Today with my 8th graders we were investigating linear equations written in slope-intercept (before I told them what slope-intercept form was) with Desmos (of course). It wasn’t anything great, students input some equations into Desmos and then found the slope of the line and its y-intercept. Then I wrote each equation on the board, wrote its slope and intercept underneath it, and then stepped away and asked them what they noticed about the equations, their slopes, and intercepts. A couple hands shot up right away, but I waited. As students stared at the board, I knew EXACTLY when they saw it. I knew because of their faces. As soon as they saw it, some got a big smile on their faces, some said quietly to themselves, “Ohhhhh I see it,” and some just threw their hands in the air. Being able to see that moment when a kid “gets it” or notices something for the first time is one of my all-time favorite things that happens in the classroom. I need to work on designing more lessons and investigations where that can happen more often.
Today was a really good day.
After reading Bob’s post (and BTW, I’m loving Bob’s class openers series this year) about geometric series, for a warm-up today I asked my geometry students about the sum of that series. It led to an amazing discussion (argument) about whether or not there even was an answer, and what that answer might be. We had some really passionate (loud) debate and ended up spending a lot longer talking about it then I had planned, but hey, when they’re that engaged I just sit back, smile, and let them go at it.When I showed them the diagram, it was priceless. Afterwards, a ton of them gave the “mind blown” motion and said their heads hurt. Win.
So my day was already going pretty good, and then after class, one of my students who had just gotten back from Japan on an exchange type program through our school gave me a pack of candy he had brought back for me. They looked like this:
Apparently these things are a HOT commodity. He said they were a type of Hi-Chew’s (which is like a Starburst type of candy that I just learned about last year), but that you can’t get this flavor in the US. When I asked what the flavor was, he said “white soda.” I laughed and asked what that meant. He didn’t know. I laughed and ate one. It was good. Can’t really put my finger on the taste either, but oh well, candy is candy.
Then, as my day was already going along swell, at lunch one of my former students who is now in high school sent me this pic. I’m assuming it was a warm-up or quick write or something for one of her classes.
I mean, come on. Great day.
Oh yeah, and the World Series starts tonight. Like I said, too much good stuff. Go Giants!!!
Everyday I greet students at the door and as they enter we do some sort of high five thing, depending on the day. On Mondays we do an upside down 3 finger high five, because it’s “M for Monday.” Anyways, every once in a while I have a student who adopts their own routine as they enter the room. Last year I had a girl who always gave me a high five after we did my high five, and this year I have an 8th grade boy who, when he comes into the room, gives me a huge, totally cheesy smile. He’s been doing this for the last couple weeks and I get a kick out of it. Today was kind of a cold and dreary day outside and he came in to the last period of the day with that big, goofy smile, and made me laugh. Sometimes it’s the little things.
Inspired by Brian’s post involving numberless word problem’s, I threw a “mostly numberless word problem” at my students for our warm-up today. When students came in the following statement was on the board: “Mr. M went out to dinner and paid for his food, tax, and tip. His total bill was $26.” I asked students, like I always do, to just silently think about the question on their own for a minute. During this time, several students tried raising their hands, looking confused and uneasy. I knew what they wanted to ask me, but I told them to just think about it. Then I told them to turn and talk with their group members and share their thoughts. It was great. Some groups immediately began trying to assign dollar amounts to dinner, tax, and tip, some lamented the fact that there wasn’t a question, and some were just confused about what was going on.
After a couple minutes I began randomly calling on students to share their thinking with the class. The responses were incredibly interesting. One student responded that he thought that the food would cost around $18. I asked why and he said because that seemed like a reasonable amount considering that I also had to pay tax and tip. Others gave specific amounts; one student said she thought the food cost $15, the tax was $3, and the tip was $8. Then I called on one boy and his response was, “Pasta.” The class of 8th graders obviously got a kick out of that and giggles ensued. I asked what he meant by that and he replied that considering the total bill was $26 including tax and tip, he thinks I ordered a pasta dish because the cost of pasta dishes that he’s seen in restaurants are usually a little less than $20. It was a really cool insight and thought that I never expected.
Finally a few accused me of not giving them enough info, and I played it up saying, “Wait, you mean I DIDN’T give you a question?! Whoops. We all make mistakes sometimes.” But instead of giving them a question, I asked them what they wondered. I immediately got questions involving how much the food cost, how much tip I left, what percent tax there was, etc. I told them I couldn’t remember all of the details, but I did remember that the tax was 10% and that I left a 20% tip (I made the percents very reasonable because this was all mental math). We decided to figure out how much my food cost. Students thought for a minute on their own and then began discussing with their groups, which again led to some really interesting insights. Some wanted to subtract 30% of 26 from itself and came up with a cost of $18.20. I asked them to prove it by working “the other way” from 18.20 and confirm their solution was accurate. they realized it wasn’t and went back to the drawing board. Other groups used guess and check and began guessing numbers and trying them. In the end, many of the groups were able to come up with an answer of $20, which we then discussed as a class and made sure that it worked.
Overall I thought this was a really cool setup for a question. It definitely got students thinking about what information they wanted to know from the problem, and let them essentially choose the question to be asked. I look forward to using more of these types of problems throughout the year. Hopefully I’ll get more answers as good as “Pasta.”
Middle school students love challenges. If you tell them that you’re not sure they can do something, they will do everything in their power to prove you wrong. That happened today in my geometry classes. We are going to be learning about points of concurrency in triangles this week so today with about 20 minutes left of class I held up some large triangles that I had cut out of old manilla folders and told them that I had a challenge for them. I told them that they needed to find the exact point on the triangle in which I could balance the triangle on the tip of a pencil. I told them that they could probably do it by simply holding the triangle and making constant adjustments, but I challenged them to find a method for finding the point on ANY triangle using any tools they wanted.
What followed was a fantastic exploration where students used rulers, compasses, and protractors to try and find the point where the triangle would balance on a pencil. They constructed angle bisectors, perpendicular bisectors, and drew midsegments among other things. I heard a ton of excitement throughout the room, and a bunch of “AWWW’s” when their triangles fell. We ended class on a cliffhanger, and promised I would show them how to find the point on Thursday. It was great.
Since I’m using SBG this year, one of the things I loved was how some other teachers designated some area of their classroom to celebrate students who have shown great perseverance or mastery of concepts. So 2 weeks ago I made a “Wall of Mastery” with the largest free space in my room. When a student masters a concept, he or she gets a post-it (each class has a different color), writes his or her name and which learning target was mastered, and gets to stick it on the wall. I looked at the wall at the end of the day today and it put a big smile on my face. Students haven’t been given the chance to master many learning targets yet (2 in my geometry classes and only 1 in my math 8 classes), as they have to show me they are proficient with a skill at some random time of my choosing, and yet, the wall is still pretty full. Every one of those post-its represents hard work and effort. Students are learning and it’s a nice reminder of that. I can’t wait to see what it looks like in a couple more weeks. I’m pretty sure that eventually we’re gonna need a bigger wall.
This is a completely selfish post about me, but I think we’re all entitled to that from time to time. I switched to a SBG system this year, one in which I don’t give an overall course grade, and I tried to get the rest of the middle school staff to do it too. Most of them voted against me, citing reasons from parent backlash to the system being confusing and hard to manage. They instead decided to use a hybrid system involving a 100 point scale and SBG, thinking that this “baby step” would help them adjust to the system. We met today to discuss how everything was going and, as I tried to tell them, they were struggling to combine the two systems. Many of them said that the issue was the 100 point scale, and if we got rid of that, everything would be much simpler. While I wanted to shout, “I TOLD YOU THIS 3 MONTHS AGO!!!” and get up and start dancing like I just scored a touchdown, all I actually did was sit quietly in the back of the room and smile. This is what it was going to take to get them past that initial fear of abandoning overall course grades and averaging student work. And while I was happy about being right all along, I was more happy about the fact that they’re starting to come around. I’m really excited about that. This is only the beginning…
So last week on Twitter I saw this post, and immediately thought, “No Way!” But after crunching some numbers it actually seemed feasible. So today I threw out the question to my geometry classes today. I started with a small hula hoop and asked them how many of them could stand comfortably inside of it. Then we used a slightly larger one and did the same thing. Then I asked them to estimate how large of a hoop we would need for all 1,200 students at our school to stand comfortably inside, then I dropped the big question on them, “What size hula hoop would we need to fit every person on the Earth?”
There was an immediate reaction and students started throwing out crazy numbers. Some said 250 or 500 miles wide, some said a hoop the size of Texas, some said a hoop with a diameter across the US, some said the size of Asia, crazy estimates but they were all really enthusiastic! Now I asked them what info they needed to solve the problem and they told me the population of the Earth, so I gave it to them. At this point the students were literally fidgeting in anticipation of getting started. I told them that I hoped they had some kind of plan in their heads about how they could figure this out. Then I said, “Go.”
What followed was what we all dream about happening in our classes. Students grouping together and diving head first into solving a problem. Some grabbed yard sticks and rulers and started measuring their feet and carpet squares. Some grabbed measuring tape and started measuring me (width of my shoulders, circumference of a circle around my feet, etc), thinking that I better represented an average human than them. It was great.
They pounded away on their calculators and scribbled numbers on whiteboards and scratch paper. Unfortunately, we ran short on time just as some groups were beginning to come up with answers. We don’t have school Thursday or Friday and because of block days this was the last time I’ll see them until Monday. They begged me to tell them the answer, and I gave in and told them. They were downright shocked. I gave them a reference of how far 31 miles was in terms of our city and they couldn’t believe it.
This happened in both of my geometry classes today. It was a seriously amazing. It’s a great reminder that the right problem can help my classroom become the place that I always strive for it to be. Awesome day.
Today we used the Desmos graphing calculator for the first time with my 8th graders. We were graphing proportional relationships and using the graph to solve problems. We’re going to be using it a ton over the next few months but this was the first time students had used it to graph. Before we started, I had them scroll down the home page and check out some of the featured graphs. The “ooo’s” and “ahhh’s” started immediately as they began finding amazing graphs. They got really excited and when we started graphing, they wanted to know about all of the features. I told them they’d have to wait and features would be revealed in the near future. They’re pretty excited.
I was in a collaboration meeting this morning with the rest of the 8th grade teachers and before the meeting I was putting some problems together for my geometry class to work on. I made an angle chasing problem involving a triangle and a couple parallel lines, but I didn’t feel like making up equations for unknown angles, so I opened up our textbook, pulled out a couple equations that I knew had integer answers from two different problems, and just wrote them into a couple of the missing angles. When I got back to my class I glanced at the problems to see how students did with them and was immediately shocked to see that they had labeled one of the angles in the diagram as having a measure of -18 degrees. Confused, I did the calculations in my head for that part of the diagram (which involved a straight angle made up of 3 adjacent angles) and discovered that one of the equations I pulled resulted in one of the angles being 135 degrees, and another being 63 degrees, which of course, would mean that the third angle had a measure of -18 degrees. WHOOPS! I couldn’t help but start laughing. I can only imagine my class, with a substitute in the room, when they discovered this. I’m sure they were incredibly confused and tried the problem a bunch of times, sure that they were doing it right but not sure why their answer was off. I owe them an apology when I see them again on Thursday. I’m sure some of them were mad at me, but I definitely got a good laugh out of it.