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Rockwood School District

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Focusing on CPA: Concrete, Pictorial, Abstract

We use a variety of resources to meet our students' needs. Math in Focus is our core resource that focuses on making mathematical connections between the Concrete (manipulative), Pictorial (visual), and Abstract (algorithmic) representations of math.


Concrete is the students' first encounter with the mathematical concept. This is done through a hands-on approach, using physical materials as a guide for students.

Plastic bricks being added together


Pictorial is the second encounter with a mathematical concept. This is done by moving to a picture stage in which drawings are used to model problems.

A drawing of one square being added to two others


Abstract is when students are familiar with the ideas taught. They progress to a more advanced or more abstract stage in which only numbers, notation, and symbols are used.

The equation two plus one equals three written out