Title
Fortune Telling


Problem Statement
Using only the number 4 and the four basic operations (+, -, x, ), write all the numbers from 1 to 31.

(Source: Adapted from Mathematics Teaching in the Middle School, May 1994)
 

 

Investigation/Exploration of the Problem

This investigation is similar to the Combinations Investigation. Let's set this problem up the same way using a spreadsheet. If we use all the combinations available to us we will have the following:

 

4*4 = 16

4/4 = 1

4 - 4 = 0

4 + 4 = 8

 

We can use combinations of these expressions to find the numbers 1-31. Click here for the spreadsheet. But there are other combinations that can be used. For example, 15 can be written in at least three different ways:

 

4*4 - 4/4 = 15

or

 4 + 4 + 4 + 4/4 + 4/4 + 4/4 = 15

or

4/4 + 4/4 + 4/4 + 4/4 + 4/4 + 4/4 + 4/4 + 4/4 + 4/4 + 4/4 + 4/4 + 4/4+ 4/4 + 4/4 + 4/4 = 15

 

 

Author & Contact
Laura Thomas

Memorial Middle School

Conyers, GA
lthomas@rockdale.k12.ga.us