C_l_e_0..Q_c Posted May 12, 2008 Share Posted May 12, 2008 At what level should the following problem be understood? Square root of 72 minus square root of 50 (to be done without a calculator, of course). I'd be interested in knowing at what level your children could answer that question, and what math program they used. Thanks! Quote Link to comment Share on other sites More sharing options...
Bev in B'ville Posted May 12, 2008 Share Posted May 12, 2008 (my youngest) this year took Algebra 1 using Dolciani's Structure and Method: Book 1. He can do this and actually enjoys these problems. He was 12 when he started this curriculum and just recently turned 13. Quote Link to comment Share on other sites More sharing options...
Pamela H in Texas Posted May 12, 2008 Share Posted May 12, 2008 My daughter also did it using the book Bev said. She was a little younger (7 when she started book, but could have been 8 when she learned that), but also enjoyed those. I haven't done it yet with my 13yo though, if that matters. Hmmmm, but now looking at it, it looks that my son could answer that kind in his head if I showed him how. Is there a curriculum that is presenting those to younger kids as mental math or "fun math?" Thanks! Quote Link to comment Share on other sites More sharing options...
In The Great White North Posted May 12, 2008 Share Posted May 12, 2008 OK, clue me in. I seem to have forgotten how to find square roots, besides the whole numbers I've memorized, without a calculator :confused: (if I ever knew.) We did Foerster Algebra last year and I don't remember this. Quote Link to comment Share on other sites More sharing options...
Kareni Posted May 12, 2008 Share Posted May 12, 2008 OK, clue me in. I seem to have forgotten how to find square roots, besides the whole numbers I've memorized, without a calculator :confused: (if I ever knew.) We did Foerster Algebra last year and I don't remember this. Okay, here's how I'm solving it. Square root of 72 is equal to the square root of the quantity 36 times 2. This equals 6 times the square root of 2. Square root of 50 is equal to the square root of the quantity 25 times 2. This equals 5 times the square root of 2. Subtracting the latter from the former leaves the square root of 2 as the answer. Curriculum used? Older brain with vague memories of years gone past. Regards, Kareni Quote Link to comment Share on other sites More sharing options...
Chris in VA Posted May 12, 2008 Share Posted May 12, 2008 I'm not sure about those sorts of square roots, but I'll tell you that dd8 is using Saxon Math 3 (just finished--yippee!) and she's been doing things like the square root of 81 minus the square root of 25 for about two months now. I'd imagine they get into the more difficult square roots next year, which would be 8-10 years old. Don't know if that's helpful or not! Quote Link to comment Share on other sites More sharing options...
Susie-Knits Posted May 12, 2008 Share Posted May 12, 2008 ... in ChalkDust PreAlgebra this year. I just challenged him to your problem and he was able solved it. My oldest didn't do PreAlgebra and picked it up in greater depth in ChalkDust Algebra 1 and MathCounts/Problem Solving. Susie Quote Link to comment Share on other sites More sharing options...
teachmom3 Posted May 12, 2008 Share Posted May 12, 2008 At what level should the following problem be understood? Square root of 72 minus square root of 50 (to be done without a calculator, of course). I'd be interested in knowing at what level your children could answer that question, and what math program they used. Hi-- Assuming you mean simplifying and combining the terms (answer: square root of 2), rather than being able to derive a numerical approximation without the use of a calculator, my children learned to do that in algebra 1. They all used UCSMP Algebra, which is a sufficient, but not an intense, algebra 1 program. HTH! Quote Link to comment Share on other sites More sharing options...
C_l_e_0..Q_c Posted May 12, 2008 Author Share Posted May 12, 2008 sqrt of 72 = sqrt of (2 * 2 * 2 * 3 * 3) = 2 * 3 * (sqrt of 2) = 6 * (sqrt of 2) sqrt of 50 = sqrt of ( 2 * 5 * 5) = 5 * (sqrt of 2) therefore 6*sqrt(2) - 5*sqrt (2) = sqrt(2) Quote Link to comment Share on other sites More sharing options...
C_l_e_0..Q_c Posted May 12, 2008 Author Share Posted May 12, 2008 I found the above in a placement test for an algebra 1 class. So far, I had considered my son ready for algebra 1, but he's never been exposed to square roots at that level. I was wondering if I had found a gap in his knowledge, or if the class in question was more advanced than average, or if his pre-algebra class was not strong enough. It would seem it's all of the above, since this math knowledge seems to be in either pre-algebra or algebra 1. I know I can explain it in 2 seconds, and he'll pick it up. But I'm worried about other possible gaps. I'll check out Chalkdust pre-algebra. Or Singapore NEM. Maybe more Singapore.. I wonder at what level they will teach this concept. Quote Link to comment Share on other sites More sharing options...
C_l_e_0..Q_c Posted May 12, 2008 Author Share Posted May 12, 2008 Assuming you mean simplifying and combining the terms (answer: square root of 2), rather than being able to derive a numerical approximation without the use of a calculator, my children learned to do that in algebra 1. They all used UCSMP Algebra, which is a sufficient, but not an intense, algebra 1 program.HTH! LOL! You know that's ironic. I'd forgotten my son knew how to extract square roots manually! He *could* have done it the long way, barring any calculation errors... Quote Link to comment Share on other sites More sharing options...
Ailaena Posted May 12, 2008 Share Posted May 12, 2008 I introduced dd to the topic in 5th grade, but it was fully covered in 6th grade in the Dolciani S&M book. Like both Bev's and Pamela's children, she loved these things. They are not in my ps'd niece's Glencoe Pre-Algebra book at all, if that helps. Quote Link to comment Share on other sites More sharing options...
Susie-Knits Posted May 12, 2008 Share Posted May 12, 2008 unless there is more than just the rt problem, I wouldn't worry too much about it. I believe you said he has a concept of what a root is. He will learn to expand on the basic idea and make mathematical inferences. The key to simplifying your sample problem is to realize since the numbers are both multiples of rt 2 then they can be subtracted and thus further simplied. Remember that each publisher's series will also cover different info in different depths in different years of study. My 2 cents, Susie Quote Link to comment Share on other sites More sharing options...
C_l_e_0..Q_c Posted May 12, 2008 Author Share Posted May 12, 2008 unless there is more than just the rt problem, I wouldn't worry too much about it. I believe you said he has a concept of what a root is He was introduced to the concept of roots in Kinder. With manipulatives, he could extract exact square roots and cubic roots, when he was 5yo! This year, with MUS Pre-algebra he learned how to extract non exact roots by hand. My son is hard to place when we switch curricula. He did Singapore 1 to 4, but balked at 5. We went back to Défi-Math 5 and 6 (local program in French, that is very very strong, but doesn't follow any standard approach - that's the program teaching square roots in Kinder.) He also did MUS pre-algebra because he wanted to play with his sister's manipulatives. Now is the time to jump to high school (starts in grade 7 here, and in Singapore too, also in French - grade 6 actually) Anyway, the short story is that all of our book series have ended, and he's got to move. I'm looking at various placement tests to look for gaps, and levels. Quote Link to comment Share on other sites More sharing options...
In The Great White North Posted May 12, 2008 Share Posted May 12, 2008 What a relief! I didn't miss it after all! I thought you were talking about finding an actual number (as in decimal places and no square root sign) for an answer. BTW, Foerster did cover this, but I had it in my brain with factoring, instead of solving square roots. Quote Link to comment Share on other sites More sharing options...
Susie-Knits Posted May 12, 2008 Share Posted May 12, 2008 ... you need to switch. My oldest started Algebra 1 in 6th and my youngest will start in 9th. My experience seems to be on both ends of the spectrum! haha Mine have had great success with ChalkDust but there are lots of good math programs out there. Happy curriculum hunting! Susie He was introduced to the concept of roots in Kinder. With manipulatives, he could extract exact square roots and cubic roots, when he was 5yo! This year, with MUS Pre-algebra he learned how to extract non exact roots by hand. My son is hard to place when we switch curricula. He did Singapore 1 to 4, but balked at 5. We went back to Défi-Math 5 and 6 (local program in French, that is very very strong, but doesn't follow any standard approach - that's the program teaching square roots in Kinder.) He also did MUS pre-algebra because he wanted to play with his sister's manipulatives. Now is the time to jump to high school (starts in grade 7 here, and in Singapore too, also in French - grade 6 actually) Anyway, the short story is that all of our book series have ended, and he's got to move. I'm looking at various placement tests to look for gaps, and levels. Quote Link to comment Share on other sites More sharing options...
Pamela H in Texas Posted May 12, 2008 Share Posted May 12, 2008 It's hard to know when/where to place asynchronous and advanced children. My daughter started algebra at 7 (as mentioned above). My son was 11 when he did BCM, but we decided he STILL wasn't ready (and I chose BCM after he tested into Algebra). Different kids just need different things. I will say that I have NEVER regretted making my kids take a course twice (and I've done it more than once with dd and probably will with ds) using different materials. I also took Algebra I twice and though I made straight 99's the second time, I felt like it gave me more than any other option could have in terms of math ability and confidence. Anyway, that probably doesn't help a whole lot. But I just figured I'd share. Quote Link to comment Share on other sites More sharing options...
Pamela H in Texas Posted May 14, 2008 Share Posted May 14, 2008 Just wanted to post....I was wrong. DS (13 in April) did know how to do it when I asked. He said it was "before K12" which he started in October so it was either Lial's BCM or Abeka Math. Don't know if that helps any.... and who said homeschool moms know what things their kids know? Quote Link to comment Share on other sites More sharing options...
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