This activity helps students solidify their understanding of the new vocabulary identifying the angles created by a transversal between two lines. To make it a wee-bit more interesting, we also look at transversals across non-parallel lines.
I'm struggling to find time to write thoughtful posts. But I am taking pictures. Here's some fun shots of our Ball Drop experiment in Algebra 1.
This past summer, I was honored by the Colorado Council of Teachers of Mathematics as the 2017 Outstanding Secondary Mathematics Teacher for Region 2. One for each region of the State. I didn't post this in September when it happened, because, honestly, it felt really weird to have people congratulating me. And then life showed up and it got lost as it moved farther down the 'to do' list.
I spent some time this past week reflecting on 2017. While going through my journal I was reminded of this wonderful little event. Part of my desire for this next year is to celebrate more. This is my first attempt.
My school district even gave me a shout out on Twitter:
I'm very thankful to all of the wonderful educators I've worked side-by-side with over the years and those who I've had the pleasure of interacting with online through the #MTBoS. Thank you for your kind words, your wisdom, your patience, and your friendship. I'm so very humbled that I get to be on this journey with such quality people. Without a doubt, I'm a better teacher because of your encouragement to try new things and to fail early and often. You all are the best! I truly believe we are better together. Always.
I spent some time searching for a card matching exercise for exponential functions. I found a couple but none that did exactly what I wanted them to do. Rather than spending an hour searching for what I wanted, I spent an hour and made it. Although, to be real, I'm not sure what I made is what I wanted either. I plan to use it early next week.
Students match percent growth and percent decay equations, graphs, descriptions, and tables. Not every function has a description or a table. I thought I'd cut down on the process of elimination solution method.
I also included some function forms students would probably not be familiar with yet but I would like them to take a stab at looking at the form of the function and guessing what the matching graph might be like.
I've included the files as both a pdf and word doc.
Update: I added an extra page with recursive definitions of most of the functions... just in case you want to add the extra step of complexity!
With systems of equations, I tried something new for review. Instead of doing the normal routine of making a review assignment and then having students solve it, and then having the students who don't do the assignment be the ones who need to do it the most--I had students make their own review assignment. Hey, why not?
Here are the directions I gave to the class (link to Google Doc here):
Here are the sections we covered this chapter:
6-1: Graphing Systems of Equations
6-3: Elimination using Addition and Subtraction
6-4: Elimination using multiplication
6-5: Applying systems of Linear Equations
6-6: Systems of Inequalities
At first, there where the obligatory moans from the classroom when I introduced the assignment. But, when I told them they only had to create 6 problem--one from each of the sections for the chapter--the mood changed. Don't get me wrong, they didn't cheer or anything, but I did have buy-in from most of the class.
When students asked me what a certain section was about, I directed them back to their textbook. I have both an in-class set and we have online pdf's so access should be an issue. Students checked their 'correct' solutions using Desmos. I appreciated how much this pushed students to understand the mechanics of solving systems of equations on a deeper level. It's one thing to use an algorithm. It's another to intentionally break the algorithm and see what you get when you break it.
Sadly, this assignment didn't fix the problem of students who really really need to work on the assignment not doing the assignment. I guess if I had the magic fairy dust to fix that, I would be a very rich man.
If I had to change one thing about this task next year, it would be that students didn't really know what I expected of them; there was some confusion as to what the end product might look like. So, I took pictures of this year's work to show to next year's students. I can usually go through the pictures without saying a word. Students start to get a pretty good intuition about what 'good work' versus 'bad work' feels like. This looks nice. This... doesn't look as nice.
Here's some examples of student-created practice tests. I've included four different levels:
-the "Oh my goodness, can I frame this?"
-the "Good attempt but struggles with organization"
-the "I appreciate how much effort you put into this but it took me some time to figure it out", and
-the "Can you walk me through this, please?"
Good attempt but can use a little more organization to help the reader understand what's happening:
Can you walk me through this, please?:
Thanks to Dan Greenberg for the idea!
I'm starting my second real book on formative assessment. I finished Embedding Formative Assessment by Wiliam and Leahy. Now I'm starting The Formative 5 by Fennel, Kobett, and Wray. Something I've noticed about both books: neither one suggests using warm-ups as a research-backed strategy in the classroom.
I'm thinking about dropping them. Granted, I've only done them for like 3 months but I'm frustrated. My actual problem is that I can't fit everything into a lesson I want to fit in. I want to:
i) have a discussion about a warm-up
ii) check and go over questions on the previous night's practice work/homework
(quick stat: 80-90% of my students do the homework on any given assignment)
iii) teach an interesting lesson/investigation/experiment/whatever
iv) and to top it all off, have students complete an exit ticket
As it turns out, that's too much to pack into one day.
I talked this out with one of our district middle school math coaches (Dan Greenberg) yesterday. He's like a ninja-math-education-guru. It's awesome. After turning my questions back on themselves several times, he helped me figure out that warm-ups are the least productive of the options I want to pursue. Rather than trying to spiral in old ideas, or bring up Visual Patterns, or Which Ones Don't Belong, or whatever other good 'extra' things I want to do in a day, maybe I could use problems from the previous night's homework as a launch for group discussions. It would help students see the value in doing the homework. It would be a natural tie in of the previous day's work to what we would be looking at today. And it would help me better understand what my students do and don't understand about what I'm attempting to teach. Those other things are totally cool, I simply need to plan time for them rather than trying to shove them into an already full plan for a day.
So, I'm thinking about letting something good go. I spent days pulling together what I believe is an all-star cast of warm-ups to use in Algebra 1 this year. It's hard.
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I teach Math and Programming at Summit Middle School in Boulder, CO.