4 Early Numeracy Concepts episode
4 Number Relationships episode
Welcome fellow Recovering Traditionalists to Episode 210: Why Good Activities Aren’t Enough – The Missing Piece That Makes Number Sense Work
Over the past three episodes, we’ve talked about the 8 foundational number sense concepts and I shared Number Strings as a powerful way to integrate multiple concepts in one activity.
I know many of you went out and tried a Number String with your students. Some of you have been doing Number Talks or Number Strings for a while now. Maybe you’ve been doing other number routines like Quick Images, counting circles, or Which One Doesn’t Belong.
But here’s what I hear from teachers all the time: “I’m DOING these activities. I’m putting in the time. But I’m not seeing the progress I expected. They’re still not thinking flexibly. What am I doing wrong?”
And when I dig deeper with these teachers, when I ask them to describe how they’re facilitating these activities, I discover something really important.
They’re doing the activities. But they’re missing the entire POINT of the activities.
And here’s the thing – it’s not their fault. Because nobody taught them what to actually listen for during these activities. Nobody showed them the difference between facilitating an activity for ANSWERS versus facilitating an activity for NUMBER SENSE. They heard about this great new activity and all that’s ever posted about these activities are the steps to do them.
THE ACTIVITY TRAP
Teachers are doing “good activities.” They’re doing Number Talks, Number Strings, Quick Images, counting activities – all the things everyone says builds number sense.
But they’re facilitating them the same way they were taught to teach math: focused on getting answers and learning procedures.
And this is the trap. You can DO a Number String and completely miss building number sense if you don’t know what to highlight. You can do Number Talks every single day and still have students stuck counting on their fingers if you’re just collecting answers instead of developing the underlying concepts.
The activity itself is not the magic. What you SAY during the activity – what you LISTEN for, what you HIGHLIGHT, what you make VISIBLE – that’s what builds number sense.
WHAT THIS LOOKS LIKE
Let me show you what I mean with a really simple example.
Let’s say you’re doing a Number String and the first problem is 3 ½ + 4 ½ and the next problem is 3 ½ + 4 ¾.
Traditional facilitation looks like teachers who ask for only the answers before moving on to the next question. There might be a little discussion about how one problem connects to another but most of the time is spent just giving problems and students giving the answers.
When they get to the 3 ½ + 4 ¾ problem after getting the answer, they might ask “how did you get that answer?” and when a student says “I took half from the ¾ to make 3 ½ a 4 and then I had 4 + 4 ¼,” they just move right on after that to the next problem.
When doing Number Sense focused facilitation, the majority of the time is spent discussing relationships. Very little time on the actual answer, and even if students are very procedural in their descriptions of their strategy, as teachers we can add in layers that help highlight number sense ideas.
When the student said “I took half from the ¾ to make 3 ½ a 4 and then I had 4 + 4 ¼,” instead of moving on this is your opportunity to dig deeper. Asking things like “hold up, there’s a ½ in ¾? Who can explain that to me?” And as a student explains it, you are drawing a fraction model that helps students see the ½ within ¾ and how that half can fill up the 3 ½ to 4 whole items and they can see the 4 ¼ left from the 4 ¾.
Do you see the difference? Same activity. Same problem. Completely different learning happening.
In the first version, the teacher collected an answer and moved on.
In the second version, the teacher made the math and the number sense ideas visible. They are explicitly addressing some underlying concepts that many of us just assume kids have, but many do not.
This might add 2 extra minutes to the discussion but it is the most powerful part of the entire routine.
WHY THIS MATTERS
When you don’t know about the 8 number sense concepts we’ve been talking about (those are the first two episodes in this math fluency series), you don’t know what to listen for in students’ responses and then call out if they don’t address it. You hear a student describe their strategy and you think, “Great, they’ve got it” and you move on.
But when you understand these concepts deeply, when you know what each one sounds like and looks like in students’ thinking, you hear so much MORE in their responses. You know what questions to ask to draw out their thinking to ensure everyone in the room understands, not just the person describing it. You know which strategies to highlight and why. You know how to connect one student’s thinking to another’s.
This is the missing piece. This is why teachers can be doing all the “right” activities but not seeing the growth they want.
The activity provides the context. But YOUR facilitation – your questions, your highlighting, your connecting – that’s what builds the concepts. The same thing goes for using math manipulatives or even visuals. Just because you put something inside a ten frame does not mean all kids are going to see the number sense relationships. It gives them the OPPORTUNITY but your facilitation and questioning is what helps them focus on those instead of just counting.
THE COMMON MISTAKES
Let me share some of the most common mistakes I see teachers make when facilitating these activities.
Mistake #1: Moving too fast
Teachers treat the activity like a speed drill instead of a thinking opportunity. They get an answer and immediately move to the next problem. There’s no time to unpack the thinking, to highlight the relationships, to connect strategies.
The fix? Slow down. You don’t need to do 15 problems, heck even 5 problems. Do 2 problems really well. If you only have a few minutes just do a string of 2 problems and spend time focusing on highlighting the relationships. Ask follow-up questions. Make the thinking visible. That leads me to….
Mistake #2: Only highlighting procedures
Teachers record strategies as a series of steps instead of as relationships between numbers. They focus on “first I did this, then I did this” instead of “here’s what I noticed about the numbers.”
When you record student thinking, you want to emphasize the relationships: “So you used 4 as a benchmark” or “You saw 8 as being made of 5 and 3 more” or “You noticed this problem was just one more than the problem before.”
Mistake #3: Accepting vague answers
A student says “I just knew it” and the teacher moves on. Or a student says “I added them” without explaining their thinking, and the teacher accepts that.
But “I just knew it” is where the good stuff is hiding! That’s where you ask, “How did you know that so quickly? What helped you figure it out? If your buddy didn’t know it, how would you explain it to them?”
Mistake #4: Not naming the concepts
Students use strategies but don’t realize WHAT they’re doing or WHY it’s powerful. They decompose a number but don’t realize they’re using part-part-whole thinking. They reference 10 but don’t realize they’re using a benchmark number.
When you NAME the concept – when you say “Ooh, you just used a benchmark number to help you! That’s such an efficient strategy” – you’re helping students become aware of their own thinking. And that awareness is what helps them use that strategy again in the future.
THE SHIFT
So here’s what I need you to understand: The activity is not the magic. What you SAY/DRAW/ASK during the activity is what builds number sense.
You could do Number Strings every single day and not build number sense if you’re just collecting answers and moving on.
OR you could do ONE well-facilitated Number String per week and build tremendous number sense – if you know what to listen for, what to ask, and what to highlight.
This is why teachers get frustrated. We’re doing the activities. We’re putting in the time. But we’re not seeing the growth we expected.
And it’s because we’re missing this crucial piece – we don’t know how to make the 8 number sense concepts visible during the activity.
We don’t know what questions to ask to draw out spatial relationship thinking versus part-part-whole thinking.
We don’t know how to listen for the underlying ideas beneath counting & cardinality.
We don’t know which student responses to highlight and connect to help the whole class see the relationships between numbers.
And again – this is not our fault. Nobody taught us this.
We were taught to teach math by showing procedures and checking for right answers. We weren’t taught to listen for conceptual understanding. We weren’t taught to facilitate mathematical discussions. We weren’t taught what number sense actually sounds like in students’ responses.
Now, I know what some of you are thinking: “Christina, this sounds like a lot. I have to know 8 concepts, listen for them all during activities, ask the right questions, facilitate discussions effectively, AND teach my required curriculum?”
And yes, I get it. When I lay it all out like this, it does sound overwhelming.
But here’s the good news: Once you know what you’re listening for, it becomes second nature.
It’s like learning to drive a car. At first, you’re consciously thinking about every single thing – checking your mirrors, pressing the pedals, using your turn signal, staying in your lane. Your brain is on overload.
But after a while, you just drive. You don’t have to consciously think about every step. Your brain has learned what to pay attention to and it responds automatically.
The same thing happens with these number sense concepts. Once you understand them deeply – once you’ve seen examples of what they look like and sound like in students’ thinking, once you’ve practiced listening for them and asking questions about them – it becomes natural. You don’t have to think so hard about it. You just hear it in students’ responses.
But getting to that point? That requires some intentional learning on YOUR part first.
You need to understand these 8 concepts at a deep level – not just what they are, but what they SOUND like when students are using them. What they LOOK like at different developmental levels. What questions draw them out. How to know which concept a student needs to develop next.
And that’s not something you can pick up from one podcast episode or one professional development session. It requires time, examples, practice, and guidance.
This is exactly why I created two pathways for teachers who want to build their students’ number sense effectively – not just DO the activities, but facilitate them in a way that actually builds these foundational concepts.
Because I realized most teachers were just like me – they learned math by following procedures. They never learned these ideas themselves. They need to understand these concepts deeply enough that they can recognize them in students’ thinking. They need specific questions to ask and strategies for highlighting the right things.
So let me share both options with you, and you can decide which one is the right fit for where you are right now.
Option 1: The 10-Day Number Sense Kickstart
This is $19, and it’s designed for teachers who are thinking, “I have a base understanding of these concepts but just want to try out a few things in my classroom to get started focusing on number sense.”
You get 10 videos meant to be watched one-a-day, but you can binge them all at once. The videos give you an action item to do in your classroom each day. You don’t get much more detail about each number sense concept than I’ve already given in these episodes, more a review of them. Instead, the intent behind the kickstart is to give you things to do in your classroom that will move towards a more number-sense focused type of learning and teaching.
This is designed for busy teachers who want just little things to try out. It’s your crash course in understanding these concepts and then doing small changes to how you teach.
Option 2: The Flexibility Formula Course
This is $97, and it’s for teachers who are thinking, “I want to master this. I want the complete system for not just understanding these concepts but knowing exactly how to develop them systematically with my students.”
In the Flexibility Formula course, you get deep dives into each of the 8 concepts with multiple examples of what they look like at different developmental levels. You get assessment look fors to help you learn to notice when kids have the number sense concepts and when they are still working on them.
These concepts develop over time. A kindergartner’s subitizing looks different from a 5th grader’s subitizing. A first grader’s part-part-whole thinking looks different from a fourth grader’s. You need to know what you’re looking for at each level. Which is why there is a course for PreK-2nd grade teachers and one designed for 3rd-5th grade. If you work with students in all grades, I recommend taking the 3rd-5th because it’s easier to adjust items down for the earlier grades….or take both so you get all the resources.
Not only the assessment pieces for each grade band but we also have number routines, story problems, and games that you are ready for you to use with your students.
Inside the course, you also learn how to connect all of this to your required curriculum so it’s not “one more thing” but becomes woven into what you’re already teaching.
This is the full system – not just understanding the concepts, but knowing how to build them, how to assess for them, and how to make them a natural part of your math instruction.
So here’s how to choose between these two options:
Choose the 10-Day Kickstart if:
- You’re new to thinking about number sense this way
- You want to get started quickly without a huge investment
- You want small, quick ways to get started in working towards a number-sense focused classroom
Choose the Flexibility Formula course if:
- You want the complete roadmap for building number sense
- You’re ready to transform your math instruction, not just try out a few activities
- You want to feel confident in every math conversation you have with students
- You want comprehensive resources that help you implement
- You want the assessments so you can pinpoint exactly where each student is in their number sense development
Both options will help you move from just DOING activities to FACILITATING them in a way that builds real number sense. The question is just how deep you want to go with building number sense with your students.
Here’s what I want you to do:
First, I want you to think about the activities you’re already doing. Number Talks, Number Strings, math centers, Quick Images, whatever it is.
Ask yourself honestly: Am I facilitating these in a way that builds number sense? Or am I just collecting answers and moving on?
Do I know what to listen for in students’ responses? Do I know what questions to ask to draw out their thinking about these 8 concepts? Do I know which strategies to highlight and why?
If you’re not sure, or if you know you’re missing this piece, then choose one of these options:
Go to buildmathminds.com/10Day-kickstart for the 10-Day Number Sense Kickstart
Or go to BuildMathMinds.com/enroll for the complete Flexibility Formula course. There’s one for PreK-2nd grade and one for 3rd-5th grade, so make sure you choose the right one for your grade level.
Pick the one that fits where you are right now and what you need most. But don’t stay stuck doing activities that aren’t actually building the understanding you want your students to have.
Because here’s the truth: The activities are only as good as how you facilitate them.
You can have the best activities in the world, but if you don’t know what to listen for and what to highlight, you’re not going to get the results you want.
Let me help you facilitate them well. Let me show you what to listen for, what to ask, and how to make these concepts visible for your students.
Now, next week I’m tackling the objection I know some of you still have about doing number sense activities. Because even as I’m talking about asking more questions and having deeper discussions during these activities, I know some of you are thinking, “But Christina, I don’t have TIME for all this questioning and discussion. I have to move through my curriculum. I can’t spend 15 minutes on one Number String when I have so much else to cover.”
I hear you. And next week, I’m going to give you some of my favorite ways to build number sense in the time you’re ALREADY spending on math, without adding a single minute to your day.
I’m going to show you what to STOP doing and what to START doing instead. How to make every minute count. How to weave this into your existing instruction instead of treating it as something separate.
Until then, really think about your facilitation. Pay attention this week to what you’re asking and what you’re highlighting. Notice if you’re just collecting answers or if you’re building understanding.
And if you realize you need help with this – if you want to know what excellent facilitation looks like and sounds like – go grab either the Kickstart or the Flexibility Formula course. The links are in the show notes at BuildMathMinds.com/210.
Until next week, my fellow Recovering Traditionalists, keep letting your students explore math, keep questioning, and most importantly, keep Building Math Minds.
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