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Day 43

So I am reading Elizabeth Green's Building a Better Teacher which in part discusses a style of teaching math in which students get to talk through concepts rather than taking notes while teachers stand and deliver. The teachers doing this call it "This kind of teaching" or "TKOT." I like David Wees' summary of TKOT here. Also, my pedagogic goals have focused in recent years on engagement. As such, I am striving to play more games and do more problem based learning (PrBL) tasks in class. Thank you MtBos!

This means that my brain is aflutter every night at bed time. I can't fall asleep until I make a mental plan to improve my plan for the next day. Overall, I haven't been getting a ton of sleep, but my lessons are improving.

However, I am still struggling in two areas. One, I am overwhelmed by possibility. I get stymied by the sheer amount of materials available online. Though a lot of the lesson I find are good to illustrate a concept and not that great at teaching a new concept in a fun and engaging way. This is especially true when that concept is like today's goal: writing the equation of the line through a point that is parallel or perpendicular to the given line. This brings me to my second struggle: the content. I get frustrated that the curriculum I teach isn't built around engaging tasks or projects. Rather, I am trying to jam in interesting tasks (PrBL, Digital portfolios, games, projects, etc) AND teach very traditional, formal Algebra. I want to have my cake and eat it too! Have I mentioned that I only have 135, 40 minute class sessions each school year to make this happen?

Enough complaining.

Green's words have bolstered what I have been learning from the MtBOS and each day I am trying to improve in some way.

Today's agenda:

I used Socrative to give a formative assessment on yesterday's goal of using the standard form of an equation. My students like using socrative. Then as usual, students run a review of the homework at the document camera. I admit that this part of my daily agenda is successful because my students do their homework everyday. 

#lucky #independantschoolproblems

So the slight change I made for today's lesson came under item #3. Rather than lecturing, I gave them clues about parallel and perpendicular. They looked at two problems solo and then they were to discuss results with their partners. Lastly, they were to graph all three on Desmos.

After, we came back together as a group (going for that you, y'all, we model), I walked through plotting the original line y = 3x - 1, the point (-3, -5) and then the lines they found algebraically. 

The next objective was for them to be able to look at equations and determine the slope of each as quickly as possible. 

Lastly, they worked this problem independently.

After a student presented his solution, we closed with an activity I like to call #algebraconfessions. in students share aloud their mistakes. 

"I wrote the parallel equation."

"I didn't make the slope negative."

"Mine was a point-slope mess."

Today's class was still fairly traditional, though I think the variety made it more engaging. I would love feedback and suggestions for making this better. :)


  1. interesting post - i think we all feel that tension between how we want our class to go and the curriculum we feel (however rightly or not) we need to deliver. it's hard to find a good way to approach every topic!

    one question popped into my mind was: did the students already know that parallel lines had the same gradient? what about perpendicular lines? because those are quick and easy investigations to do with the students. for example: draw the line y = 2x-5. draw a line parallel to it. what's its equation? draw another line parallel to it....what's its equation? there's a parallel line that goes through the point (0,-79). what's its equation? there's another parallel line that goes through the point (5, 11). why is this problem more challenging? what's a wrong answer someone might give (and why might they give that answer?)? how could you find the right answer?

    perpendicular gradients is always fun as well, because i notice that most students will not independently say "negative reciprocal" or "m1 * m2 = -1," but they come up with great rules anyway!

    i also like to mix it up a bit with questions like 2x - 3y = 7 is parallel with 4x - By = 9. Find b. 2x - 3y = 7 is NOT parallel with 10x - 15y = 35. explain why not.

    finally, i really like your algebra confessions - great way to normalize mistakes!!! really nice idea - i will have to steal that one! :)

    1. Thank you for reading my post! In regards to curriculum, there are some topics that are more procedural and with the given time I have, don't lend themselves to a better approach.... but I can still keep trying! :)

      My students did already know the slope connection to parallel and perpendicular. They discover it on a homework assignment given coordinates and directions to find slope. Your comment makes me want to rethink that choice and to instead make it an in class activity, maybe incorporate desmos... maybe make it a post for their blogs...


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