Number Sense vs. Number Facts

Have you ever asked your child what 2 + 3 is? Or 3 + 4? Or 24 + 63? Maybe you’ve asked her what 2 x 5 is? Or 4 x 6? Maybe you even have a set of flashcards to organize this whole process. No doubt you know that it’s very important to memorize your math facts…to know your multiplication table inside and out. And it is. But there’s more to it all than memorization.

I quiz my kids all the time on their math facts. I make it silly and challenging and rewarding in my own style, but when you pare it all down, I’m just drilling them. They’re just practicing number facts. And while I know it’s important that they can access those facts quickly, I most want them to have a deep grasp of number sense.

What is number sense? I’m so glad you asked! Because describing number sense requires me to use words that are music to a parent’s and teacher’s ears. Number sense is the ability to think flexibly, to notice patterns and relationships, to predict, to estimate, to determine the reasonableness of an answer, and to reflect.

Wowza. Those are skills that apply far beyond numbers and mathematics! And I want them for my kids.

So here’s what I’ve started doing:

Instead of asking, “What is 2 + 3?”, I have changed the format of the question. Now I ask, “How can I make 5?”

The first time I asked that question, the 5-year-old looked at me quizzically. The gears were turning. I gave him time to consider what I meant. Then he busted out with, “2 + 3!!” Nice. Predictable. Then I said, “Right on! Now find another way to make 5.” He paused for a bit longer this time. Then, “2 + 1+ 1?” Interesting choice. I showed him on my fingers a two, a one, and another one. He counted them up and declared that he needed another one. Right on, buddy.

We continued like this for a bit longer. At some point I asked how we could make 5 if we had 6 or 7. Then we laughed about one thing or another and probably went outside to ride bikes over dirt piles. And maybe, just maybe, as he was riding over those dirt piles, my kid was wondering what else might make 5.

(Mathematically…the question “What is 2 + 3?” has only one answer, while the answer “5” has an infinite number of questions. Thinking of those questions is an interesting and rich process that requires practicing mental flexibility. As your child learns more mathematical operations, the question “How can I make 5?” only gets more interesting, whereas the question “What is 2 + 3?” is old and basic.)