Updated October 28, 2026

The Concrete Representational Abstract (CRA) approach in mathematics allows all students to access content and gain deep understanding. When instruction jumps straight to picking an operation, students start guessing, especially with number stories.  Let’s look at how to teach story problems using CRA.

In my last post, we looked at the CRA framework in early math and why students move back and forth between concrete, representational, and abstract thinking. One reason students are successful when they use Structures of Equality (SoE) is that it integrates all components of CRA. We’ve talked about how visual representations help students “see the math”. Today, we’ll see how we can combine models with hands-on exploration and symbolic representation to promote conceptual understanding.

What is Structures of Equality? A quick refresher. 

SoE is a comprehension-first framework that helps students understand what’s happening in a word problem. Students first name the math main idea, the relationship in the story. They then represent that relationship using one of 3 structures.

• Parts Equal Total (PET)
• Repeated Equal Groups (REG)
• Compare

Each structure includes labels, values, and a representation of equality. 

If you’re new to the structures, learn more about the foundations of SoE here.

I’m going to show you how the CRA framework shows up in SoE, using a number story we’ll represent with the Compare structure.

How CRA shows up in Structures of Equality

Let’s use this math story:

Victor has 6 Pokemon cards. Charlie has 3. How many more Pokemon cards does Victor have than Charlie?

Before anyone draws a model, we talk about the story. “What’s happening in this story?” and “Can you describe the relationship occurring in the story?” Then students name the math main idea. This story describes two amounts being compared, so we represent that relationship with a Compare structure. 

Concrete

We act out the story. Six students stand in a line to show Victor’s cards, with each student holding 1 card. Students can see exactly where the two lines are equal, and they can see the extra students in Victor’s line. Those extra students are the “more.” 

Some days, this is all we do. We stand on the floor and talk, and that’s okay. From there, you might bring in bulletin board paper representing the Compare model, Unifix cubes, or even real cards. Each time, connect the new model back to the students standing in line. 

Representational

Students use laminated sentence strips or draw a Compare structure on paper to visually represent what is happening in the number story. One bar represents Victor’s 6 cards, and a shorter bar represents Charlie’s 3 cards. Each one gets a label that says what it’s comparing. At this stage, they can see equality and that the value of Victor’s cards is more. What they can’t see yet is how much more (the difference between Victor’s cards and Charlie’s cards, and it’s the unknown value the story is asking about).

Abstract

Writing a number sentence isn’t part of SoE. Once students understand the story and can explain their model, though, the structure becomes their bridge to equations that match what’s happening. In this story, the equations could be: 

Using the Compare structure, students are able to explain how each equation could match the situation.

Often, all three representations show up within the same problem. Students move back and forth depending on the story and where their understanding breaks down. A student who gets tangled up in an equation might go back to the structure, or even back to the cubes, to check whether their thinking matches the story. Moving between representations is a sign they’re thinking.

CRA and SoE in action 

If you’d like to see more ideas on how to teach story problems with CRA, check out the videos below. (While you’re there, don’t forget to subscribe to my YouTube channel!)

📹 Concrete: Compare Structure of Equality with Bulletin Board Paper

📹 Representational: Compare Structure of Equality with More 

Why CRA and SoE go hand in hand

Through Structures of Equality (SoE), the Concrete Representational Abstract (CRA) approach becomes naturally integrated. By visually representing mathematical concepts and connecting them to procedural tasks like writing equations, students gain deep understanding. Rich discussions strengthen their ability to model number stories accurately.

If you want to go deeper, Chapter 4 of Structures of Equality, “Seeing Is Understanding,” shows how manipulatives and visual models help students make sense of math stories before they ever compute. Get the book.