logo
Lesson Materials

Math Magic or How to use the powers of two!

Think of any number from 1 to 31.
Click on ALL of the check boxes in the groups where your number appears.
Click the 'Your Number is' button and the result is the number you were thinking of. Want to try another number? Just click 'RESET' and try again.

group1
Group One 		group2
Group Two 		group3
Group Three
group4
Group Four 		group5
Group Five

Objective

6.22 The student will investigate and describe concepts of positive exponents, perfect squares, and square roots. Calculators will be used to develop exponential patterns.

 How it Works Close 

Let's say you pick 28. It is in cards 3, 4, and 5. Now look at those cards. Do you notice anything special? Add the first number of those three cards. Add 4 + 8 + 16. You get 28! What is so special about 4, 8, and 16?
Notice that the first number of all the cards is a power of 2. We can add powers of 2 and make any whole number.

 Task Close 

This 'trick' actually is very old but it is still performed even to this day. Usually, the five groups of numbers are written down on five cards. (Magicians use six cards and refer to these as the age cards, so-called because one 'trick' is using these to guess someone's age, provided that the person is not over 63 years of age.)
Can you make this six-card set?


 Hands-On Activities Close 

Refer to the "King's Reward" and "Grain of rice" activity at left. Can you make a visual display to represent these stories?

 Other Web Sites Close 
  1. Exponents defined.
  2. Click on quiz link after reading.
 Puzzles & Problems tangram Close 

What is 21? What is 20?
What is 31 and 30?
What is 27 to the 1 and 0 power?
Write a "rule" for any number to the 1 and 0 power.