Teaching Conics in Algebra 2

I really like opening the day with an open question. They’ve been kind of easy to think of so far. But, what about conics? What’s a good group of open questions that can be used with conic section lessons? Before I could think of that, I really had to look at the new standards for Conics. In doing that, I realized I really hadn’t examined exactly what the kids are supposed to learn. So, I had to research and think about that for a while first.

I did a little research about conic section topics and standards that need to be covered in Algebra 2. I checked this publication on the California Dept. of Education website: California Common Core State Standards for Mathematics. You’ve probably all seen it, if you’ve been working in California.

Here’s the conics standard for California – yes, there’s only one, but it’s loaded (p. 83):

3.1 Given a quadratic equation of the form  ax² + bx + cy² + dy + e = 0, use the method for completing the square to put the equation into standard form; identify whether the graph of the equation is a circle, ellipse, parabola, or hyperbola and graph the equation. [In Algebra II, this standard addresses only circles and parabolas.] CA

Um… okay. Let me think about that. first of all, is this the same or different for what we’ve been doing at my school for teaching conics. Do we need to address the directrix and focus or foci? Because, I talk about those whenever I talk about conics. Even when introducing them in Geometry.

Here are the Geometry standards (p. 74):

Translate between the geometric description and the equation for a conic section.

1. Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

2. Derive the equation of a parabola given a focus and directrix.

In the past, I taught about the foci of an ellipse and parabola and hyperbola. Last year, we didn’t test on graphing hyperbolas. According to the Algebra 2 standard above, it seems like it’s all four, except for that part in the brackets. Is that only for other States? I needed to find out. After all, I’m serving on a County wide committee to discuss teaching this class and we should really know what those apparently contradictory statements mean. The bold is supposed to be California.

So…. here’s what I found out… Go to this website IXL, scroll down to whatever standard in which you are interested, hold your cursor over the standard and a sample questions will pop up. Wow. Great stuff. No foci/directrix stuff until Pre-Calculus. Okay – I guess they’ll handle that in Pre-Calc. Looks like just graphing parabolas, those that open horizontally or vertically, and graphing circles. For circles, be able to find the center. I think they still need to be able to tell whether the conic is a circle, ellipse, parabola or hyperbola from the equation, though.  Please make a comment below if you understand this all to be different than what I’m writing here. This seems much less than what I’ve taught in the past. So, maybe that’s a good thing. 🙂

Next, what will the lessons be? Then, I checked the NCTM website, Teachers Pay Teachers the NRICH websites for ideas related to those standards. And, of course, Desmos. Well, on the day I had to start the topic, I didn’t have a good ‘open question’ opener. I just asked kids about the equation of a parabola, in vertex form. I asked about the equation of a circle. I put it on the board. I asked if they’d seen that before. I asked them to notice that there’s a x-squared and a y-squared term. I asked if that meant it’s a function. So, it was a weak start compared to what I would have liked. But, it was the day before break and my goal was to introduce conic sections. I had them watch this Conics video from YouTube This was pretty much a vocabulary lesson with a graphic that was pretty good for getting them to understand the basic concept of what conic sections are.

Then, the fun began…  as they started to use the Desmos activity, Polygraphs: Conics, found here. Now, I’m figuring out my unit plan. I have the week off. I plan to find open questions, interesting activities and relevant homework for them. Something that spirals old stuff, too. I plan to write more about it, too….  Ideas?





Kids really bombed the quiz…

Dear Mathies,

So, teaching logs, and missing two days last week, I gave a quiz to see where the kids are. I’m feeling pressured, because of the February break, to get a test in next week. It’s also the end of the grading period that Friday before the break. So, I’m feeling like a quiz is needed to let me and the kids know where we are this week.

Well, it seems like we’re overall pretty far from where we’d like to be. 🙂

So, do I labor through the grading, or do I hand them back without grading them, and allow them to work through them again? Do I worry about cheating, grade inflation, lack of “data” for issuing the grade for the reporting period? Yeah, I do worry about all that. I also worry about their stress level, because I want them to like math and math class. And, logs are not one of the easier Algebra 2 topics. They will learn more if they enjoy themselves and aren’t experiencing ‘stress-brain.’ But, I could feel the tension in the room as they we reviewed for the quiz and as they took the quiz.

So, I want to get creative. I want them to get the feedback they need, without the low score. So, I’m thinking that I will give them the quiz back today and let them correct them with a pen. Then, if they want to turn it in or retake it, they can decide. So, there’s still some accountability and they have a bit less anxiety and a bit more control.

My questions for you are:

  1. What do you think of this idea?
  2. Do you have a better idea?
  3. How have you handled these conflicting pressures around assessment?
  4. What else should I be thinking about? What am I missing here?

If you can give me feedback on any of these things, I’d appreciate it!

Here’s what happened: I did the above, and many want to retake, but many kept their score. They got some feedback, for sure. However, I didn’t let them keep the quizzes. So, some asked, “How will I study for the re-take?” Great question…

I’m going to send a couple of tutorial links (via Remind and put links on my website) and have them review their assignments to ‘study’. I hope this will help them learn how to study, too. Maybe we’ll focus on that some more, too. Regularly.