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.

(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.

Numbers are building blocks. (2)(2)(3) = 6 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.

(You can download the graphic organizer for

**free**in this 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.

10?

-10?

4?

-4?

11?

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.

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.

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.

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

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