Unit 5 was our second of three units in our curriculum centered around linear functions. Students had spent all of November focusing on graphing and slope-intercept form, and now it was time to get more algebraic since the foundation had been laid.
We basically went through topics in this unit in the same order as the last unit and then added more to the end. We started off with slope, this time introducing the slope formula and how to calculate slope from coordinates, tables, and word problems.
Many of my students seemed to prefer this method for a change, because it meant they didn’t have to graph anything and they didn’t have to remember “rise over run” and they didn’t have to remember when their rise or run was positive or negative. We didn’t spend as much time on slope during this unit because we had already spent quite a few days on it during the last unit.
After slope we went right into direct variation, skipping parent functions this time. We focused more on how to find the constant of variation and how to solve word problems involving direct variation during this unit.
This was too rushed. I would have spent at least one more day working on direct variation problems. Thankfully we should have time to review these types of problems when we discuss inverse variation later this year.
I taught point-slope form for the first time. Last year we had only done slope-intercept, and we are still not doing standard form. I again don’t think that we did enough practice with this. A lot of my students are struggling to remember the formula and what is supposed to go where.
The divide in my students between those who liked point-slope and those who liked slope-intercept was very interesting. A lot of students ALWAYS wanted to solve for slope-intercept form. I tried to keep telling them that they didn’t have to do that but they didn’t seem to care. Maybe they had caught such a focus on solving for y that it was stuck in their heads. I’m not entirely sure.
After teaching point-slope form is where things started to differ from the previous unit. We did not do linear inequalities in this unit, since they are almost always represented in either standard or slope-intercept form. Instead of working with linear inequalities, we introduced a few new concepts.
We spent about a day talking about VUXHOY. Most of my students do remember this (YAY!) and are pretty good now about being able to graph and write equations that just have an x or a y.
I tried to come up with some good “real-life” situations that would have zero rate of change or an undefined rate of change but I was terrible at it and I didn’t get much back from Google. If anyone has some good scenarios for this let me know!
We worked with parallel and perpendicular lines for the next two days. During the first day, students completed an inquiry worksheet where they graphed pairs of lines and were asked to notice and wonder about the lines. Then on the second day we completed the notes and did a few more practice problems.
They seem to understand parallel pretty well but are definitely still struggling with perpendicular. Thankfully this is technically a geometry standard here so this is just to give them some prior knowledge going into next year.
The last topic of this unit was line of best fit. Again, this was very rushed as we were heading into winter break. I would’ve liked at least one more day on this topic to do some sort of in-class activity, but the students still seemed to grasp this concept pretty well.
I think that next year I would hold off on ever saying the words “direct variation” until this second unit on linear functions, because there was little to no connection made by my students between the direct variation problems we did in unit 4 and this unit.
One thing that (so far) I’m really liking is that we did not go directly from this unit into systems of linear functions. Especially because we are on a block schedule (and I see these students for 85 minutes every day all year) it is very easy for them to get burnt out on topics. Linear functions for three straight months would have been terribly long I think, no matter how many activities or projects we would have tried to incorporate. This will also give them a chance to review their linear functions later in the year before we begin prepping for their state test.
Overall I really enjoyed the flow of these two units and I truly believe that it led to a better foundation and conceptual understanding of linear functions for my students. Next year though there will have to be significantly more practice on the skills required to really master these topics.