I can definitely say 5th Grade fractions seem to be where teachers struggle the most. Keep that in mind when dissecting the progression document and watching the video. Any ideas, suggestions or thoughts on how to make this any easier for both teachers and students based on your own experiences would be GREAT!
1. Begin by reading pages 11-14 of the Math Progression Document and look for new understanding and/or important aspects of fractions in the 4th grade. Please try and comment about a concept or new understanding from this document.2. Watch the following video on standard 5NF from EngageNY Studio Talks located here: Click Here
3. Post One Comment about something new you learned, an important aspect of 5th grade fractions that other grade levels need to know or an instructional strategy/model that you would use to help solidify fractions in the 5th grade. Try and relate your new learning of 5th grade fractions to what you learned previously in grades 3 and 4.
4. Post one comment responding to another participant in order to add to their thinking, suggest additional ideas or engage in a meaningful educational conversation about fractions thus far.
After viewing the document for 5th grade, I was drawn to the visual models on the right. From looking at the visual, I could immediately see how things were broken down even before checking what was written to the left. The visuals are helpful for the student to learn and for the teacher to see the child's thought process.
ReplyDelete(While watching the video, I could only think of Dana's comment yesterday about how the man in the video being so fluent writing in reverse!)
In the video, I loved the use of bar models. Last year, I observed a fifth grade math class (Dana...it was Joyce Monacelli). It was the first time I saw common core math live. They were using bar models to find common denominators, and it completely was easy to follow for the students and myself.
The video said bar models...
1. visualize the problem
2. help find common denominators
3. help write an equation
4. allow students to estimate the reasonableness of the answer.
THIS IS ALL TRUE. I am a step by step learner so of course this would help in my own though process while teaching.
Did anyone have to watch the one demonstration again using the board word problem? I admit I did to keep up. Again I believe this strategy takes repetition not only with the students, but the teacher as well in order to be clear.
You are very correct Jen it takes time. And that is why its tough to just start teaching the bar model in 5th grade. Its a much easier transition when they have been seeing it earlier on with easier problems. I have seen so many 5th grade teachers struggle with this when the students have no background in using models.
DeleteI agree Jen. He is going pretty fast. I had to stop and replay a few times because I wanted to make sure I "got it". I need to have surgery to have a replay button installed so when I'm going to fast kids can unwind and go back.
DeleteOur school has been using bar modeling in grades 3 and 4 for two years now and for K, 1 and 2 for just one year. It will be so great when the students come to me in 3rd grade with an understanding of the correct terminology and how bar models work. Many teachers are resistant to the time it takes to teach the foundation information, but I believe that the students need this background in order to find success in the harder tasks in the upper grades.
DeleteJessi mentioned to share ideas that would also enhance learning because this is a difficult year...
ReplyDeleteWhat if there were more "real life" models to use. For years the kids will be drawing the visuals, but what about use real life visuals.
Examples
Using Oblong Tissue boxes for units to separate. (We know classrooms go through tissues)
Cereal boxes (the mini packs)
Just an idea to make it more appealing even if helps one or two students that are struggling with visuals.
Love!! Or even committing to once a week a real world real model word problem for them to solve!?! That way they get the real life visual and can connect it to real world applications and use!
DeleteJen, great idea with the tissues boxes! Real life models will really draw a lot of kids in and provide some incredible concrete experiences!
DeleteJen, I also liked your creative idea using the tissue boxes representing units to separate. It makes it more realistic and manipulative to enhance student learning. I also had to pause the video to think about how I would present this to my students. I did think one of the final demonstrations might be confusing for them, but I am enjoying the bar models.
DeleteFirst of all, thank you Jesse for shattering my illusion, I mean clearing up my confusion, about the reverse writing the presenter seems to be doing :) . Of course, now my curiosity is piqued about the mirror and what that is like to use and why we can't see it... This makes me think about how it is easy to be distracted by other things when doing math (or anything, I guess). How often I have rued using the very manipulatives that I introduced to help with math because they were a distraction for some. (Perhaps because I didn't give some time with them first to explore/"play", as well as spell out procedures for them. And maybe I wasn't remembering what it's like to be a child and was only thinking about the time crunch that only an adult/teacher would feel at that moment...)
ReplyDeleteAs for working with bar models, I really like using them, and would love to see them used more in our series - not just to introduce a lesson. "Step by Step Model Drawing" by Char Forsten is a great resource if you are just getting started with them, since most/all of us didn't grow up with that strategy. Also, I like to have students use Thinking Blocks to get used to seeing/using bar models.
[ http://www.mathplayground.com/thinkingblocks.html ] (I think many "math" websites are more game than math, but thinking blocks is not one of them.) It's hard to squeeze that kind of computer time into a math lesson, but if there's some flexible time later, it's a good way for them to use the computer as a learning tool...
Anybody else catch that in the document and in the video LCD was termed a distraction? I was pleasantly surprised by the candor. In my faint and possibly faulty memories of math class growing up, finding the least common denominator was taught as if it were law. I've told students that if they are really good with their fact families, they will often see a simpler denominator than the one that would come from what the video terms as splitting the unit fraction (multiplying according to the denominators), but it isn't necessary to see the simpler relationship... I'm relieved to see that I wasn't being subversive in revealing this...:)
Reminding students that they are using the identity property when making equivalent fractions is a key, too. From the beginning we teachers need to make sure we are using the appropriate terms and concepts when teaching this - not just saying that you multiply by 3, but by 3/3, and pointing out that it works because it's the identity property, not just a trick to be remembered...
I also chuckled when the document had Ludmilla and Lazarus making hummus. I'm fairly certain most of my students would have been lost on that one, but it would have been fun to feed them some hummus to give a cultural context... On the same problem, the document says that 9/10 of a cup of lemon juice would have been close enough to not ruin the recipe, but I'm not sure that students unfamiliar with cooking would have reached that conclusion. I think they may be more legalistic with a recipe, and can see a question like this being on a state exam with students possibly losing credit for not reaching the same conclusion...Maybe I'm paranoid?
Finally ( I think), the division with models and then going right into the inverse multiplicative relationship seems like a powerful strategy. It also seems like it would need a significant amount of repetition and representation to really ingrain into students. They really seem to need a lot more time than we give them to digest multiplication and division with fractions. (Perhaps because of the previously taught rule that expires about multiplication makes bigger and division makes smaller?)
Yikes!! I didn't realize how long I rambled since I was typing in such a small box. Sorry!
DeleteDana: Awesome post, thank you for really taking the time to share, question and apply what you saw. I actually read it twice because i enjoyed it :)
DeleteWe are definitely going to dive more into multiplication and division next week so i look forward to more thoughts on that.
Anytime we have real world applications it is great, but your right it needs to also be relevant! Cooking seems to be the most commonly used, wish we could venture from always using cooking and give them more applications!
Last thing, thank you for point out the importance of using the right terminology and properties, this is SO crucial for teachers to understand and often over looked.
Now I'm in my fifth grade element! 1 minute and 45 seconds in I had to replay. It's not necessary to find a least common denominator to add and subtract and it can be a distraction to the process!? Did I hear correctly? yes. Well my interest was piqued for sure! True confessions, I'm new at using the models. It doesn't necessarily come first for me because heck I know how to do this stuff :-) But I am a visual learner so I am forever making diagrams for my students. Those diagrams usually consist of bar diagrams. So.... technically I guess I was doing this before common core came out with it. Now the trick is going to be to go heavier on the bar models before letting them discover what they can.
ReplyDeleteSOOOOO glad he mentioned the identity property. I think it's important for kiddos to pull all that stuff together and see how this is all connected.
I was also glad to hear him say to write the problems horizontally when dealing with fractions. It sure is less likely that errors will occur.
5NF4 I love using rectangular area models when multiplying a fraction times a fraction. It's like a hidden picture kids see when it is all done. It was interesting to note he said "after practice with models students can discover the algorithm. Hmmm. I wonder if mine discovered or if I told them? I'm going to have to watch myself and see this year when I start teaching this.
5.NF7 The first time for division with fractions. This is a tricky one for fifth graders. The word reciprocal wasn't even mentioned. I think I like that. In the past when I have taught this students would keep asking which one do I flip? It is especially confusing when a fraction is divided by a whole number. Students are still hung up on a big number divided by a smaller number gives you a smaller number, instead of understanding the true idea of what division really is. More models, more models, more models. Can I please have some more time?
Becky,
DeleteReferring to your comments under 5NF4...
I like how you said I wonder if my students discovered the algorithm or I told them?
I'm one that always does not give enough wait time with questions and also does not always check for true understanding. I need to work on that. The new math really wants students to build understanding, and I know I have to check if they are by allowing them to discover.
I think an idea would be to have more students come in front of the class and show the work and see what they discover. Students often love to play the teacher.
Ha ha i did the same thing when i watched this video for the first time last year! That first two minutes is VERY powerful and more teachers need to hear it. 5th grade really is the year to pull it all together with fractions and use anything and everything to make it word. Models are key, but you will find some students are ready to move on to the conceptual understanding and just go ahead and solve!!
DeleteGreat thoughts!!
I have spent the past two years working with fifth grade students and the bar models. It is amazing the foundation that they build. It is important to be consistent and trust the module instruction. It is easy to fall back on what we know based on how it was taught years ago. I have found that the "tricks" that we learned to solve problems lack a foundation of understanding, but the concrete methods that the module presents will eventually lead students to discover the "tricks or short cuts" on their own with understanding. I really like the fraction models that are presented at the fifth grade level. The foundation that the models build allows you to instruct students on concepts that are more advanced then 5th grade students have been able to master in years past.
ReplyDeleteAs far as the glass wall in the video goes, I think I should put in a purchase order for my classroom! (just had to comment on this LOL!)
You said it perfect Heidi! But now the question lies how do we get teachers to change their way of thinking and instruction to follow suite? Thats the true struggle. I do find once they step outside their comfort zone and try it the see amazing things happen!!
DeleteHeidi - I agree with trusting the modules. We have to keep falling back on the premise that we are teaching the students the foundations of the math and not just the "tricks". I can relate it to 3rd grade, teaching multiplication, most of my students mastered their multiplication facts, but the struggling students could figure out the math fact if needed using a variety of models and strategies.
DeleteAfter viewing the video, I really liked the use of bar models for teaching all four operations with fractions. I was also taken aback when he first stated that we didn't need to find a common denominator first. The visual aspect using the bar models will really help the students who possibly don't understand the process of computing the regular way. I am all for modifying and trying new procedures when teaching math. When watching the video I thought thats really neat how he did that!
ReplyDeleteUpon reading the Math Progression Document for fifth grade and relating it to what was previously learned in grades 3 and 4, I felt that it was important to begin using the bar models in the earlier grades was imperative. These skills intensified much more in fifth grade and the students need the previous exposure to make the process appear more seamless. Using the number line and area models were also useful tools when teaching students how to multiply and divide fractions. I have used the area models during instruction with my students. Some of them have a difficult time visually perceiving these diagrams.
Exactly!! Although i dont think all teachers will ditch the finding common denominators first method. We can hope that maybe they will show both :-)
DeleteWow, as I read the document I thought...thank goodness I do not teach 5th grade math! While the pictures off to the side do help, the paragraphs of information are overwhelming to me. Thankfully as I listened to the video much of the information became so much clearer to me. For 5.NF.7b using the bar models will help the students not only solve the problems, but understand why and where the answers are coming from. So many times in the past, we were taught to just do it this way but some really never understood why we did it or what the answer stands for. I try to remember to ask my students to tell me what the answer stands for, especially in a word problem. As far as the multiplication and division they are using the Singapore strategies. I use these and have found them to be so valuable for the students. Once again, if teachers continually spiral the previous learners, students will have a much easier time learning and understanding these new concepts.
ReplyDeleteKaty: very important point you made, they need to SPEAK about fractions constantly so that it becomes part of their normal explanations. They start this very young when talking about numbers and it its crucial to continue this with fractions!
DeleteWow, each year the math models get more and more intricate. They rely on a deep understanding of the fraction concepts. I always tell my students that the picture/ model helps "prove" your answer. It becomes clear again how important it is for teachers to lay the foundation in the earlier grades.
ReplyDeleteI really like how the standards stress the inverse relationships while students are multiplying and dividing fractions (which relates to the fact families in the earlier grades) I also noticed again the power of the identity property while multiplying and dividing.