CRA+Approach

**CRA Approach**

**Content** The CRA (Concrete-Representational-Abstract) approach uses a three part instructional strategy to teach math content.

**Grade Level** The CRA approach can be implemented in any grade level, but its suggested use is for students with learning disabilities in grades 6-12. The following example would be useful in an Algebra I class. (8th-9th grade)

**Curriculum Standards** M.O.A1.1- formulate algebraic expressions for use in equations and inequalities that require planning to accurately model real-world problems

M.O.A1.2- create and solve multi-step linear equations, absolute value equations, and linear inequalities in one variable, (with and without technology); apply skills toward solving practical problems such as distance, mixtures or motion and judge the reasonableness of solutions.

M.O.A1.8- compute and interpret the expected value of random variables in simple cases using simulations and rules of probability (with and without technology).

**Description of Practices** The CRA approach is a three stage instructional strategy that allows each phase to build upon the last one.

The first stage is the //Concrete// stage. During this stage of the strategy, the student is taught using concrete manipulatives such as base ten blocks, fractions strips or counting chips. The second stage is the //Representational// stage. During this stage of the strategy, the student uses semiconcrete representations, such as drawings, to transform the concrete manipulatives into representations. The final stage is the //Abstract// stage. During this stage, the student uses only numbers, notation and mathematical symbols (+,-,x,division) to model the math concept or skill being taught.

The CRA approach can be used to solve simple algebra equations with an unknown coefficient:
 * Concrete Stage: To model the equation 9=3x in the concrete stage, the teacher can use paper plates and counting chips as manipulatives. The teacher should set up 3 plates to represent the whole number of 3 in the equation. The student should be given 9 chips and be asked to evenly distribute the chips across the 3 plates. When the student has run out of chips, there should be 3 chips on each plate. This represents the unknown coefficient (x) in the problem.
 * Representational Stage: During this stage, the student should create representations of the equation using drawings. The student could draw three boxes and evenly distribute 9 tallies across the three boxes. Once the student has placed the tallies in the boxes, they will be able to see that the mission coefficient is 3 because there are 3 tallies in each box.
 * Abstract Stage: For this stage, the student will use only symbols and numbers to solve the equation. Through the use of the concrete and representational stages of the strategy, the student should understand they must use division to find the missing coefficient.

**Implementation Considerations** Implementation of the CRA approach is best suited for a small group or one-on-one setting. The teacher must be able to supervise all stages of the CRA approach, especially the concrete and representational stages to check for understanding.

**Example** This following link gives an example of the CRA Approach being implemented in a middle school math setting. The video is rather long, but it gives a full description and a full lesson using this approach: "http://www.youtube.com/embed/y6n8Ncw33Z0"

The following website gives great descriptions and examples of implementation using the CRA approach: []

**Citation** Witzel, B. S., Riccomini, P. J., & Schneider, E. (2008). Implementing CRA with secondary students with learning disabilities in mathematics. //Intervention in school and clinic//, //43//(5), 270-276.