FairProspects Posted October 17, 2012 Share Posted October 17, 2012 For problem #97 on page 57, you are supposed to divide 156 by 6 using long division. But, I'm confused as to why the answer key expects the child to start with 20 for the quotient, since all the other examples (except for the one directly above on the page) have them starting with 10 times the divisor and working from there. Even in the example right above using 20 as a starting quotient, the divisor is 5, which makes sense because 20 x 5 = 100 and I could see ds getting that easily, but why would he be expected to start working on the dividend 156 with 6 x 20 and not 6 x 10? :confused: I'm pretty sure that they don't expect times tables to be memorized that high. Also, I am really thrown off because this is the way I learned long division: 156/6 6 goes into 15, 2 times 2 x 6 = 12 15-12 = 3 3 bring down the 6 = 36 36/6 = 6 I realize that is not a very efficient way of understanding what is occurring, or looking at the number as a whole, but is there something I can read to understand the BA/Singapore method? When ds struggles, I don't know why he should start that way or how to help him understand because I haven't learned this method very well and can't scaffold it. Quote Link to comment Share on other sites More sharing options...

letsplaymath Posted October 17, 2012 Share Posted October 17, 2012 I haven't seen BA, but I'm guessing they assumed most students are familiar with the doubles and could see an easy parallel between 6x2=12 and 6x20=120. As far as using the zero (20 instead of 2), that emphasizes the place-value meaning of what is happening with the numbers. The way you (we!) learned kept the meaning hidden behind a set of steps to follow. We could just as easily have been little robots the teachers programmed with "follow the recipe and don't ask questions". Quote Link to comment Share on other sites More sharing options...

Rosie Posted October 18, 2012 Share Posted October 18, 2012 For problem #97 on page 57, you are supposed to divide 156 by 6 using long division. But, I'm confused as to why the answer key expects the child to start with 20 for the quotient, since all the other examples (except for the one directly above on the page) have them starting with 10 times the divisor and working from there. Even in the example right above using 20 as a starting quotient, the divisor is 5, which makes sense because 20 x 5 = 100 and I could see ds getting that easily, but why would he be expected to start working on the dividend 156 with 6 x 20 and not 6 x 10? :confused: I'm pretty sure that they don't expect times tables to be memorized that high. Also, I am really thrown off because this is the way I learned long division: 156/6 6 goes into 15, 2 times 2 x 6 = 12 15-12 = 3 3 bring down the 6 = 36 36/6 = 6 I realize that is not a very efficient way of understanding what is occurring, or looking at the number as a whole, but is there something I can read to understand the BA/Singapore method? When ds struggles, I don't know why he should start that way or how to help him understand because I haven't learned this method very well and can't scaffold it. I can't answer your specific question since I haven't ordered 3C yet, but I know that in 3B they do expect them to know what 6x20 is. I was taught the way you were, with no understanding, just knowing that I got the right answer by going through the steps. I'm teaching my dd the way Crewton Ramone shows (with some slight changes) and it is going really well! You might want to check it out HERE. Quote Link to comment Share on other sites More sharing options...

Rivka Posted October 18, 2012 Share Posted October 18, 2012 For problem #97 on page 57, you are supposed to divide 156 by 6 using long division. But, I'm confused as to why the answer key expects the child to start with 20 for the quotient, since all the other examples (except for the one directly above on the page) have them starting with 10 times the divisor and working from there. Even in the example right above using 20 as a starting quotient, the divisor is 5, which makes sense because 20 x 5 = 100 and I could see ds getting that easily, but why would he be expected to start working on the dividend 156 with 6 x 20 and not 6 x 10? :confused: I'm pretty sure that they don't expect times tables to be memorized that high. They don't expect kids to have memorized the times tables through the teens, but they do expect them to be able to extrapolate from the regular times tables to x 20, x 200, etc. You're supposed to start by looking at the whole numbers and guessing that 6 goes in at least a certain number of times. Guessing that it goes in "at least 10 times" would still work; it would just be less efficient. For my DD, the thought process would be, "How many times would 6 go in? At least 10 times? ...That would just make 60, wow, it would go in a lot more times than that. How about 20 times, okay, 120 is much closer." I was taught long division the same way you were, but I think this way makes SO much more sense conceptually. I'm fast and accurate with the old-fashioned way, but if pressed I would have a hard time explaining why it works. The BA way, the sense of place value is preserved. I also like that if your estimate is off, it's no biggie - it might add an extra step, but it doesn't mean you did anything "wrong." It was helpful, with my DD, to consistently phrase it in terms of the monsters/donuts problems in the Guide until she fully grasped the process. "So 6 monsters are sharing 156 donuts. Each monster will get at least 20, right? If you hand out 20 to each, how many donuts will that use up? Okay, so 120 have been used up - subtract it from 156 and find out how many are left. 36, okay, so each monster gets 6 more donuts and you don't have any left after that. They each get 20 + 6 = 26 donuts." Quote Link to comment Share on other sites More sharing options...

justLisa Posted October 18, 2012 Share Posted October 18, 2012 They don't expect kids to have memorized the times tables through the teens, but they do expect them to be able to extrapolate from the regular times tables to x 20, x 200, etc. You're supposed to start by looking at the whole numbers and guessing that 6 goes in at least a certain number of times. Guessing that it goes in "at least 10 times" would still work; it would just be less efficient. For my DD, the thought process would be, "How many times would 6 go in? At least 10 times? ...That would just make 60, wow, it would go in a lot more times than that. How about 20 times, okay, 120 is much closer." I was taught long division the same way you were, but I think this way makes SO much more sense conceptually. I'm fast and accurate with the old-fashioned way, but if pressed I would have a hard time explaining why it works. The BA way, the sense of place value is preserved. I also like that if your estimate is off, it's no biggie - it might add an extra step, but it doesn't mean you did anything "wrong." It was helpful, with my DD, to consistently phrase it in terms of the monsters/donuts problems in the Guide until she fully grasped the process. "So 6 monsters are sharing 156 donuts. Each monster will get at least 20, right? If you hand out 20 to each, how many donuts will that use up? Okay, so 120 have been used up - subtract it from 156 and find out how many are left. 36, okay, so each monster gets 6 more donuts and you don't have any left after that. They each get 20 + 6 = 26 donuts." This is helpful. Dang I was taught by the algorithm and had no clue "why." We are about to review 2 digit divisors and I'm already banging my head. Quote Link to comment Share on other sites More sharing options...

FairProspects Posted October 18, 2012 Author Share Posted October 18, 2012 I can't answer your specific question since I haven't ordered 3C yet, but I know that in 3B they do expect them to know what 6x20 is. I was taught the way you were, with no understanding, just knowing that I got the right answer by going through the steps. I'm teaching my dd the way Crewton Ramone shows (with some slight changes) and it is going really well! You might want to check it out HERE. Thanks! He does know or could figure out what 20 x 6 is from 3B, but he doesn't have it memorized and probably wouldn't think to start there and work backwards. I'll have to check out the Crewton Ramone link. They don't expect kids to have memorized the times tables through the teens, but they do expect them to be able to extrapolate from the regular times tables to x 20, x 200, etc. You're supposed to start by looking at the whole numbers and guessing that 6 goes in at least a certain number of times. Guessing that it goes in "at least 10 times" would still work; it would just be less efficient. For my DD, the thought process would be, "How many times would 6 go in? At least 10 times? ...That would just make 60, wow, it would go in a lot more times than that. How about 20 times, okay, 120 is much closer." I was taught long division the same way you were, but I think this way makes SO much more sense conceptually. I'm fast and accurate with the old-fashioned way, but if pressed I would have a hard time explaining why it works. The BA way, the sense of place value is preserved. I also like that if your estimate is off, it's no biggie - it might add an extra step, but it doesn't mean you did anything "wrong." It was helpful, with my DD, to consistently phrase it in terms of the monsters/donuts problems in the Guide until she fully grasped the process. "So 6 monsters are sharing 156 donuts. Each monster will get at least 20, right? If you hand out 20 to each, how many donuts will that use up? Okay, so 120 have been used up - subtract it from 156 and find out how many are left. 36, okay, so each monster gets 6 more donuts and you don't have any left after that. They each get 20 + 6 = 26 donuts." The monsters and donuts thing is how we have been doing it too, but ds just never starts with 20. At least it only adds an extra step, but that automatic mental calculation is just not gonna be there. I thought maybe I was missing a trick where they explained why you start with 20, but I guess not. We'll just keep plugging along. Quote Link to comment Share on other sites More sharing options...

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