Day 64: Slope

I left school yesterday not feeling so great about Geometry. Yesterday was pretty tough mentally for me. We talked about them problem at the beginning of class, only 2 of the 20 students didn’t try the problem which was great!

I am going to write more on that tomorrow… I need a little more time to think about how to tweak it for next year. One thing I do know is I didn’t have a clear idea of what I wanted students to get out of the problem, I pretty much went in blind.

In algebra we started slope. I like looking back at Dan’s Algebra slides and trying some of his old techniques.

I started class with this on the board:

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Students started to weave through different relationships, completing a table for each.

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There were so many different, crazy, cool ways students were working through these. After a while the tables started looking like this:

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We talked about all the different ways students saw this, then I had them fill in the missing values.

Day64.5Everything tied together at this point and words like slope and rise over run started coming up. We plotted the values and saw that to get from one point on the line to another, students could go down three units and right one or down twelve units and right four.

I threw this at em’

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Students derived the slope formula and we talked about how taking the difference of two values is the same as finding the distance between them. I liked using the tables as a technique to lower the entry points for students and gradually increasing the difficulty and refining the language of what calculations were happening.

Tomorrow is another new day!

Day 60: Slope

For the past two days algebra has been diving into the idea of slope. Fawn Nguyen has an awesome activity and post on using stairs to get students thinking about slope as steepness. This can be found right here.

All my classes pretty much reached the same point as her’s on the first day. I am not going to re-create an identical post to hers so go check her’s out… Seriously!

On the second day however I moved the class in a little different direction…

I lost quite a bit of student engagement when I pushed students to think about what we could do with the different bases/heights we measured. We went through all the operations and I asked students “What operation would be the best for COMPARING the base and the height?”

We settled on division. Some classes looked at the base/height some looked at the height/base. We talked about what a large base and small height would look like as a stair case and vise-versa. After that each group measured a the base and height of a particular case and we threw all those measurements into a spread sheet and ranked them.

There was some great conversation on what ranking the numbers from smallest to largest related to in terms of least/most steep.

I held on ever further in introducing the word slope.

After I had students measure the base and height of an individual step, we talked this and how measuring something in millimeters is a whole lot more precise than using inches. We also talked about how the measurements of each step are proportional to the measurements of the overall height and base.

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Then we dove into this:

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This activity came from James Cleveland over at The Roots of the Equation. I love this because it drives home the idea of slope as a ratio. I threw student’s rankings up on the board and then we quickly calculated the height/base of each.

Only at this point did I introduce the word slope, we talked a little more about what it measured and found the slope between a few points.

A great couple days of classroom action, students really seemed to enjoy the openness of these activities… even though they were complaining a little.

Day 59: Observation

An administrator came into Algebra today and I have my first of two formal evaluations for the school year.

I used Fawn’s Staircase and Steepness for the second year in a row. As always there were some hiccups along the way (like rulers turning into helicopter rotors and reaching maximum velocity). I want to write about the lesson tomorrow and use today to reflect on the positives and negatives of the lesson.

Positives

  • Students were challenged in multiple ways (use appropriate tools, make sense of calculations, put thinking into words).
  • The activity made math social.
  • I had student buy-in across all ability levels.
  • The students who had learned slope last year, had a tough time recalling the information (this says to me that there is value in the activity across all ability levels).

Negative

  • I did not spend enough time pre-loading students with expectations for the day. Behaviors became an issues because students were uncomfortable with their thinking being challenged + loss of interest.
  • All around time management could have been better.

STRUGGLE FOR THE YEAR (pretty much on a daily basis): I try and present math in a way which removes the mindset of memorizing equations/learning through repetition. When trying to do so, I have a hard time balancing that mindset and finding a form of classroom management that pairs well with it. I want my classroom to be social, which in turn is noisy. But students tend to push to the point where it becomes unproductive on a daily basis.

GAHHHHHHHHH….. IT IS SO HARD TO FIND THE RIGHT BALANCE.