Grade 2: 2.NBT
Based on my experience thus far, 2nd grade seems to be the level where teachers begin to struggle with the different models and conceptual understanding that needs to be taught. Pay close attention to this section, as it is crucial in laying the foundation for Operations. Also, if you have have experience with teaching these Common Core Standards and Models, please share any additional classroom experience you may have!
1. Begin by reading pages 8-11 of the Math Progression Document and look for new understanding and/or important aspects of base-ten understanding and numbers within 1000. Please try and comment about a concept or new understanding from this document.
2. Watch the following video on standard 2.NBT from EngageNY Studio Talks located here: Click Here
3. Post One Comment about something new you learned, an important aspect of 2nd grade that other grade levels need to know or an instructional strategy/model that you would use to help solidify addition and subtraction. Try and relate your new learning of 2nd grade to what you learned previously in grades K and 1.
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 second grade. Offer a suggestion to help with fluency or a resource you may have used.
As I watched the video and read the document, I continue to see where students must understand how to bundle and unbundle numbers and develop proficiency with mental computation. It is valuable for me to know that students at this age continue to extend their knowledge of skip counting to prepare for multiplication. Being fluent with multiplication facts is a critical skill students must have in the upper grades. I did want to comment on the addition illustration on page 9 of the progression document. I completely understand the concept, but I think it is a totally new way for "old school people" (like me) to change their "math thinking".
ReplyDeleteJanelle: Great point, i find that is the hardest part, you have to re-train your brain to think about math not as a step-by-step process as we learned it but more about the conceptual understanding of the how and why. The beauty of this though is that kids know no different so they are the perfect slate to learn on.
DeleteNot only is it a totally new way for "old school" teachers (like me)....it is an new way for parents. Some of the parents are not necessarily "old", but the strategies for solving math problems have changed so much. It makes helping a chiild with homework difficult. Parents are not used to "explain your thinking" or draw a model to show your thinking.
ReplyDeleteThe comment was suppose to be reply to Janelle's Comment. sorry.
DeleteNow here is my comment :)
ReplyDeleteThe similarity I am noticing so far between K-2 is the consistent direction to draw and model or use manipulatives to represent numbers. This helps the students understand what the number means and represents instead of them just seeing a bunch of digits. I am surprised that there are so many different strategies used to add and subtract numbers in grade 2. I wonder if teachers at this level think students are not given adequate time to digest one strategy before seeing another. I know our third graders see several strategies in a very short time. We were shocked the first time we had to teach commutative property of multiplication and the distributive property of multiplication within 3 days of each other, and this is one month into school. These are difficult concepts for new third graders to digest.
I agree with you on how there are so many strategies introduced to teach one concept before students have actually mastered one. I am noticing within the modules, they various strategies are taught and like when they have the option to choose the method that works best for them. I am also teaching third grade and am finding currently that telling elapsed time on a number line is very difficult.
DeleteDrawing models continues to be a large part of 5th grade curriculum as well. I have found that when Kelly and I teach math, we teach it the "module way" involving thorough explanation with models, but we do also still teach algorithms and quick tricks that will help the students as well as their parents.
DeleteI believe the equal mix is key. Also, i am a firm believer if a model is not "working" or helping move on. They are there to help not hurt and every model doesnt help every kid!
DeleteJulie i just had this conversation yesterday about the time on the number line, I do know if i would teach that until they had a better concept of time and the number line separately before showing that model. I prefer the fractions on the clock :-)
So true! It is very difficult to show time by skipping ahead on a number, or backward, when they struggle telling time as it is. We don't have much liberty since we adopted the modules and have to move on with a new lesson each day. It is a struggle! I like the idea of fractions on a clock - snuck that in there when discussing halves and quarters :)
DeleteI'm glad you are finding time to sneak in telling time. It is disturbing how many 8th graders cannot tell time on an analog clock.
DeleteAfter reading this portion, I found it interesting how they composed units in separate rows. I have not see this in addition before, only in expanded form decomposing just one number. Not having taught math for the past 2 years, I am learning the way of the common core. It actually makes so much sense and illustrates what these numbers actually mean. Jumps on a number line, from the video, was new to me as well. I liked how that was thought out, but I am not sure my third graders could do that independently...maybe guided. These strategies are a great way to teach place value. Bundling continues within each grade, which is another new vocabulary word with the newer math language.
ReplyDeleteAs a special education teacher, I have found value in teaching children what we call "the long way", using models and such. Students can begin to understand what the math means so that when we teach the "old way", or standard algorithm, students can see the connection between the models and the algorithm.
DeleteAs a special education teacher, I LOVE the progression of concrete to pictorial being emphasized. For our learners really struggling, tis still allows tem an entry point and a possibility of being able to participate in a lesson utilizing their strengths. Kids not reaching their learning targets at the same rate as their peers Can continue to use these strategies as their gen ed peers are moving into pictorial and abstract.
DeleteAfter watching the video and reading the article, there is clearly a continued emphasis on creating models, bundling numbers, composing and decomposing. I wanted to comment on the first model on page 10 with regards to where to place the number when regrouping. "Digits representing newly composed units are placed below the addends, on the line." This allows students to see the origin of the "regrouped" number, rather than having the regrouped number separated. I also like that strategies are taught to make computations easier for students.
ReplyDeleteKelly, I agree there is definitely an emphasis on creating models, composing and decomposing. I liked how they would reorder numbers so that they could be added easier with other numbers.
DeleteFluency continues to be important here, as well. As the kids get into middle school, they will need to know their basic facts with fluency as well as really understand commutative property in order to develop the most effective game plan for solving number sentences and algebraic sequences. I never thought about the development of that fluency until I saw it in the progressions document.
DeleteOne of the new methods that I learned in the video included drawing the number line and making jumps for 100s, 10s, and 1s. I thought this was very useful for adding numbers. I was a little skeptic of changing subtraction to addition. The only reason I say that is because I felt it was over the head for the 2nd graders. It seemed like a lot of thinking that the young student may have trouble completing. However, I have never been in a 2nd grade math class, so they would probably surprise me. I liked how the understanding of 100 is 10 10s, which is very similar to how a ten is 10 1s. This allows for background knowledge to make the concept easier for students.
ReplyDeleteIt took me several moments to understand the sample problem on page 9, right column, of the progressions document in which the addition is completed left to right, starting by adding two hundreds and one hundred to equal three hundreds. Then I really did a double take when 7 tens and 4 tens were added to make 11 tens or one hundred and one 10. Wow, blew me away, but I think that the kids would understand better, having been raised in a deeper understanding of the base ten system than the rest of us were. I would love to see which common errors of regrouping are now being avoided. Equally as interesting, what common errors of borrowing are being eliminated based on alternative problem solving strategies. How much better my middle schoolers will be able to manipulate numbers!
ReplyDeleteA second thing I noticed in the progressions document was an emphasis on fluency. When we started introducing this concept of fluency a few years ago to our middle schoolers, I paralleled their new experience with foreign language class (Spanish or French). Sure, they can say some words and maybe even put together a sentence, but they certainly are not fluent. And, while they would be understood if they traveled abroad, it could prove to be a very frustrating process for speaker and listener. The same is true when you are speaking "math." Being fluent allows you to solve so many more problems with much less frustration. They bought into it, sort of.... Obviously I liked the progressions document better than the video :)
Adding on the number line was new to me. I had not seen addition done in that way. It seemed odd that the computations were done starting with the hundreds place instead of right to left, the way I was taught. After watching the video it made sense and I can understand the importance of teaching students how to decompose numbers so that it reinforces fluency in addition and subtraction within 100. Students need to have a thorough understanding of place value and properties of operation when adding and subtracting by the end of second grade.
ReplyDeleteI agree! The whole number line concept was new to me too...I am still not sure if I am a fan but I am trying to get used to it. I agree that the decomposition is very important to obtain fluency. I think anytime a student can compose and decompose numbers you are going to have greater fluency. I am hoping that these new methods help with any "borrowing" issues we have had in the past with subtraction.
DeleteI actually really liked the method of adding 278 & 147 on page 9 of the document. Sometimes I feel silly that I never even thought of something so similar to what we do yet so different. I personally like this method better than what I am used to. We are so trained in the old ways that sometimes I don't look for any other ways. Not only do I like the idea of left to right but also the regrouping with the pictures. I also am a fan of informally using the commutative and associative properties. The earlier we introduce the properties, hopefully the better. As far as the video goes...again I love how the manipulatives show the regrouping (straws are my favorite). I think it is very impressive that 2nd graders can (hopefully) read and write numbers to 1000 using base ten numerals and number names.
ReplyDelete