Well, as I gear up for online Number Sense 101 course (The Number Sense 101 course has been reworked and is now called The Flexibility Formula) to open up for registration, I always like to provide some free content around number sense so that you can implement number sense into your classroom, whether you take the full course or not.

Watch the video or read the transcript below:

Here are links to products/activities mentioned in this vlog. (Some may be affiliate links which just means that if you do purchase using my link, the company you purchased from sends me some money. Find more info HERE about that.)

• MathRacks: https://mathrack.com/
• Number Rack App: https://apps.mathlearningcenter.org/number-rack/
• Number Sense Routines Book: https://amzn.to/2MbvVcW
• Number Paths: https://buildmathminds.com/product/1-20-number-path/

The Number Sense courses have been reworked and are now called The Flexibility Formula

Key Take-Away #1: Provide Experiences

So often we have kids who see school math as separated from real math and that just should not be the case, number one. And number two, when we connect it to their real lives, they get to see the mathematics in action and it isn’t just this abstract concept to them. When we can take a concept we’re trying to work on and put it into something real life for them, they can see the mathematics in all new ways, ways that we cannot directly teach to them. They need to experience it and see how numbers work together.

For example, let’s say that we’re working with kids and we want to talk about how numbers compare to each other, like four compared to five and really, we’re wanting to talk about how five is one more than four, that five is greater than four, all of those kinds of concepts that we want kids to understand when they’re looking at two numbers and trying to compare them.

Well, if we just give them 4 and 5 as digits on a piece of paper, it doesn’t connect as well for them. If we put it into a story format and we say something like,

“Sierra has four cookies. Her brother has five cookies. Who has more? How many more?”

The image that that portrays, so many kids can bring that image up in their mind, that they aren’t even seeing 4 and 5 as digits, they’re seeing amounts.

Like this, you’ll see kids who will model that problem by counting out four things, counting out five things, and maybe they do need to count because that’s the stage they’re in, but you’ll also see kids who can just visualize those amounts, but I wanted to bring the visual up here so we could talk about. And even for the kids who are visualizing something and who don’t need to physically count out the amounts, the image that they are conjuring up when we put it into some kind of a context for them, creates an image like this or similar to this.

And when they have that image, they can do so much more, and they can talk about how those numbers relate to each other in various different ways and in ways that may be different than the way we were seeing it. Let’s say I was really hoping that kids might be able to understand that five is more than four and it’s one more than four.

You definitely will get those kids who will see that extra one sticking out there and can talk about and verbalize that extra one that’s sitting out there. And then you can help formalize that thinking and talk about, so five, is one more than four, or four is one less than five. You can attach the more proper verbiage that you want kids to talk about, but when they can physically see it with their eyes, say, “Oh, that’s what they mean when we’re saying one more than or one less than.”

If we just have the digits, they don’t see those things. And the other cool piece that I talked about is they may see something completely different. You may have some kids who see that both sets really have four in it.

And that is a huge mathematical idea that a lot of kids really struggle with: that within five, you still have four things. Even though you have five, you have the amounts that are smaller than it as well. And you don’t see that unless you’re putting it into some kind of a context that kids can create visuals to go along with those contexts.

This is why my first piece of advice for building number sense with your kids is provide experiences, help them catch number sense, because you cannot directly teach it.

Key Take-Away #2: Use Manipulatives and Visuals

Often this is known as the CRA model. So, it stands for Concrete to Representational, to Abstract. So let’s say, for example, we’re trying to work on addition. And we’re doing 8 + 7. You don’t just start with 8 + 7 on a piece of paper. They don’t have any visuals or manipulatives, anything to connect 8 + 7 too. So any time we’re starting with something new, we wanna start with concrete, give them physical things to move, touch, and model the problem with. And then we attach a representation which is often times a model or a drawing and then we attach the abstract symbols.

Let’s take a look at what that would look like with 8 + 7.

I don’t wanna jump straight to just 8 + 7, so instead, I ask them to show it on a MathRack™, and I might even give it to them in a story problem format. I might say something using a popular context for the MathRack™ which is a bunk bed. It could be something like, “Sierra is having a slumber party. She has all the girls sitting on her bunk bed. There are seven girls on the top bunk and there are eight girls on the bottom bunk. How many girls are on the bunk bed?”

Now the cool part is that they can model this with the MathRack™ and I am actually showing it with an app just so I could write on it and kind of show you the strategies that kids talk about, but you should have them actually have physical MathRacks™. Those are also known as Rekenreks.

Having them model it and then the whole idea is how do you actually figure out how many are there. Because even though we have eight and seven, you might have some kiddos who are sitting there counting one by one by one by one, but you might have other kids who are grouping. And they would never see this grouping except because it’s in a MathRack™. If I just had seven things in a line and eight things in a line, or in like little piles, nothing’s begging me to group that information or those numbers together. But when we can model it with a MathRack™, that really brings out some groupings and some relationships that kids can see.

One of the most popular ones that kids see is the groupings of fives. They will find the fives. And so they’ll see five and five and they know five and five make ten, and then they’ll grab the two and the three.

Now, of course, on a real MathRack™, they’re not writing the numbers on there. So it’s very concrete. They’re just moving it with their hands, they’re seeing it visually and grouping things with the concrete manipulative. However, we don’t want kids to always stay in that concrete phase. We really do need to move them through to the abstract so that when they see 8 + 7, they just know what 8 + 7 is or they have a strategy even when it doesn’t have a visual attached to it. But in order to get kids to that strategy point, we have to create the visuals that help manifest those strategies.

This whole strategy of finding five and making a 10 from those fives is an awesome strategy, but again, it can’t be taught. Kids have to catch that strategy and they’re gonna catch it if we provide manipulatives and visuals that help them see those groupings. Once they see those groupings, then we can help them attach a representation to it and one of my favorite ways to do a representation is using a number path because kids don’t have to draw all the little rectangles. The rectangles are already there for them and they just circle the amounts that they’re seeing. They’re modeling it on the number path.

So that’s the representational phase and then when we attach the symbols, the digits to it, then it’s becoming more abstract. We’re tying that concrete and the visual representation to the abstract symbols. Man, when you can do all three of those things with your students, it just makes some awesome connections for your kiddos that they can’t see if we just jump straight to the abstract.

So any time your kiddos are needing to learn something that’s new to them or that they’re struggling with, I highly encourage that you drop back down and get some concrete manipulatives for them to work with and attach it to a representation and then attach that to the abstract. All three of those together will help build their understanding.

Key Take-Away #3: Develop a Daily Routine

Alright, now our last one is that I really want to encourage you to make building number sense a daily routine. If you don’t set aside time every single day, it’s going to go by the wayside. It will because the pressures of what you need to be teaching, all of those standards, the next lesson in your textbook, whatever it is that you’re using as your guide, will get in the way because you’re always going to be behind. It’s just the fact of teaching.

But, number sense is so important. When we look at our standards and we say this is the end standard I need to get kids to, our standards don’t talk about how we actually get them there. With all the information and knowledge kids need to know in order to do that standard and number sense is usually the root of a lot of it. But it’s not built into our textbooks because it’s kind of assumed that kids know this. Our textbooks are jumping kids straight to the final product and they’re not giving kids enough time to play and to make connections around numbers. So if you don’t make a concerted effort to build that into your day, it’s not going to happen.

Now, whether it’s that you decide you are going to do story problems, you’re going to put things in context every single day, or maybe, you’re going to do some manipulatives and working with concrete stuff every single day. Just make a time where that’s going to be it. And, it does not have to be during your math time. The cool part of developing some kind of routine is that you want it to be a short thing that you do in five or even ten minutes.

Whatever the concept is that you want to work on, make it be short and it can be part of your math time or it could be, as you’re looking at your schedule and you’ve got five minutes between reading and PE. That’s the time where you can do your number sense routine.

It can be the things that I mentioned here or I’m also going to highly recommend the book, Number Sense Routines by Jessica Shumway. There is one that’s for the early grades and then there is one for 3rd-5th. You want the early grades book, it is one of my favorites. It talks about some of the stuff I talk about here but gives you other specific routines like counting circles and dot patterns and things like that that you can do. So it is definitely worth the cost of the book. I highly recommend it.

Now, no matter what time of year you are reading this, whether it’s the start of the year, mid-year, or towards the end of the year, it is never too late to get started on building number sense. You know the old saying of the best time to plant a tree was 10 years ago, but the next best time is right now. Yes, it’s wonderful if you can start your year off building number sense but if you’re coming to this post part way through, the next best time is right now. Start building your kids number sense.

If you want help with that, I’ve got some upcoming webinars, we’ve got a full course all on developing number sense from Pre-K to second grade that I would love to have you join in as well. So if you’d like that and if you’re interested in that, be watching for emails from me. If you’re not on my email list, look up above, there’s a spot where you can sign up to be notified about stuff, so join my email list.

Another way you can join my email list is grab the little freebie that’s right here. I’ve compiled all of my recommendations that I just gave you here in this video in one nice little cheat sheet that you can print off and have posted right next to your desk as you’re planning lessons, or wherever you want to put it as a reminder of the things that you can be doing to build number sense so it doesn’t go by the wayside.

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