Sometimes math is like a stinking onion. You encounter a student who is having a problem, so you peel back a layer to discover more misconceptions which leads to more and more problems until you have a big stinking mess and lots of tears. The good thing though, is a stinking onion can be cooked in a way that tastes delicious.

We are deep into our division unit, and many students are struggling with strategies to divide by 8 and 9. These are much larger numbers that we are working with, so the most fragile students are even more sensitive as they calculate their answers. Red faces, frustrated brows, and a lack of perseverance sets in quickly.

A student that was trying to divide 48 by 8 was really struggling. She had already tried to solve it by making equal groups, she had tried repeated subtraction, she had tried to figure out the related multiplication fact, but she kept getting lost in the process. We decided to find the related multiplication fact together.

I asked her to try thinking of a friendly eight fact. 8 x 2 felt good, she was able to solve that. She then jumped to 8 x 5. She counted by fives until she had 40. I waited to see if she’d make the connection that 8 x 6 is just one more eight added to the group. I waited, and waited. Nothing. So I wrote it out for her…8 x 6. I asked her, “What is 40 and 8 more?”

Nothing.

I mean, there was complete and utter silence.

I was actually speechless that she made it this far and didn’t know how to add 40 and 8! In a calm and non-judgmental way, I wrote out the following sequence on a dry erase board:

0 + 8

10 + 8

20 + 8

30 + 8

40 + 8

After she solved the first two, she immediately saw the pattern and we both breathed a sigh of relief. I didn’t leave the school day feeling very good though. This concern has been in the front of my mind all night. How is this child supposed to learn to multiply and divide when her number sense is so fragmented?

So many of us (I am guilty of this myself) have stressed memorization of math facts without any strategy or number sense behind it. This moment today has convinced me that this type of practice MUST happen regularly for students, and those strategies need to be shared out loud often. Extending patterns is essential for students to become strong mathematicians. It is part of the math practice standards and truly is an important skill.

How do you promote number sense (or extend patterns) in your classroom?