What is Number Sense and Why It’s So Essential

The number one concern I hear from teachers is that their students struggle with number sense and they want to build that for their kiddos.

However, although we know our kiddos don’t have a good sense of numbers, it’s hard to define what Number Sense is.

If you don’t have a clear definition of it, how can you help your kiddos develop it??

Watch the video below to learn the 4 Number Relationships that make up Number Sense and Why it’s so essential that you slow down and build that foundation for your kiddos.

To request the eBook and assessment Christina references at the end of the video please go here and request the Number Sense eBook. 

What is Number Sense?

In Howden’s quote, she says that it’s a good intuition about numbers, and their relationships…every time that I’ve seen that quote, it has bugged me.

I do not like that part of the quote, because it doesn’t tell me what to do, how do I teach that?

It wasn’t until I saw John Van de Walle’s work, and his colleagues, in Teaching Student-Centered Mathematics that I really found, what I feel like is, what Number Sense truly is. 

This is something tangible that I can take and do with my kiddos. They talk about four relationships that kids need in order to develop their sense of numbers.  Helping kids develop these, helps them “catch” number sense:

1. Spatial Relationships. This goes along with subitizing, but it’s having a visual to go with a numeral. It’s not just having those visuals, but talking about how they relate.

I can have a visual of three, and I can have a visual of four, but really, what do those visuals tell me about three and about four? What kind of relationships can be built once we have those visual pictures?

Giving kids those visuals to go with the number is the first place to start. Then, once you have those visuals, you can move into the next three.

2. One and two more and less.  If I just have the digit six, and ask the kids what’s one more, just knowing that the digit seven is next, doesn’t really tell me much about it. But, if I have a visual like a MathRack, one is showing six, the other is showing seven, that helps me understand better about six and seven, and how it is one less, and one more than each other.

3. Benchmarks of 5 and 10. We want to give kiddos visuals of quantities, but the visuals matter. I could have a line of nine things, and that would be a visual representation of nine.  But it doesn’t help me develop what nine really is in relationship to other amounts.

By taking those nine things, putting them into a 10 frame, that helps develop how 9 relates to 5, and how it relates to 10. So, along with seeing that it’s nine individual things, we get to develop those relationships to the benchmarks as well.

4. Part-Part-Whole. This is being able to understand that a whole can be broken into parts, and that parts come together to make a whole. Textbooks do a great job of having us break all of these apart.  We do lots of activities with number bonds, fact families, and whatever else you may call it, but it’s being able to show all the parts that make the whole.

It’s also really important to spend time talking about not just what are all the ways you can break apart seven, but when would you break seven into a one and a six versus a two and a five? What’s the point of being able to break that number apart?

Why Number Sense is SOOOO Essential?

We have all of these standards being thrown at us, that we need to be able to teach in a year, but really it’s not about focusing on that standard.

If you focus on developing sense for your students, all of these standards become so much easier to do.

Let’s look at a really quick example. Let’s say I’m working on the standard in 2nd grade about developing fluency with their facts, like 9 plus 7. I can just have kids memorize 9 plus 7, no big deal.

But, if we spend time developing relationships….AND we have visuals to go along with 9 plus 7,  some kids are going to see that, “wow, 9 plus 7 is really like having 10 plus 6, I can take one, and give it, and fill the 10 frame.” Imagine the amounts in a ten frame, “I can fill the 10 frame, and then I just have 6 left over.” That’s awesome!

It seems like that takes a lot of time, it would be faster if they just memorized it. But the power of building Number Sense is that it lasts beyond just like facts like this.

Let’s say we move into problems where we have to add and subtract and become fluent within a thousand. Like when doing 299+357….yes, I could stack it and do the traditional algorithm….but that problem would be so much nicer if I could just move one over, and create 300, and then all I’ve got is 300 + 356!!

Having Number Sense really isn’t even just for whole numbers. As kids start to move into decimals, doing a problem like 3.99 + 0.17 becomes so much nicer, right? Think about how much nicer that problem can be when we think, “Ah! I get that benchmark of the whole number, the benchmark of 4, I just gotta bring 0.01 over. Now I have 4, and 0.16!”

And on into the dreaded fractions…if I have 3  1/2 plus 5  3/4, how can I make one of those nicer? How could I make it friendlier?

Being able to build these relationships for kids isn’t about teaching the strategies, it’s about developing relationships that kids can see and notice and use on all types of problems.

So, those four Number Sense relationships are the real key ones that I want you to be developing.

Get the Spatial Relationships going in your classroom, get One and Two More & Less {which moves into 10 more and less, 100 more and less}.  Then the Benchmarks of 5 and 10 {when you’re doing fractions and decimals, those benchmarks become the whole numbers and the halves}. All the while you are building Part-Part-Whole; being able to break numbers apart, and know when to break them apart, is an essential piece of that.

If we can develop those things for our kids, it makes all of the other standards so much easier.

I know it’s hard to slow down and spend some time focusing on Number Sense, but if you do, you could actually speed up through a whole lot more of the standards, and your curriculum, because kids will get it a whole lot faster.

Instead of having to spend three or four days on a lesson, because it’s not clicking with the kids…slow down and take the time to develop their Number Sense.

Then the standards that we need to be addressing this year become a whole lot easier.