Today we spent the first part of class taking our 3rd version of the systems of equations quiz. I had 9 students in each class to improve so I think it was worth it. Overall I am disappointed because I still have many students who just still don't get it. UGH!
Here Goes Nothing is an activity that the students can do pretty quickly. It helps the students to further analyze the nature of 2 to the zero power. I am glad that we did the Graphing Alice activity on chart paper so we had them hanging in the room to help us. I also wish that I had at least done one graph on chart paper of A Wonderland Lost - just for discussion purposes. The teacher's guide really adds to this activity so make sure you read through it before you teach it.
Since we did Here Goes Nothing quicker than I expected I had my students to graph #5 from A New Kind of Cake on chart paper. This is a comparison of y=2^x and y=x^2 and I really like it. We will discuss it tomorrow.
Showing posts with label zero power. Show all posts
Showing posts with label zero power. Show all posts
Tuesday, March 10, 2015
Tuesday, March 3, 2015
IMP Alice Day 2 - Graphing Alice - raising to the zero power
I remember Sonya New telling me how much she loved Alice because it gives a context for any number raised to the zero power equaling one. Now I have taught it with the Alice context and it is so exciting! For years I have just told my students to memorize it as a fact. Today I got to use the Alice context... Just in case you might be reading this and you don't know what I'm talking about let me share.
As I'm sure you know Alice (in Alice in Wonderland) shrinks when she drinks the beverage and grows when she eats the cake. The first activity in the unit tells the students to imagine that Alice's height doubles for every ounce of cake she eats and is cut in half for every ounce of beverage she drinks. In graphing Alice they are asked to graph the two situations for 1-6 ounces. For the cake situaion you are graphing y=2^x and the beverage situation is y=.5^x. The outputs (y values) are actually giving you what you will be multiplying Alice's original height by. The x values represent the number of ounces eaten or drank. The teacher's guide advises you to talk about what happens when she eats zero ounces. This would mean you are raising 2 to the zero power. It was so awesome to have the context to explain that when she eats zero ounces of cake her multiplier (y value) is 1 because multiplying by 1 doesn't change Alice's height!! My students can't appreciate how exciting it is to be able to explain the why. I told them today that I have never been able to explain why anything to the zero power equals one and I just got blank stares. Haha! Some of you may be looking at the computer screen like...
It doesn't matter. I know I am a math nerd but today's lesson made me HAPPY! And I felt the need to write about it even though I am sure it is hard to follow.
As I'm sure you know Alice (in Alice in Wonderland) shrinks when she drinks the beverage and grows when she eats the cake. The first activity in the unit tells the students to imagine that Alice's height doubles for every ounce of cake she eats and is cut in half for every ounce of beverage she drinks. In graphing Alice they are asked to graph the two situations for 1-6 ounces. For the cake situaion you are graphing y=2^x and the beverage situation is y=.5^x. The outputs (y values) are actually giving you what you will be multiplying Alice's original height by. The x values represent the number of ounces eaten or drank. The teacher's guide advises you to talk about what happens when she eats zero ounces. This would mean you are raising 2 to the zero power. It was so awesome to have the context to explain that when she eats zero ounces of cake her multiplier (y value) is 1 because multiplying by 1 doesn't change Alice's height!! My students can't appreciate how exciting it is to be able to explain the why. I told them today that I have never been able to explain why anything to the zero power equals one and I just got blank stares. Haha! Some of you may be looking at the computer screen like...
It doesn't matter. I know I am a math nerd but today's lesson made me HAPPY! And I felt the need to write about it even though I am sure it is hard to follow.
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