Number routines have become popular in the elementary schools, but do you know what they are and how to use them properly?

I’m Christina Tondevold, The Recovering Traditionalist and today, we’re gonna take a look at How Number Routines Are Not A Time To Teach, They Are A Time To Listen, in our quest to build our math minds so we can build the math minds of our students.

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Number Sense Routines K-3 by Jessica Shumway

Number Sense Routines 3-5 by Jessica Shumway
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I was recently doing an interview for my Build Math Minds podcast with Vicky Tilson. Vicky, all the credit for this video goes to you. During that interview, Vicky and I were talking about all the things that she has learned through my online courses. She was talking about the changes that they have seen happening at their school in the math instruction and student learning, based upon the things that they have learned from the courses. She made a comment, that I told her I was gonna use and make a video about. Her comment was that number routines are not a time to teach, they are a time to listen. That is what prompted me to do this video.

What is a Number Routine?

They are very quick. Maybe 5 to 15 minutes is all that you spend doing a number routine. They are meant to build students’ understanding around numbers. They are not meant to teach a certain concept or to reteach something. This is a time to build number sense. They are repeatable routines that you can change out the content, so kids aren’t always having to listen and learn the instructions for the activity. They can just focus on the mathematical conversations that you’re having during the routine.

So let’s take a look at one, for example.

A common routine is to do quick images with kids. Basically, this is where you flash an image and then you have that image disappear and you ask the students, “How many did you see?”

We’ll do one here in a minute but the cool thing is that that routine, the system, basically never changes. So the kids know what to expect. They even start to get familiar with what kinds of questions you’re gonna ask. The focus is just on the mathematical content. They aren’t having to really think about what’s coming next and thinking, ‘What am I supposed to do here?’ Because they are already used to this routine. 

In the early grades, we will flash images with just like 5 dots or 4 dots, up through 20 in the early grades. Even as kids get older, they still need to be doing these quick images. So you can do quick images by just creating ones with your base 10 blocks. And this isn’t very fancy, just a regular piece of paper that I printed some images on.

These images actually come from inside of the Flexibility Formula courses. Participants get these images and they can create their own images using the templates that we give them. So here’s a quick little image. You would show it, leave it up there for a little bit of time, and then you take it down and you have a discussion about what they saw.

It’s not just about getting the answer. I am more paying attention to how, how did they see that? And what does that tell me about their number sense?

Here’s one where you can take the traditional placement of like dot patterns but replace them with coins, images of coins. So it’s still the same pattern, where I’m showing it. I take it away, I ask “what did you see?” But also, I’m asking for different ways.

It’s not just about how much was there. It’s more about how they’re seeing it and how they knew how much was there. And then you get to have conversations about who saw similar things.  You get to build all kinds of connections.

Here’s another example for multiplication. You can show this image, make it disappear and then build their conversation around it, ‘What did they see?’ 

Okay last one, you can even do it with fractions. Here’s an image, what amount is shaded? I’m gonna take it away. Then we’re gonna talk about: how did they know how much was shaded? How did you see that? And again, what I’m listening for is not just how much was on there (did they get the right answer?) I am listening for the number sense that’s encapsulated in their thinking process.

As I said before, a lot of times people think that number sense routines are a time where you can teach a certain concept or reteach. That’s not the case. 

I love this quote from Jessica Shumway. Jessica has these fabulous books, Number Sense Routines. There’s one for K – 3 and 3 – 5. This one comes from the K-3 book on page 18. She describes number sense routines in this way:

“Students need quick, explicit daily experiences with number sense concepts. Routines provide that structure, no matter what you are teaching during the mini-lesson or during the active learning portion of the math block. The routine does not always need to be related or connected to the math lesson for that day or the math unit for the month. It’s purpose is to provide a daily experience, with a number sense concept. The ultimate goal is that students make connections over time, build an understanding of relationships among numbers and operations. And ultimately, apply their number sense understanding in problem-solving.”

So as she says, you don’t have to have number sense routines that are tied to the things that they’re gonna be learning in their math time.

Number Sense Routines Should be Student-Centered

You shouldn’t buy a resource of pre-made number sense routines. You can, I’m sure you can Google and find it but that’s not the way that they are meant to be used. Number routines are meant to be based upon your students’ needs. That changes based upon the group of students you have at the time and the things that they learn.

As they learn something new, you’ve got to switch up your routines. So in order to know what number sense concepts that you should focus on during your number sense routines, you need to listen. You have to listen, it is not a time for you to teach them things. It is a time for you to listen to what your students are saying. That gives you information about their number sense.

Let’s revisit one of these quick images. Let’s come back to this one.

If I put this up and I have students who can’t recognize that the amount inside each space is 7, and they’re counting every single one of those dots to figure out the total on this. That tells me something about their number sense.

Versus if I see kids who know it’s 7 but that’s all that they’re seeing. So they count up like 7, 14, 21..they’re kind of skip-counting along the way. 

Versus a kid who might say something like, “well I know two 7s is 14 and another 14 and another 14.” 

And another kid might say, “well I know three 7s is 21. So I just double it to figure out the total there.”

There are so many different ways that children could look at that image and determine the total number of dots, and it’s all based upon their number sense. But if we use that number sense routine as a time to teach them something.

If I put this up here and I tell the kids, “Okay, do you guys see that there’s 7 here? We have 7 in 6 spots. 7 x 6, let’s figure out what 7 x 6 is. Do you see how there’s 3 groups of 7 and we could double that?”

If I try to teach them the distributive property of how they can chunk that up and do 7 x 3 and then 7 x 3 and then put it together, that’s not what we should be doing during a number sense routine. During that number sense routine, you put the image up and you step back and you listen.

How are the students thinking about this? And again, this is just one example of a number routine. There are lots of number routines and you can Google and find all kinds of types of number sense routines. Again, I love the books. I think the books are very essential because they give you that information about how to actually do them.

You can Google and find them but it doesn’t really tell you much about how to do them in your classroom. So number routines, again, should be focused on bringing out your students’ number sense. And then using that insight for you to then determine what future number routines your students will benefit from.

Pay Attention to The Positives

Now here’s one of the last things I want you to take away from this. When you are listening to your students, the number one thing to keep in mind is: pay attention to the positives. You will be so tempted, when you’re doing number routines, to focus on the things that your students are not able to do, the things they are not noticing. But instead, I want to encourage you to pay attention to the positives, the things that your students do know and then build from there.

When you focus on the things they don’t know, you’re focusing on their gaps and then the tendency is that you’ll want to fill them up. And that’s when you’ll get into that trap of trying to teach during your number sense routines. But that’s not what number routines are about, so really focus in on the positives.

Start with what your students are able to do and then design number routines that build from what they know. Your goal as the facilitator, is to help them see connections to more and more things as the year goes through. 

In Conclusion,

Inside of my courses we go into great detail about what number sense is, how to observe your students. We go into how to make those connections between things that they know and the things that we’re trying to help them build their understanding around. We also go into numbers routines that are some of my favorites, and how to do them in your classroom, in order to build your students’ flexibility with numbers.

I know not everyone can take one of my online courses. So before the courses ever open up, we also do free training. To get you started on this journey of doing more listening and not just teaching, come join me for my free webinar, The Three Keys to Building Math Fluency for Elementary Students.

We’re going to talk about what to listen for. Number routines are a great way to hear what your students are thinking about numbers. But you need to know what to listen for, what is it that they are telling you when they’re talking? What do we need to know about their number sense journey and what things do we need to watch out for?

In the webinar, we’re going to talk about three things that help you build your students’ fluency and one of them is building their number sense. After the webinar, you will know what number sense concepts to be listening for during your number routines. Head on over to buildmathminds.com/webinar to get registered for this live webinar.

I hope that I will see you there. And I hope that this video has helped you build your math mind, so you can go build the math minds of your students. Have a great day. 

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