Repeat or Revise?

Last week I wrote about my idea for an activity for investigating SSS. Helpful ideas were provided in the comments: using straws and string, Geogebra, and Polystrips to name a few. The year before we used the string and straws for this concept. It worked well.

Despite having something that was okay last year, I changed it. I shouldn’t have. Despite asking for your advice, I didn’t take it. I should have.

This year? Bleah. The strips were too hard to cut out and keep track of. They didn’t fit together well. The set that shouldn’t have formed a triangle? Some of them forced it by cutting off more of one side. The next day I tried to “fix” it. We talked about what should have happened.  I don’t feel good about the way this lesson went. It was muddled. There was no a-ha moment.

So I’ve been wondering why I felt the need to do something differently this year. I don’t have a good answer. I think part of it is my fear of becoming the teacher who doesn’t change her lesson plans from year to year. I never want to say last year was good enough, I’ll just do that again. I want every lesson to be great. I know I’m not there yet. I don’t know if I’ll ever get there, but I’m trying.

How often do you repeat lessons from year to year? How often do you just tweak? How often do you scrap it all and start over?

I guess I’m just wondering when I’ll be satisfied with my lessons and my teaching. And if I ever should be.

Functions

We’re in the “World of Functions” unit in IMP4. This may be my favorite unit in the whole curriculum.

Instead of a separate sections on linear, quadratic, radical, rational, exponential, …, we’re studying functions. Delving deeper into the relationship between the table, the graph, and the equation. Working on translating from one form to another to another. We’re doing application problems too. Lots of them.

Of course, they’ve used to working from multiple representations. They’ve been doing it for almost four years now.

This week we began algebra of functions.

I gave my students the following graph and asked them to draw , , and .¹

I didn’t tell them what to do. They didn’t need me to. They figured it out. They helped each other. They debated. They used numerical examples. They figured it out.²

Did they all do it perfectly on the first try? No. After working on it in their groups? Yep, most of them. Did they all try? Yep. Not one person sat there waiting for me to tell them what to do. No one said “I can’t.” A few are still working on solidifying their understanding of this. I’m okay with that. Not everyone gets it at the same time.

I’m blown away on a daily basis by my seniors in IMP4. Both by the mathematical understanding they’re demonstrating and they willingness with which they tackle new problems. I’m not sure which impresses me more.

¹While not exactly a “What Can You Do with This” image, I still like it.

²We also discussed when f/g would be undefined and why f*g needs a scale. Any other ideas as to where we could have taken this?

Side-Side-Side?

One of my classes is at an impasse. They all agree that having proportional sides does not guarantee similarity in a quadrilateral (yay for the students who thought to grab a rhombus and a square from the tub of shapes to prove their point!). Yet we’re stuck on triangles. Half of the students are convinced of side-side-side similarity in triangles, the other half are not. They have been unable to get anyone to change their minds.

I believe they are waiting for me to tell them who is correct.

So, I’m going to try this.

Instructions:

• Measure each side and record.
• Determine if the sides are proportional (they are).
• Determine the scale factor (left as an exercise to the reader).
• Then carefully cut out each segment (kinda worried about this part).
• Next create a triangle out of each set (one triangle will use the letter only sides, one the primed letters).
• Measure the angles. (thinking they may need to tape the triangle together)
• Determine if SSS guarantees similarity in triangles.

I tried it. It seemed doable.

We’ll see how it goes.  Any suggestions, advice, insights, criticism is/are of course welcome.

(There are two more sets in the .pdf -bonus, one set is special.)