Chrysalis Academy Posted October 11, 2015 Share Posted October 11, 2015 I need some advice about how to help dd, who is getting a little bit stuck. She is working through the 2nd book in the Arbor School math series, Crocodiles & Coconuts. She loves it and has done well with it so far, working through all the problems, reading the solutions and understanding any errors she makes, then taking the tests, which she's gotten above 90% on consistently. She's on the last couple of lessons in the book and struggling a little bit with graphing parabolas and hyperbolas. In looking at the lessons, the scope & sequence, and trying to figure out how to help her, I'm seeing that this scope & sequence is a little bit odd, and it is my sense that graphing parabolas and hyperbolas is a pretty advanced Algebra 1 topic that usually comes after Quadratics are covered. If that is the case, I'm wondering how much to sweat this - if she will be revisiting it later, is it a hill to die on now? If it is, will you help me understand 1) what are the key foundational concepts that must be understood solidly in order to learn this, so I can figure out if one of them is weak, and b) if there are any resources you can suggest for additional practice on parabolic functions and graphing parabolas - everything I can easily find would require that quadratics & polynomials were already covered, which is not the case here. I'm really wondering if perhaps this trouble is just a function of the kind of odd scope and sequence, so will you comment on this, too? Arbor School's sequence has 3 books, the first one, Jousting Armadillos, is PreAlgebra including solving single variable linear equations. Here is the scope & sequence of the next two books: Book 2 - Crocodiles & Coconuts: Equations in Two variables Chapter 1 - Two-variable equations & the Cartesian Coordinate Plane Chapter 2 - Functions Chapter 3 - Simultaneous Equations Chapter 4 - The Conic Sections Book 3 - Chuckles the Rocket Dog: Polynomials and Quadratics Chapter 1 - Exponents Chapter 2 - Introduction to Polynomials Chapter 3 - Factoring and Solving Quadratic Equations Chapter 4 - Polynomials in Rational Expressions Chapter 5 - Advanced Factoring and the Quadratic formula So my question is, wouldn't you normally cover conic sections after quadratics? It makes me wonder if we should just come back and revisit these lessons at some point in Book 3 Advice and comments are eagerly awaited, TIA! ETA: Edited for clarity Quote Link to comment Share on other sites More sharing options...
JanetC Posted October 11, 2015 Share Posted October 11, 2015 I believe my DD had to graph parabolas in algebra 1 in Life of Fred. I passed my book on, though so can't check for sure. I would need to see the problems and what she is doing to try to guess what fundamental concepts she may be missing. The big worry would be that this is a more conceptual introduction to parabolas, basically applying the fundamental concepts of graphing and functions covered in earlier chapters to an unfamiliar situation. So, yes, you could be leaving a big hole by moving on. 1 Quote Link to comment Share on other sites More sharing options...
regentrude Posted October 11, 2015 Share Posted October 11, 2015 I can't imagine covering conic section before quadratics. That makes absolutely no sense to me. Normally you'd cover those after, so the student can relate the equations to a graph. How do you even graph conics without understanding quadratic equations? 3 Quote Link to comment Share on other sites More sharing options...
Tsuga Posted October 11, 2015 Share Posted October 11, 2015 I was going to say the same thing. I'm not a math teacher but my experience, and what I see my step-kids doing, is definitely they equations (raw numeric relationships) before the graphs, then you plot it in two dimensions. That said-- I remember thinking when the teacher brought out the cone all sliced up, thinking, "Why didn't they show us this when they taught us the quadratic equation? Eighth grade would have been so much easier!" Still, they either need to be together or the equation first. It's hard to get a grasp on parabolas mathematically without an equation. 1 Quote Link to comment Share on other sites More sharing options...
Chrysalis Academy Posted October 11, 2015 Author Share Posted October 11, 2015 I can't imagine covering conic section before quadratics. That makes absolutely no sense to me. Normally you'd cover those after, so the student can relate the equations to a graph. How do you even graph conics without understanding quadratic equations? That's kind of what I'm thinking. He's led them through lessons on fractional equations, two-intercept form, and fractional equations with exponents, and she's done fine with those lessons, although my sense is she could use more practice on the last topic. Now the last two lessons are on parabolas and hyperbolas. My sense is that this is meant to be a very conceptual introduction to graphing the kind of functions he's had them working with, but they really haven't covered polynomials and quadratics explicitly yet. Here is what he says at the beginning of the chapter: "In this chapter you'll be working with fractional equations and looking at how they relate to geometry." I think maybe this is part of the discovery aspect of this program? He wants to lead them to see how parabolic functions are a natural extension of what they have been doing so far? But I'm not sure how to help her without reference to quadratics. The next book has a detailed chapter reviewing exponents and radicals, which I'm very happy about, and I think it's going to help her a lot. And then it dives into polynomials and quadratics. It just seems like the conic sections will make more sense after she's covered that. I'm really thinking of just pausing here and covering the material in the next book, and then revisiting this again at the end. This is where a discovery based math program can get me into trouble - I don't have a sufficiently solid grasp of the big picture to understand exactly where he is going with this method and order of introducing the material. In looking more closely I see that he is trying to guide the discovery, but I think she's just not making the jump. Quote Link to comment Share on other sites More sharing options...
Chrysalis Academy Posted October 11, 2015 Author Share Posted October 11, 2015 I was just talking to Shannon about the lesson, and she says she can see that he's leading her toward a discovery, and she felt like she was following along and getting it, just on the cusp of a discovery, but hit a wall Friday. She was coming down with a cold, so in a little bit of brain fog, and consequently getting really frustrated and weepy - this isn't normal for her, she has gotten really good at asking for help finding alternative explanations if she's not getting something. So I suspect the virus was wreaking some havoc on Friday. I told her to stop, but that her brain would keep working on it in the background and it might be easier to understand after a second look. She said she wants to try again on Monday and see if she can get where he is taking her with a fresh brain. But if she gets really stuck, we'll just put this aside for now and revisit it after she's worked on polynomials and quadratic equations. 3 Quote Link to comment Share on other sites More sharing options...
kiana Posted October 11, 2015 Share Posted October 11, 2015 Looking at the TOC's for the books I'd put it aside now and come back to look at this section after each chapter or two of the next book. I have a feeling that he's probably trying to do a very conceptual explanation so that when he does come back to it, it's somewhat familiar. 3 Quote Link to comment Share on other sites More sharing options...
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