Year 2 Lesson Plan 2: Exponents, Powers of Ten, Scientific Notation for Large Numbers

  1. (2 min) Reminders
    1. Homework must be turned in on time.
    2. Every week bring your calculator and pencil.

  2. (10 min) Exponents
    An exponent tells how many times a number is to be multiplied by itself. What is 2 x 2 x 2 x 2 ? [16] It can also be written as 24. 4 is the exponent or the power of 2. We say that 2 is raised to the 4th power.

    DO NOT CONFUSE 24 WITH 2 x 4. THEY ARE NOT THE SAME.
    2 x 4 = 8 and 24=16.

    What is 4 x 4 x 4? [64] How would you write it with an exponent? [43]
    What is 32? [9] What is 53? [125]



    There is a story about exponents:
    Once upon a time there was a rich king who had a mathematical wise man.
    the wise man told the king that he would work for a small price.
    He brought a checkerboard to the king and said: On the first square put 
    one grain of rice.  On the second square, double that. On every square,
    double the number of grains of rice that were oon the previous square.  
    The king agreed, but he lost his entire kingdom to the wise man.
    
    The king owed the wise man 18 quntillion
    grains of rice.  This is more rice than has ever been grown in the 
    history of the world!!!

  3. (10 min) Powers of 10
    We write 10 X 10 X 10 = 1000 as 103. Powers of 10 are very easy to work with because all you do is count the zeroes.
       4 x 105 = 4 x 100000 = 400000       
       6 x 108 = 6 x 100000000 = 600000000
    
    Scientists must work with very large numbers. For example the distance from the sun to the planet Neptune is about 2,790,000,000 miles. We can express this as:
    2.79 x 1000000000 or ...
    2.79 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 or...
    2.79 x 109

    These numbers are easier to write and compute when expressed as scientific notation. In scientific notation, the number is expressed as a number between 1 and 10 and then multiplied by a power of 10. The number of the exponent is the number of zeros added on the end. If there is a decimal point, you have to move the decimal point to the right, counting for each, and then add zero's on the end to finish off.

       1.997 x 103 = 1997
       1492 = 1.492 x 103
     
    We will not discuss negative (-) exponents for very small numbers.

  4. (Remainder of class) In-class exercise

  5. Hand out homework to students as they successfully complete the in-class exercise
A resource that can be used in conjuction with this lesson is the book or video Powers of Ten by Philip Morrison and Phylis Morrison. 1982, Scientific American Books. It is also available as a video in many districts media libraries.