Building number sense is the best way to foster depth of understanding, confidence, and enjoyment of math.  And who doesn’t want that?!  

               Number Sense is… good intuition about numbers and their relationships.  It develops gradually as a result of exploring numbers, visualizing them in a variety of contexts, and relating them in ways that are not limited by traditional algorithms.  – Howden 1989

In a prior blog post, 3 ROUTINES TO BUILD NUMBER SENSE we mentioned using the following:

• Number Talks
• Manipulatives
• Number lines

So, let’s explore three more!

1. Subitizing

I’m not a fan of emphasizing speed in Math, but subitizing is a way to help students quickly grasp the VALUE of a number by simply looking at a group of dots.

Subitizing is the ability to immediately recognize “how many” in a small set.   

Many students who have a great deal of experience with the game of dominos do this and are able to quickly grasp the dot pattern of a 5, and can, in turn, recognize the difference between a 5 and a 6, even though they are so similar.  Students will see a 5 pattern as two sets of two with a one in the middle; as opposed to a 6, which is a three and three.  Using these has SO many benefits, but one that I love is that it draws in your more artistic kids, who understand visuals deeply and SEE patterns.  It is a bridge builder between the typical left-brain math instruction and our right-brained kiddos.

One way to include this into your math routine is with the use of Subitizing Cards.

These cards can be used in a variety of ways, but two of my favorites are: a matching game (like concentration) where the student looks for two (or four) cards depicting the same amount and matches them;  OR they can be used in a game of War, where the kids divide the cards; each kid plays the top card; and the one with the larger amount takes both cards. 

 2. Decomposing Numbers

Another way to build number sense in your students is by regularly decomposing numbers.  This means the breaking down of numbers into their sub parts. 

Decomposing can look like breaking 10 into 5+5, or 4 + 6, or 3 + 7.  Kids who have experience with (not just memorized) the different ways 10 can be broken down, develop lots of flexibility with numbers. I’ve seen this a LOT first-hand when my students are adding or subtracting 2- and 3- digit numbers, with carrying and borrowing, respectively.  Students who have a deeper sense of the relationship to 10 make far fewer mistakes in this.

But, decomposing numbers doesn’t stop with ways to make 10.  It can also include multiplication.  For instance, what are all the ways we can get to 36? 1 x 36, 2 x 18, 3 x 12, 4 x 9 –   This seamlessly leads into factorization.  After that, older students greatly benefit from decomposing fractions and mixed numbers.  7/8 can be decomposed into 3/8 + 4/8. Number sense is not just for lower elementary!

3. Math Games for Number Sense

“Scientists have recently determined that it takes approximately 400 repetitions to create a new synapse in the brain – unless it is done with PLAY, in which case, it takes between 10 – 20 repetitions.”  Dr. Kary Purvis

As teachers, we sometimes skimp on playtime because our curriculum is always hanging over our heads, and we struggle every day to cover what we need to.  But what if we didn’t NEED as much time?  Strategically implementing game time can do just that, especially when it comes to things like math facts. Learning them through play is a GAME CHANGER!  Kids are motivated, and it is FUN; not to mention, the lowered anxiety for those who have developed math fears. So, whenever you can implement games to reinforce math skills, DO IT!  It will NOT be a waste of time.  In fact, you’ll be way ahead in building those synapses!

So, I hope you will try implementing subitizing, decomposing numbers, and games regularly into your math routines.  If you do, PLEASE share how it has impacted number sense in your math class!

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