Day: February 18, 2009

Inequalities and Quadratics

In Algebra II,, we’ve recently been delving into quadratics. I recently blogged about how I taught completing the square and the quadratic formula, and put up a bunch of resources. Since then, we’ve moved on to graphing quadratics, followed by inequalities.

The complete topic list for inequalities is:

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I’ve been trying something new, which is creating packets for students to work on. In essence, I’m creating my own textbook for these sorts of questions. I thought I’d share them with you in case they prove useful [1]. I’m pretty proud of them — and they way they fit together and build up understanding, not just providing a method to solving problems.

1. PACKET 1: Linear and Quadratic Inequalities on the Number Line (PDF version)
2. Additional Homework on Quadratic Inequalities (PDF version)
3. PACKET II: Linear and Quadratic Inequalities on the Coordinate Plane (PDF version)

4. PACKET III: Systems of Inequalities (Linear and Linear-Quadratic) (PDF version)
5. Additional Homework on Systems of Inequalities (PDF version)
6. Pop Quiz on Inequalities and Quadratics (PDF version)

Hopefully they’ll be useful to someone else out there!

[1] The formatting might be a bit off for you… It looks slightly off (meaning the pages don’t end where I intended them to end) on my mac but fine on my PC. I think you need to make sure that on a Mac you select all and convert the font to “Gill Sans” (on a PC, I think it’s called “Gill Sans MT”, which is creating the problem).

UPDATE: PDFs posted, without typographic weirdnesses.

On Time

Last week I was rushing to get to one of my classes, after not being able to get away from one of those hallway conversations with a fellow teacher. I made it down the four flights of stairs and as I walked into the room panting, the students — looking at the clock — hollered “just 5 more seconds Mr. Shah… if you came in just 5 seconds later you would have been late!” Indeed, they were right.

This moment struck me deeply.

Why? This is the moment that tells me I’ve succeeded. I have clear expectations with my students regarding certain things, including being on time to class. And I make damned well sure that if I give myself permission to call out those who come in late, I’m going to be in the classroom every day on time.

I like that they’ve internalized it. This moment could never have happened otherwise.

Another failed AMC 10/12

So my school offered the AMC 10 and the AMC 12 (math competitions) last week. And although we have a number of pretty strong math students, none of them broke the 100 point mark. No student in recent history — apparently — at my school has done that. The fact is that to do well on these competitions, you have to be familiar with the types of questions and methods to solving them. There are techniques to doing well, tricks that any student who has seen enough of these can put away in their mathematical arsenal. These contests require a different way of thinking, a different way of approaching problems.

I am the faculty adviser for my school’s math club, and I just go with the flow. I listen to what the students want and we do it. Sometimes students bring an interesting problem or an extension of a problem. Sometimes I bring a problem. Sometimes we watch a video. Sometimes we work on contest problems.

Last year and this year, the students haven’t wanted to dedicate time outside of math club to doing math. We have only 25 minutes a week to meet. Well, frankly my dear, you can’t get through much in that time — especially if students don’t want to concertedly work on problems outside of math club, and then use math club to present solutions or failed methods of attack. When it comes down to it, to do well on these contests, you need to practice.

I’m okay with students not wanting to spend time outside of mathclub working on math problems. They are all busy and well-rounded and are juggling a ton of different things.

Still… I am waiting for the day when someone in mathclub says: “Everyone, I am going to solve every one of these 25 competitions problems by next week” and goes at it. Whether or not they succeed, it’s irrelevant to me. That’s the kid I want to take under my wing.

PS. I finally got around to taking the AMC12 under testing conditions (75 minutes, no calculator). I scored a 108. Which is around the same score I got last year and when I was in high school.