Monday, March 14, 2016

Happy Pi Day - Dominos, Measurement, and Differentiation


So today is Pi Day, as in 3.14.  My math students think about pie, and an infinitely long decimal, and sometimes stories of a classmate long ago who could reel off the first 25 digits, or the first 100 digits.  However, I want the students to come away with an understanding that Pi is actually the ratio of every (yes, every) circle's circumference to its diagonal. Pi is an irrational number, meaning it cannot be written as a fraction with integer numerator and non-zero integer denominator.  We didn't have a chance to organize a pie-a-palooza for today, so I brought in round cookies (okay, a stretch to think of them as mini-pies, but they certainly are desserts and they are mostly round). 
 I intended to have my students watch my favorite Pi Day video  (you've got to check this out!!), especially because after its mesmerizing 3 minute 14 seconds (hey, wait a minute....) it explains the math in a very accessible way.  Then they would measure the cookies, measuring circumference with a string, and diameter and finding the ratio, and going from there.  Thanks to my colleague for sharing her idea, which was a table for measuring lots of round objects.  I borrowed it, wrote "cookie" in the first row, stacked a variety of round objects on the table,  and added some differentiation for my different classes as follows:  

My seventh graders watched the video and measured, calculating ratios.  We will discuss their results tomorrow.
One eighth grade class watched the video, measured, then built a scatter plot of their results with the data and drew a line of fit. I will show them how to find the line's equation tomorrow.
The other eighth grade class did all of the above and generated equations for the line of fit, which we wrote on the board.  Tomorrow we will compare equations, thinking the slope of each should be near 3.14.  Hmmmm. 

So, I spent Pi Day without eating a bite of pie, which is fine with me.  My students came away from Pi Day having eaten a well-measured cookie, understanding that Pi is irrational, and that it is the ratio of circumference to diameter of each and every circle.  Everyone was engaged! It was a very good day.


Sunday, March 6, 2016

"Hall Math" or "How to Accomplish Review, Collaboration, Movement and Confidence with a Few Index Cards"

My high school algebra class is working with linear equations.  There is a lot of vocabulary.  Much of the vocabulary sounds vaguely similar so it is easy for the students to feel "mushy" about the whole unit.  In my book, "mushy" is not good, and leads to "mushier" as we move forward into inequalities, linear systems, and eventually quadratic equations.  Ideally, students will have facility with equation solving tools, with which they can manipulate linear equations into various forms.  And, they can see that certain forms of linear equations lend themselves to different applications.  We aren't there yet, but closer.  As I write this, I realize I need to design a lesson where they read problems and identify which form of the linear equation would be more applicable.  

This Algebra I class is particularly fidgety after lunch, so I proposed "hall math" to them.  The eight questions above were taped in the hall, within view of my room.  I asked them how they should comport themselves in the hall, and we reviewed.  Then I asked how many times I should have to prompt them to keep the noise down before I called them all back in.  They suggested five! (not surprised)  I told them that they would get one warning before I rounded them up, but I was sure they could handle it, and this was a trial run to see if we could have more hall math in the future... And, I asked them to pair up as follows:  If you are comfortable with the material, find someone less comfortable, and vice versa.  I gave them each clipboards with an eight-graph sheet attached and off they went.  They were fantastic!  

Last year, I attended the National Council of Teachers of Math conference which was held in Boston.   May I say, what a treat to be among hundreds of people who are enthused about mathematics?  I had sort of forgotten that many people continue to believe that Math is a mystery, or it became a mystery to them at some point in school and it moved forward without them.  That's a topic for another day. But, one of the sessions I went to was about incorporating some social conscience into math class.  It's easy to start; rather than having Roxanne contemplate which deal is better at the health club, you can formulate problems that involve giving, or that highlight some local or global concerns.

Here's an example of slope-intercept form in action:
Alex has set a goal of donating 76 books to the Boys and Girls club. He started by using part of his birthday money to buy 10 books.  Each week he uses some of his allowance to choose 4 books from the sale rack at the local bookstore. 

a. Write an equation representing Alex's progress toward his goal as a function of how many weeks have passed. 

b. Graph the equation.

c. How many books will Alex have left to donate after 6 weeks have passed?

Thanks for reading along... I'm excited about hall math... "Get thee to a laminator".