Math magic tricks can liven up any math class and create a sense of wonder and curiosity about math. Not only that, math magic creates a new context for algebraic reasoning as students go beyond "What's the answer?" to explore "What's the trick?"
Abracadabra! Your number is 13! Images courtesy of Wendy Petti. 
Operate on a starting number and always end up with a given number.
One type of number trick involves adding, subtracting, multiplying, or dividing by a starting number and subtracting the original number in such a way that each participant always arrives at a certain number:
Think of a number between 1 and 100.
Multiply your number by 4.
Add 12.
Multiply this number by 2.
Add 16.
Divide this number by 8.
Subtract your original number.
Your new number is 5!Think of a number between 1 and 100.
Double your number.
Add 15.
Multiply this number by 3.
Add 33.
Divide this number by 6.
Subtract your original number.
Now your number is 13!1
Rearrange digits.
Another type of number trick involves rearranging and recombining digits:
Write a threedigit number (with three different digits).
Mix up the digits to get another threedigit number.
Subtract the smaller number from the larger.
Add the digits in the difference. (If you get a twodigit answer, add the two digits to get a single digit.)
Subtract 5 to get a final number.
Your number is 4!2
(This trick works with numbers up to eight digits, when each digit is different.)Write a threedigit number. The first and last digits should have a difference of more than one.
Reverse the digits and write down this new number.
Subtract the smaller number from the larger one.
Circle your answer.
Reverse the digits and add this new number to the circled number.
Your number is 1089!3
The starting number appears in a final custom number.
Some number tricks come back to a form of the starting number(s):
Here is a magic number: 12,345,679 (Write it on the board.)
Pick a number from 1 to 9.
Multiply your number by 9.
Multiply the magic number by your new number.
Surprise! Look at the number you have now!
(It's a string of nine digits made up entirely of each person's starting number. When starting with 2, the new number is 222,222,222.)4Write the year of your birth.
Double it.
Add 5.
Multiply by 50.
Add your age.
Add 365.
Subtract 615.
The first four digits are the year of your birth. The last two digits are your age.5
You can find math magic in
What do you get when you cut a Mobius strip in half?Â (a longer Mobius strip!) 
The resources at the end of this article encompass a variety of math magic ideas presented in kidfriendly fashion.

Adapt number tricks for younger students by asking them to choose a starting number less than 20 or even less than 10.
Provide calculators as needed for multiplying and dividing, or for doublechecking answers.
After enjoying a math magic show, guide students in understanding how one of the tricks works. See "How Did You Do That?" below.
Challenge older or advanced students to figure out on their own how a trick works and then explain it so everyone else can understand. Students could work in small groups to explain a trick quickly and effectively.
Ask students to develop their own math magic tricks.
Many math magic tricks call on students to compute with the four basic operations  sometimes applied to very large numbers. In the context of math magic, computational practice is fun.
If a trick works for some students and not others, it's amazing how eager they can be to find and fix their mistakes so the trick will come out right.
Best of all, many students have an inner motivation to understand how math magic tricks work, and that curiosity can lead them to embrace and apply both new and familiar concepts and skills, including algebra.
For the most part, the resources cited in this article do not explain their tricks, because "Magicians never reveal their secrets!" You might choose for the tricks to stay in the realm of magic, to intrigue and delight your students. There can be value enough in students' enthusiastic manipulation of numbers as they are being wowed. But there can be value, as well, in revealing a few magicians' secrets.
Most math magic tricks can be understood with algebraic reasoning. Students as young as fourth grade can grasp how simpler tricks work if you guide them step by step through the reasoning and explain the algebraic notation. For example, the first trick can be explained like this:
Think of a number between 1 and 100.  Let's represent this number as n. 
Multiply your number by 4.  We can show this as 4n (4 times n). 
Add 12.  4n + 12 
Multiply this number by 2.  2 (4n + 12) = 8n + 24 (using the Distributive Property) 
Add 16.  (8n + 24) + 16 = 8n + (24 + 16) = 8n + 40 (using the Associative Property) 
Divide this number by 8.  = + = n + 5 
Subtract your original number.  n + 5 â n = (n â n) + 5 = 0 + 5
(using the Commutative and Associative Properties) 
Your number is 5!  0 + 5 = 5 
It's a wonderful feeling when students beg to know how a trick works and exclaim over the algebraic reasoning that proves it. Demystifying a math magic trick can help students appreciate the greater "magic" and utility of algebra, number properties, and patterns, driven by their own need to know.
But don't overdo it! There's a lot to be said for retaining some of the mystery too, and letting students enjoy the wonder of the "magic."
Notes: 1 This trick is from Mathemagic.