Can We Really Teach Number Sense?

Are your students struggling with number sense? Are you looking for ways to help students improve their number sense? This post is filled with number sense teaching ideas, free resources and links to places to learn more about number talks in math class.

In 2013, NPR published "Scientists Put a 'Sixth Sense' For Numbers on Brain Map". The article summarized scientists' findings on a region of the brain responsible for our ability to estimate quantities.  

Quantities of pencils on the floor, quantities of tiles on the ceiling, quantities of flowers in a vase. Without counting, how close can you get to estimating the correct number of objects you see?

Leading the study was Ben Harvey who was quoted as saying, "The better you are at number sensing, the better you seem to do on standardized mathematical tests."

As Math Teachers, we know how hard it is to teach number sense. It's one of those things we weave in daily as we teach more concrete topics.

We also know how difficult standardized tests can be!

Looking at number sense through the lens of this study makes it seem as innate as hearing, smelling or seeing. So is it even possible to teach number sense? From a Growth Mindset point of view, of course it is! We can ALWAYS get better at math if we work at it. 

My husband and I don't care what career our daughter eventually chooses. Our #1 goal is for her to be happy. From when she enters kindergarten to the day she graduates, a big part of that happiness will be centered around her feelings about school. And those feelings, tragically, will have to do a lot with how she does on tests. So we have started doing what we can to build her number sense.

Free Math Word Wall for even and odd numbers

(You can download this Even and Odd Numbers Math Word Wall for free here in my Dropbox.)

This Even and Odd Numbers Math Word Wall came from a conversation I had with my daughter. 

Little Miss A: "4 plus 7 is 12!"

Me: Immediately begin on long diatribe that even plus odd always equals odd.

Me 10 seconds into it: Backtrack to more age-appropriate conversation that calculators are tools and our brains are smarter.

prime number vs. composite number discovery activity

What makes a prime number prime? One idea for introducing prime vs. composite numbers is this prime number investigation activity. Students try to arrange given numbers of paper squares into rectangles. If they can make a rectangle, their number is composite. If not, it's prime. 

using algebra tiles to build understanding of factoring quadratics

Algebra tiles are great for building all sorts of skills like multiplying binomials, solving equations and factoring quadraticsThere is a free paper set of algebra tiles linked here. To make them thicker and easier to handle, you can laminate then cut the algebra tile printable. 

I loved this idea from Karyn's Blog about equivalent fractions on a multiplication chart: 

When students struggle with multiplication they can end up feeling really bad about themselves! I see this a lot in Algebra 2 when we factor quadratics. Students who don't have their times tables memorized think they "can't" factor, when really it's not at all an algebra issue but is instead a math facts issue. 

This multiplication chart may be a little easier for kids to read. It takes out the duplicate products, highlights the squares and uses clear rows and columns. You can find the pdf free in my dropbox here.

Prime Factors, GCF and LCM Math Pennant Activity

Numbers are building blocks. (2)(2)(3) = 12 like H+H+O = water. We can break down numbers into their "prime fingerprints" just like compounds can be broken down into their elements. This prime and composite numbers pennant asks student to break down composite numbers into their prime factors, find the GCF of two composite numbers less than 100 and find the LCM of two composite numbers less than 12. 

GCF and especially LCM are weird concepts for kids. Have you seen this cake method for finding them? I love it. It makes LCM so easy! You can get this word wall reference for GCF and LCM free in this post

Prime factorizing visual math word wall

I recently completed a 4th grade math word wall and in it included this set of visual references for prime factoring. A few teachers commented that these references would also be helpful for older kids, so I added them to my dropbox. You can get these prime factoring references here (free).

(You can download this integers graphic organizer for free in this post.)

 Integer Rules Visual References for Addition and Subtraction

I reached out to math teacher and blogger Don Steward about creating some printables based on the visual integers references he had created. Don said that he'd be happy for this to happen. You can find the above poster (plus 3 others covering addition and subtraction) free in this visual integer rules post.

When I taught mainstream Algebra 2, even my strongest students would make mistakes with integer operations. They'd get to the end of solving a complicated radical equation and get tripped up on x - 7 = -3. 


A manipulative for integer operations

When it came time to write my thesis, I wrote it on integers and the integer operations manipulative I created to help make integer operations more concrete. 

Linking integers to temperature with a vertical number line may also help some kids internalize these abstract numbers. 

Divisibility Rules Pennant

Getting back to numbers as building blocks... I made this divisibility rules pennant for students to reference as they are reducing fractions, factoring numbers, finding square roots, etc. 

Divisibility Rules Pennant

I posted a list of prime numbers and a list of square numbers on my classroom math word wall. We also have a divisibility rules poster with the same rules as this pennant. 

Solving equations graphic organizer

Another area where my students have struggled is with solving equations. I made them this solving equations graphic organizer (free) that focuses on the + and - signs as it guides students through the solving process. 

It was amazing to me how fast my students were able to solve equations when 30 minutes earlier they didn't even know where to start.

A cool way to build number sense in algebra is with algebra tiles. Here is a way to show solving equations using algebra tiles. There are 3 examples with lots of photos, and a link to this free solving mat, in the post. 

I recently added this number classification reference to my 8th grade math word wall to help students visualize different types of numbers. 

how to get started with number talks

I had been hestitant for years to give number talks a try in my classes, mainly because I wasn't 100% sure how they worked. When I finally sat down to figure them out and bring them to my class, I wished I hadn't waited so long.

In my consumer math class we worked with percents for our number talks. There is a free set of slides to bring percents number talks to your class in this post.

With my daughter, we have begun asking her to estimate the number of My Little Ponies she sees in a box or how many crayons are on the table. She has also shown a lot of interest in the Even and Odd Word Wall, building rectangles (even) and jagged shapes (odd) with the pieces that she takes off the wall. 

Our hope is to get her number sense ready for later when there will be a time crunch to perform so that her school years may be as happy as ours were years ago.

Here are a few more resources for teaching Number Sense:

Jo Boaler's What is Number Sense video

Don Steward's Directed Number Arithmetic Sped Up

The 5 tips in this post from Top Notch Teaching 

10 questions in: How many piano tuners are in NYC?

Blog post: Number Talks in High School Math

Blog post: Integer Rules Visual References

Scaffolded Math and Science blog


  1. This is so awesome and presented at the perfect time. Thank you!

    1. I'm so happy to hear this! Thank you Mrs. Walker!