Concrete-Representational-Abstract (CRA)

Overview

CRA is a sequential instructional approach during which students move from working with concrete materials to creating representational drawings to using abstract symbols. Using this concrete-representational-abstract sequence helps students develop the thorough mental representations that are foundational for conceptual understanding.

Use It in the Classroom

Watch how CRA can be used to teach difficult math concepts. By using algebra tiles, students can connect concrete objects to abstract algebraic expressions.

When teaching a math concept within Algebraic Thinking, such as algebraic expressions or factoring quadratics, teachers can first model with concrete objects like algebra tiles. Then, when students demonstrate mastery with these objects, teachers can work with students to draw the algebra tiles that represent the algebraic expressions. Finally, teachers can introduce the concept with only numbers and math symbols to target abstract understanding. This same process also works to develop Number Sense and Operations.

Design It into Your Product

Videos are chosen as examples of strategies in action. These choices are not endorsements of the products or evidence of use of research to develop the feature.

Learn how ST Math uses CRA to build mathematical understanding. All math concepts are first presented visually in games requiring digital manipulation of objects. As students progress, the math symbols are slowly introduced until a student sees the full equation represented in the game they are playing.

Products can use CRA to sequence and present their lessons using digital features such as virtual manipulatives and drawing tools. These elements can support Speed of Processing and moving concepts from Short-term to Long-term Memory.

View References

Resources

Below are additional examples, research, and professional development. These resources are possible representations of this strategy, not endorsements.

Examples

CRA Instructional Approach

Informational guide on CRA

Examples

CRA Intervention Template

Description, procedures, and critical components of implementing CRA

Examples

CRA Video

Walk through of CRA with a fraction lesson

Examples

Sequence of Instruction

Detailed explanation of CRA and how to implement it