tag:blogger.com,1999:blog-1907702537884089718.post6253179809475734740..comments2022-08-15T05:36:19.642-07:00Comments on Exit 10A: Trying to Make Some Sense Out of Long DivisionJoe Schwartzhttp://www.blogger.com/profile/02304083254248927187noreply@blogger.comBlogger13125tag:blogger.com,1999:blog-1907702537884089718.post-14895230504843242922019-03-10T11:22:42.385-07:002019-03-10T11:22:42.385-07:00That's a really good question. As you can see...That's a really good question. As you can see from the date of the post, it's been a while! But I think this developed over a period of about two weeks. Kids progressed through the various stages at different times. At some point (maybe the following year?) we started with dividing actual base-10 blocks, then moved on.Joe Schwartzhttps://www.blogger.com/profile/02304083254248927187noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-23056930753971490852019-03-09T10:48:23.857-08:002019-03-09T10:48:23.857-08:00Thank you for sharing this! I am curious, did all ...Thank you for sharing this! I am curious, did all of this progress in one week? Could you share how much time you took from start to finish with the different phases you shared in this post?NeolaBhttps://www.blogger.com/profile/05723693082664327108noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-1743928233178383362019-01-17T11:09:07.435-08:002019-01-17T11:09:07.435-08:00This task is one that actually appears in the 6th ...This task is one that actually appears in the 6th grade frameworks for Georgia ("School Fundraiser") and the progression towards the traditional algorithm is also in our frameworks tasks in 6th grade ("Scaffolding Division through Strip Model Diagramming")! It all looks extremely familiar to me! Anonymoushttps://www.blogger.com/profile/07986794277071843475noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-17725099354880561212014-09-20T20:19:33.189-07:002014-09-20T20:19:33.189-07:00Thanks for your comments. Yes, double-digit divis...Thanks for your comments. Yes, double-digit divisors are tough to handle! I'm glad you'll be giving this a try. Let me know how it works with your class.Joe Schwartzhttps://www.blogger.com/profile/02304083254248927187noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-31491473790455676462014-09-19T02:50:53.262-07:002014-09-19T02:50:53.262-07:00I love this! Thank you for sharing! I teach 5th gr...I love this! Thank you for sharing! I teach 5th grade and we are supposed to be able to divide with double digit divisors, but they haven't mastered the basics. I will be giving this method a try! Maybe if we can visualize it this way, we can take on double digit divisors. Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-34762691683253496402014-04-20T06:37:12.373-07:002014-04-20T06:37:12.373-07:00OK, now I get it! No, that comment was not meant ...OK, now I get it! No, that comment was not meant to mean it was a less preferred way, and it was not expressed to the student. Clearly there are some kids ready for "short division", and we may want to explore introducing this to them as the next, natural step in the progression.<br />Thanks for your positive words and for taking the time to comment. Joe Schwartzhttps://www.blogger.com/profile/02304083254248927187noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-56580586981190998562014-04-20T05:23:38.920-07:002014-04-20T05:23:38.920-07:00"It brought back bad memories for Jeff" ..."It brought back bad memories for Jeff" was the caption on the last example, so I thought that this is a less preferred way of doing the problem<br /><br />I do like how there are multiple ways of dividing and you encourage accuracy, comfort with method, and efficiency of process.<br /><br />The last example I've seen referred to as "short division" because it is the traditional long division algorithm but you are only recording the remainder and doing the subtraction mentally.<br /><br />Again, this is a very powerful way to teach and your students are very fortunate to experience this.MrChttps://www.blogger.com/profile/15834292039619837268noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-41166258070964841192014-04-20T05:09:27.871-07:002014-04-20T05:09:27.871-07:00Are you referring to the last example? It was not...Are you referring to the last example? It was not my intention to judge it. I had never seen division done that way.Joe Schwartzhttps://www.blogger.com/profile/02304083254248927187noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-48424604086731604272014-04-19T07:52:13.145-07:002014-04-19T07:52:13.145-07:00But why after all the "find your own way"... But why after all the "find your own way" do you pass judgement on "short division" as it could be considered a next step in algorithm after long division?MrChttps://www.blogger.com/profile/15834292039619837268noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-47905745483173783722014-04-18T09:50:21.573-07:002014-04-18T09:50:21.573-07:00Thanks Nicora. Asking the kids to explain what it...Thanks Nicora. Asking the kids to explain what it is that they're doing is something I know is important, but do not remember to do often enough. Perhaps it makes more sense to give them fewer problems to do and more time to explain and reflect? Joe Schwartzhttps://www.blogger.com/profile/02304083254248927187noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-22875109471187107022014-04-14T09:35:36.069-07:002014-04-14T09:35:36.069-07:00Joe- I think this is so neat. I love how the stud...Joe- I think this is so neat. I love how the students progress (and how you keep track of it) from doing what makes sense to them with the diagram to moving toward the traditional algorithm. It's great how you allowed the students to build on what they knew. I would be really interested to hear (or see in writing) their explanations for what they were doing. It sounds like they are developing a deep understanding for why the algorithm works--which I think is an amazing accomplishment! I'm still thinking about your question about how to use the diagram reinforce equal grouping. But, as you said, since that wasn't your goal, maybe it's not as important here. And just so you know, I am loving reading your blog--it's giving me so many ideas! Nicora Placahttps://www.blogger.com/profile/16724981389472015421noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-88682102643582898162014-04-02T14:34:41.114-07:002014-04-02T14:34:41.114-07:00That's a great problem (although we'd cert...That's a great problem (although we'd certainly need some background knowledge regarding pallets). I'm looking forward to reading about it. Did your kids have any visuals or manipulatives to help? <br />In the past we would've used base 10 blocks, and done all the requisite regrouping involved. This was painstaking and took lots of time, but did build good understanding. What it didn't do was explain how it all fit in the traditional long division tableau.<br />I thought that the traditional algorithm was grade 5, but yes it is grade 6. Maybe it's just me, but I think it's a bit unrealistic to ask kids to handle dividing 4 digit dividends and 2 digit divisors and decimals to hundredths through grade 5 efficiently without a traditional algorithm. The numbers just seem too big. I hate to say this, but I suppose we'll have to wait and see what the PARCC has in store for us division-wise. Maybe we're over-thinking it?Joe Schwartzhttps://www.blogger.com/profile/02304083254248927187noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-58182508480668098202014-04-02T06:16:05.652-07:002014-04-02T06:16:05.652-07:00Absolutely Joe!!!! Division is a monster! Althou...Absolutely Joe!!!! Division is a monster! Although CCSS doesn't specifically address the traditional algorithm of division until 6th grade...this ugly beast continues to rear its head in the 3-5 classroom. The problem is that it is difficult to conceptually have the students mimic what's happening in the traditional algorithm (within a context) which leads to DMBS. I came across this from John Van de Walle last week and tried it with a 4th grade class on Monday! The context served the math beautifully...You're one post ahead of me here:-) <br /><br />A school is participating in a doughnut fundraiser and the shipments have been delivered. <br />• Each pallet has 10 cartons<br />• Each carton has 10 boxes <br />• Each box has 10 donuts<br />The shipment consists of 4 pallets, 6 cartons, 4 boxes, and 8 individually wrapped doughnuts. If the doughnuts needed to be shared among the 5 classes, what is the most EFFICIENT way they could share the doughnuts between the classes?<br /><br />This task asks that students disseminate the doughnuts the most efficient way possible. The most efficient way to share the doughnuts is to keep as many pallets, cartons and boxes unopened as possible. The underlying mathematics of this task mimics the division algorithm and this context makes the understanding of "procedures" accessible to students.<br /><br />Give it a try! Love to see how it goes for you and your peeps!<br />Graham<br /><br />Anonymoushttps://www.blogger.com/profile/08525114028095675402noreply@blogger.com