4th Grade: 4.NBT
1. Begin by reading pages 13-17 of the Math Progression Document and look for new understanding and/or important aspects of the 4th Grade NBT standards
2. Watch the following video on standard 4NBT from EngageNY Studio Talks located here: Click Here
3. Post One Comment about something new you learned about multiplication and division that other grade levels need to know or an instructional strategy/model that you would use to help in the 4th grade instruction of the 4NBT standards.
Think about some of the following questions:
-what model would you use and why?
-why teach partial products?
-why does base-ten foundations play such an important role in multiplying and dividing?
- why has common core shifted more towards conceptual understanding instead of the "old way" of teaching an algorithms?
4. The 4th grade Progression is very Model involved. Please also comment on each other posts addressing your questions, comments and concerns about these Models and their application in the classroom. (Take a second look at Page 17 and discuss the different methods if applicable)
So, I found the 4th grade section of the progression document very involved. After reviewing the models and strategies, I can see where they could all be helpful. My struggle is more what to do as a 5th grade teacher. At this point when we use multiplication for solving problems, we usually see only two different methods…standard algorithm and showing partial products. We also teach the area model to assist with conceptual understanding, but do not typically use that when solving for word problems etc. At times I worry that in the future, students will have too many options available to solve problems, and not perform any of them completely accurately.
ReplyDeleteWith regard to the division model on page 16 (division as finding group size), we also use a model similar to that in 5th grade. I find the model we use extremely useful to explain the conceptual understanding, but it is so time consuming I can’t fathom using it as a daily tool. At the end of the video, the instructor states that students should be given ample time to explore the multitude of strategies available, but I am not sure we have that amount of time available in daily classroom life.
Time is a struggle for us as well. We spend 85 minutes daily on math and we may just finish the Module lesson that allows for 60 minutes. The modules are packed and very time consuming. Going through this year, being my first, I am not tweaking the modules much. Maybe after having taught them a full year, I'd feel more confident in supplementing or pulling some material out. Do you use the modules?
DeleteJanelle...I also heard Nick the video guy mention that time needs to be given for students to experiment to develop enduring understanding. I am all for that; however, the fast paced design of the modules don't really allow for that luxury. In addition, most students do not have the stamina. I am hoping that stimina will improve as students are exposed in the lower grades.
DeleteI understand what you're saying about having too many options available. As a special education teacher, I want to give my students as many options possible so that they can choose the one that works best for him/her. Along the way, they may understand aspect of each option, but never really become great at any option. I know my other teachers have said they only show one method for that very reason. I also agree that there is a limited amount of time to teach these major concepts, and teachers needs to balance fluency practice with other important concepts in the curriculum.
DeleteThe best advice i can give is to make it a goal as a teacher to help students pick what works and help them get good at it. I understand this can be difficult with so many students but it really is a key component for success, and it truly is differentiated instruction at its best!
DeleteAfter reading the Progression Document, of all the models listed, I would be most inclined to use the area model. This model involves the students decomposing the factors into their units and then solving for the areas of each box. We have used area models with our students before as a strategy for multiplying larger numbers, and they are usually fairly successful. I also think teaching the distributive property makes sense for the students because again, they are breaking numbers apart into place value units, which they should be proficient at by 4th grade. The method that I have a harder time with is multiplying numbers by solving for the partial products. Conceptually, I understand how this requires students to truly understand what they are multiplying by as they are forced to utilize their place value reasoning, however, when it comes time to actually teach the standard algorithm, I believe students might become confused, as the standard algorithm follows a different set of “rules”. For dividing numbers, I found that 4th grade follows a similar model to 5th grade. It lays the foundation for understanding how numbers are divided into equal groups, but is very time consuming.
ReplyDeleteSorry...I did it again. I posted again instead of clicking reply to Kelly's response.
DeleteYes, students usually complete area models successfully. Using the distributive property is also very helpful. Both of these methods continue to build upon the importance of students understanding place value.
ReplyDeleteWhat I learned was how to multiply using quadrants. I have not seen this method before. This model is helpful in demonstrating double digit multiplication and decomposing the numbers into a model that is visual and slightly easier to solve. However, there are so many steps involved, which creates a larger margin of error in my opinion. Common core seems to really stress the importance of understanding numbers and the entire base ten system as opposed to teaching tricks and faster methods of arriving at the answer. They really focus on understanding the system. The old way seems much easier and efficient, but this way does seem to dig deeper into the meaning of numbers. Page 17 was confusing to me and I needed to reread it to understand myself. This is the struggle... I need to study the math modules deeply to gain understanding myself, before I can begin to expect an 8 year old to understand. I do agree with the heavy emphasis on place value, it really lays the foundation for many mathematical concepts.
ReplyDeleteI have really made an effort to constantly refer back to "the value of a place" in a particular number. Student success depends on them knowing and understanding that a digit can have a different value depending on where it sits in particular number.
DeleteHi Julie...yes, we are in our third year of modules.
DeleteDo you find that you have tweaked them each year, or do you pretty much stick to the script?
DeleteWe pretty much stick to the lessons as they are presented. However, the modules are periodically updated and improved.
DeleteLet me start off by saying...WOW...I can't imagine teaching fourth grade module math the first year when students had zero background knowledge. LewPort IEC is in year 3 of math modules, so I think things are starting to get a little easier for teachers and students. Nick the video guy refers to developing "flexible thinking and deep thinking". In the "get everything in an instant world" we all live in, students and adults are NOT accustomed to deep thinking activities. I think it is very interesting that the modules are taking students through lessons that require and encourage decomposing numbers into their smallest of parts. Not only does this require a knowledge of how place value works, it requires patience, stamina, and did I mention patience? When students are encouraged to tap into this stamina and patience, some will enjoy it, some will become anxious, some will become angry, some will quit, and some will have their parents write a note to the teacher saying they don't get it. Who knows....module math might even develop character.
ReplyDeleteOk...now onto my math post....
I found my math mind connected best to the area model. We spend a lot of time in third grade with multiplication using areas models. No matter what model is being used, you must "attend to precision". This attention to detail is what most students, teachers, and parents are not accustomed to when solving a math algorithm.
Having students understand how base ten works is a foundational skill that travels throught the grade levels. We just had that same conversation recently in class when introducing grams and kilograms, which also works on a base 10 system.
I had a really difficult time understanding the example of "division to find side lengths". I may need a tutorial on that one. I would also like to know if the new terminology is "bundling and rebundling" as opposed to grouping / regrounding. Finally, are we encouraging students to put "rebundles" at top or below? I saw Nick the video guy do both.
Yes Mrs. Defranco it is a difficult transition and thats why i believe a slower roll-out would have yielded much better buy-in and results! But the Commissioner told us..."students will rise to the occasion" and from what i saw "most" did.
DeleteIn regards to the terminology remember to always go back to the standards. Because it doesnt specifically state unbundling i tell teachers to use all forms of the vocabulary for exposure.
Math Modules put the "carry'overs" on the bottom, remember these videos are not module based but standards based so it really is a school districts preference, i just like to see an entire school district do the same!
Interesting that you found your math mind connecting to the area model - I found that to be the one I liked least. I was thinking about my learners with special needs and I think it would be too much for them in the top right box. I had trouble following it at first, but then once I reasoned through it, figured it out. But then, I am an immigrant to these strategies and instruction, not having learned it from a young age.
DeleteI really like the "area" way of multiplying. This becomes very important at the high middle/high school level for multiplying polynomials. We often refer to it as the "box" method. I think it is a great way to keep students organized with their work. The partial products makes multiplication much easier because it breaks down multi-digit multiplication into simple divisions that the students are already fluent in. I think the common core has shifted toward conceptual understanding versus the algorithms because students are better able to assimilate the information using the visual representations and other diagrams. The algorithms are easily confused, especially if you do not know where one part of the algorithm comes from. Using the conceptual understanding allows student to develop a sense of where the algorithm comes from. This is why I have been a big proponent of the common core standards (but not the way they were implemented).
ReplyDeleteI am not in a math class this year, so it is good to hear that you like the shift toward conceptual understanding versus the algorithms. This year, I am departmentalizing and am only in ELA and Social Studies. My students, however, seem to really be struggling with 8th grade math. Eleven out of 24 students are failing math this marking period. My counterpart is spending all of her Study Skills periods on math as well as extra time before school every day and an extra 30 minutes that is supposed to be used for SSR working with these students. She even takes them from my Study Skills time to provide additional math support. They just can’t seem to grasp it. I’ve never had this many students struggle with math before.
DeleteI understand your pain. My study skills classes are focused on completing the math homework. Students spend all period trying to get the homework done, which I allow because they need the practice with the content, but I do not get anytime to pre-teach or re-teach the material they may be struggling with. I am hoping that it become easier for the students as students enter the high school with more years experience with the Common Core Curriculum.
DeleteYes Kyle! That is what is so important, the correlation that happens amongst the grade levels. Im so happy you brought that up. Box method in Algebra 1 and reverse tabular in Algebra II is easy if they used these methods in 4th and 5th grade. Thats the best part of my job is that i get to see this coherence k-algebra II. It is so powerful!
DeleteI do agree though, the roll-out was not done correctly and therefor there is a negative cloud over the CC Standards when they actually are amazing if done correctly.
I also enjoy the area model - I think because it is so similar to one of the methods I used to teach for multiplying binomials (box method). I just can't believe I am comparing this strategy to a strategy we use in algebra! Crazy how times change:)
DeleteAs a Special Education Teacher teaching at the secondary level, this is all new to me. One of the concepts that I learned was how to multiple using the area model. I had to watch it twice to really understand what Nick was doing, but it is an interesting way to think about and manipulate the numbers. It seems like a lot more work than the way I was taught to multiply two digit numbers and it seems like there are more opportunities to make errors. I was surprised when he said this model is used through secondary math. When do students start learning algorithms?
ReplyDeleteWe also use the area models in 5th grade and I actually really like them. We do, however, teach the standard algorithm in 5th grade.
DeleteAn algorithm is always taught last. So at the end of 3rd grade units on adding and subtracting it is shown as multiplying and dividing is ultimately shown at the end. remember the key is for a student to get to the algorithm and be able to use it with conceptually understanding not by completing memorized steps. So many people think kids never do the algorithms but they do! You may also have students who stick with models and that's ok too, but, end goal is the algorithm!
DeleteOk, I have to echo some earlier sentiments that WOW fourth grade seems almost as model heavy as kindergarten did. (Kudos to all fourth grade teachers!) One thing I noticed with the decomposition strategy for multiplying multi-digit numbers was the use of distributive property. Since my seventh graders are learning distributive property with algebraic terms, this was interesting to me to watch. I was thinking that if these strategies are taught earlier, then we, as seventh grade teachers, are merely adding to the kids' knowledge of how distributive property works.
ReplyDeleteAs for the multi-digit addition, I love the modeling. I've said it before, but it just makes so much sense that we model and move onto algorithms to catch all learners. Some fourth graders may still be working with the models at the end of the unit, but that's how their minds think and where they are at as learners. Having graded the NYS assessments for several years now, we are issued a state approved answer, but generally there is another bullet that allows us to give credit if other logical mathematical process are used to arrive at an accurate conclusion. This means that even if a student shows the columns and bundles, (s)he can receive full credit. In fact, it's probably better that they show this type of work so we can follow their thinking and find mistakes more easily.
One other thing ..... I am continually struck by the way we are teaching kids to decompose numbers and then "re"compose them. This is such a great way to teach number sense without explicitly teaching number sense. Throughout my teaching, I have always stressed checking to make sure that your answer makes sense. Sometimes, the kids will say "Yes" even when it is clear that their answer doesn't make sense. But they don't know that it doesn't, because they don't have good number sense. This gets trickier when we get into algebra. Who knows when those x's make sense, but if the kids have grown up though this process, then they will have more strategies to better check their work.
DeleteNot to sound like a parrot but... WOW. I think 4th grade has always been a heavy year but this is intense! Although I may not be a fan of all the models, I love the multiple options kids have. From the expectation of using precise language when describing products to the need for understanding the role of the comma to the multiple ways to multiply and divide...there is a lot to cover. I really liked the left to right idea vs. the traditional right to left. Although I personally like the area model for multiplication, I'm wondering if kids could get confused on what each square means as far as place value. I like the expanded form for more practice with properties. On one negative note, I hate to admit it but I was not a fan of the division to find side length. But like everything, I may just need time and practice.
ReplyDelete