Exponent Operations and Arithmetic/Geometric Progressions

Summary:

In accordance with our theme of learning for understanding, students explored some exponent operations today. Our objective was to simply think through these operations rather than try and commit rules to memory.

For example, take the problem 2^5 divided by 2^3. There is a rule which states that when dividing exponential values with the same base, you can simply find the difference in the exponents, meaning the answer would be 2^2. But blind acceptance of a rule is not a true learning experience. Students wrote out the expanded version of the original problem as
2^5 = 2 x 2 x 2 x 2 x 2 = 32
and 2^3 = 2 x 2 x 2 = 8
and 32 divided by 8 = 4 or 2^2
This thinking process leads us naturally to the rule by way of understanding, not blind acceptance.

Students also examined two math sequences today, arithmetic and geometric. Both terms are easily found online using a basic search and we made connections between these terms and the linear and exponential relationships we study in class.

Home Nugget #35
Assigned onTuesday December 19, 2006
Due on Wednesday December 20, 2006
From the Practice Sheet labelled for use after 6-1 all problems

Focus Correction Areas (FCAs)
1 point: all problems completed
3 points: explanations or evidence of your work is provided for:
#1-4
#11,12
#17-21