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Last week we talked about how to determine where the breakdown is happening in your students’ math work. We have a skill we want to target, and now the work shifts to figuring out what to actually do in order to teach that skill.
The first thing I’m thinking about is whether that skill is actually specific enough. It’s really easy to name something like “number sense” or even “comparing numbers” and feel like we have a direction, but both of those are still too broad to build a week of instruction around. There are too many subskills wrapped up in them.
I want to get much tighter than that so I can actually plan something meaningful.
- Comparing Numbers ->
- Comparing 2-Digit Numbers ->
- Comparing 2-digit numbers using numbers or visual models
Those are all very different instructional paths, even though they sound similar on the surface. Once I have that level of clarity, I’m not just pulling random activities but rather am teaching toward a specific skill.
What Will Success Look Like?
Before I plan anything, I want a clear picture of what it looks like when a student has this skill. Not just that they “understand it,” but what it specifically looks like when they show that understanding.
I’ll usually go to released state assessment questions for this. I look up the standard that’s closest to the skill I’m targeting and read through a mix of multiple-choice and short-answer questions. I’m not necessarily looking up these questions to make a test. I’m using them to define the endpoint and to make that endpoint very clear for myself.
What kinds of problems are students expected to solve? What does the wording look like? What are they being asked to do?
That becomes my target for the week.
If you’re using my 5 Day Focus Math Intervention units, this part is already done for you. That’s what the pre and post-assessments are built around. They show you exactly what success looks like for that specific skill, so you’re not trying to piece that together on your own.
Building The Pathway
Once I know what I’m teaching and what success looks like, I need a plan for how I’m going to move students from where they are to where they need to be. This is where CRA comes in, but not in the way it’s often talked about.
CRA is not a schedule where each day is assigned a different stage. It’s not hands-on one day, drawings the next, and abstract at the end. That’s too rigid and it doesn’t actually match what students need.
CRA is about levels of support.
Concrete is anything students can physically interact with. Representational is anything they can see and draw. Abstract is where they’re working with numbers and symbols alone. Those three modes give students different ways to access the same idea but with very different levels of support.
When I introduce a new skill, I’m thinking about how much support my students need to make sense of it. Starting with something concrete often gives more students a way in, especially if this is a skill that has already been a point of struggle. From there, I’m connecting that thinking to visual models and then eventually to numbers and equations.
But I’m not moving through those in a straight line or assigning them to specific days. I’m using them as tools and adjusting based on what students are showing me.
Planning the week
When I sit down to plan a week, I’m thinking about where my students are starting, where I want them to end up, and how I can gradually remove support over time.
Some groups need to stay with hands-on materials longer before anything starts to click. Some groups move quickly into models and need to go back and forth between representations to solidify their thinking. Some skills don’t need a heavy concrete start at all, and beginning with a model is enough.
The goal isn’t to say you “did the CRA model”. The goal is to build understanding and then slowly decrease support as you expect more independence from students.
What this can look like in practice
If I’m working on something like adding and subtracting decade numbers, I might start with linking cubes so students can physically build and combine quantities. From there, I’ll connect that to drawings and then to equations, but I’m watching how they respond at each step and adjusting as needed. **You can see this in more depth here at the strategy library**
If I’m working on comparing 2-digit numbers, I might use multiple tools across the week. Linking cubes, place value charts, drawings. I’m not assigning one representation per day. I’m choosing what helps students make sense of the math and then pulling that support away as they’re ready. *Read More in the Strategy Library*
If I’m working on comparing fractions, I might start in a story context, move into pattern blocks or fraction bars, then to paper strips, and eventually to numbers and symbols. Again, I’m connecting ideas and reducing support over time, not following a fixed sequence. *Read More in the Strategy Library*
What I’m paying attention to as I teach
As the week goes on, I’m constantly watching what students can do without support.
Can they still solve the problem when the tools are gone? Do they need to go back to a model to make sense of what they’re doing? Are they ready to work abstractly, or am I pushing too fast?
Those answers tell me what the next step needs to be. This is exactly what we will discuss further next week when we delve into progress monitoring and assessment.
