The Concrete Representational Abstract (CRA) approach in mathematics allows all students to access content and gain deep understanding. Given that many students struggle with comprehension, particularly in number stories, let’s explore how to teach story problems using CRA.

One reason students are successful when they use Structures of Equality is because it effectively integrates all components of CRA. We’ve talked about how visual representations help students “see the math”. Today, we’ll explore how we can combine models with hands-on exploration and symbolic representation to promote conceptual understanding.

A quick Structures of Equality (SoE) refresher

SoE is a reading comprehension tool that helps students understand what’s happening in a word problem. Through the use of graphic organizers, there are 3 different structures students can use to successfully represent number stories:

• Parts Equal Total
• Repeated Equal Groups
• Compare

For those of you unfamiliar with SoE, you may find it beneficial to learn more about the foundations of SoE.

I’m going to show you how the CRA method shows up in SoE, using a number story that lends itself to the Compare structure.

How CRA is embedded into SoE practices

What does it look like to use SoE at the Concrete, Representational, and Abstract stages? Let’s consider the following number story:

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

After asking students questions about the context of the story and helping them understand the math main idea, it’s time to begin work with the structures. This problem can be represented with a Compare structure.

Concrete

First, 6 students stand in one line to model Victor’s Pokemon cards, with each student representing 1 card. Then, 3 students stand lined up next to them to represent Charlie’s cards. In this model, students can see the point up to which the values are equal along with the extra or “more” students.

Representational

Students use laminated sentence strips or draw a Compare structure on paper to visually represent what is happening in the number story. At this stage, they can see equality and that the value of Victor’s cards is more. What they can’t see is how much more.

Abstract

Structures of Equality is a reading comprehension tool to help students understand what is being asked in a number story. While a number sentence is not a component of SoE, you can see how these representations could help students write equations that match the context of the story. In this case, the numeric representations could be:

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

Ideally, you would use concrete, representational, and abstract models within the same problem to help students make mathematical connections.

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 

Conclusion

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 further enhance their ability to model number stories effectively.