SoCal Sandra Posted May 8, 2011 Share Posted May 8, 2011 My dss solved the following problem, which is problem 25 from Review 11, on page 115 of SM 5B workbook: "June spent 3/5 of her money in the first week and 1/3 of the remainder in the second week. She spent $110 altogether. How much money did she have left?" I used algebra and the SM bar model to work out the problem, but my ds solved it in his head. He got the correct answer, $40, but I don't understand what he did. Here's his explanation of what he did: "I dropped the 0 from 110 and treated it like 11. The largest multiple of 3 that you can get out of 11 is 9. I added the zeroes back to the numbers, so the amount spent on the first day was $90, which means $20 was spent on the second day. Two times $20 is $40 dollars. $40 was left. Also, three times $20 is $60 dollars, which added to $90 equals $150, and $150 minus $110 equals $40. When I asked ds why he divided the $90 by three he said it was because 3/5 of the money was spent on the first day. I don't quite understand how all of this got ds to the correct answer. He thinks differently than I do, so perhaps I'm missing something. Does anyone understand the logic in his approach? Or did he just make a lucky guess? TIA Quote Link to comment Share on other sites More sharing options...
kiwi mum Posted May 8, 2011 Share Posted May 8, 2011 I can do this in my head too, but I don't get his logic. I think the 90 was a lucky guess. (Open to being proved wrong though ;-) ) Quote Link to comment Share on other sites More sharing options...
meet me in paris Posted May 8, 2011 Share Posted May 8, 2011 I think dividing the 90 by 3 was a smart move - it definitely lets you work "backwards" to find the same ratio (90 / 3 = 30, 30 x 5 = 150, so your ratio is 90:150 = 3:5). In that case, $60 is left, and 1/3 of 60 is 20, so 90+20 was spent, and $40 left. So, I think his logic was right on (although dropping the zero happened to work in this problem, but it might not in others). Maybe he just had a roundabout way of explaining it (my daughter is like this). Quote Link to comment Share on other sites More sharing options...
Capt_Uhura Posted May 8, 2011 Share Posted May 8, 2011 HELP! I'm having a brain fart. Please someone work that out with bar diagrams from me! I'm currently working through SM CWP 5 challenging problems only. :001_huh: Quote Link to comment Share on other sites More sharing options...
Narrow Gate Academy Posted May 8, 2011 Share Posted May 8, 2011 "June spent 3/5 of her money in the first week and 1/3 of the remainder in the second week. She spent $110 altogether. How much money did she have left?" Here's his explanation of what he did: "I dropped the 0 from 110 and treated it like 11. The largest multiple of 3 that you can get out of 11 is 9. I added the zeroes back to the numbers, so the amount spent on the first day was $90, which means $20 was spent on the second day. Two times $20 is $40 dollars. $40 was left. Also, three times $20 is $60 dollars, which added to $90 equals $150, and $150 minus $110 equals $40. When I asked ds why he divided the $90 by three he said it was because 3/5 of the money was spent on the first day. I don't quite understand how all of this got ds to the correct answer. He thinks differently than I do, so perhaps I'm missing something. Does anyone understand the logic in his approach? Or did he just make a lucky guess? TIA Dropping the 0 to temporarily work with smaller numbers and then adding it back on is fine. If you divide by ten and then multiply by ten, most of the time it does not change the overall answer. The problem I see with your son's logic is that he is making the assumption that the amount spent will be a multiple of thirty (which he has simplified to 3). The amount could just as easily have been 84 or 96 or some number that is not a multiple of 30. While this technique works in the world of elementary word problems, it does not necessarily work well in real life applications. I think he ended up with a lucky guess and would make sure that he understands how to solve the problem without making that initial assumption. HELP! I'm having a brain fart. Please someone work that out with bar diagrams from me! I'm currently working through SM CWP 5 challenging problems only. :001_huh: Here's what I would do... Amount spent in the first week [--][--][--][--][--] Next I adjust the number of boxes so I can easily mark off 1/3 of the remainder (the black boxes). On paper I just take each of my rectangular boxes and divide it into three pieces so it ends up looking like the bars below. Amount spent in the first week [--][--][--][--][--][--][--][--][--][--][--][--][--][--][--] Amount spent in the second week = 1/3 of the remaining 6 (black) boxes or 2 boxes. I color these in on the bar. [--][--][--][--][--][--][--][--][--][--][--][--][--][--][--] Total amount spent is 11 boxes = 9 from week 1 + 2 from week 2 = $110 (I would draw a bracket over the 11 colored boxes on my diagram and write $110) $110/11 = $10 for each box so the 4 black boxesboxes remaining would be $40 HTH Quote Link to comment Share on other sites More sharing options...
angela in ohio Posted May 8, 2011 Share Posted May 8, 2011 Dropping the 0 to temporarily work with smaller numbers and then adding it back on is fine. If you divide by ten and then multiply by ten, most of the time it does not change the overall answer. The problem I see with your son's logic is that he is making the assumption that the amount spent will be a multiple of thirty (which he has simplified to 3). The amount could just as easily have been 84 or 96 or some number that is not a multiple of 30. While this technique works in the world of elementary word problems, it does not necessarily work well in real life applications. I think he ended up with a lucky guess and would make sure that he understands how to solve the problem without making that initial assumption. :iagree: My dd tends to do this, and I always have to back her up so that she has the skill correct to tackle ANY problem. Quote Link to comment Share on other sites More sharing options...
Capt_Uhura Posted May 8, 2011 Share Posted May 8, 2011 Here's what I would do... Amount spent in the first week [--][--][--][--][--] Next I adjust the number of boxes so I can easily mark off 1/3 of the remainder (the black boxes). On paper I just take each of my rectangular boxes and divide it into three pieces so it ends up looking like the bars below. Amount spent in the first week [--][--][--][--][--][--][--][--][--][--][--][--][--][--][--] Amount spent in the second week = 1/3 of the remaining 6 (black) boxes or 2 boxes. I color these in on the bar. [--][--][--][--][--][--][--][--][--][--][--][--][--][--][--] Total amount spent is 11 boxes = 9 from week 1 + 2 from week 2 = $110 (I would draw a bracket over the 11 colored boxes on my diagram and write $110) $110/11 = $10 for each box so the 4 black boxesboxes remaining would be $40 HTH thank you! I was on the right track! YEAH!!!!!!!!!!!! But figured I must be on the wrong track lol. I'll finish it later and then compare to what you've done. Thanks again, Capt Uhura Quote Link to comment Share on other sites More sharing options...
Capt_Uhura Posted May 8, 2011 Share Posted May 8, 2011 AARGH I had misread the problem! Got it! THanks! Quote Link to comment Share on other sites More sharing options...
Pata Posted May 9, 2011 Share Posted May 9, 2011 FWIW, a very dear friend of mine who used to teach math in Singapore gave me a manual that teaches the various ways to solve challenging word problems. One of the methods is to guess the number, then plug it in and see if it works. Your son may have had made a guess, but it did work and Singapore says that's ok. I believe their philosophy is that by guessing, the student will learn about the relationships of the numbers and see what works and what doesn't. I would still make sure he knew the math behind it though by giving him a few more problems that are similar, as I'm sure that Singapore doesn't want the student to guess at every problem :D. Quote Link to comment Share on other sites More sharing options...
Surfside Academy Posted May 9, 2011 Share Posted May 9, 2011 I'm intrigued by Singapore's bar method. In what book do they introduce this method? Would it be found in their Intensive Practice books? Quote Link to comment Share on other sites More sharing options...
Pata Posted May 10, 2011 Share Posted May 10, 2011 You need to use it in the IP books, but the method is explained in the textbook and in the home instructor's guide. Quote Link to comment Share on other sites More sharing options...
SoCal Sandra Posted May 10, 2011 Author Share Posted May 10, 2011 You've helped me zero in on the problem and I think my son is either not recognizing the steps he is taking or is unskilled at communicating them. This isn't the first time that he has solved a problem in a way that seems backward to me, but this time he solved it so very quickly that I think he failed to distinguish the steps he was taking. You've given me quite a bit of insight and I think he jumped straight to the end, recognized a ratio, dropped the zero from the 110 for a quick "guess and check" and solved the problem. SM 5B covers both ratio and estimation, so he has used those a lot recently. Since they may have made their way into his approach to this problem, perhaps that means that SM taught the concepts effectively. I will monitor this. I check every single problem and ds is required to correct every problem he gets wrong. Since we use the textbook, the workbook, parts of the extra practice book and parts of the intensive practice book, correcting even a few errors makes math a big part of our lives. Regarding the bar models, they are introduced in the textbook and sometimes modeled in the workbook, but I think the best examples are found in the "Friendly Notes" section of the extra practice book. We use the standards edition now, but I think the U.S. edition called the section something else. The instructor's guide also gives a good narrative description of using the bar models. Thanks again, Math Mavens! Quote Link to comment Share on other sites More sharing options...
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