Slideshow (flash): The Reason for Numbers
            Slideshow script: The Reason for Numbers

Teacher Notes:

Numbers are important to mathematics and science.  Students may take the beauty of numbers for granted, not realizing how difficult it was to develop practical symbols for expressing quantity.

You may want to introduce the idea of the “magic” of math by using a Magic Square to start a discussion.  We recommend the famous Magic Square used in a painting by Albrecht  Durer (1471-1528), a German painter and printmaker during the Renaissance.            The magic squares all add up to 34 whether you add rows, columns, diagonals or corners.

 If students have not learned some of these philosophies in the readings, you might want to extend discussions.  It is very important for students to understand these skills and the difficulties to develop them.

ANSWERS:

Part I. 1. rational; 2. rational; 3.  irrational; 4. irrational; 5. rational; 6. rational; 7. irrational

Rational can be expressed as a fraction or ratio; irrational cannot be expressed as a fraction

Part II.

1.  Look at the  chart in text.
    

2. Accurate means to be close to the right answer; precise means exactly.  Accurate is preferable because you can be precise and way off the correct answer.
    

3. In our world of perception, it cannot because there are no two headed worms.
    

4. Actually it creates one drop of water, which is why we use a different type of measuring system instead of adding, using ml.
    

5. Number refers to a quantity; numeral is the symbol that represents the number
    

6. Iraq
   . 

7. No, it has been a difficult concept.  It has changed many times from base 10, base 12, and base 60.  Depending on the ruler of an area and how they traded depended on how standard they became.
    

8. By measuring a certain quantity and state this is the standard or by developing a standard which to compare
    

9. ½ ml
    

10. Googol means a very large number, referring to the amount of calculations needed to find answers