AEC Posted October 4, 2012 Share Posted October 4, 2012 Background: DS10 has just finished SM 4B (IP, WB, sprints). We'll start 5A next week and I expect he'll move through it quickly as his arithmetic is solid (multi-digit, decimals/fractions, pos/neg numbers, on paper and mental). I'd figured we'd do 5A/5B and then jump into AoPS pre-algebra. We also do CWP, running about 1/2 a year behind on purpose. I wanted the 'math' in the word problems to be easy so he could focus on the problem setup aspect. So far, that's worked well. Issue: Twice in the last two days he's hit upon a problem in CWP4 he didn't know how to solve, and where the picture SM would want you to construct wasn't immediately obvious to me, either. Then he sees me resort to algebra to see what the answer is so I can work backwards and explain how they'd want you to setup the problem. Being a curious sort, he of course said 'hey...what's this algebra stuff? Could you teach me that and we'll skip all this diagram nonsense?' Question: Now I'm not sure what to do. I won't just tell him the 'rules' for solving simultaneous equations for the same reason we didn't just learn the rules for arithmetic. If we're gonna do algebra we're going to learn it correctly. Further, I think there's value in the comprehension provided by the visual method of problem setup. AND YET - the boy is asking for algebra. I can't just let that go! Options: -> say "you'll learn it soon enough, meanwhile let's stick with this method" and march on through CWP4, SM 5A/5B, CWP5 till we're done. -> go buy the AoPS pre-alg book and do some of that alongside the SM roadmap. Will that satisfy his desire 'for algebra'? -> decide we're done with SM and jump to AoPS pre-alg. He'd pass the AoPS pre-test, no problems. He won't pass the SM 5B pretest, thought (won't know the percentage, ratio or geometry problems). Thoughts? Quote Link to comment Share on other sites More sharing options...
boscopup Posted October 4, 2012 Share Posted October 4, 2012 My son and I recently hit some problems in Singapore where algebra was easier than the bar model. I went ahead and showed him some basic stuff, emphasizing the whole way that you had to do the same thing to both sides to keep the equations equal. When he did a page of word problems that day, he used bar model for the problems where that seemed easier and algebra for the problems where that seemed easier. We're also planning to do AoPS after 5B. IIRC, there is some basic introduction to algebra in 5B somewhere. I forget which section. The why and how is covered thoroughly in AoPS, so I'm not concerned. I just don't teach it as a trick. I explain every step of the way why I'm doing what I'm doing. DS had also used balances in MM4A to solve some linear equations, including using two balances (equations) to solve for two variables, so he has seen the â€whyâ€. You could go ahead and get AoPS now and read through the linear equation explanations yourself, so you know how to teach that part. I've taught DS a few things from AoPS while doing Singapore. I'm working through the book ahead of him, so I can answer questions intelligently. :) Quote Link to comment Share on other sites More sharing options...
ErinE Posted October 4, 2012 Share Posted October 4, 2012 I'll chime in with Boscopup and say start teaching him basic algebra. I've run into the same issue where using algebra to find the answer is easier than using pictures. I've introduced the idea of a variable and explained as I worked through the problem exactly what I'm doing and why I'm doing it. DS10 loves our "algebra" sessions and I think it will make algebraic concepts less of an unknown when he begins a more formal study. Quote Link to comment Share on other sites More sharing options...
Angie in VA Posted October 4, 2012 Share Posted October 4, 2012 (edited) Crewton Ramone. (I've watched his videos.) Hands on Equations. (I've never used.) Just posted a link to HBC's 30% off HoE on the K-8 board this morning. Edited October 4, 2012 by Angie in VA Added info. Quote Link to comment Share on other sites More sharing options...
Chrysalis Academy Posted October 4, 2012 Share Posted October 4, 2012 One of my favorite things about Life of Fred is the introduction of the ideas of variables and unknowns and basic algebraic concepts from the beginning - I mean even in the Elementary series. I've picked up on the author's technique - he'll show something the "arithmetic" way, then show how you would solve that in Algebra 1, Algebra 2, Calculus, etc. using more sophisticated tools - and I will show dd, and explain "that's algebra". Whenever she does something (in MM) solving for variables or unknowns, I point out that she's "doing algebra." So we've completely demystified the idea of algebra, and introduced it as this exciting way to solve problems, so she's eager to do it. I'm not familiar with Singapore's S&S, but we are coming up on a basic introduction to equations in MM5A Ch 1, and there are more balance problems too. I decided to get hands-on equations, too. I plan to continue working through the rest of MM (5&6) but to keep feeding the interest and excitement about algebra and hopefully LOF and HOE will help . . . Not sure if this helps any. I am another who is often mystified by the bar model thing (we use Singapore word problems), and while I usually try to figure it out and teach it that way, if it seems really counterintuitive to me, I just show her the algebraic method. We didn't start using these more Asian-style curricula till 4th grade, though, so maybe if we had done it from the beginning it would be more obvious to me - but at this point, I can't see forcing the bar models and making it more confusing if there is a simple alternative that she can grasp conceptually. Quote Link to comment Share on other sites More sharing options...
dbmamaz Posted October 4, 2012 Share Posted October 4, 2012 also check out real life algebra and challenge math from Zaccaro. RLA seems lower level than Challenge math. amazon . . . Quote Link to comment Share on other sites More sharing options...
FairProspects Posted October 4, 2012 Share Posted October 4, 2012 Is there a problem with using algebra? The algebra is easier for ds than the arithmetic, so I've always just put it into algebra when we get stuck. Is there some reason I shouldn't? Quote Link to comment Share on other sites More sharing options...
acurtis75 Posted October 4, 2012 Share Posted October 4, 2012 Dd and I reviewed the bar model concept and use it on some problems but neither one of us really cares for it so we've used basic algebra instead at times. We only use CWP as a supplement. We use MUS as our spine and the concept of "mystery numbers"/ variables was introduced in the alpha level while learning basic addition. We've since played with hands on equations and other stuff for fun. Dd prefers using algebra to using the bar models. Quote Link to comment Share on other sites More sharing options...
justLisa Posted October 4, 2012 Share Posted October 4, 2012 There is a section in MM using bar models and x to make an equation. That makes much more sense. Quote Link to comment Share on other sites More sharing options...
Chrysalis Academy Posted October 4, 2012 Share Posted October 4, 2012 OMG, get Hands-On Equations! The UPS man :001_wub: delivered it right as we were finishing our MM lesson, so we watched the video and did the first lesson. Miss P loved it!!!! I'm so glad we got it! Quote Link to comment Share on other sites More sharing options...
Mommy22alyns Posted October 4, 2012 Share Posted October 4, 2012 Hands on Equations!!! Loving it here. Quote Link to comment Share on other sites More sharing options...
crazyforlatin Posted October 4, 2012 Share Posted October 4, 2012 I like the bar method, but it hasn't resonated with DD as I had hoped. She much prefers the HoE way (eg. balance, algebraic equation) and I'm fine with that. I love HOE's verbal book, which is what you could add in with level 5 math. Quote Link to comment Share on other sites More sharing options...
besroma Posted October 4, 2012 Share Posted October 4, 2012 I agree with the LOF recommendation. Quote Link to comment Share on other sites More sharing options...
Beth in SW WA Posted October 4, 2012 Share Posted October 4, 2012 Crewton Ramone. (I've watched his videos.) Hands on Equations. (I've never used.) Just posted a link to HBC's 30% off HoE on the K-8 board this morning. :iagree: Quote Link to comment Share on other sites More sharing options...
boscopup Posted October 4, 2012 Share Posted October 4, 2012 Is there a problem with using algebra? The algebra is easier for ds than the arithmetic, so I've always just put it into algebra when we get stuck. Is there some reason I shouldn't? Some problems are really easy to solve once you draw the bar models, to the point that you can see the answer right away without doing a lot of calculating. But many of them, algebra is just as easy or easier, and if your kid understands the algebra way, I see no problem with doing it that way. Quote Link to comment Share on other sites More sharing options...
Hunter Posted October 4, 2012 Share Posted October 4, 2012 If you google "algebra tiles" and "algebra blocks" you will find some free resources. Quote Link to comment Share on other sites More sharing options...
letsplaymath Posted October 5, 2012 Share Posted October 5, 2012 I like using word algebra to teach students how to think through math problems. Quote Link to comment Share on other sites More sharing options...
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