If you’ve been in math education longer than five minutes, you’ve heard of the CRA model: 

Concrete → Representational → Abstract.

And if you’ve been in classrooms longer than five minutes, you’ve probably seen it misused.

Too often, CRA is treated like a staircase students climb once and never revisit. Concrete in Unit 1. Drawings in Unit 2. Numbers forever after. Done.

But that version of CRA is incomplete—and honestly, it sells students short.

The CRA model is not a ladder. It’s a learning system. Better yet, it’s a Venn diagram where concrete, representational, and abstract thinking constantly overlap and reinforce one another.

Let’s talk about what that really means in practice.

Concrete
Students manipulate real objects: counters, base-ten blocks, fraction tiles, number lines, arrays, etc. This is where ideas become touchable.

Representational
Students draw or visualize those ideas: pictures, models, bar diagrams, area models, tape diagrams.

Abstract
Students use symbols and numbers: equations, algorithms, expressions, and traditional notation.

All three matter. None are optional. And none should live in isolation.

Here’s the trap:

Students use blocks for a few lessons.
Then they draw for a unit.
Then we declare them “ready” for numbers only.

Sounds efficient. It’s not.

When CRA becomes a one-way progression, struggling students lose their supports too early, and confident students miss chances to deepen conceptual understanding. We end up with students who can perform steps but can’t explain why those steps work.

That’s not mastery. That’s memorization in a trench coat.

In strong classrooms:

• Students solve with numbers and check with models.

• Students draw representations to explain abstract thinking.

• Students return to concrete tools when concepts become complex.

The three modes coexist.

Concrete supports representational.
Representational strengthens abstract.
Abstract sharpens concrete understanding.

It’s a feedback loop—not a finish line.

Here’s a realistic example with multiplication:

• A student builds 4 groups of 6 using counters (concrete).

• Draws an array or tape diagram (representational).

• Writes 4 × 6 = 24 (abstract).

Later, when working on multi-digit multiplication:

• They solve using the standard algorithm (abstract).

• Sketch an area model to justify their steps (representational).

• Pull base-ten blocks to make sense of regrouping (concrete).
  
  

That’s CRA working as intended.

Let’s be honest: anchor charts sometimes get a bad rap for being “decorations” or classroom clutter. But when used with purpose, they act as cognitive scaffolds that make the invisible visible.

Here’s how anchor charts actively support CRA:

🔹 Visual reinforcement of connections

Anchor charts help students link concrete experience to representations and abstract symbols. Research on visual learning suggests that external representations (such as diagrams and charts) serve as thinking tools, not just pretty pictures.

🔹 Multiple representations on display

Instead of collapsing math into a single procedure, anchor charts can show several pathways — manipulatives, drawings, symbols — side by side. That reflects the overlap and Venn diagram nature of CRA.

🔹 Support for diverse learners

Visual, linguistic, and symbolic elements in an anchor chart support learners with different strengths and needs. This matters because CRA is most effective when all students can access the meaning behind the thinking, not just the algorithm.

🔹 Memory and independence

Anchor charts help with retention. Students don’t need to memorize every step; they can refer to the visual reasoning processes that helped them understand the math in the first place.

Small groups are where CRA truly shines.

You can:

• Reintroduce concrete tools for students who need conceptual repair

• Push representational reasoning for students ready to explain

• Extend abstract thinking for students prepared to generalize
  
  

Same task. Different entry points. Same math goal.

That’s differentiation without chaos.