit that was crossed out in the

original number.

Performance: A Permutation Trick

1.Take 3 blank cards and write any single digit on the first card, any

single digit on the second card (please do not make both digits zeros),

and a decimal point on the third card.

2.Without revealing the numbers chosen, find all possible decimal numbers

that can be formed by rearranging the three cards. There should be six.

3.Sum the six numbers.

4.Multiply this sum by 100.

5.Divide this result by 11.

6.Divide this result by 3.

7.Finally, divide this result by the sum of the two digits that were first

selected.

8.You can predict the answer.

Performance: The Reappearing Number

1.Write down any two-digit prime number greater than 13.

2.Attach a zero to this number and form a six-digit number by repeating

these three digits.

3.Pass the paper to 5 other people. Have each of them do successive

divisions by the primes: 2, 5, 7, 11, and 13. The first person divides

the six-digit number by 2, the second person divides the resulting

quotient by 5, the third person divides the second quotient by 7, and so

on. In all the divisions, the remainders are zeros. When the final

division is completed, the last quotient is written on the paper and

passed back to the person who thought of the number.

4.When you get the paper back, you will recognize the two-digit prime

number on the paper.

Performance: Permutation Prediction

1.Think of a number.

2.Perform the computations:

a.Multiply the number by 2.

b.Add 6 to the product.

c.Add this result to the square of the original number.

d.Subtract 5 from this sum.

e.Take the square root of the difference.

3.Predict the original number selected.

Performance: Divining from a Table

1.Have someone think of a number from 1 to 60.

2.Give them the six cards.

Card 1: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35,

37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59

Card 2: 4, 5, 6, 7, 12, 13, 14, 15, 20, 21, 22, 23, 28, 29, 30, 31, 36,

37,

38, 39, 44, 45, 46, 47, 52, 53, 54, 55, 60, 13

Card 3:8, 9, 10, 11, 12, 13, 14, 15, 24, 25, 26, 27, 28, 29, 30, 31, 40,

41,

42, 43, 44, 45, 46, 47, 56, 57, 58, 59, 60, 13

Card 4:2, 3, 6, 7, 10, 11, 14, 15, 18, 19, 22, 23, 26, 27, 30, 31, 34, 35,

38,

39, 42, 43, 46, 47, 50, 51, 54, 55, 58, 59

Card 5:16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 48,

49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 30, 60

Card 6:32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48,

49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 41

3.Ask for all the cards containing her/his number.

4.From the cards returned to you, you can predict her/his number.

Performance: The Domino Chain

1.Mix the 28-piece set of dominoes and place them face up on a table.

2.Ask your subject to form a single chain using all the dominoes and

matching them end to end as in normal play.

3.You can predict the beginning and ending numbers in the domino chain.

Performance: Sum Fun

1.Number 6 slips of paper from 1 to 6.

2.Arrange your pieces of paper like this:

3 1 2

4 6 5

Add pieces of paper which are adjacent to each other:

Solution: 4, 3, 10, 11, 7, 7, 7

3.Rearrange your slips of paper until all the answers are different from

each other- 7 different answers. Record your arrangement.

4.Rearrange your slips of paper so that you have only 3 different answers.

Performance: Was It a Rat I Saw (Palindrome)

1.Definition: reads the same from left to right and from right to left.

2.Examples: MOM, RADAR, ABBA, 747, 222, 54145, REDIVIDER

3.You can create your own Type I (1 addition step) or

Type 2 (2 addition step) as follows:

Reverse digits and add:

Type 1: 43 + 34 = 77

Type 2: 85 + 58 = 143

+341

--------

484

Show that 153 is Type 2 and 79 is Type 6.

Try 24 steps for 98 to get 8813200023188

Performance: 6174

1.Take any 4-digit number as long as the 4 digits are not all the same.

2.Using these 4 digits, make as big a number as possible.

3.Using these same 4 digits, make as small a number as possible.

4.Subtract the answer to step 3 from the answer to step 2.

5.Repeat steps 2-4 till you get the answer 6174. (Try 3 digits and see!)

Performance: Mental Math

1.Multiply by 11:

352458

111111

--------------------------------------------------------------------------------

385 264638

(8 = 3 + 5)(6 = 2+4)?

Performance: 7/11

1.Write a number < 10

2.Write another number < 10

3.Add the first 2 numbers

4.Add the second and third numbers

5.Add the 3rd and 4th numbers

6.Continue this pattern until there are 10 numbers in the column.

7.Add up all numbers

(Short cut: Multiply the 7th number by 11)

Ex. 7, 2, 9, 11, 20, 31, 51, 82, 133, 215 = 561

(51 x 11 = 561)

Performance: Predicting the Remainder

1.Write a 3-digit number

2.Add the 3 digits until you get a single digit.

3.Have volunteer divide the 3-digit number by 9

4.Remainder should be 7 (unless the single digit is 9, remainder is 0)

Performance: Divining a Number

1.Write a number between 1 and 10 inclusive

2.Multiply by 3

3.Divide bye 2

4.If you note that a fraction remains, key 1

5.Multiply by 3 again, and divide by 2

6.If a fraction, key 2

7.Add 2

8.Subtract 11

9.If a subject cannot do that without getting a negative number, add key

numbers and that's the number they had.

10.If subject can do it, key 4

11.Add 5

12.Subtract 14

13.If cannot without negative number, add key numbers to get their number.

If can, total key numbers and add another 4.

Performance:Which Hand

1.Tell subject to put a dime in one hand, and a penny in the other without

you seeing which is which.

2.Tell subject to multiply the value of the coin in the right hand by any

even number you pick.

3.Tell subject to multiply the value of the coin in the left hand by any

odd number you pick.

4.Add the results and have them tell you if their sum is even or odd.

5.If even, penny is in the right hand and the dime in the left. If odd,

dime is in the right hand and the penny in the left.

Performance: Tapping the Hours:

1.Have the subject think of any number on the watch dial.

2.Tell them to start with their number and count to 20 as you tap. When

they reach twenty, they should say stop.

3.Tap 8 random numbers, 9th tap should be on 12 and then continue until

they say stop going counterclockwise on consecutive numbers.

4.When they say stop, it will be on their number.

Performance: Predicting a Number

1.Write down the year of your birth.

2.Write down the year when something interesting happened and add the two

years together.

3.Add to this sum your age this year.

4.Add to this sum the number of years since the interesting event

happened.

5.Sum will always be twice the current year.

Performance: Guessing the Total:

1.Have subject roll three dice. They should add the faces that are up.

2.Have them select on the die and add the number on the bottom face.

3.Roll that die again and add the new "up" face to the total

4.Make sure they leave dice as they now are and you can tell them their

total by adding the faces showing up plus 7.

Performance: Royal Pairs:

1.Before trick, remove kings and queens from deck. Separate kings into 1

pile and queens into another, but in the same suit order. Place one on

top of the other.

2.Allow someone to cut as many times as they want.

3.Split into two piles, 4 cards each, without disturbing the order.

4.Top of each deck will be a pair.

Performance: Four-Ace Trick

1.Before trick, put 4 aces in positions 9, 10, 11, and 12 in deck.

2.Have subject pick a number between 10 and 20.

3.Deal that many off the deck.

4.Add digits of that number and put that many back on top of deck.

5.Take top card and set aside.

6.Repeat until you have four cards out of the deck.

7.These four cards will be the aces.

Performance: The Magic of Manhattan:

1.Have someone cut the deck approximately in half.

2.Pick up either half and count the number of cards.

3.Add the digits, and counting from the bottom, go to that card number.

Have subject remember the card.

4.Replace that 1/2 deck on top of the other half deck.

5.Spell out T H E M A G I C O F M A N H A T T A N

(or any other 19 letter phrase or word)

6.Spelling ends on selected card.

Professor's Nightmare

K. Chun

Effect: Teacher shows three separate pieces of rope each of a different

size. There is a short piece, a medium size piece, and a long piece. The

teacher folds the three pieces and when the ropes are opened out again,

all three pieces are seen to be of the same size.

Modification: Have students measure and cut the ropes and the

rest of the class estimate the length.

Performance: Hold the three ropes in your left hand as illustrated in figure 1.

The shortest rope is to the left towards the joint of the thumb, then the

medium size rope and finally the long rope.

Grip the hanging end of the shortest rope with your right hand

from behind the other two ropes and bring it to the top placing it to the

extreme right of the three ends besides the original short end as in figure 2.

Take the hanging end of the middle sized rope and place it to the

right of the four ends in your hand. Finally take the hanging end of the

longest rope and place it to the extreme right. The position at this

stage is as in figure 3. Your extended fingers cover the fold of the

shortest rope from the students' view.

Separate the three ends to your right and pull out the ropes. Let

them hang down. All three ropes appear to be of the same size.

Performance: Professor's NightMare

Performer shows three separate pieces of rope each of a different size.

There is a very short piece, a medium size piece, and a long piece. The

performer folds the three pieces and when the ropes are opened out again,

all three pieces are seen to be of the same size. A perfect illusion. If

required, the ropes can again be restored to their original different

sizes and tossed out for examination.

Preparation:

Cut ropes / string as follows:

1/2 of small + 1/2 of long = 1 medium

3-Paper Experiment

Tear 3 pieces of paper and draw:

1) Circle, 2) Square, 3) Triangle

Write the "1" in the circle

"2" in the square

"3" in the triangle

Opposite side write :

"4" on the back of the circle

"5" on back of the square

"6" on back of the triangle

place paper with 4,5, 6 side up ... mix them up to form any 3-digit number: 456, 654, 564,645, etc.

Take center paper and

turn it over ...

add up the 3 numbers ....

you have come up with a number between 1 & 15

....

solution: 12

Astrology ...

a, b, c, d ...................

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

think of a number from 10 to 20 ... place your finger on a - 1, b- 2, c-

3, d-4, 10-5, 11-6, ... till you come to your

thought out number ....ex. 11 ....

12- 7, 1-8, 2-9, 3-10,4-11...

now you count your number again, but in the opposite direction ... counter

clockwise ...

start your count with the circle you finished on ... starting with 1 ...

ex. 4-1, 3-2, 2-3, 1-4, 12-5, 11-6, 10-7, 9-8, 8-9, 7-10, 6-11

now you have come o a sign .... which is the number 6 ......

Folded paper ...

Take a paper and fold in 1/2, fold in 1/2 2 more time ... into 8 separate

rectangles ... unfold the paper and fill information with: upper left

corner A ... B ... C .... D

H ... G ... F ... E

Take your paper and fold in any manner ... along long axis, or fold paper in on self ... fold in or outward to a

single unit ... take your scissors and trim off the edges of folded paper

... you will come out with separate rectangles ...

sort paper with face up and face down letters .... and choose either one

... study letters and try to form a word with all the letters ... if you

can't make up a word, then choose other stack ... you got a word ....

CAGE

interactive symbols ...matrix

arrow square cross

circle heart star

rectangle triangle diamond

place your finger on any design and spell out the design ...move finger

from space to space for each letter .. .you can move left/right, up and

down ... not diagonally ...

once a space is gone, you can't move there ...

now that you have finished spelling, you're not on the rectangle ... it's gone, you can't go there anymore

arrow square cross

circle heart star

triangle diamond

move 5 times ... you're not on circle

arrow square cross

heart star

triangle diamond

move 2 times ... you're not on triangle

arrow square cross

heart star

diamond

move 3 times ... take away arrow & diamond ...

square cross

heart star

move 3 times ... take away square

cross heart star

move 1 time ... get rid of heart & cross ...

star

you are the star!

Cards ...

1)

deal 2 stacks of 5 cards each ... left/right ...

look at card on top of left pile ... remember it

pick up right stack, and option ... you can deal cards away to deck that

was placed on side ... you can

determine to get rid of 1-4 cards ... the remaining card goes on top the

left stack and buries it away ....

your card is in the middle somewhere .... pick up pile and turn face up, mix the cards as follows ...

deal the top card to table, then the next card under the stack ... down

and under till you run out of cards ...

now the pile is mixed ... take the pile and face down on table and remove

the top card ... face down ... say the card you remember out loud ... not

that one ...

second card ... nope ...

third card ... ah ... yes ... that's it !

2) Shuffle cards ...

cut into 3 piles/ approx. equal ... choose only 1 pile and put the others

away ...

should have between 10-20 cards ... count them ... now the number is

random ....

add the 2 digits together .... whatever the total, deal that many cards to

discard ...

hold the cards and deal down for 2 groups ... you can put 1 to right and left or 2/2, or 3/3, or 4/4 ...

you now have 1 pile to left, 1 on right and maybe some in hand ... take

either of 2 piles and discard ...

look at bottom card of pile ... that's yours ... take the pile and place

on left hand ...

I'll find your card by spelling Max Maven or counting 8 ... and put the

cards to the bottom of the packet ....

the top card is yours!

3) 4 cards ... each suit ... take out any of each ....

S, H, D, C

Take spade and face up ... on it the heart, club, then diamond ... pick up

4 cards and place face up ... turn over diamond ... cut the packet ...

transfer from top to bottom, take top 2 cards and turn over as one, cut

the cards any way, turn the entire packet over and repeat procedure...

take top 2 cards and turn over as one, cut the cards any way

option ... you can do this again or not do it ... take top single card and turn over ..

take top 2 cards and turn over as one, take top 3 cards and turn over as

one, turn over entire packet .....

at this point, all mixed ... nevertheless, it could have a lot of

combinations, but only 1 is reverse ...

spread out packet ....

solution: heart!

Performance: Royal Pairs:

1.Before trick, remove kings and queens from deck. Separate kings into 1

pile and queens into another, but in the same suit order. Place one on

top of the other.

2.Allow someone to cut as many times as they want.

3.Split into two piles, 4 cards each, without disturbing the order.

4.Top of each deck will be a pair.

Performance: Four-Ace Trick

1.Before trick, put 4 aces in positions 9, 10, 11, and 12 in deck.

2.Have subject pick a number between 10 and 20.

3.Deal that many off the deck.

4.Add digits of that number and put that many back on top of deck.

5.Take top card and set aside.

6.Repeat until you have four cards out of the deck.

7.These four cards will be the aces.

Performance: The Surprise In Hawaii:

1.Have someone cut the deck approximately in half.

2.Pick up either half and count the number of cards.

3.Add the digits, and counting from the bottom, go to that card number.

Have subject remember the card.

4.Replace that 1/2 deck on top of the other half deck.

5.Spell out T H E S U R P R I S E I N H A W A I I

(or any other 19 letter phrase or word)

6.Spelling ends on selected card.