Exponents

A textbook was adopted and given to me.  What will I do with it?  (A question any teacher must asked her/himself!)  The textbook we have has a typical two-page spread with three (or more) worked examples followed by two pages of "Guided Practice," "Independent Practice", and "Practice and Problem Solving." 

For the section on Exponents, the stated goal is:  Represent numbers by using exponents.  This is not students' first experience with exponents, so the examples and exercises such as find 5^2 and 2^6, write 49 with a base of 7, and compare 15 and 4^2 did not seem very challenging.  Many students reach first for their calculators so these become even more trivial.

After examing the section and the teacher notes, I did find some tasks that I thought seemed a bit more interesting and encouraged students to think more about the meaning of exponents.  How would you characterize the cognitive demands of these tasks?

• Guess/Check/Revise:  Guess the missing exponent and use your calculator to check.
• 3^?=729; 2^?=4096; 9^?=4,782,969; 4^?=1024
• Explain how you can find the value of 2^11 if you know that 2^10=1024.
• Is 6^3 = 3^6?  Explain.
• In as many ways as you can, represent 64 using powers.

Note:  Of course the textbook does not use ^, but I didn't feel like taking the effort to format this entry.