&KDSWHUEnrichment:
Be a Math Magician
Objective To use expressions and equations • To explain a number trick
algebraically
Some magic tricks have more to do with math than with magic.
A magician told Mr. Green that she would read his mind if he
followed her instructions carefully.
“Choose a number from 2 through 9. Choose 2, choose 9, or
anything in between. Are you ready? Good. Multiply your
number by the sum of 6 plus 3. This gives you a new number.
Add its digits. Subtract 3 from that sum to find your
key number.”“Take your key number, and change it to a letter of the alphabet this way. For 1,
the letter is A; for 2, it is B, and so on. Find your letter and think of two names:
the name of a state that begins with that letter and the name of a large animal that
begins with the last letter of the state’s name. Think hard, so I can read your mind.”
“Mr. Green, you are thinking of an alligator in Florida, aren’t you?” Mr. Green
couldn’t believe it! The magician was right. Did she really read his mind?If you analyze the trick carefully, you will find that it is really very simple.
- The sum of 6 3 is 9. The product of 9 and any number from 2–9 is a
two-digit number whose digit sum is 9. - Subtracting 3 from 9 gives 6. The sixth letter of the alphabet is F.Only one
state begins with the letter F—Florida. - Most people who have Florida in mind will think of an alligator when they
are asked about a large animal whose name begins with the letter A.
This number trick relies on arithmetic and common knowledge. In this lesson, you
will try some more tricks and then analyze them to figure out how they work.
Try the trick below with several different starting numbers.
Steps of Trick 1: a.Pick a number.
b.Multiply it by 3.
c.Add 6 to the product.
d.Divide the sum by 3.
e.Subtract the original number.
Did you get 2 every time? To see
how this works, you need to use
a little algebra. The table below
gives the steps for the number 246
and for “any number” n. The right
column shows why the result will
always be 2.Steps of Trick With 246 With n
a.Pick a number. 246 n
b.Multiply it by 3. 738 3 n
c.Add 6 to the product. 744 3 n 6
d.Divide the sum by 3. 248 n 2
e.Subtract the original number. 2 2