1 00:00:00,000 --> 00:00:12,800 Hello and welcome to Making Number Sense Makes Sense, a podcast for elementary teachers, 2 00:00:12,800 --> 00:00:17,680 specifically early elementary teachers, looking to really make an impact in the number sense 3 00:00:17,680 --> 00:00:23,720 of their students. Welcome back to the Making Number Sense Makes Sense podcast. Today, I'm 4 00:00:23,720 --> 00:00:31,000 going to talk to you about subitizing. When I first started teaching, I had no idea what 5 00:00:31,000 --> 00:00:39,440 subitizing even was. So now I kind of think of subitizing like a turtle covered in flowers. 6 00:00:39,440 --> 00:00:46,200 I know a turtle covered in flowers. I'll explain. So the other day, I was driving, you know, 7 00:00:46,200 --> 00:00:51,400 listening to music, driving, and I turned to the side and I had to do a double take. I 8 00:00:51,400 --> 00:01:00,080 was like, what is that? So I see on my left a giant turtle, probably like a tortoise. And 9 00:01:00,080 --> 00:01:06,200 it's person, I don't know, owner, I guess, we're just strolling along the sidewalk. And 10 00:01:06,200 --> 00:01:12,240 this turtle was covered in pink flowers. And I definitely had to do a double take. I was 11 00:01:12,240 --> 00:01:19,720 like, did I, did I just see that? Is that really just a tortoise covered in flowers, just walking 12 00:01:19,720 --> 00:01:24,320 in the neighborhood? And it sure enough was. I was like, oh man, I wish I could have taken 13 00:01:24,320 --> 00:01:29,120 a picture because I have never seen a turtle covered in flowers before in real life. I 14 00:01:29,120 --> 00:01:36,160 wouldn't even think to do that. So subitizing is a lot like that. When you are subitizing, 15 00:01:36,160 --> 00:01:45,080 your students are seeing an image with some numeral on it or value on it. So when your 16 00:01:45,080 --> 00:01:51,480 students are subitizing, they're looking at an image and trying to figure out how many 17 00:01:51,480 --> 00:01:59,840 things they're seeing without counting by once. So subitizing is the ability to instantly 18 00:01:59,840 --> 00:02:06,440 recognize a number of objects without counting. And some of your students may come in already 19 00:02:06,440 --> 00:02:13,240 being able to subitize small numbers like one, two or three objects, especially in familiar 20 00:02:13,240 --> 00:02:19,000 items like on a dice base. So a lot of times if students play games at home, they know 21 00:02:19,000 --> 00:02:24,920 what the number, the dot arrangement of a dice looks like for numbers one to six, and 22 00:02:24,920 --> 00:02:29,560 they don't need to count it, they just see it and know that is subitizing. And dice is 23 00:02:29,560 --> 00:02:34,400 just my example, but it could be finger patterns like if you ask a student to show you five 24 00:02:34,400 --> 00:02:39,360 fingers, they'll probably just put up their hand with five on it and not have to count 25 00:02:39,360 --> 00:02:44,840 each and every finger, they just know that one full hand is five. That ability to know 26 00:02:44,840 --> 00:02:49,800 your numbers like that is subitizing. Make things just a little complicated. There's 27 00:02:49,800 --> 00:02:55,800 actually two different types of subitizing. There's perceptual subitizing and conceptual 28 00:02:55,800 --> 00:03:04,280 subitizing us as people can really only subitize around five items. When you start to see bigger 29 00:03:04,280 --> 00:03:08,600 items that you're still able to subitize, what's actually happening is you're seeing 30 00:03:08,600 --> 00:03:14,920 its parts. So for example, if you're looking at a dice face and you're looking at the six, 31 00:03:14,920 --> 00:03:21,280 we know it's a six because it's a common arrangement. But you might also see the six as a column 32 00:03:21,280 --> 00:03:29,640 of three and three. You might also see just two three groups of two, so two, two and two. 33 00:03:29,640 --> 00:03:35,440 You might also see four on top and then two extras on the bottom. You can see find those 34 00:03:35,440 --> 00:03:43,360 little numbers inside the bigger number. So why is that an important skill to have? Well, 35 00:03:43,360 --> 00:03:48,600 subitizing on its face may seem like a skill that kids only really need in isolation, but 36 00:03:48,600 --> 00:03:54,240 that's really not the case. It helps your students develop more sophisticated number 37 00:03:54,240 --> 00:04:00,280 strategies and counting strategies than just counting by once. It helps kids really one 38 00:04:00,280 --> 00:04:05,960 number to another number and kind of see the smaller numbers inside bigger numbers that's 39 00:04:05,960 --> 00:04:11,200 composing and decomposing numbers. So if you're thinking of the number five, then kids will 40 00:04:11,200 --> 00:04:16,280 start to learn that five is also the same as three and two is the same as four and one 41 00:04:16,280 --> 00:04:21,320 is the same as five and zero. So really beginning familiar with those number pairs that make 42 00:04:21,320 --> 00:04:26,280 up bigger numbers helps with addition and subtraction as kids move throughout the grade 43 00:04:26,280 --> 00:04:30,640 levels. As of now, I've been using dice face number patterns that only really go up to 44 00:04:30,640 --> 00:04:36,680 10. But when you start being able to subitize and see the bigger numbers and smaller numbers, 45 00:04:36,680 --> 00:04:40,520 you can start to add those to mental math and addition strategies. If I show you the 46 00:04:40,520 --> 00:04:47,760 number sentence 35 plus 12. Now 35 plus 12, some people will just know what the answer 47 00:04:47,760 --> 00:04:52,120 is. But if you're familiar with your number patterns and trying to figure it out in your 48 00:04:52,120 --> 00:04:57,800 head mental math, you might start to break apart those bigger numbers into smaller numbers. 49 00:04:57,800 --> 00:05:04,680 So one way you might do that is if you think of the number 12, 12 is the same as 10 and 50 00:05:04,680 --> 00:05:12,360 two and 10 is an easier number to add on to other numbers than 12 is. So I have 35 plus 51 00:05:12,360 --> 00:05:20,200 12 was my original question. And I broke my 12 into 10 and two. So then I'm thinking 35 52 00:05:20,200 --> 00:05:26,680 plus 10 is 45. And I have that number in my head. And I remember that I have my two other 53 00:05:26,680 --> 00:05:32,920 my two extras, because my original number was 12. So from there, you can do 45 and count 54 00:05:32,920 --> 00:05:39,120 on 454647. Or you might just know that five and two is seven. If you're familiar with 55 00:05:39,120 --> 00:05:43,560 your smaller number pairs, the numbers that make up seven, the numbers that make up eight, 56 00:05:43,560 --> 00:05:48,040 the numbers that make up nine, use that information to get the answer. So from there, you've broken 57 00:05:48,040 --> 00:05:53,160 apart the numbers, you've really been able to manipulate the numbers in your brain to 58 00:05:53,160 --> 00:05:59,480 solve this addition problem. And that's something that I know personally, I never really did. 59 00:05:59,480 --> 00:06:05,040 It wasn't until I took a class as a teacher about developing number sense, did I even 60 00:06:05,040 --> 00:06:10,080 really start to think about that like manipulating numbers in my head to solve questions like 61 00:06:10,080 --> 00:06:17,320 that was never something that I naturally did. And it's so helpful teaching your students, 62 00:06:17,320 --> 00:06:21,440 especially when they're young, to see numbers as things that are flexible things that can 63 00:06:21,440 --> 00:06:28,360 be switched around compensated, it starts to create just a giant world of possibility 64 00:06:28,360 --> 00:06:32,640 around numbers, which is something that a lot of people who are not traditionally in 65 00:06:32,640 --> 00:06:37,600 air quotes math people don't realize that you can do math can seem very rigid. And it 66 00:06:37,600 --> 00:06:42,480 has to be like this, because there's only one right answer. But the creativity comes 67 00:06:42,480 --> 00:06:48,960 in being able to dive into the different ways that you might get to that answer. And growing 68 00:06:48,960 --> 00:06:54,720 up for me, the emphasis was always on did you get the right answer? Not how can you 69 00:06:54,720 --> 00:06:59,440 approach this problem in a way that makes sense to you. So then you can solve it and 70 00:06:59,440 --> 00:07:04,440 get the right answer without having to use a standard algorithm, just really understanding 71 00:07:04,440 --> 00:07:09,600 numbers and understanding math. So I hope that I have convinced you, or at least started 72 00:07:09,600 --> 00:07:15,480 to convince you that subitizing is a very, very important skill for your students to 73 00:07:15,480 --> 00:07:22,360 develop. And it can be a really fun skill to practice throughout your entire math block. 74 00:07:22,360 --> 00:07:27,320 So next, I'm going to give you some ideas of ways that you can include subitizing activities 75 00:07:27,320 --> 00:07:33,360 in your math block that your students might really enjoy. One of my favorite ways to use 76 00:07:33,360 --> 00:07:40,360 subitizing in the classroom is like I said before, just using dice. So using games with 77 00:07:40,360 --> 00:07:45,040 dice, there's so many different things that you can do with dice and not just traditional 78 00:07:45,040 --> 00:07:51,080 one to six dice, you might use a 10 frame dice or five frame dice. That's another way 79 00:07:51,080 --> 00:07:58,720 for kids to really get to know the way that numbers look. And 10 frames, five frames, even 80 00:07:58,720 --> 00:08:04,880 spinners, if you create a spinner that has a five frame on it 10 frame on it. And using 81 00:08:04,880 --> 00:08:09,320 those things over and over in lots of different types of games is a great way to practice 82 00:08:09,320 --> 00:08:15,440 subitizing. I said a 10 frame if you're unfamiliar with a 10 frame, it's basically a rectangle 83 00:08:15,440 --> 00:08:21,240 with 10 squares in it. So it's five squares on top, five squares on bottom, all together 84 00:08:21,240 --> 00:08:27,200 is a 10 frame. And that's another great way for kids to organize numbers organizing counting 85 00:08:27,200 --> 00:08:31,320 into groups of 10, which is really important in our number system that's based in 10. So 86 00:08:31,320 --> 00:08:37,760 10 frames are a great way to practice subitizing as well with numbers higher than six. Something 87 00:08:37,760 --> 00:08:42,600 else that you can do I like to use this as a warm up or a number sense routine is quick 88 00:08:42,600 --> 00:08:49,420 images. So quick images is like it sounds like you show students an image very quickly 89 00:08:49,420 --> 00:08:54,920 like three seconds tops, and then hide it again. And then your students have to figure 90 00:08:54,920 --> 00:09:01,520 out how many things you were showing. So let's say I had a 10 frame with six items in it. 91 00:09:01,520 --> 00:09:06,680 So five on top and one on the bottom, I'll show my kids my 10 frame with six on it and 92 00:09:06,680 --> 00:09:10,760 then hide it really quickly. And so then the kids would have to talk to me about what they 93 00:09:10,760 --> 00:09:16,200 see. So some kids might say, Oh, I know it's six because I saw the top line was full and 94 00:09:16,200 --> 00:09:22,560 had one extra so five and one extra. If I might arrange my six differently for my next 95 00:09:22,560 --> 00:09:29,340 quick image. So instead of having five on top and one on the bottom, I might do three 96 00:09:29,340 --> 00:09:34,520 on the left and three on the right. And then the kids might say, Oh, I know that that is 97 00:09:34,520 --> 00:09:40,920 six because I saw three and three. You could also switch the colors. So maybe I do three 98 00:09:40,920 --> 00:09:46,080 reds and three yellows. And then they could also see three and three is six. He'd like 99 00:09:46,080 --> 00:09:51,640 some more ideas on how to use quick images. I will leave a link in the show notes to my 100 00:09:51,640 --> 00:09:57,320 free quick image kind of sample quick image freebie that you can use in your classroom. 101 00:09:57,320 --> 00:10:01,880 And that's in Google slides. So you can print off your Google slides or just project it and 102 00:10:01,880 --> 00:10:06,200 show your kids really quick and then hide it again. Now quick images doesn't have to just 103 00:10:06,200 --> 00:10:14,040 be 10 frames. It can also be finger patterns. It can be dice. It can be a wreck and wreck. 104 00:10:14,040 --> 00:10:18,160 It can be tile arrangements. There's lots of different ways that quick images can be 105 00:10:18,160 --> 00:10:22,360 used and what kind of images you show your students. So like I said, I will leave a link 106 00:10:22,360 --> 00:10:26,560 to my quick image freebie in the show notes and a blog post that talks all about quick 107 00:10:26,560 --> 00:10:31,960 images and how can you you can use them in your classroom. I mentioned it briefly before, 108 00:10:31,960 --> 00:10:37,720 but using dice in your classroom is a great way to practice subitizing. Again, if you'd 109 00:10:37,720 --> 00:10:43,280 like some more specific examples of games that you can play to practice subitizing, 110 00:10:43,280 --> 00:10:50,120 I'll have pictures and ideas all linked in the blog post that is in the show notes of 111 00:10:50,120 --> 00:10:55,320 this episode. So quick recap. 112 00:10:55,320 --> 00:11:00,200 Subitizing is a amazing skill to help your students develop number sense. You can use 113 00:11:00,200 --> 00:11:06,160 subitizing in your math block as a warm up. You can use it as a kind of wrap up to the 114 00:11:06,160 --> 00:11:13,400 end of your math block or use the thing that some of the tools like 10 frames dice finger 115 00:11:13,400 --> 00:11:19,760 patterns in your math stations or math centers to reinforce the skill. Get your kids familiar 116 00:11:19,760 --> 00:11:27,160 with all different kinds of number patterns and then they can move from the very concrete 117 00:11:27,160 --> 00:11:32,400 to conceptual understanding of numbers as they move throughout the year on your way. 118 00:11:32,400 --> 00:11:37,280 Don't forget to check out the quick images freebie and the accompanying blog post to 119 00:11:37,280 --> 00:11:42,680 see all of this written out as well as pictures of some games that you might like to play 120 00:11:42,680 --> 00:11:48,720 with your students in their centers. I do love talking about math, obviously, but there 121 00:11:48,720 --> 00:11:52,920 are some things I feel like I just need to share because it was just it's just so comical 122 00:11:52,920 --> 00:11:56,760 like some of the things that these kids do you're just like how that even happened. So 123 00:11:56,760 --> 00:12:02,000 one of my students was working on his drawing. He was so happy to show it to me and he kept 124 00:12:02,000 --> 00:12:06,520 talking about his shoes and I'm like why does he keep telling me about his shoes like I 125 00:12:06,520 --> 00:12:11,240 see their shoes I'm glad you added the detail but move away from the shoes. So I look at 126 00:12:11,240 --> 00:12:16,680 him a little bit later and I was like, hmm, he has two different shoes on today. And I 127 00:12:16,680 --> 00:12:20,440 was like, oh, maybe that's why he kept telling me about his shoes because he had two different 128 00:12:20,440 --> 00:12:24,280 shoes on. I was like, oh, wow, well, I mean, there's nothing we can do about that now like 129 00:12:24,280 --> 00:12:27,840 you're at school we can't change your shoes. I look a little closer. How about they're 130 00:12:27,840 --> 00:12:32,600 both the left foot. So not only did you have two different shoes on, but they were both 131 00:12:32,600 --> 00:12:36,400 the left foot. And I was like, well, it makes sense. He was talking about his shoes. They're 132 00:12:36,400 --> 00:12:41,120 probably uncomfortable. Like I don't even I don't even know how that happened. But I 133 00:12:41,120 --> 00:12:45,480 will say, I have walked out the house in slippers before only to have to turn around and be 134 00:12:45,480 --> 00:12:49,960 like, I need to put real shoes on. So I guess it happens to the best of us. If you have 135 00:12:49,960 --> 00:12:54,960 been enjoying the podcast, I would love it if you left a review or sent me a message to 136 00:12:54,960 --> 00:12:59,920 let me know what episodes you'd like to hear in the future. Until then, I will see you 137 00:12:59,920 --> 00:13:25,200 next time and don't forget to get your freebie on the way out.