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Magnitude of Numbers (Exponentials)
Prevoius Knowledge: Basic knowledge of positive and negative exponents.

Objective: To understand the relationship between an exponent and the magnitude of a number.

Materials:
  • Physical representation of a number line, for example:  a rope hung along a wall of a classroom or chalk drawn line along a sidewalk.
  • Index cards.
  • Clothespins or tape to affix index cards to the “number line”.


Group Size:  11+

Procedure:
  1. The teacher should choose a base, “b”, ahead of class time and fill out the index card as follows:  b-5, b-4, …, b-1, b0, b1, …, b4, b5.  (For smaller classes or larger bases, the largest power used can be 3 or 4.
  2. Distribute the index cards randomly to students as they enter the classroom or after they have already entered.  Discuss with students that they will be placing their index card in the appropriate space on the number line provided.
  3. Allow students with the index cards a maximum of 2 minutes to place their card in the proper space.  Once all cards have been placed on the number line and all students have gone back to their seats, discussion about the placement of the cards will take place as to whether they are placed correctly or not.
  4. Students that were not chosen to place cards will be given the opportunity to suggest a replacement of any misplaced card.  This process will continue until all students are satisfied with the placement of all cards.
  5. The teacher will write each number in exponential form and standard form to ensure that each placement is correct.


Extensions:
  1. Students can create exponential graphs by plotting the exponent on the x-axis and the value of the exponential number on the y-axis.
  2. Various bases can also be used to find the similarities and differences in the behavior of their graphs.


Science-integrated: A number line is set up to reflect the number of meters, in powers of ten.  Place each quantity on the number line.
  1. The distance between the Earth and the Sun.  Hint: It takes light 8.5 minutes to travel from the sun to the Earth, moving at a speed of 3.0 x 108 m/sec
    (Answer: 1.5 x 1011m)
  2. The diameter of a penny.  Hint: A penny is 19 mm across, and, 1000 mm is equivalent to one meter.
    (Answer: 1.9 x 10-2m)
  3. The diameter of a human hair.  A hair is 1/1000 inch or 0.00254 cm across, and, 100 cm = 1 meter.
    (Answer: 2.5 x 10-5m)
  4. The diameter of a photoplankton cell, which is 5 micrometers.  Hint: One million (1 x 106) micrometers equals one meter.
    (Answer: 5 x 106m)



G Redden

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