Questioning
I think I generally follow knowledge-level questions with higher-leveled questions as I teach, but for my lesson on exponents I tried to plan out specific questions and navigate through the topic based on higher level questions to emphasize critical thinking. I had discovered a day or two before that the students had a pretty good grasp on basic powers - most of them could easily calculate 2^2 or 5^3 or 10^2 - so I thought I'd take it a step further and cover multiplication of integers and fractions raised to a power. As has been the case for my past few lessons, I ran out of time at the end. There was so much I wanted to cover with them and I only had 1 period :( Looking back, I guess I bombarded them with a lot of new information, but hopefully, as one of the students commented about our teaching in the classroom, I "broke it down real good." I knew they needed to review multiplication and addition of integers and this lesson was a perfect chance to incorporate that.
Some of my leveled questions:
What is 2x2? 2x2x2?
How do we write that?
How would you show 2^7?
What is -3x-3?
How about -1x-1x-1? (wrong answer by all) How did you get that? (correction)
How can we rewrite 2^4 = 2x2x2x2? (hint: What if I grouped these twos so that 2^4 = (2x2)x(2x2)?)
I was so excited when I got a "2 squared times 2 squared," followed by a "2+2=4," followed by another observation, "2x2=4." I could tell they were thinking :) I went on to tell them the rule for adding exponents when the base is the same. After writing 2^1, 2^2,...,2^5 in a column on the board, they were able to compute the other column of 2,4,...,32.
What do you think 2^0 is? (all said "0")
What does the calculator say 2^0 is?
What is the pattern in the second column?
So what is 2^0?
I had planned to go on to negative exponents using the information we had covered but as I said earlier, I ran out of time. I enjoy using this questioning strategy because I like when the students can figure things out on their own. This isn't possible all of the time and sometimes they need extra guidance, but I think it boosts their confidence and improves their critical thinking skills.
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