Concrete-Representational-Abstract

What is the Concrete-Representational-Abstract (CRA) instructional approach?
CRA is a gradual systematic approach to teaching mathematics. Each stage builds on to the previous stage and therefore must be taught in sequence. This three step approach has been found to be highly effective in teaching math concepts.

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Concrete Stage:
The first step is called the concrete stage. It is known as the “doing” stage and involves physically manipulating objects to solve a math problem. It is critical that that students use manipulatives that represent the concept being studied. Students must be fluent in manipulation of the concrete materials and must be able to explain the connection to the concept or procedure.

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Representational Stage:
At the representational level of understanding, also known as the “seeing stage”, students learn to problem-solve by drawing pictures, models, charts, etc. The visuals represent the concrete objects students manipulated when problem-solving at the concrete level. Not all students will progress to the representational stage at the same rate. Some students may need more time at the concrete level.

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Abstract Stage:
The final step in this approach is called the abstract stage. It is known as the “symbolic” stage and involves using only numbers and symbols to solve a math problem. Students who struggle to solve problems at the abstract level often need to spend more time building understanding at either the representational or concrete level.

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How to move students from concrete to representational:
Provide scaffolding by asking students to draw pictures to show what they have done with the manipulatives. This can be a simultaneous process until students are comfortable making representations without the use of the manipulatives.

How to move students from representational to abstract:
Ask students to write numerical expressions to match their drawings (i.e. number sentences). Students may continue to draw pictures until they are comfortable in the abstract level.

How does CRA relate to Unit 1 in 3rd grade?
In Unit 1 (Addition and Subtraction within 1,000) the standard states that students will be able to fluently add and subtract within 1,000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction (MAFS.3.NBT.1.2). We know that students used the algorithm to add and subtract in 2nd grade, so we often think they should automatically be able to use the algorithm in this unit as well. In 3rd grade, it is still important that we allow students to progress through the CRA stages so they will have conceptual understanding of the standard.

For more information about CRA instruction, visit these websites: https://makingeducationfun.wordpress.com/2012/04/29/concrete-representational-abstract-cra/ and http://www.coedu.usf.edu/main/departments/sped/mathvids/strategies/cra.html . Also, there is a Mini PDM located on the math icon in IDEAS that is focused on CRA.

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