How to Teach Comparing Numbers Conceptual and Concrete Activities

hey everyone in today's video we're going to kick off fun four part Series where we are going to talk about conceptual and concrete ideas to help students really develop their number sense now last summer did four-part series with some number sense routines here are those four videos if you want to check them out they're still very relevant and great great routines to implement in your classroom next year the first one shared was about Circle counting the next one was quick images have whole video for fill the grid and then number sense activity called picture it all four of those routines are great ones to get started in your classroom but in this series we're talking about number sense still because again I'm k- through2 teacher you guys are through2 teachers and number sense is really those building blocks of all things mathematical right and want to focus on both some conceptual understanding as well as some concrete activities some handson real activities that you can take and use in your classroom for different number sense skills so each week for the next four weeks we will pick one number sense topic and will share some ideas to help your students develop their conceptual knowledge and then I'll also share some concrete activities that you can use with your students to give you quick rundown of what's ahead today we are going to focus on comparing numbers next week we will talk about patterns on aund chart so some number sense knowledge with some larger numbers numbers the week after that we're going to talk about place value specifically tens and ones although for your second grade teachers we will talk little bit about that hundreds place but we'll focus lot on tens and ones and for that last week we're going to focus on computation very beginning computation with addition and subtraction so really hope you enjoyed this series if you're ready to dive into comparing numbers give this video like subscribe to my channel let's get started all right so before we dive into some specific ideas for comparing numbers just quickly want to talk about what conceptual knowledge in math really is conceptual approach to teaching math really focuses on having students understand and kind of think flexibly about mathematics instead of just memorizing like an algorithm to give you like through 2 example we could teach subtraction few different ways to our students one way that would not be concep ual is to just teach students kind of what the minus sign looks like what it is so they can see that little Dash there and then we can tell them hey if you see problem that has this minus sign you're going to have the first number here we have 5 - 1 equals and what you do is you take that first number and then you're going to take away however many are in this second number to get your answer so we're kind of just teaching them when you see this symbol this is what you do but we're not explaining what subtraction really is conceptual understanding of subtraction would be for students to actually understand what that means we have five of something we take it away to get some sort of answer it goes bit deeper than that but that's kind of the basis of this conceptual understanding so with each of the videos that I'm going to make I'm going to talk about some ways that you can help your students conceptualize whatever skill we're working on when students have conceptual understanding of all sorts of different math skills it really helps them as they get older into trickier mathematical computations because they can really think about things flexibly they can solve things different ways they can make connections between mouth skills and so lot of our mouth skills we learn really build off one another so that being said let's dive into comparing numbers comparing numbers is an important number sense skill for your students to master because it shows us that they really understand what the digits represent right so let me just share quick example of way that you should not teach how to compare numbers for example you don't want to show students number line and tell them if number is larger it will be on this side of the number line and if it's smaller it'll be on this side so just see where they are in the number line and then you can compare them same with the 100 chart you don't want to tell them hey just look at 100 chart if the number is smaller it'll be at the Top If the number is larger it'll be at the bottom both of those are true both of those are things that you do want students to notice but neither of them help students understand the concept of which number is larger or smaller smaller that's like teaching them that minus sign right that's like hey this is what you do to solve it but they don't understand what they're doing so again I'm not saying don't tell students that I'm saying don't use that as the only way for students to understand which number's bigger and which numberers smaller I'm hoping by sharing non-example each time it'll really exemplify the conceptual understanding little better so if that works if you like that idea let me know down in the comments so can do that for each of the videos okay so what do we do to help students understand comparing numbers and comparing things first let's take away numbers completely and let's have students compare objects using the words more and less so like to put the words more and less up on the board this is especially for K1 like to put them up on the board and then like to compare objects now you can do this many different ways for example can show students both of these cups and can ask them which of these cups is going to hold more water which one's going to hold more water and then my students likely would say this pink one of course and I'd ask them why how do you know it's going to hold more water can we prove this in some way and they'll probably give me some examples they'll say it's larger it's wider we can prove this by actually pouring water in here and seeing if it will fit in the smaller cup they'll give me many different examples to show why this one holds more now using the same two tools here will also ask them to rephrase that and explain which one holds less water and want them to actually use the words more and less as they share their statements so want them to practice using those words as they're explaining their reasoning do add words in they're like greater I'll say so this pink cup holds greater amount of water would you say that's correct and kind of have them talk through this process so they hear more they hear greater and then asked them would you say this cup holds more than this cup again just hearing those phrases over and over they're all kind of looking at me like yeah Miss Jones told you the pink one holds more but by introducing these phrases it sets them up for what's coming later still using objects you can go ahead and have students start to compare groups of things so you can do this on board or you can actually grab some physical objects just to show you would do both by the way would do some examples on the board and then would also grab some things and put them in my hand but for example would say draw line down the middle draw like three triangles over here and we will draw 1 2 3 four circles so this can just be drawn on the board or like said would do both images and I'd also have like three blue cubes four red cubes you could do it either way and would ask students can you go ahead and compare these images using the words more or less and again more and less is on the board I'm giving them those words again so they can practice using them in mathematical way and then students will go ahead and compare they might say there are more circles than triangles would ask other students do you agree do you disagree how do you know how can you prove this and listen to their reasoning well they might say okay well you know there's four circles over here and there's three triangles over here and four is more than three okay well how do we really know that and then can show students that we can line them up so again if you're using the physical ones line them up and show that there's more of the other one and here would just draw them next to each other and show that there's one more Circle then there are triangles and don't have to say one more than we're just again focusing on more and less and then if students offer the more word would then again just like did with the Cups have them also use the less word so I'd ask another student in the class ask for volunteer can you compare these images using the word less once students are comfortable and familiar with comparing groups of objects that's when we introduce those numerals those numbers those digits so that way students understand when they say four and three what they really mean you can do that with the same image just shared here so would even say yesterday we compared these two groups of objects and we said that there were more circles than there were triangles and that there were less triangles than there were circles now let's put numbers to that so we can see we would count them up and we would write four and we would write three and then would ask them again the same exact image would say now can you use the words more and less but instead of saying circles or triangles can you use these numbers can you use the number words and here would of course be looking for students to say four is more than three and three is less than four so these ideas really help students understand what more and less really means instead of again just showing them hey the number is larger if it's on this side of number line and it's smaller if it's on this side and when you think about bringing it further what students were doing at the beginning here is they were really comparing volumes which isn't something they're going to think about until way later but building this number sense knowledge only helps them understand it more when the concept comes once students are comfortable comparing numbers accurately using the words more and less some easy warm-ups you can do would include putting up images like this now here you can see an image for kindergarten for first grade and for second grade and you would simply put up three to four different numbers and you would ask students can you compare these numbers using the words more or less just like we did earlier but now they're looking at group of numbers here instead of just two and they can choose which ones they want to use using those words more or less you can see here by these images that you could totally tailor this to your students so in kindergarten and really have numbers 1 through five right now first grade would definitely include numbers 1 through 20 and in second grade we have bunch of three-digit numbers and of course in small groups you can tailor this even more as hope you noticed earlier you don't want to just end it when students go ahead and share this is more than this or this is less than this you want to ask students if they agree if they can restate it if they can say it in another way and when you get to those higher numbers there I'm looking for my second and first grade students to hopefully give me some place value knowledge to defend their answers so if they are comparing three-digit numbers want them to be able to explain to me that you know they know this number is larger than this one because while they both have the same amount of hundreds this one has more TENS for example one last quick way to help students conceptualize this idea of comparing numbers is to use story problems when we use story problems it helps take mathematical ideas and make them real for quick example you could ask the class okay have question for you would you like me to bring in 10 brownies for each student or one brownie for each student why now you'll likely get lot of different answers some of your students are going to say want 10 brownies 10 is way more than just one but then other students might say well 10 brownies is way too many I'll get tummy ache so don't want 10 brownies I'll just do the one brownie I'll take the the lesser amount right that was just silly example off the top of my head but by taking these story problems it helps them make mental image and actually you know conceptualize what these numbers really mean instead of just 10 or one well 10 what one what what am comparing here now that you have some ideas to help your students conceptualize this skill let me share some concrete ideas that will help your students practice all right as for some concrete ways to have students practice comparing numbers there's many different ways you can do this first and foremost you'll want to have some sort of manipulative so you can use little bearss you can use cubes as your students get older you'll want to use some base 10 blocks so they can make larger numbers but this is going to help them really see and visualize the numbers that they are comparing so for quick one went ahead and have this deck of cards here it's Avengers yes it's awesome my sister got it for me but what did is simply took out all of the face cards and for this would have them do it with partner and have them each flip card so I'll flip one 10 and then my partner flipped two and then would have them go ahead and make each number so they would need to actually show using whatever manipulative they have so four here's 10 and here's two and then they would have to say whose is larger it's basically game of war except we're not going to play war just yet because want them to build it and they'll say 10 is more than two and on the board you'll have more or the word greater than you'll have whatever sentence stem you want them using for this activity and as you walk around you want to make sure students are saying it so the student who has the larger number will say 10 is greater than two but then also the student who has the smaller number you want to hear them say 2 is less than 10 and then they flip again flip three partner flips an eight I'll have to show it so tell my students whenever walk around should be able to see the number should be able to see it and then should be able to ask them compare these numbers using your number first go ahead and this student will say8 is more than three or greater than three and this student will say three is less than eight so very simple just grab deck of cards and some manipulatives and have them practice using those phrases so that first one just needs deck of cards and some manipulatives do also have ton of activities for all sorts of number sense skills and really all math skills in my sjt math club so wanted to show you few of these this first one is called mix order and make and within it you know it's club for through2 teachers so there are some differentiated cards for kindergarten ones for first grade and ones for second grade so here is just an example of the kindergarten cards and these are numbers 1 through 20 and put them specifically so you could just start with 1 through 10 if if you wanted to so students would first mix up the cards they would flip three 1 2 and three and then they would have to order them first based on what they think about these numbers so 1 6 and 8 and then to kind of prove their thinking this is where they make it down here so using cubes or using those Bears whatever they want here's one here is where they will make six six and then over on the other side is where they will make eight so they'll mix they'll order them and they'll make it and this is where again they check 1 is less than 6 Which is less than 8 so here they're ordering numbers but in order to order numbers of course they need to compare them to know what order they should go in 1 6 and 8 then they will clear this board they'll put it over here they'll mix and flip again and then repeat this process and then when all the cards are done they'll shuffle them back up and continue to do this process over and over now here is picture of the first grade version you can see there are some larger numbers for first grade we have them practice within 100 and then let me show you the second grade version just so you can see what that's like so kindergarten first and second grade it's the same exact concept and there are more numbers only printed out one page there's bunch of them so here with the second grade version recommend that you laminate the board and have that written in the club too because when they actually make their numbers they're going to be larger these are within 1,000 so they mix up the numbers they'll flip three 178 289 450 they'll order them first based on what they think they know and then they will make them down here now we'll Pretend This is you know dry erase marker want to see their 100 1 2 3 4 5 6 7 1 2 3 4 5 6 7 8 178 and then over here won't do it all but they'll essentially draw them all out drawing on their base 10 knowledge this helps me have students compare how many hundreds are in the numbers how many tens are in the numbers and how many ones there are another comparing game in the sjt math club is called collect and compare and this is two-player game so player one will put their game piece over here player two will put their game piece over here students will go ahead and take turns rolling the dice moving that many spaces one two and collecting however many they land on so here we'll collect two again switch it up with some fun manipulatives and they'll have ball player two moves five and they will collect two as well students will basically continue rolling and collecting however many they need until they get to the very end and once student makes it once player one makes it all the way through the board and lands here and player two makes it here they will count up how many they have in each group so let's pretend player one ended up getting 31 and player two ended up getting 27 they will determine the winner by whose ever total is larger which in this case would be player one now if those numbers get too high there's another way you can play this for kindergarten for example what would have them do let me move these over is would have them each roll the dice and move that many spaces 1 2 3 landed on three and player two landed on three 1 2 three they landed on four now in order to decide who would actually keep that amount it has to be Whoever has the larger amount so over here player one has four so or sorry player two has four so player one will put theirs back so this way the numbers aren't as High when they get to the end so they'll be pairing each time they roll and if it's tie they both get to keep it another fun game we have in the club is called Bug collector and compare this is simple one it's two-player game so students will write their name let's pretend I'm playing against my brother so will go ahead and spin land on nine will take out nine little bugs we pretend if you actually have bug like erasers or bug themed something that that can help add to it but any manipulative will do so again making the number and then player two will go they get six 1 2 3 4 5 6 we write down the numbers 9 6 who has the larger number that's me so Circle it as we go back and forth throughout the entire time we will see at the end whoever had the most higher number so whoever has the most circled numbers collected the most bugs is the winner I'm hoping you'll notice the theme with these games and that is that students not only have to compare the digits but they have to compare the actual amount by making them and just to show you one more example this is second grade example that is also in the sjt math club again all of these are just under the number sense portion have games and activities for addition subtraction geometry for everything so just to show you I'm not going to go through each one but essentially this is three-digit spin-off since that bug collector one was really for kindergarten and first here each student would take their turn spinning how many hundreds how many tens and how many ones they need for their number and then so this would be student one this would be student two or this is an independent game up to you and then they would need to compare the two numbers and this is where they would actually introduce those symbols as well so they would write the symbol too to compare so just wanted to show you that we have plenty of second grade games as well so there you have some teacher ideas and some Student Activities to really help your students understand what it means to compare hair numbers this is just part one of my four-part series and hope you will join me next week where we are going to talk about patterns on hundreds chart or 120 chart whatever you use and really get students to think about some larger numbers as well if you enjoyed these ideas and activities and they helped you think little bit differently about the way you might teach math would love to know and if you have other ways that you teach this skill let me know down in the comments love to read your comments love to learn from you like from each other and you know it's just fun as always hope you enjoyed this video please give it thumbs up so know make sure you are subscribe to my channel and click that Bell that way you're notified of every new video see you in the next one bye