When we talk about number decomposition, we mean that children are able to break apart numbers into different numbers into different parts. So knowing that the number five can be split into three and two, or that three and two can be combined to make five, that is all number decomposition. It’s super important because it really supports strong understanding of addition and subtraction.
~ Zeba from Episode 70 of The Kindergarten Cafe Podcast
Episode Summary
In this episode, I explore the key difference between math fluency and memorization, focusing on the vital role of number decomposition for young learners. I share insights on how breaking down numbers fosters flexibility in thinking and confidence in addition and subtraction. Practical strategies include hands-on activities and games that promote true understanding over rote memorization. I explain differentiating instruction to support all students, ultimately providing a roadmap for enhancing math instruction and building a solid foundation for future learning.
In this episode I share:
- Understanding Number Decomposition
- Teaching Approaches for Number Decomposition
- Transitioning to Abstract Thinking
- Reinforcing Concepts with Concrete Objects
- Importance of Understanding Over Memorization
Previous Episodes:
Resources Mentioned:
- Number Decomposition Math Games | Decomposing and Composing Numbers Under 10
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Read the Transcript
[0:00] Hey, teacher friends, we are continuing the math series, and today I’m talking about the difference between math fluency and math memorization and what I mean by that. So we’ll get into it in terms of number decomposition. All right, let’s get started.
[0:16] Music. You’re listening to the kindergarten cafe podcast where kindergarten teachers come to learn classroom tested tips and tricks and teaching ideas they can use in their classroom right away i’m Zeba creator and founder of kindergarten cafe and i help kindergarten teachers with everything they need from arrival to dismissal in order to save time, work smarter, not harder, and support students with engaging and purposeful lessons. I’m here to cheer you on through your successes and breakthroughs and offer support and resources so you never have to feel stuck or alone. Ready to start saving time and reducing your stress all while using effective and purposeful lessons that students love? Let’s get started. Music.
[1:09] When we talk about number decomposition, we mean that children are able to break apart numbers into different numbers, into different parts. So knowing that the number five can be split into three and two, or that three and two can be combined to make five, that is all number decomposition. It’s super important because it really supports strong understanding of addition and subtraction, it helps students think flexibly with numbers, which is crucial for solving math problems in kindergarten, but also throughout their entire math career. So for example, to know that if I have seven and five, seven plus five, and I’m not sure what that is, well, I can break apart the five into three, because I know seven and three make 10. And then I can use the remaining two to make 12. So 7 plus 5 equals 12.
[2:03] So that’s a really good strategy that kids can learn to do when they’re in older grades for adding bigger numbers and adding numbers in their head that they’re not sure about. Honestly, I wish this is the kind of teaching I had been taught as a kid because I was always told just to memorize facts. I was told to memorize math facts and that did not work for my brain at all. And so kids, you know, they would do a little like timed quiz and they’d be doing, you know, seven plus five. And I’d be like using my fingers to figure it out because I didn’t know. And like then you get to bigger numbers and you can’t use your fingers. And it’s just the memorizing, not how my brain worked. So if I had been taught this, learning this as a teacher, I was like,
[2:51] oh, I wish I had learned that. I wish I had learned that as a kid. So that’s why number decomposition is so important. And for the older grades especially. But we can teach that foundational skill in kindergarten by helping kids really understand how numbers up to 10 can be broken apart. or even in kindergarten, I’d say up to five, numbers up to five. And then in first grade, they’ll focus more on like numbers to 10, but how numbers can be broken up into other numbers. And that just helps kids be very flexible with their numbers when they’re adding, subtracting, doing all kinds of math. So I kind of got into this with my own personal experience, but when we’re teaching number decomposition, I think it can be really easy to slip into a memorizing framework of like the kids just need to memorize the math facts of three and two make five. But as I said with myself, as a learner, the kids aren’t then, they’re not understanding the math they’re doing. They’re just memorizing it. And memorizing can go well, or it might not. And it doesn’t help kids be flexible with numbers and use it in a different way when they’re out of the context of the memorization of that number pair or that number fact, math fact.
[4:05] When I was first teaching number decomposition, and we were having kids do like an assessment with it, it just felt kind of icky to me as like, I’m just checking to see if they’ve memorized the math fact. And I wasn’t quite seeing the foundational component to it that they really understood it. So I worked a lot on getting better about this because I didn’t want kids to just memorize the math facts. I wanted them to truly understand the number of decomposition. So some of the ways that I do that are always starting with concrete materials and visuals. So we do this with subitizing. We talked about this a couple weeks ago. If I show them five dots, they are talking about how they see three and two dots, and that makes five. That’s number decomposition right there. But it’s starting with concrete object, the dot right in front of them. If they’re sorting objects, maybe they’re sorting objects by different colors or types, They’re seeing how they had started with 10 animals, and now they have three bears and two lions and five gorillas. I’m totally making this up. But my point is they can see how 10 can be broken up into those smaller groups. They’re seeing it being broken up right in front of them.
[5:23] Love coin tosses or like two-sided chips, like I have the red and yellow chips. Toss them up, see where they land. they know they have five chips. Three are red, two are yellow.
[5:36] Oh, three and two make five. They’re really seeing it right in front of them, hands on. After they’re seeing it right in front of them, touching them, concrete, hands-on, all that stuff, you gradually start to remove some of those visuals and the concreteness. So that would mean covering up a portion of the objects and guessing how many are hidden. There’s a fun game you can get online called Splat, and you have like the subitizing, you have like the dots on the screen, and then Splat, like a paint blob, covers up some of the dots, and then the kids have to figure out how many are hidden. So it’s that next step of you have the full visual, but you’re hiding some. And so then the kids can take away the device that’s hiding it and actually count and figure out, okay, so there were five chips, but now some are under the cup. And I see two in front of me. That means there must be, I don’t know, two or three under the cup. Let’s take off the cup and let’s count. So you’re starting to remove that concreteness, but it’s still there if they need it. And then as they get better and better at being like, oh, I know I see two, so that must mean there’s three.
[6:50] As you get better and better at that, then you can start completely removing the concreteness altogether. So you can move into total abstraction of like number bonds or, you know, using the whiteboard or equation sheets where they’re just breaking apart the numbers on paper. But they’ve had that complete understanding beforehand, before you went to the abstract. So you know that even if at this point they know it so well, they know the number of parts to five so well that it is like memorizing, it’s not memorizing without understanding. That’s I think the key difference is when you start with the slow progression of fully concrete hands-on objects and visuals and then partially covered concrete visuals hands-on games to then going to fully abstract with no visuals. You know that the kids have fully understood memorized the parts to five but they understand.
[7:51] Why two and three make five because they’ve seen it they’ve seen that two red and three yellow chips make five chips and so oftentimes when we’re playing these hands-on games i’ll add in the like writing where they’re writing the number bond or they’re writing an equation on a worksheet to go with the game that helps bridge the gap to just switching straight to the abstract with no visuals, no hands-on objects. Remember, if you do have a kid where you’ve moved on to the fully abstract, you’re doing the worksheet, the number bond worksheet, and they’re having a hard time.
[8:27] Bring back those hands-on objects. Bring back the chips or the different colored cubes and say, okay, I’ve got five cubes. Two are yellow. Three are red. This is your number bond. What could we write? Five on the top because there’s five cubes. Now, what are the different colors? So if kids are struggling with that abstract, with just the numbers, with the memorizing, bring back the objects so that they have a stronger foundational understanding of why the different numbers can make other numbers. That’s really important. If kids are struggling, like I said, you can bring in those concrete objects. You can do daily practice. The more you practice, the more kids can get better at it. You could just pull a quick group of like, okay, I’m going to have five chips. Let’s toss some of them. Some are red, some are yellow. Let’s write it down. Let’s write it into our number bonds and just do that repeated practice every day until they’re really understanding that two and three, four and one, five and zero, those are the numbers that make five.
[9:29] You could even do lots of game-like resources. I have a whole bunch of those in my number decomposition pack for you that are just really fun for the kids so they don’t even realize they’re practicing. They don’t feel like they’re memorizing the number of combinations and the math facts, but it’s all working towards that understanding. So definitely check that out if you have kids working on number decomposition.
[9:54] Just remember our recap is that we don’t want kids just to memorize facts with no understanding. We want them to have that solid foundation in number decomposition to help with being flexible with numbers and adding and subtracting later on. And that when we’re teaching that number decomposition, because we don’t want them just to be memorized, we want to go from the concrete of actual objects, actual pictures right in front of the kids hands on and move then a way to covering some so some are hidden and then be fully abstract once they’ve shown that they can do the other activities really well then you can work on just numbers but if they start to struggle again bring back in those objects bring back in those concrete counters and objects and dots and all that to help the kids so those are some great ways to have number
[10:44] decomposition in your math block. And if you’re looking for more tips on math centers, definitely check in next week because I’m going to talk about managing math centers and how I handle that. And our quote of the day, a boy six-year-old said, I had a cough drop this morning.
[11:01] And another boy said, what’s that? And the original boy said, you know, it makes your cough drop.
[11:09] I know that had nothing to do with number decomposition, but it is the winter and people are always coughing and getting sick. So I thought you could relate to that. So if you have a cough, check out Cough Drops to make your cough drop. So if you enjoyed this episode, send me a DM on Instagram with the code word number decomposition or just math. Both work. Let me know you liked it. Let me know what you’re looking forward to and we’ll talk in the next episode.
[11:40] Music.
[11:45] Thanks so much for listening to the Kindergarten Cafe podcast. Be sure to check out the show notes for more information and resources or just head straight to kindergartencafe.org for all the goodies. If you liked this episode, the best ways to show your support are to subscribe, leave a review or send it to a friend. I’ll be back next week with even more kindergarten tips. See you then.