Kids should answer their own questions.

I believe that everyone "learns" better when they find the answer to their own question. Why is school not set up like that?

In other news,  I have had two interesting things happen this week.

The first: 7th grade students have discovered, by patterns, what any number to the 0 power is.

I then asked, "what is zero to the zero power?" We spent a good 15 minutes discussing this and what our options might be. I went as far as to show why was cannot divide by zero and my students were still not agreeing on one answer. Therefore, that was their homework last night. Prove what zero to the zero power is.
Today, I let them work in groups that had the same answer to put their "proof" on the board.
I saw: 0^0 = 0 because 0^1= 0, 0^2 = 0, ... the pattern is that the answer will always be 0, therefore 0 ^0 = 0
and
0^0 = 1, because any number to the zero power is 1. 2^4= 16, 2 ^3 = 8, 2^2 = 4, 2 ^1 = 2, 2^0 = 1 (divide by 2 each time). Therefore 0^0 = 1
and
0^0 = undefined. Zero has no value, and you cannot divide nothing by nothing (paraphrasing my students' work).
I went through each proof and demonstrated why it was right or wrong. I was happy with all of their answers. I enjoyed seeing how my students are starting to notice patterns and are able to think more like mathematicians.

The other interesting thing was when a student said to me, "Why don't you teach us?"

What a great teachable moment and a loaded question. I am interested to hear how others would respond before I give my answer. Of course, this requires people to be reading my blog...is anyone out there?

(un)Hear it?

I found this site today: unhearit.com
It brings up the age old question of why some songs get stuck in our head. Think about the music lessons that could be attached to this! I am excited with the possibilities and look forward to hearing ideas.

FOIL'ed again

Trying to teach FOIL, without just telling them.

I wanted my kids to discover it and to fight with the idea. Trying to make this topic apply to a "lab" or the real world was difficult for me. So, I stole the ol' adding areas of rectangles together.
1. Add two different colored slips of paper onto a normal sheet of paper

2. Find the total area

3. It was helpful to draw an example on the board as well (if my students had their own white boards, I could imagine this could be a great activity, or even better cutting their own paper).

4. Let them ask the questions, fill in the information, and teacher help guide questions

5. When the quest arrises about the 4th rectangle, I added a little red rectangle to our model.

6. We got to the total area by adding all of the rectangles, but now what is the total measurement of the L and W?

7. Write that as two binomials multiplied together.

8. Set that equal to our total area

9. Let the students discover FOIL

I was happy to see my students struggle. In the past I have seen the difficulty to just follow the steps. But here, I was able to see the struggle with the concept. I think the students feel like they came upon this pattern, more than being told to memorize steps.

We were able to have discussions about
a. what variables to assign to what
b. what to include in our dimensions
c. how to solve the problem of that extra space (the 4th/red rectangle)
d. discover how to multiply two binomials together

Did my students grasp the concept? I don't know yet. I wish I could have had about 10 more minutes of class time (we went off on a tangent about multiplying exponents in the beginning of class). The students that were engaged in our discussion have the tools to grasp the concept during their homework tonight. However, the students that turn off during our discussions will be lost tonight. They will ask me to "teach" them tomorrow, since I "didn't" today.