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?

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Love this post! I encounter this all the time. Even when I blog about how I help kids with number sense I get comments that it takes to much time and questions about why I don’t just teach them how to do it. It is so important for kids to develop this number sense or their knowledge becomes fragmented and you have to re-teach them “how to do it” every year. I have a huge group of kids right now in a new school I am working in that are third graders who really have no concept of number. Almost half the class has all this fragmented knowledge and I keep finding myself going back to things and trying to build the knowledge they should have built in first and second grade.

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I think the focus on literacy in early grades (for good reason) is why we have a lot of students fall through the cracks like this in early grades. We are SO good at catching those struggling readers, and we put a lot of resources in place to catch them them. I wish that we could put an equal focus on math and number sense specifically.

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Have you considered using Number Talks as part of your math routine? My school started using Number Talks a few years ago and it has helped immensely with the types of problems you describe because students are asked to talk through various mental math strategies for solving problems. It’s also an easy way for the teacher to see and address underlying misconceptions that affect computational ability. Obviously not a replacement for building a solid number sense foundation, but it does help keep those mental math and place value strategies fresh in students’ minds so they can use them when needed.

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OK Jessica, you are the second person to suggest this to me! Is this a book or a resource that I can look up and purchase? I’d LOVE to include that in my routine, and it sounds like it could be something quick to include. Thank you so much for the suggestion!

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It’s a book. You can purchase it on amazon. Typically there are 3 or 4 equations that are related to each other in some way or that build on each other in a pattern that students can use to help them. There is a number talk for each day for each grade level and they get progressively more complex as the school year goes on. I’d suggest watching some videos of people using Number Talk with their students and then decide whether you want to buy the book (or convince your school to buy it!). My school started out with one copy for all primary teachers to share and one copy for all intermediate teachers. We liked it so much that now every teacher has a copy! I hope you like it as much as I do.

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Thank you SO much. I am definitely going to check it out, it sounds right up my alley. I will certainly blog about how I’ve used it as well, I am sure. I’m thinking that could be a good spring break read (if our spring break isn’t used up with snow days).

Thanks again for the information! I really appreciate any help I can get with number sense ideas.

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HI. just read this blog, months after youv’e written it. but it touches on some things that I have been thinking about. To students, math and computation seem synonymous, but in fact isn’t noticing patterns and relationships at the core of math thinking? Sure, we all need to know our number facts, but it’s looking for and discovering patterns seems,like you did with yourplus 8 list seems to be a really fine way of working.

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