MATH-MAGIC NUMBER 1

Card Values:Ace = 1 2 = 2 3 = 3 … 10 = 10 J = 11 Q = 12 K = 13

For this activity, we’ll select two volunteers. Each will choose a card from the deck and show the rest of the class. The class will verify that the calculations are correct.

The first person will do the following: Take the value of your card, multiply it by 4, add 5, then multiply by 5.

The second person will do the following: Take the value of the card, multiply by 2, subtract 10, then divide by 2.

Neither person will tell me their individual numbers, but instead, they will take the resulting number from each part and add them together. When finished, verify with the class that this is the correct value. Then tell JUST this value.

MATH-MAGIC NUMBER 2Doug will show you a card trick. You need to determine how it is done and why it works (if it really does always work). This trick will involve three cards along with the operations of addition and division.

Card Values: Ace = 1, 2 = 2, … 9 = 9, Ten/Jack/Queen/King = 0

Draw three cards – only requirement is that all three must have different face values (so you couldn’t have a Jack and a Queen since both are worth 0, and you couldn’t have a pair of 4’s, etc). Once you have them, arrange them to form all possible 2 digit numbers. It is okay to have a two digit number that starts with a 0.

Add up all of these two digit numbers and write down the sum. Then take the original three face values and add them together. Divide the larger sum by the smaller sum and find the quotient (the answer from the division problem).

What is your result? Why?

MATH-MAGIC NUMBER 3Doug will show you a card trick. You need to determine how it is done and why it works (if it really does always work). This trick will involve three cards along with the operations of addition and subtraction.

Card Values: Ace = 1, 2 = 2, … 9 = 9, Ten/Jack/Queen/King = 0

Draw three cards – only requirement is that you can’t end with 3 of a kind. Once you have them, arrange them to form the largest possible 3 digit number, and the smallest possible 3 digit number (it is okay if the number ends up 005, this is still a 3-digit number).Now take the large number and subtract the smaller number – this will form a 3 digit number (again, it is okay if the first digit is a 0).

With this new number, write it backwards (abc would become cba). Then add these two together.

What is your result? Why?