tag:blogger.com,1999:blog-30226356.post3418809371379660890..comments2016-12-11T21:47:43.153-08:00Comments on The Exponential Curve: Constructing and Deconstructing EquationsDan Wekselgreenehttp://www.blogger.com/profile/08696028020767073620noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-30226356.post-7580866645998785042013-11-08T12:04:13.277-08:002013-11-08T12:04:13.277-08:00I love the FAL lessons. I recently used the lesso...I love the FAL lessons. I recently used the lesson called "Solving Linear Equations in One Variable" with my 8th graders and it went great! It is a great one to use when dealing with variables on both sides and when equations can be always, never, or sometimes true.Annie Foresthttp://showyourthinkingmath.blogspot.comnoreply@blogger.comtag:blogger.com,1999:blog-30226356.post-25404453330285141812013-10-10T20:50:52.976-07:002013-10-10T20:50:52.976-07:00I like it! I use a similar method called "unw...I like it! I use a similar method called "unwrapping the onion." http://untilnextstop.blogspot.de/2012/11/visualizing-order-of-operations.html It worked very well with my 7th-graders last year (who went from having never seen variables to solving quite complex equations)!untilnextstophttp://www.blogger.com/profile/15285583728476473117noreply@blogger.comtag:blogger.com,1999:blog-30226356.post-19641465105899949492013-10-03T07:49:20.433-07:002013-10-03T07:49:20.433-07:00I do a variety of different things. Something tha...I do a variety of different things. Something that I do, which sounds similar to your current method, is that I have students analyze what is happening to the variable within the equation. They have to analyze this step by step and create a list of all of the actions that occurred. I then ask them how to undo these actions. most start undoing in the wrong order so I make the analogy of putting on clothes in the morning and taking them off at night. They typically get it and are then able to make a list of the correct actions they need to take. To help remediate students knowledge on this, particularly as I teach a lot of upper level math know, I ask a series of questions. "What do you want," "what has been done to it" and "what do you need to do to undo it." Same thing I know, but I also get them to attend to even the visual structure of equations. <br /><br />You can often tell visually what things are "most closely attached to the variable." In this respect, those things are like the sock on your foot and things that are attached less tightly are the shoe. The visual structure is pretty helpful for a lot of students.Chris Painterhttp://www.blogger.com/profile/16549385444649576076noreply@blogger.comtag:blogger.com,1999:blog-30226356.post-8187156000190612292013-10-02T16:58:30.108-07:002013-10-02T16:58:30.108-07:00@ CalcDave,
Using substitution is exactly what I ...@ CalcDave,<br /><br />Using substitution is exactly what I did when students were given a constructed equation and had to figure out what the steps were. Some students were able to see the order without that crutch, and others could only see it when I had them work through the operations with a sample x.<br /><br />Starting at the bottom and working up is actually how I did it several years ago when I tried this before. It makes sense to me to do it that way. But when I was reading through the FAL, they have it starting from the top. I was wondering why, but I figured they know what they are doing and probably have a reason, so I decided to go with that. I think it may be because, when they are typically solving equations, they will be expected to start at the top and work their way down, so the idea is to habituate them to the typical order of writing the steps? Maybe the trade-off is a little more confusion at the outset for less confusion later. I'm definitely not convinced either way yet...<br /><br />@ Miss Gray<br />I haven't applied it to more complicated equations yet. And I'm not sure that this method can apply on its own, without adding in other steps, when there are variables on both sides. There is another FAL that deals with number of solutions, and I plan on looking more into that one before tackling the next phase of equation solving. How do you introduce variables on both sides?Dan Wekselgreenehttp://www.blogger.com/profile/08696028020767073620noreply@blogger.comtag:blogger.com,1999:blog-30226356.post-53031181141486754842013-10-02T16:12:02.058-07:002013-10-02T16:12:02.058-07:00We use this method when we do literal equations. I...We use this method when we do literal equations. I was wondering if you have applies it to equations with variables on both sides (ex no solution, all real etc), if so how did you do it?<br /><br /><br />Miss Grayhttp://www.blogger.com/profile/01834270553533545584noreply@blogger.comtag:blogger.com,1999:blog-30226356.post-5043849725836755292013-10-02T16:07:14.406-07:002013-10-02T16:07:14.406-07:00Maybe you could start with the substitution to see...Maybe you could start with the substitution to see how that goes. Replace x with your favorite number and then get a value. Use the order of steps to build up the function.<br /><br />Also, I wonder if it would be slightly better on the board if you continued the second column at the bottom and worked up. Then the corresponding parts are next to one another rather than reversed.<br /><br />I like the idea here, though!CalcDavehttp://www.blogger.com/profile/14039458440867020542noreply@blogger.com