tag:blogger.com,1999:blog-30226356.post3493181804862796877..comments2024-02-16T23:32:12.073-08:00Comments on The Exponential Curve: Algebra 1: Solving EquationsDan Wekselgreenehttp://www.blogger.com/profile/08696028020767073620noreply@blogger.comBlogger11125tag:blogger.com,1999:blog-30226356.post-22475354101014073112009-09-22T08:08:03.624-07:002009-09-22T08:08:03.624-07:00I think it's excellent if they love mapping ou...I think it's excellent if they love mapping out the steps, as it will really reinforce the order of operations for them. I think students will naturally move out of reliance on this kind of scaffolding as they get better at it (they will naturally look for short cuts) or as problems demand it.Dan Wekselgreenehttps://www.blogger.com/profile/08696028020767073620noreply@blogger.comtag:blogger.com,1999:blog-30226356.post-83817976215478339312009-09-22T04:25:03.449-07:002009-09-22T04:25:03.449-07:00I used the order of operations boxes with my sixth...I used the order of operations boxes with my sixth graders last year as an intro to solving two step equations. I then couldn't convince my students to do the standard isolate a variable method. They loved mapping out every step. The order of operations boxes are in the NYC Impact Math curriculum for 6th grade.Vaporizing Boxeshttps://www.blogger.com/profile/17769170706394161647noreply@blogger.comtag:blogger.com,1999:blog-30226356.post-75840085933397430852009-09-19T07:00:23.140-07:002009-09-19T07:00:23.140-07:00I have used Mr. K's method (which I stole from...I have used Mr. K's method (which I stole from his blog) during summer school. I could not believed how well it worked. We spent some time with the boxes and then moved on. What the boxes helped the kids to understand was the undoing process. It seems as if many times students are not sure where to start or how to undo 16x = 32. I will find them somtimes subtracting the 16. This tells me that they don't really understand the whole order of operations concept.Kim Hugheyhttps://www.blogger.com/profile/14765229714690518433noreply@blogger.comtag:blogger.com,1999:blog-30226356.post-87516135481879334022009-09-17T09:37:21.726-07:002009-09-17T09:37:21.726-07:00Dan,
You are an absolute machine. I am embarasse...Dan, <br />You are an absolute machine. I am embarassed to admit that I have never seen these the bar modeling or order of operations before. (maybe I have seen the order of ops, but it was probably on your blog :). This year I introduced equations to my 7th graders using the balance scale. Use circles for the x's and squares for the units. It was amazing how quickly kids picked up on it and transfered it to equations like: <br />2x + 3 = 5x -7 .David Coxhttp://coxmathblog.wordpress.comnoreply@blogger.comtag:blogger.com,1999:blog-30226356.post-76194520543315078452009-09-13T09:34:22.904-07:002009-09-13T09:34:22.904-07:00Dan - Thanks for posting this. I really like the v...Dan - Thanks for posting this. I really like the visual. I'll give this a try with students who struggle. My inclination would be to go with the standard approach for most kids, and reserve this as the backup for those struggling more. I would demonstrate this skill to the entire class once or twice to broaden the conceptual understanding in general. I think after it's been introduced, maybe ask kids to solve some equations using the method they like best. From there you can decide how best to get those bar approach more comfortable with the traditional approach.Nickhttp://www.ateacher.org/blog/noreply@blogger.comtag:blogger.com,1999:blog-30226356.post-64799402570503391612009-09-12T18:03:10.694-07:002009-09-12T18:03:10.694-07:00Mr. Sweeney -
Thanks for the info. Your process ...Mr. Sweeney -<br /><br />Thanks for the info. Your process sounds like it's pretty effective - though I don't think I have the brain space to employ something like that this year.<br /><br />Any youtube clips of you guys singing and dancing? :)Dan Wekselgreenehttps://www.blogger.com/profile/08696028020767073620noreply@blogger.comtag:blogger.com,1999:blog-30226356.post-51419123586080314832009-09-12T17:57:56.493-07:002009-09-12T17:57:56.493-07:00Mr. K -
I remember that post from way back when, ...Mr. K -<br /><br />I remember that post from way back when, when I didn't think about Algebra 1. Thanks for linking to it again.<br /><br />I believe that the original NCTM article that I was thinking of did it like you do. This new article got me thinking though - I like how the boxes correspond to the intermediate steps of the traditional method. I wonder if this would help the transition, especially for equations that are more than just two-steppers.<br /><br />This method does have more stuff to write and keep track of, but at the same time, it is totally procedural (as long as they have mastered the order of operations) and does extend to most basic equations. So a lower skilled kid could solve an equation like -3(2 + -5x) + 30 = -36 by applying the box method.<br /><br />Or maybe another way to look at the benefits is that it forces students to constantly think about the order of operations as they work, pushing them toward mastery? One can hope? :)Dan Wekselgreenehttps://www.blogger.com/profile/08696028020767073620noreply@blogger.comtag:blogger.com,1999:blog-30226356.post-77318401709181626812009-09-12T17:22:27.312-07:002009-09-12T17:22:27.312-07:00I've not tried that approach, but I can tell y...I've not tried that approach, but I can tell you what I do with my classes which has been pretty effective.<br /><br />I start by teaching the unit to the best of my abilities, but there are always a few students who lag behind like you said. I then have a song and dance we do as a class which reinforces the steps they need to take to solve the equations. It might sound silly, but it really helps them understand that when they get stuck, there are steps they can follow.<br /><br />After the unit is over, throughout the year I do a "skills drill" sheet for 10 minutes at the beginning of about two classes a week. They are 6 problems long, each of which show off some different part of solving equations. I look them over really quickly as they finish. Students that make a certain number of mistakes have to meet with me outside of class either during our study hall period or after school for a few minutes to go over it together. If a student gets through 3 of these sheets and only makes 2 mistakes between them, then they move on to a new topic for skills drill(graphing equations). If they get through all of the skills drills topics(rarely happens, but provides a carrot for them) then they can have the 10 minutes of class to work silently on something else or read a book. I've had a lot of success with these skills drills, but it does take time out of classes.<br /><br />Another strategy I've used for this was having my students create wiki pages for each important topic for our exam as a group project. I intentionally made students who struggled with a particular topic responsible for explaining that topic. Students who excelled at most things were grouped together for the newest material. I was a little worried about it at first, but it worked out quite nicely in the end.Mr. Sweeneyhttps://www.blogger.com/profile/09576574228194571537noreply@blogger.comtag:blogger.com,1999:blog-30226356.post-90433928502399142422009-09-12T17:09:23.523-07:002009-09-12T17:09:23.523-07:00The second method is very similar to the way I tea...The second method is very similar to <a href="http://blog.mathsage.com/?p=164" rel="nofollow">the way I teach it</a>.<br /><br />The tradeoff that I see between the two is that your method makes the process a little bit clearer, at the expense of accessibility for the low performing kids - I believe part of the success is that they can just do this, and worry about the why it works after they have the process down. It seems possible that having them write the expressions in the tp boxes might just be more stuff to put in their head.Mr. Khttp://feeds2.feedburner.com/MathStoriesnoreply@blogger.comtag:blogger.com,1999:blog-30226356.post-16508818384771015762009-09-12T16:39:23.361-07:002009-09-12T16:39:23.361-07:00The difference in abilities is a constant struggle...The difference in abilities is a constant struggle in my class. All of the students have taken algebra 1 already in 8th grade; we make them all take algebra 1 again with us as freshmen, because even those who have passed the class in middle school tend not to actually be able to do any algebra (procedurally, let alone conceptually).<br /><br />But they all remember different pieces here and there. I'm sure quite a few will already know how to solve equations like 2x + 5 = 11. And you're right, when they do know how to do something (or just think they do), they become very resistant to trying "the long way".<br /><br />However, I doubt those same kids can solve 5 - (2/3)x = -3. Using these visual methods might really help them, even though they "know a faster way". So I would probably push them to try these methods anyway.<br /><br />I will do a diagnostic before we start the unit, though, to determine if there are students who really have already mastered solving equations. I might have a total of 4 or 5 out of all my algebra 1 students. For those kids, I will probably come up with some alternate assignments for them to work on during this unit. Then I would give them the choice: learn the same topic in a new way, or learn a new topic independently. Both have value.Dan Wekselgreenehttps://www.blogger.com/profile/08696028020767073620noreply@blogger.comtag:blogger.com,1999:blog-30226356.post-7161449431380683742009-09-12T16:24:00.004-07:002009-09-12T16:24:00.004-07:00This is pretty intuitive to me, so I hope it will ...This is pretty intuitive to me, so I hope it will be to your students. My concern would be that, for the students who pick up on how to solve equations quickly, this will just be obnoxious busy work and they will complain or act out. Otherwise, it seems like it's certainly worth a try! I'm looking forward to hearing how it goes down.Alison Blankhttps://www.blogger.com/profile/03495865487502079654noreply@blogger.com