Friday, March 13, 2015

IMP Alice Days 6-7 - Piece After Piece, Many Meals for Alice, and In Search of the Law

For Many Meals for Alice and In Search of the Law I really put my Ipads to use. I am learning better ways to implement using the Ipads. I gave each group a few minutes to brainstorm on each problem and then told them that at the end of the allotted time they had to put SOMETHING on the Ipad (using the Educreations app). The Airserver app allows you to project up to 10 Ipads at a time so I have an Ipad in each group (sometimes more). I had told my students that if you have an Ipad you HAVE to be mirroring the screen. I can see all the screens on my computer. This has been a tremendous help for keeping my students from using the Ipads for purposes other than the math! When I turn on my projector where the students can see everyone else's work it is interesting. I am still amazed how my students will approach problems so differently when I don't stand at the board and show them an example of what to do (which causes them to all try to do it my way). We have an easy way to compare and critique the work without it being totally obvious whose group it came from. Then they are able to edit their work when it is needed. Formative assessment on the fly!!
I had a student volunteer to "teach" - she was great!

The context given in All About Alice provides such a neat alternative to simply just giving the students the rules of exponents. Piece after Piece establishes the rule for multiplying powers with the same base. Some of my students wanted to ADD 2^3 and 2^5 so to help them I told them to remember that we are always looking at what we are MULTIPLYING Alice's height by. I am interested to see how other IMP teachers handle this...

Many Meals for Alice establishes the rule for raising a power to a power. The original power is for the number of ounces of cake she eats at each meal - #1 is 3 ounces of base 2 cake so it is actually 2^3. Then the students figure out what is happening to her height after certain numbers of meals. In the end they have hopefully developed the idea that (2^3)^4 means that Alice ate 4 meals where she had 3 ounces of base 2 cake. It takes a few times of looking at it to start making the connection. I LOVE #3.

In Search of the Law actually has the students to explore exponent rules that I have not usually put much thought into. It took me a minute or two of exploring myself - I actually had to tell my students to start working on #1 while I went to read the teacher's guide! When I glanced over the activity the day before I taught it I didn't realize it was going to throw me a curve. Anyway...this activity is actually not difficult AT ALL. It gives the students several scenarios to just work with exponents.