1) The document explores difference patterns for squares, cubes, and 4th powers in tables ranging from 0 to 102, 0 to 103, and 0 to 104 respectively.
2) It notes that extending the tables to -10, the patterns continue to hold and asks what pattern could be used to predict the differences in a 5th power table without directly calculating it.
3) It has the reader look back at the exploration from a teacher's perspective regarding lower level skills involved, appropriateness for students just beginning exponents, and gains/losses of using calculators versus doing calculations by hand.
2. -102 -92 -82 -72 -62 -52 -42 -32 -22 -12 02
100 81 64 49 36 25 16 9 4 1 0
-19 -17 -15 -13 -11 -9 -7 -5 -3 -1
2 2 2 2 2 2 2 2 2
d.) extend to -10do the patterns continue to hold in the extended tables?
e.)Find a pattern in the results from pats abc above that would allow you to predict what
you would find if you made a difference table for fifth powers. To veriry the prediction directly
would be a lot of work. Instead, check youor overall patter in a very simple case, first powers.
9. Look back at questions 8 from the point of view of a teacher.
a. what lower level skill are involved
b. would question 8 be appropriate for students who have just begun to work with
exponents or whose subtraction skills are weak? Could question 8 be modified to make it less
demanding, yet still reach the same goals.
c. what would be gained and what would be lost if students did all the calculations in
question 8 on a calculator or computer?