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.
Today was extra fun because of some students throwing little bits of linguini all over the class. Oh joy!
The teacher with whom I share a classroom is doing a cool project (relating to the sine and cosine) and among the art supplies was a package of uncooked linguini off to the side of the room today. A student thought it would be so funny to steal the linguini, break it into little bits and throw it at people whenever I had my back turned to them. What distresses me more is that this student is very bright and somewhat of a ring leader and so his behavior is immediately copied by others.
I made two of the students who I saw doing this sweep the floor after school. Parents notified.
I could be much better at teaching high school if I could multitask better. I used to think I was good at multitasking, but I’m really horrible at it.
In my classes today, I meant to assign homework, pass back graded papers, give work to students who were absent, make copies of a handout needed for class, carry supplies from one classroom to another classroom. I didn’t do any of those things. Oh, and there were a couple more things I know I forgot, but I don’t know what they are because I forgot. (My bad memory is also a big problem.) The issue is that I’m not willing to set aside class time for these kinds of things because I’m always freaking out about having the most learning possible out of every class period. For example, in my imagination, while students are working productively on a task I’ll be able to walk around a pass back papers. However, that never happens in reality. Students invariably need help, or someone knocks at the door, or the phone rings, or someone needs to go to the office, and then I forget to do what I thought I would do.
Another issue is that I need to get from the fourth floor to the fifth floor between third and fourth periods, and I have a really hard time making this transition smoothly during the five-minute passing period. Arriving disheveled causes me to forget things as well.
There is no way I will become massively better at multitasking, so the solution is that I need to do is to make students responsible for as many tasks as possible. I can hear Harry Wong yelling “Procedures, procedures, procedures!!”
I’ve been insisting on passing papers back myself up to now because I’ve been trying to learn students’ names. But now I think I can let students pass back papers or put them in some central place. That’s at least one thing I can try to do. Other tips from seasoned teachers?
Our school district is large and uses a centralized web-based system for taking attendance. I think it’s interesting that this system has a separate web page to tell users whether the service is working properly. Hmmm… Any guesses from readers about what this means about the reliability of the service?
A minor setback over the weekend. The copier is in our school’s office. The office is often locked during school because staff or admin are not there. When us teachers need to make copies, we have been relying on the teacher who room is next to the office to let us into the office through his side door. This is really not a good solution and the teacher, rightly so, has decided not to allow us to come through his room. So now, our ability to make copies is restricted. We found out today the copier is out of toner, so maybe it doesn’t matter anyway.
And now nice anecdote to end the post: Today in third period, I noticed one of my students (who previously complained about being in a group with people she did not know) helping another student. She was explaining things methodically and not just giving the other student the answers. She was doing it so earnestly and she seemed so pleased that she understood the material enough to be able to explain it. I thanked her for her thoughtfulness at the end of class. Hooray!