What is number sense?

Do you ever hear people talk about terms in education and wonder, "Hmmm...I THINK I know what that means..." or "That isn't what I THOUGHT that was..."?

Me too.

I hear people say "reader's workshop" and I wonder if they define it the same way I do.  I hear people say "project based learning" and "formative assessment" and "close reading" and I wonder if I really know what they mean.  Feel the same way?

I think the same can be said for "number sense".  I know teachers are always talking about "number sense"--but I bet each one of us defines it differently and has different ideas about what it means.  So I'm curious...when you hear the term "number sense"--what thoughts go through your mind?  Here's what a few "experts" say...

  1. Number sense essentially refers to a student's “fluidity and flexibility with numbers,” (Gersten & Chard, 2001).
Marilyn Burns describes students with a strong number sense in the following way: “[They] can think and reason flexibly with numbers, use numbers to solve problems, spot unreasonable answers, understand how numbers can be taken apart and put together in different wayssee connections among operations, figure mentally, and make reasonable estimates.”

The National Council of Teachers in 1989 identified the following five components that characterize number sense:
Number meaning

Number relationships
Number magnitude
Operations involving numbers and referents for number
Referents for numbers and quantities

Using number lines can accomplish SO much of this...if the number line activities force students to think and reason.  I truly believe number line use can be one of the most valuable teaching tools we have available to us--and we can model how to use number lines on the fly OR can provide careful, scaffolded practice in small doses to really keep students thinking and analyzing.  Number line problems are very easy to create--but if you want a ton of great problems all ready to print and use, you might be interested in these!  I'd love to know what you think... 


  1. Oh..... the biggie!! Number sense to me is how well kids understand the meaning of a number.... it's value, it's relationship to other numbers, how to use the number.

  2. Number sense is the kids being able to manipulate different numbers to understand how numbers can relate to each other!

  3. I agree with Marilyn Burns's definition, especially the ability to mentally manipulate numbers to solve problems as well as the ability to "spot unreasonable answers."

    1. That is an area that I think I often miss or forget about...the ability to spot the "unreasonable answer". It is important for students to be able to see a number sentence, first know what that means, then tell if it's true or false, and prove or support their thinking.

  4. Third times a charm...so if my comments come up three times, I'm sorry! I couldn't see them. I think number sense is having a good foundation of base ten and seeing numbers in relationship to one another. Kids that really get base ten seem to be able to manipulate numbers and know what a reasonable answer would be.

  5. I agree with TeacherNana and Sherri, as well as Marilyn Burns. Number Sense is that deep understanding of numbers--not having to count everything on your fingers because you UNDERSTAND what numbers mean and can see their relationships. It develops with manipulatives and needs to become number fluency so students can see mistakes and improbable answers. This is something I'm reading about this summer, so your items look like a good resource!

  6. I agree with all so far. Number sense is the ability to see the relationship between numbers and understand that relationship. Those students who do not master this concept struggle with Math consistently. I have used manipulatives in the past and just this past year put the number line into more use. Do not feel I ma proficient in this area but I keep working at it.

  7. I think number sense also means that they can rename the number different ways and understand how much it is worth. For example, 458 could be 4 hundreds 5 tens and 8 ones OR 45 tens 8 ones OR 458 ones. Being able to play around with with the numbers, making reasonable estimates (250/6- the answer would fall between 30 and 40) and how to use what they know about a number to make math easier for themselves. My kids struggled a lot with this as we piloted new math curriculum, I'm hoping this year will be easier as they have had some experience! (and I can't wait to get my hands on those K friends-it will be a lot easier then!)

    :) Kaitlyn
    Smiles and Sunshine

  8. I am loving all these definitions! I always tell my students that they need to be able to play with numbers and make them work for them. If a student can understand a number well enough to manipulate it and make it easy to work with in a given situation they have some sort number sense.

  9. Good topic! I think in the upper grades number sense starts with a firm understanding of place value. I love using the area model for multiplication to really reinforce the concept of place value during multiplication. I also think it's important that students be able to estimate the answer to an equation. If their estimates are way off I know we'll need to work on developing number sense,

  10. Number sense is a huge thing in New Zealand, so much so that it is one of four mathematical areas we teach. Statistics, geometry and measurement, problem solving, and then the big one - Number sense and algebraic thinking. To me and my kids, it's about knowing what a number is, how to use it, and what each of the parts of it means. One of the activities we do as a warm up is we "target" a number, and challenge ourselves to think of all the ways we can "Read, say, and do/make" that number. A it like what you have in the photo in your post.

    Learning to be awesome

  11. Meg,

    You are completely right, number sense is so vital for students success in Math. It is the backbone students need to be successful in comprehending all math concepts.

  12. I teavh 3Rd grade. Most of the students that I have had that struggled in math had poor number sense. They could not spot unreasonable answers and struggled to break apart or put together numbers. Students need number sense.

  13. What a great topic. I feel it is important for students to understand the meanings of numbers & how they relate to the real world. I tthink kids should be able to use different strategies to solve problems & build a solid foundation for learning. We use number lines quite often & with almost every concept taught. They allow students to see relationships between numbers, make reasonable estimations about the numbers in front of them, and create connections.

  14. Number sense is belong able to manipulate numbers easily. Students need to be flexible with numbers and be able to think outside the box. They should also have a good grasp of place value.

  15. I think that number sense is so important, as it is a person's ability to recognize numbers, identify their values, and understand how to use numbers in a variety of ways. I try to do a short activity every day to strengthen number sense. Just a quick warm-up to get students thinking about numbers and using math vocabulary goes a long way.
    In terms of assessing number sense, the best way is through discussions. Its the only way to really see if students understanding is where it needs to be. I try to hold quick math interviews with my students during each new concept. It can be time consuming but so valuable!
    Such an important topic! Thanks for writing about it!

  16. I liked the definition by Marilyn Burns that you noted in your piece. I had a hard time teaching this to the extent that my kids really got "number sense" in that form under their belts. I understand the importance of it, but it seems like such an abstract part of math in my brain and I have problems making it more concrete for them (and me!). Looking forward to figuring it out a little more for my students this year!