## Thursday, 7 January 2016

### MPM2D - Day 74: y = 2^x and Negative Exponents

We have what I think is a weird curriculum expectation lumped in with quadratics in grade 10:

I feel like it's a one-off lesson so I kept it until the end in the hopes that my students wouldn't forget it.

We started by looking at patterns.

They did well at seeing the pattern and answering the questions that follow. We jumped onto Desmos and looked at the two graphs as we zoomed further and further out. We also looked at what happens to the exponential as x becomes a very big negative number, and tied that into the pattern above.

Next, we watched James Tanton's video. I really like his explanation of 0 and negative exponents related to the piece of paper (around the 3 minute mark). Here is the link. My students didn't want to stop watching as they wanted to know about exponent ½, which is not in the curriculum for this course :)

We looked at y = 3^x next to see that the same patterns hold true and then looked for a way of evaluating a power with a negative exponent without having to make a table and use the pattern.

We went through some examples together - I chose students to answer using my popsicle sticks. These were fine.

And the first row of the next set of examples went well, also. Then we got to (-2)^(-4) and my ability to take a quick question and turn it into a 10 minute class discussion hit. (Seriously, other teachers seem to finish a lesson with 20 minutes to spare and I don't get through the lesson.) Anyway, we had a lot of discussion about whether the answer should be positive or negative and whether the brackets were needed. I should say that the students were discussing it as I only asked what they thought of each others' answers without adding to the discussion. In the end, those who said yes to brackets convinced those who were saying that brackets did not matter.

I consolidated what they had figured out here:

And that was all we had time for. Here is today's homework.