Can We Really Teach Number Sense?

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 Factors, GCF and LCM Math Pennant Activity

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. 


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. 

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. 

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

Scaffolded Math and Science

Fun Quadratic Formula Activities

Of all Algebra and Algebra 2 topics, quadratics is by far my favorite. What I love most that students start SO intimidated and by the end are old pros. So much growth happens during this unit. I love seeing my students grow more confident as they learn how to solve quadratics in different ways.

I've written a ton about quadratics on my blog and the activities we do during this part of our curriculum. In this post I want to highlight a few fun Quadratic Formula activities. 

Free Quadratic Formula Template

Get Laid Off? Here Are 7 Tips for Teachers Who Have Been Laid Off

7 Tips for the Laid Off teacher

First of all -- DON'T PANIC!

Everyone gets laid off. Everyone. If it's not from that first job at Dunkin' Donuts, it's after 27 loyal years into a company. The point is, it happens to everyone. And it's a good thing.

Even if it's not a good thing, even if you LOVED your job and are DEVASTATED to be let go, it's still most productive to look at it as a good thing. 

Think about all the people in this world. There's a place for every single one of them and you will find another - better - place. 

This I am sure of.

I've been laid off a few times. While initially it was always a shock to get the boot, looking back it really wasn't all that shocking. I was miserable at every one of those jobs and I needed the push to find something better.

So what do you do if you get laid off? Here are some tips from an old pro! :)