March 4th, C Block Honors PreCalculus
The bell rings at 11:03, the projected instructions tell students to take out their homework (a concept map, inspired by Elizabeth's post) and compare with their neighbors. Which ideas are the same? Which are different? Did you skip those things on purpose or because you decided they weren't important enough to include? Individual students share with me their struggles and successes as I take attendance. A student returns quizzes from last class, most of them remember to record their grades in their chart and students who received perfect scores tape their stars to the "Perfect Score, First Try!" wall. A student tells me she couldn't find the example concept map online; I briefly panicked it hadn't uploaded, then we figured out she didn't realize the files were multi-page and she had to scroll to get to the example. I asked if anyone wanted to share something about their concept map but no one really did. One student said that he thought it was interesting, he had made webs and maps in science and english class before, but never in math. Everyone hands in their concept map in the class inbox.
At 11:12 we transition to making observations about the problems they solved last class. Usually we do work and discuss in the same day but last class was short? Maybe? Somehow we are discussing things today but luckily these are my Honors PreCalc kids, they have organized binders and can find the work quickly. I ask them to notice and wonder about solving polynomials of higher degree. A student wants to tell me that the degree of the polynomial tells you how many roots there are, but she says "the exponent is how many solutions there are" For once, I remember to write down exactly what a student says! I then write down the example x^4+x^3+2 and ask her how many solutions. She realizes it's the highest exponent so we add that word in. I tell her that what she said is perfectly clear, and then ask the class if they remember the word for 'the highest exponent' and get a lot of blank stares (could've sworn I just used this term...) but eventually someone clicks in and says "Degree!" I ask them to be even more specific - what kinds of solutions did they get when solving degree 4 polynomials? (I set it up last class so they had one example with 2 real and 2 imaginary, another example with 4 imaginary.) And then push them - is it possible to get one imaginary? Why not? What else did you notice? Someone recognizes that all the imaginary solutions are plus or minus, so I mention the word conjugate and then ask why that matters? We make up an example and I have them multiply out (x-i)(x+i) to see that the resulting polynomial won't have any imaginary coefficients. Several students are totally convinced that there have to be an even number of imaginary solutions, but I'm not so sure about the rest of the class, so I ask if they want to do another example. One student nods so we discuss the number and type of possible roots of degree three polynomials. When I asked if it could have four imaginary roots a couple students are so caught up in the fact that imaginary roots have to be even they say yes. And then smile at their mistake when someone points out that four is greater than three.
11:24 We transition to independent review. I have sample problems available for each of the topics that will be on the test next week and emphasize that even if students are confident in solving polynomials since we just finished that topic they should read through the problems because they ask for the answer in different forms (real solutions vs. all solutions vs. factored). A student asks if they can retake a quiz and I tell the whole class that now is a great time to do any make up work or retakes they need to do, since any of those tasks results in them practicing the topics that will be on the test. Things get busy as half the class wants me to answer a question about their quiz or the graded assignment from last week. I run around in circles for a while until most people are working on something, then I walk in circles answering questions. Progress reports go out this week but I'm behind in grading so I flip through the assignments in the inbox to make sure that everyone who has resubmitted the graded assignment did so correctly. I spot a few with issues and instruct those students how to complete that section.
12:05 All is quiet. Everyone is working. I can breathe for a moment, but only one, someone else has a question.
12:15 Most students haven't done the review problems on operations with complex numbers. I really want them to realize that |a|*|b|=|a*b|, which isn't something we discussed in class. I get everyone's attention and tell them to do those problems right now if they haven't yet, then hurry up and notice something. The student who told me at the beginning of class he hadn't done a concept map in math before shared that he didn't feel like it was useful last night, but today as he did all the review problems he felt that he understood everything much better. (YAY!!) I told him I was glad to hear that and we chatted about how your brain works off of connections; the more you access a memory the better you remember it, so the more connections you have to an idea the easier it is to access.
12:20 I am about to get everyone's attention to talk about the complex number pattern, but notice one of my students who doesn't participate much is tutoring her partner. I wait.
12:23 Attention everyone! Please do this complex number problem that I am writing on the board. A student guesses that the pattern is |a|*|b|=|a*b| and I say yes! I project the journal questions (What did you notice or wonder? How should you study for the test?) and the homework (study, here are the relevant sections in the book). A student goes up to the review problems that she hasn't gotten to and lines them up so she can take a photo with her phone. Smart use of technology!
12:28 The bell rings. I experience immediate regret for telling students the pattern after one of them guessed rather than making sure everyone did out the work to see why. That would have been an excellent homework problem. Hindsight...
Note: This post is for Day in the Life, Single Class Edition. Read all the DITLife posts and submit your own!