Here’s a great Geometry activity relating to triangles and points of concurrency (incenter, orthocenter, circumcenter, centroid). I stole this from a friend in Utah.
Cut out some cardboard shapes. Take a shape (start with a circle) and rest it on top of something stable (like a soup can or paper cup). Pour salt on top until you get a nice pile of salt and the three-dimensional pile of salt doesn’t change anymore. (Use something to catch all the salt so you don’t make a mess.) For a circle, you’ll get a cone. For a triangle, you’ll get this.
Neat, huh? Now to all you Geometry fans out there, what are those lines formed by the ridges of the pyramid and where is that apex? Is it the incenter, circumcenter, centroid or some other point of concurrency?
It’s a very fun activity that makes these ideas relating to triangle centers become more tangible. Also very fun is trying to predict what kind of three-dimensional shape will result when you pour salt over other shapes, like a star or semicircle or the letter E, etc..
I’ve been using this algebra balance in my Algebra 1 classes to illustrate concepts having to do with equations. This balance is unique in that it has two pans on each side. The yellow pans represent positive quantities and the red pans represent negative quantities. The white chips and the green containers (representing the “x”) have the same weight so you can easily set up simple equations using the pan.
It’s been a minor hit so far. Students seem to understand that you can maintain the balance by adding or taking something away from each side of the balance. This and next week we’re working on making the appropriate moves on the balance and solving equations without the aid of the balance. I’ve gotten students used to solving equations like “2x-1=9” by inspection; the unintended consequence of this is that students are a bit puzzled why I’m going through so much effort how to add 1 to both sides, etc.
At the parent-teacher conferences this Thursday, I met a parent of a student who is currently in jail. (It was good to find out why he has been missing from school for about a month.) The parent claims that the student did not commit any crimes and asked me to write a letter on the student’s behalf. This student was a positive force in my class, and I have missed having him there. He was making good progress in mathematics. His close circle of friends seem to be harder to control in class without him there–he was a good influence on his friends as he would often be on task and they would emulate him (after making fun of him to his face).
I made sure to to write “Ph.D.” after my name in the letter. I hope this letter will help; my student’s future is at stake.
Parent-teacher conferences took place tonight. There wasn’t a huge turn out, but it was nice to meet parents. Students act very differently when they’re by themselves (instead of around their peers) and they act even more differently when around their parents! I was kicking myself tonight for not keeping up my Spanish skills–that was the major impediment tonight.
Grades for next grading period due tomorrow. I’ve been thinking a lot about the purpose of these mid-semester grades. The purpose is to send feedback to students, so I’m not as concerned about the grades matching up numerically with students’ performance as I am with the grades sending the appropriate messages. For example, one student was so thrilled to hear that he is going to get a B in my class. He told me he’s never gotten a B in math before. His mother was so proud. Truthfully, he is closer to getting a C than a B, but I’d rather him get a B now and work hard to maintain it (or improve it to an A!) rather than feel like he’ll never be good at math.
In third period, a student called me over to his group. “Teacher, what does ching chong <insert other random Asian sounds> chong mean?” He had his whole group in stitches. The first time he asked the question, I didn’t realize what he was doing and I said, “I don’t understand what you are trying to say.” (Duh, I’m slow.) He tried to call me over many other times with the same question and I ignored his subsequent attempts. I was busy responding to other students’ mathematical questions.
At the time I didn’t think much of it, but now I realized how bothered I am by the student’s actions and the reactions of his peers (one is an A student). I can’t do anything about my ethnicity (Asian) being different from most of my students so I’m not going to overthink that. I do wish that I was a lot quicker on my feet than I am. I’m usually the last one to get a joke and can never think of the right thing to say in a situation until much later.
This and other incidents at school make me wonder why high schoolers seem to be so fixated about ethnicity. There was another conflict between Hispanic and Armenian students at school this week, apparently.
Today’s professional development meeting at school was productive. We spent much of the time talking about students, especially those that are having issues that are causing them to miss school or do poorly at school. It was great to hear the concern from all of colleagues. This is why we do what we do.