lazy 0ch0

Simplified Probability Bingo

I teach an Algebra 1 course and the other day we were studying experimental and theoretical probability. I saw a Probability Bingo activity on Dave Ferris’s and Sarah Hagan’s blogs and wanted to try it. The problem was I saw it the day of the lesson and didn’t really have a bunch of prep time. In fact, I had about 15 minutes. (I changed my previous plans at the last moment.)

What do teachers do? We adapt at the last second. Here’s what I did and it took about 10 minutes of prep.

I colored several pieces of paper in different colors.

I also created 2×2 squares in Word and printed them out on 1/3 sheets of paper. During the lesson, I put all of the colored paper in a small cup. I told the students I was going to pull out two pieces or paper, one at a time. I asked the students to predict what I was going to pull out by filling in their tables by putting two colors in each corner of the table.

I proceeded to pull out the pieces of paper from the cup. If the combination they wrote down was pulled from the cup, they crossed it out. The first student to have their 2×2 grid entirely crossed out wins.

We played twice. Afterwards, we discussed the probabilities of choosing each combination of colors. They then dived into some practice problems on probability. It was great because the formal “learning” about probability took place after I had them engaged in the activity and not the other way around.

I found that the students thoroughly enjoyed the activity. It was a simple game and they didn’t even care what they won (which was nothing). They just wanted their colors pulled from the cup. Plus, it was an awesome hook into basic probability….especially since it only took 10 minutes of actual prep time. Next time, I may try and go with full-blown bingo.

Speed Dating

I’ve heard this strategy being used by several teachers in the MTBoS, but I most notably remember Kate Nowak being the one I heard it from first. It was a total success.

If you don’t know already, here’s the deal. Set up the classroom so that students are facing each other. Create a worksheet with problems you need the students to study/review. After handing it out, I gave the students a few minutes to become “masters” at one problem (I assigned them each a problem). I had 22 students, so I had 22 problems. After this, each student will “teach” their problem to the person across from them – for my problem set this was about 3 minutes (for both students to teach). After the 3 minutes, one side of the students got up and moved one seat to the left. Now they were across from a different classmate and the 3 minutes would start again – and each new pair would teach their problem. Each new pair now had a fresh start on explaining their problem and understanding a new one. (Sort of like real-world speed dating.) This process repeated until the end of the period. Oh, and I put out whiteboards on the tables to help with all this.

I floated around as they worked and assisted as necessary, but I wasn’t really part of the picture all that much. I loved this! I felt a bit weird in that I wasn’t doing much throughout the period. Then I came to my senses: it was the power of student-centered learning taking over me.

Because each student was only required to “master” one problem, they weren’t overwhelmed. And because they had to explain that question several times over the course of the class period, they really became well-versed on the concept that their problem related to. Conversely, because there was a student walking them through a problem they hadn’t seen before, I was able to incorporate peer tutoring and bring the learning to them in a more native way. They were talking about math all period – teaching and learning from one another – and hardly realized it.

It was totally my fault, but I didn’t get around to getting in an exit slip to gauge their thoughts on the activity. In fact, the bell rang as we were closing up. But if I had to guess from the looks of it, they really liked speed dating.

Height Problem from Graphing Stories

This week in my Precal class, we were working on increasing, decreasing, and constant functions. I showed them a Graphing Story. These problems are perfect for analyzing graphs of functions. I chose the one that asks the viewer to graph height vs. time based on a lady swinging on a rope in Costa Rica.

If you haven’t already, first watch it for yourself here.

I’ve done some of the other graphing stories before and I love them. We did this one, discussed various aspects of the graph, and eventually hit on increasing, decreasing and constant intervals of the function. Its a great activity, but an interesting debate arose regarding the given answer.

You notice that the answer (i.e. graph) has a relatively large increase during 7-10 seconds.

When I initially displayed the solution to my students, they debated whether this interval was accurate. They found it intriguing that, according to the solution, she swung roughly 32 meters higher than her original height on the platform. Some of them said yes, it was possible for her to swing 44 meters in the air. I mean, looking at the video her upswing does look VERY high – much higher than the platform she started jumped from. Some students said no, that the camera angle was playing tricks on us. It was such an awesome discussion, and to be honest, I told them I wasn’t sure about who was right, but I’d do my best to find out.

After school I spoke to a physics teacher at my school, Shane Coleman (who these students also have), about the problem to get his scientific opinion. He informed me that it is physically impossible for the lady to have swung as high as 44 meters, unless she was pushed hard, had extra momentum when she left the platform, or pumped her legs on the swing, none of which happened. He told me for the footage in the clip, her kinetic energy would not have exceeded her potential energy. In other words, she wouldn’t have been able to swing higher than her original height; it would have been less and less with every swing. I probably should have known this, because its sort of common sense, but whatever. So then I brought all this back to my Precalc kids and it made for a pretty good discussion while we ironed out the actual solution. Later that day, the students probed even more while in Shane’s class. Awesome.

Now here’s my question: have my students, Shane, and I missed something here or is the solution inaccurate? If so, my follow up question is what assumption(s) could we make about the swing that would make the given solution valid?

On a slightly different note, isn’t it also interesting that her height is 0 at two different instances, yet she never reaches the ground?

Friday Letters

This summer I got a dynamite idea from Rebecka Perterson at TMC14. The premise is that students have the option of writing you a letter on Fridays instead of doing the Warm Up or bell work activity. Then, no matter how short or how long their letter, you write them back and give it to them on Monday.

When I first informed the students about Friday letters, I could see a refreshing look on most of their faces. But things got even more interesting when told them I would respond to every letter I received. Without one letter being written, I could tell I had already made a lasting impression.

So here’s my box. It was literally a 5 minute job. Literally. It’s a small lidless cardboard box with a file folder taped to the top wrapped in blue paper. In other words, it’s the saddest mailbox ever. The kids got a pretty good kick out of it. One of the kids said “it’s the thought that counts!”

Last week was the first Friday the students had the opportunity to write me. I provided the kids with 1/4 sheets of paper and post it notes for those that chose to write. I received 17 letters, which I was stoked about. For the most part they were light hearted, things like “I really like your class so far” to “What’s your favorite color?” to “The first Varsity basketball game is December 3, can you come?” I thoroughly enjoyed reading and responding to them all. I suspect the letters will get more intriguing as the year goes on.

Friday letters opens up a private line of communication with my students that I’ve never had before. I’d like to think that my communication was always pretty good, but Friday letters adds a new dimension. It allows students to communicate to me their questions, feelings, and thoughts in a way that is accessible, non-judgmental, and meaningful. They feel that their voice is heard while getting individual attention from me. Plus, I really get to know my kids, which I love…they’re all so unique. This will really afford me the opportunity to learn who they are as people and tap into their strengths.

How will this ultimately effect my classroom this year? Will students just eventually stop writing and be “over” it? We’ll see. I’d love to hear similar things that other teachers have done to open up this type of communication with their kids.