Johns Hopkins University Secondary Support Initiative (JHUSSI)  

CRA Approach


The CRA approach to mathematics bridges the gap between tangible manipulatives and abstract number systems (Making Education Fun, 2012).


Purpose of Strategy/Approach


Use the CRA method to teach polynomial multiplication will allow students to “see” and interact with the concept before memorizing the algorithm. The concrete stage allows students to manipulate Algebra Tiles as representations of variables and units. Next students experience the representational stage by creating diagrams to represent the problems. Finally, students will be required to complete the algorithm without any concrete or representational assistance. The research indicates that CRA can be very effective in assisting students with understanding an algorithm even if they do not have a lot of experience at concrete and representational levels.


Rationale of Lesson


Understanding how to perform the arithmetic operation of multiplication on polynomials is fundamental to understanding that polynomials form a system analogous to the integers, namely they are closed under the operations of addition, subtraction, and multiplication and can be added, subtracted, and multiplied.


Acknowledgment of Content Expert and Consultants


Dr. Francine Johnson


  • Algebra Tiles (enough for each student)
  • grid paper
  • computer and projection system or SMART board

References and Web Resources


CRA Approach References and Web Resources