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Why I Don't Teach Rounding Tricks (anymore!)

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Why I Don't Teach Rounding Tricks (anymore!)

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Round Numbers Using a Number Line | Discover how to round numbers using a number line. Find out more by looking at my FB Live post. Preview the items used here:... | By Mr Elementary Math | - Welcome to Math Mondays with Mr. Elementary Math. I'm Greg Coleman, coming live to you from Atlanta, Georgia. For those of you who don't know me, let me just give you a little bit information about myself. In 2003, I became a teacher, and in 2010, I had the awesome pleasure of becoming a math coach. In addition, I'm a educational blogger who loves sharing math ideas and resources with my fellow elementary school teachers, so welcome back for another Facebook Live session, thank you for coming along this journey with me. Can we close it out? Alright, sorry about the delay, guys. Anyhow, my name is Greg Coleman and welcome to Math Mondays with Mr. Elementary Math, I'm glad that you're here on this journey with me for Math Mondays, if you've been on this journey with me, which I hope many of you will have, what you notice is I've been talking about number sense over the last couple of weeks. So, I started out by talking about using an interactive number line, and then, I moved on to three math routines to help build number sense. Then last week I talked about the use of ten frames in building number sense. This week, what I'm gonna share with you guys is how to use the number line to round numbers. So, we gonna do this for our third and fourth grade students, if you're here in that place and this is the right topic for you, I'm glad you're here. So, just enough about me and enough about what we're gonna do, what I wanna do is just share a little story with you guys tonight. So, before I became a math coach, I was actually a third grade teacher, third grade teachers, thumbs up! If you're a third grade teacher. Alright, so that was my last grade that I taught, third grade, and one of the important skills in that was rounding, so, I just have this rounding rhyme, it was kind of like a rhyme, and I used to say five or higher go up, four or lower let it rest. Five or higher round up, four or longer let it rest. So I would use that, and use it with different numbers, so if my students had to round the number 163 to the nearest 10, I would have them recite that, and then I would show them the number that we're talking about, the digit that they had to look at and if they had to round up, or let it rest, and make it a zero, so basically, it would say, okay, 163, we practiced that, it'd be 160, round to the nearest 10. So, I was excited about that, because when I start this, okay, the students are really getting it, they know that rhyme really good, but, when it came to an assessment, at the end, I was like, okay, they gonna do well on this, 'cause they got this, they have this. What I noticed is, my students didn't do real well on that! And I was like, why didn't they do well with rounding? So after some reflection on myself, I was thinking, man, I really thought they had it, because of the rhyme! I realized that they needed something more, so I had to start thinking of ideas to get my students to really understand rounding, as opposed to just the rule, because that's what I realized that I was giving to them, just the rule, and they didn't really understand that! So, I discovered and thought about how to use a number line to help students round. So, I'm gonna share with you guys tonight some of those ideas and strategies that I hope, well, I found out or discovered, using the number line, to help round numbers. Are you ready? Alright. So let's get into the math. So, I'mma start out by talking to you about some important ideas about rounding numbers, so we're gonna start here. So if you think about the brain and how it works, pretty much, the brain really has a great processing tool, and it's a great processing tool, and it's really good, because it remembers numbers, certain numbers that are friendly numbers, we call it, another word is nice number, another word you might use are benchmark numbers. Numbers like that might be like five, 10, 25, or 100, so, the brain really can recognize those numbers and memorize those numbers really quick. So another of the ideas that's important with rounding is, when you're teaching it, make sure you provide a context for rounding. So we do that, everything, we talk about rounding in numbers or estimation in our language, so for example, instead of saying, Last night, boys and girls, I know 26 of you guys played video games, you can say, About 30 of you guys played video games last night, and how that's great is because 30 could mean that it was 25 kids who played video games, it could mean 26 kids who played video games, it could even be 29 kids, but it would open up the question a little bit more, or the statement. So, when you are talking about rounding, make sure you reference things that are in the news, there are all kind of numbers that are rounded all the time that they use. And last but certainly not least, an important idea is to use a number line when rounding, it's a great tool, because the number line really shows students visual, it's a visual model to show them where numbers are, and the relationship between numbers. So, enough of that, let me share with you some of those ideas that I spoke about with rounding. So, in my TPT pack, I have one that's called it's a rounding bundle, I have composed all of these pieces that I'mma share with you guys tonight, okay? So the first one here is a sheet, and this pretty much starts at 60, it ends at 69, starts at 70, and ends at 79. This is the sheet, and it starts at zero and ends all the way at 100, it's a way of building your number line. So what's important, the first activity that I would use with students is building a number line, and I would start with small numbers, starting with zero to 100. So what I would do is I would cut this particular tool right across that dash, and once I cut it, it would look like this. So what we have is, we have 80, then we have, I would tape it together in the back so it would be a continuous model, 90, so it would look like this, and then, as I move on, it would tape together to kinda look just like this. So, this right here is a sample of how the number line looks, and what you notice here is that I've colored in the decades, so all of the decades are pretty much colored in a different color, and I'm gonna share with you how I would use this activity, so, this activity I would use as my first introduction to rounding with students, and this is not just a one-day activity, it's something that you can do over time, so I might start with this, this might be a two or three-day activity that I extend. So, with this activity, you also wanna purchase coloring, color-coded labels that look like this, I purchased these at my local Office Depot, okay? And, if you decided not to, that they were kinda expensive, what you can also do is you can circle in those cells the color of the decade, okay? So let me show you what I mean. So, one of the questions I would ask my student is, I would have them look at this number line, and I would have them say, okay guys, we're looking numbers between zero and 10, so, let's start with zero, is zero closer to zero, or is it closer to 10? Zero would be closer to zero, 'cause it is zero. So let's put a yellow dot here, and yellow and yellow. Is one closer to zero, or is it closer to 10? So, the kids could either look and they say, it's one away from zero, or it's nine away from 10, so it's closer to zero, because it's only one away from zero, so that means another yellow dot. Two, is it closer to 10 or is it closer to zero? They would say, Two is closer to zero, because it's two away from zero. So I would ask them what dot they put down, they would put a yellow dot. So mind you, I'm putting the yellow and the dots down now, but the students would actually do this, I would have my kids on a carpet, and we go through this whole number line starting at zero and ended at 100, and pretty much, they would go through the process of putting these dots down, and they would be using the language that I'm saying, it's closer to this number because of this. So we would go to three. Three is closer to zero because it's three away from zero, and it's seven away from 10. Four. Four is four away from zero, and it's six away from 10, so it's closer to zero, we continue this process. So here, hmm, I have the number five, and notice, guys, five is halfway between the numbers, zero and 10, it's five away from five, it's five away from zero, and five is also five away from 10, so, in the US, what we did is, we come up with a rule so that everyone would understand this. If we have a number that's halfway between two numbers, you would round up to the nearest number. Or the nearest decade, or the nearest multiple of 10. So, if that's the case, five is halfway between, because it's half between these two numbers, it rounds to, what? 10! So, what color dot would I put underneath the five? I hear you guys, we would put a red dot underneath it, because five rounds to 10, and it's five numbers away. Six, is it closer to 10, or zero? Six is four numbers from 10, so it's closer to 10, and it's six numbers away from zero, so it's closer. Now we continue that process. Seven is three numbers away from 10, so it rounds to 10. Eight is two numbers away from 10, so it rounds to 10. Nine is how many numbers? Is one number away from 10, so it rounds to 10. 10 is 10, so, 10 rounds to 10. Eleven, it is, we look at the next decade, it's between 10 and 20, so is it closer to 10 or 20? It's one number away from 10, so another red dot. 12, is it closer to 10, or is it closer to 20? It's two numbers away from 10, so we can do a red dot. So we will continue this process all the way to all of our numbers, and the finished product would look like this, let me show you. So this would be an example of the finished product. So you notice that we have all of our numbers completed, I just wanna pan that out so you guys can see it, so you can see all the finished product. So it goes all the way down, all the numbers go all the way down to, let me make it clear so you guys can see, it goes to 100. So, notice, one of the things I would ask after we do this activity, notice, this would take a long time with the class, right? So I would ask the students, what do they notice? So that's always an important math question to ask students, what do they notice? And they're gonna see various things. One of the points that they'll see is you start seeing patterns, all the greens are numbers that round to 70, in this case, all the blues round to 60, so 55, 56, 57, 58, 59, 60, 61, 62, 63, 64 all round to 60, so it's the same pattern, and there are 10 numbers that round to that 10! So that's really interesting thing for students to notice. After we do this, I will give the students a opportunity to have a rounding reflection. So, the rounding reflection looks very much like this, and this is the actual template that came from the bundle. So, pretty much the students would work together in pairs or in groups to answer these. Which numbers round to 10? Which numbers round to 20, which numbers round to 30, which numbers round to 40, which numbers round to 50. So notice, I didn't say which number rounded, I said which numbers, because I want students to really understand how rounding is about closeness and proximity to decades, and they can really see that with this tool, so this is a reflection tool that they can use for that. So after doing this, I pretty much referenced this, so I would hang it up in my room, okay? So I would always have this in the room, and hanging up, 'cause this a great tool for kids to always reference. So after we did that building of this kind of number line, I would do activities like this. So, I have already a prepared number line, and what I would say is round this number, which is 163, to the nearest 10. So we have a number line, we have 100, it starts at 100 and it ends at 200, and the students would first have to say, what number is half, or midway between 100 and 200? We would identify that as being 50. And then, I would ask, where would the number 163 belong on this number line? So I would expect the students to say somewhere like, does it belong here? I hope they say no! Does it belong here? No, does it belong here? No, does it belong around here? So it would be around here, because this would be 160, this is 100, let me write this down, and we record this so the kids see it, 165, 170. So, 163 is this one right here, so I'mma highlight this one for you all, and I would put a star just like that and have the kids see that. So I would say, okay, guys, which two 10s is 163 between? It's between 160 and 170. So my question is, if 100, this was kinda sloppy, I know it's sloppy. If it was written. So if 163 is here, is it closer to 160, or is it closer to 170? So the kids would instantly see that it's very close to 160, so they know the answer's 160, okay? You can do this with different numbers on a number line, you can say, round the number 145, or 146, what 10 would that be between, and where would that be on a number line? So they can really use this tool to really find the number first, and then, they can see what two 10s it's between, and then determine which 10 it's closest to, okay? So you can continue to do activities like this, and you could do it with, after much practice, so I'll say, after much practice, they would round numbers, 163 to the nearest 100, so it would be the same type of format, we have a number line starting at 100, ending at 200, we mark off our midpoint, halfway between 100 and 200 is 150, so, I would ask them to find 163 on our number line, it'd belong right around here, so, let me write 163, alright. So, we would go into our example, remember what we talked about on the smaller number line. Halfway between any number bigger than the halfway part would round to the nearest 100, or go up. So, kids would see that 163 is only 37 numbers away from 200, but it's 63 numbers away from 100, so it's far away from this number, but it's closer to 200, so they can visually see that. I think that's really critical for students to be able to look and say, okay, it's only this amount of space versus this amount of space. So this is really an important idea for students, so notice, 163 is a lot closer to here because this yellow mark designates it, and it's further away from 100, so, this is really an important concept, and when kids can see it, they pick up on it, and then they can reference the two that we did initially with building the 100s chart, or building the numbers to 100 and what numbers round to that, so, after much activity, I would probably extend that activity and ask a broader question, and ask, which numbers round to 160? So you can do something like that, so open up the question, which numbers round to 160? So they already know 163 rounds to 160, so they should be able to tell me some other ones, so they should be able to say 161, 162, 164, they all round to 160, so that's a broader question that you can ask too, and all of these kind of questions and number lines like this, I included in the rounding bundle to help you guys out. Alright, so after I did a lot of practice with this, I would move on to what I call my rounding triangle, so let me share the rounding triangle with you guys. So, the rounding triangle's a activity that is great for small groups, it's really great for a small group instruction, because you have the kids have a dry erase board, you give 'em markers, and you have a dry erase board and a marker, so, you pretty much have the kids really understand where numbers lie and what numbers are between what numbers, they can do this. So, if I ask them to round 234 to the nearest 10, we would have to figure out what two 10s 234 is between! So, it's between, what? I hear you, 230, which I'm writing, and 200 and what? I hear you, 40, alright. So, it's between 230, and 240. Then I would say, what is the mid number, or what's halfway between 230 and 240? So, halfway between would be right here, what number's halfway between? It's 235, I hear you guys, 235. Are you with me? Thumbs up if you're with me. Alright. So, halfway between is 235, then we have to figure out our number, 234, where's that in relationship? So 234 is about right here. So, our number 234, 234 is right here, and what we would do is ask, is that number closer to 230, or is it closer to 240? And the students can really see that it's only four numbers away from 230, but it's six numbers away from 240. So, 234 basically rounds to 230, and kids could instantly see that using this tool, so I call this my rounding triangle, so this is just another idea, you can use this with rounding to 10s, rounding to 100s, rounding to 1,000s, so you can use this for small and large numbers, but I would only do this after I have given time and experiences and practice building first my number line, determining what numbers round to that, then, using this type of number line, and then extending it to here, okay? So, those are some of the ideas that I wanted to share with you guys today, so I also talked about this rounding bundle, this rounding bundle. So, let me share some other things that are in the rounding bundle that help. So, we talked about the rounding triangle, that's also in the bundle, so we have practice with the rounding triangle that's here. We also have our number lines, so check out our number lines, guys, so all the activities we talked about here with rounding number lines, we have number line activities where kids have experiences and practice with that, 'cause it's really important, and, if you need something with a exit ticket to check for understanding on a daily basis and not get til like the final test, we have exit tickets too, so exit tickets are included in that. And let me show you the flip and go cards, so, I also have flip and go cards, which I included in that and ask questions true or false, 256 rounded to the nearest 100 is 200, they have to explain that, alright? And last, but certainly not least, let me get to some of the real fun stuff. So, you know you guys have bulletin boards and, like me, we have to have quality work on our bulletin boards, so here's a activity, it's called the true or false round off, okay? And the kids have to prove the statement that they have, and determine if that statement is true or if it's false, so for here, example here says, John believes that 42 rounded to the nearest 10s place is 40, circle whether that's true or false, and they have to explain, so this is a great activity that you can do which is a performance task that students have to do. So, that's another one, and last, but certainly not least, this is the most fun thing and kids absolutely love this, they go like crazy over this one, this is called rounding face-off. So let me explain this game. After I have had adequate experiences with kids doing the number line, rounding numbers on a number line, I would give them this, so, let me show you how this pretty much works. So, inside this folder, you have numbers rounded to the nearest 10, so multiples of 10. And the kids have cards that look like this. So, these cards basically have numbers that they have to round to, so, two kids can play against one another. So, they would flip their cards down, so you have two different kinds playing, one kid would use this pile, the other kid would use this pile. So I would have another student say, one, two, three, go! And then what the kids would have to do is flip over their card, each, so this student would have to round this number to the nearest 10, 51, this student would have to round 35 to the nearest 10, and they have to place that on the appropriate places, so the student who placed it on that square first, gets both cards, so 51 to the nearest 10 is 50, 35 to the nearest 10 is 40. So, as a scaffold, like I said, they have to have a lot of experiences with number lines. Make sure, if you have kids who are still struggling, have them use this, or have this number line that we did at the beginning of our introduction of rounding, have them refer to this, and use this with this, so, they would do another one, they would put that card, so that kid would get it, so then they would say, one, two, three, go! So, one kid would have to round this number, 76 to the nearest 10, the other kid would have to round 92 to the nearest 10, so the first kid who did that would place it correctly on the square would get both cards. The kids love this game, and they go wild over this game, so this is just another tool that's in the rounding bundle to help you guys with rounding, so, just a recap on what I did. Today we shared some rounding activities, I showed you how to build a number line, and how to use a number line to round numbers, and different types of number lines that you can use to round numbers. I hope you use some, or all of these, and if you do, please share with me, I'd love to see your photos of how you use these in your classroom. So, please tag me on my Instagram account, it's @mrelementarymath, once again, you can tag me @mrelementarymath, so you can share with me, 'cause I heard some people saying that they're teaching rounding this week, some of you guys said this week, some of you guys said you all teaching it next week, so these are just some activities to help you get started. Fourth grade teachers, you can use any of these activities, but the bundle really only includes numbers within 1,000, I would say use the rounding triangle, and use it with numbers to 1,000, or 10,000, that's a great tool to use. So, I hope you enjoyed what you saw, if you did, please subscribe to my Facebook notifications, you can press that, because next Monday, at 8:30, for Math Mondays, I'm gonna be sharing for my teachers who are coming back right after Labor Day, yes, Labor Day is coming up, we'll be sharing ideas for back-to-school, math ideas, so it's one particular math idea for getting to know your students with numbers, okay? So I'll be sharing that with K-5 teachers, come back, and see it, if you have any friends you think would like it, have them come on back and check me out, okay? I hope you enjoyed what you saw today, if you have any questions, I will stick around for the next half hour or 45 minutes, and I will answer all of your questions, so I thank you for coming to this Facebook Live and making this a success, because without you, I wouldn't be here, so thank you guys, thank you, thank you, and remember, we're on a journey to make math simply clear and fun, I'll see you next Monday, thanks for coming out.

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Easy Activity for Rounding Numbers to the Nearest 10

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