Carl's Teaching Blog

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Category: Clog (Page 5 of 7)

CLOG: Unfinished Business

Today’s class began with the awkward dance of finishing what we left off the last class. The source of the awkwardness 40% of the kids unaware of what we did yesterday and needing to get caught up.

To combat the awkwardness I typically try and quickly get those 3 up to speed, but the students were responsible, and did what they had to do the day before end up sitting their bored. Today that wouldn’t work because it would require too much circulating. Instead I tried to do a comprehensive recap of what happened last class, and then ask the absentee kids to ignore front page of the assignment and instead join the rest of the class on the back page. Instead I caught all of them working on the front because they wanted to work linearly. What ended up happening was the worst of both worlds, where I had to wait for the whole class to finish so I could have the discussion, leaving some of the other students doodling in their notebooks for longer than I’d like. Guh.

Luckily, the discussion was great, as kids were saying exactly the things I hoped them they would say. I felt like Hannibal at the end of an A-Team episode when it was all said and done.


Clog: Just because it worked last year… #MTBoS30

Today we worked on reviewing average, median and mode before talking about how to use those tools to make arguments around a set of data. Students were given basketball statistics and data about restaurants in NYC and a set of statements that weren’t correct about the data and asked them to reword the statement so it actually reflected the data. After that I wanted to get into the “Hot Dog Festival” worksheet when my teenagers started acting like teenagers and nothing got done.

Do you ever find worksheets on your computer from last year and think “This worksheet was the Jam! I’m going to roll this out tomorrow and it will be awesome!” I had a worksheet like that today, and I was really excited about how awesome it was going to be. As class started, I realized before I even started teaching it, that it wasn’t going to go well. The beginning of this worksheet had some jokes in it that I forgot about. Naturally, bedlam broke loose when I asked the goofiest kid in the class to read the prompt out loud knowing that there is only w0 minutes to go in the 90-minute block, and that everyone was a little punchy. My one small joke about sausages set off the class and these two boys couldn’t stop laughing about it. I overlooked the joke when I chose this worksheet because I was too focused on how the task fit mathematically in the unit. The moral of the story is that you shouldn’t rest on your laurels just because something worked last year.

Hopefully we can finish the hotdog activity on Thursday, and then we can get into the outlier activity. This activity is another one that I did last year. Naturally, I will spend much more time preparing for Thursday’s class than I did today. (I might even write a blog post about it.

Are you wondering what the joke was? Ask me in the comments!


Edit, ok here is a link to the worksheet, you can see what threw them off in there:


CLOG: Moving towards symbolic representation

We have spent our time this past few weeks turning an interest in patterns into an interest in modeling. Each day we have done activities to get the students to think about number sense, and also about relationships and functions. Next we will focus on linear and quadratics simultaneously and look at both as examples of functions that we can use to describe how things grow and change. Teaching the two functions simultaneously will hopefully strengthen kids’ understanding of what functions are and what they could be more so than focusing immediately and solely on linear.

I taught my class twice, as per usual. The way our school is scheduled, we only see kids on Tuesdays-Thursday classes for 90 minutes each. The class has only met on 6 occasions (and one of those was taught by a sub who wasn’t given my subplans). At times it feels like we should be further along, but I want to remember to be patient.

Tuesday we looked at the penny circle on Desmos. We also opened up class with three visual patterns, one linear, one quadratic, and one exponential followed by a Contemplate then Calculate activity from This helped going into the penny circle because they were familiar with the types of equations, and also with counting things. The best part about Desmos activities are that it let’s the students work independently on tasks, and learn from each other. It is certainly because of these benefits that the universe conjured up a perfect storm of misplaced computer cart key and a soft lockdown drill kept me from actually using computers with my kids, and I ended up having a few kids walk through it with the smart board. Luckily I made a worksheet so I could see what kids are thinking about the activity, and the kids could still engage in this whole-class format. The students were able to see how the different equations look on a coordinate graph.

Following the activity we did an Interpreting Distance Time Graphs from the Shell Centre, which we did not have time to finish.

On Thursday we started with a visual pattern that worked out pretty well. This was the 5th one of these that I have done, but it was the first time I asked for symbolic equations for the patterns. I was surprised that students didn’t offer some kind of equation earlier, but I still wanted to wait until this point because we could start working with equations soon. To formally begin working with equations we looked at a modified version of Tina’s quilt squares, which has been a staple of my introduction to quadratics for years. Kids then worked on finding the number of grey squares and the number of white squares and eventually we had time to talk about the equations.

Clog: Getting ready for the next Episode

Today we finished up the first little “Episode” of my class, the goal of which was to  be able to identify relationships and functions as well as expose them to the terms ‘linear’ and ‘quadratic’ to describe their work with visual patterns. We had finished 8 different kinds of patterns by the time this class rolled around, including this one from youcubed. Since are now experts, I asked them to create their own patterns of blocks and put them on the board using Post-It notes, sort of a play on VNPS. Later on they were able to classify the patterns that they made as either Linear or Quadratic once they learned that that is a word used in math. The majority of the patterns they created were linear, which left me wondering if I should have exposed them to more non-linear patterns or if I just have a linear bunch of students.


Following this activity the students worked on a little reflection to wrap up this first Episode. I had this idea of breaking my class into little Episodes over winter break while my wife and I shamelessly barreled our way through Agents of Shield and The Blacklist on Netflix. Surely, some of the structures that the writers use to draw viewers into their stories could be adopted by teachers as they plan their units. My plan is to have these clear distinct units at the end of which is a little reflection, it’s roughly the “big idea” from the last 4 classes. Since the “big ideas” are the characters in my 2nd period show, the end of the Episode should highlight a new piece of information about one of the “big ideas.” The reflection on these things will help students keep track of all the important connections and representations. As we start future classes I plan to use the students reflections as part of a little introduction. This introduction could be mirror the “In the last episode…” or “Previously on Agents of Shield” announcements they have on TV which are followed by replays of key scenes from the series. So on the days where the concepts from this Episode stand to make particularly strong connections the ideas from the next Episode, I will try to adopt that by bringing back some of the more interesting reflections that student wrote.

What is the next Episode going to be about? Understanding! Specifically, getting to different forms of linear and quadratic equations with lots of understanding. We can look at difference tables, and break apart the meaning of the y-intercept and other variables in the equations, as well as looking at how these things reflect in the graph. I will work in some instructional activities and some problem strings in addition to counting circles as a way to help kids build some number sense. Since today’s post-it notes were a success, it seems like I will have to use more manipulatives, and try some Vertical Non Permanent Surface Problem Solving. If you have any ideas of things I should try, or other ways to make my class as addictive as a Netflix bing, let me know in the comments!

CLOG: First Class Of The Cycle

This Tuesday was the first math class I was teaching all year. This means Monday night I was wringing out my twitter feed like wet dish rag, trying to squeeze out every drop of teaching ideas into my class the next day. The turnover and structure of our school means that every marking period gives teachers the first day of school ‘blank page’ feeling.

My first day of school for this quarter needed to have some routines to build number sense, promote discourse, and get the kids prepared for an exploration of quadratics that put procedural knowledge in the backseat.  I settled on starting Tuesday with a counting circle for 10 minutes each class.  Sadie’s post from a few years ago seemed to be within six-degrees of separation of any post you can find on counting circles, and it pretty much convinced me to start my first class with this routine. As the cycle goes on I may try to work in a Problem String or some other routine.The idea is to start class each day with everyone working together and talking, as opposed to my usual Do Now-Review.

I like to think of this class as a unit in quadratics that puts procedures on the back burner. To plant the seed for some discourse around the quadratics I asked to get in groups and have a little conversation about two different kinds of visual patterns and to talk in small groups about what similarities and differences they saw in the two patterns.  The worksheet I used is below, and was a lightly modified version of one from last year.

Download (PDF, 50KB)

The worksheet didn’t really help promote the group work the way I would have wanted, in part because the task could have been more group optimized, and I could have really pushed the kids to stick to the group roles I had prepared. But the biggest problem was that I had only 5 students who showed up to class. Low attendance is a regular occurrence at our school, but this was basically a tutoring session. I had the whole class sit around the same table and instead of using chart paper had each group just write on a mini-whiteboard and slide the result down to the group at the other end of the table.

The two groups worked differently, one visual, one comparing the differences, so it was good. I asked them to describe their work to each other. Then on their paper, paraphrase what they saw in the other approach and how it connects to their own work. It showed that I will need to work on helping students describe their thinking in order to let everyone be successful this cycle.

The last thing we did in the class was talk about functions, and for this I dusted off a tried and true function lesson. The thing that this assignment needs is to have more challenging problems for the students who are able to finish the work quickly. If I could have an “important stuff” section of future assignments, and then “tough stuff” or “fun stuff” sections and ask student just to work on whatever they think is worth their time I would probably be more successful. I would also be just that much closer to Bowen and Darryl, whose idea I would be stealing.

For a first class it was pretty good. I hope to keep posting here throughout the cycle. The next post will be a talk about what ended up happening when I had to miss the second class of the cycle because of a meeting I had to attend.

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