Today went well (I think). It felt much more relaxed, perhaps because I got the timing right for one of the few times this year. The students have also seemed more relaxed the last few days, joking around with me more at the beginning of class (although they still get too quiet as we move deeper into class and content).
The opener (pdf) was designed to reinforce some basic distributive property stuff, give them some practice on solving equations with variables on both sides (formal assessment over that is on Monday), and to remind them/introduce them to the concept of a sequence. They did reasonably well with these, although I’m still concerned with the number of students who can’t do problems like 1a correctly (with a calculator).
The lesson (pdf) was then an introduction to recursive sequences (this is leading to writing linear equations and the concept of slope). It was also an opportunity to show them one of the features of their graphing calculators – the ANS key. (Not all of the students have graphing calculators, but I made new groups this week to make sure at least one student in each group, and usually more, has a graphing calculator).
So they built the patterns out of toothpicks and pretty easily saw the rules for number of toothpicks and perimeter. I then showed them how they could build a recursive routine into their calculators using braces and the ANS key so that they could quickly generate results for additional figures. They then pretty easily came up with the number of toothpicks and the perimeter for figure 25. (As cool as this is, we’ll eventually transition to, “Well, what if we needed to know figure 125, or 1125? Wouldn’t it be nice to have a quicker way?” Bingo, let’s right an expression/equation.)
They fairly easily then replicated this process with a sequence of squares, although I did lose a few students who were more interested in creating artwork with the toothpicks. My favorite quote of the week was from a student who said, “Mr. Fisch, do you ever worry that parents are going to call you when they find out we were playing with toothpicks in Algebra class?”
Their homework was to prepare for their assessment over Solving Equations with Variables on Both Sides on Monday (and, yes, I’m a little worried about giving it on a Monday), and to plan how they might want to participate in Homecoming Week (pdf) next week.