Teaching Approach Using the CRA Scaffold
I would use this CRA scaffold to systematically teach fraction addition over three carefully sequenced lessons, using the example . Beginning with the CONCRETE stage, I'd distribute fraction circles and have students physically explore the problem. They'd handle the piece and the piece, discovering through manipulation that two ¼ pieces completely cover one ½ piece. This hands-on experience helps them build the foundational understanding that fractions must represent equal-sized parts to be combined meaningfully. Students would physically combine their fraction pieces and see that they create three-fourths of a whole circle, establishing the concrete reality that .
Moving to the REPRESENTATIONAL stage, we'd transition from manipulatives to paper. Using the same problem, I'd model how to draw rectangle models divided into equal parts. Students would shade of one rectangle, then realize they need to subdivide that same rectangle to show as 2/4 to match the from the second rectangle. This visual bridging is crucial—it helps them understand why we need common denominators before introducing the mathematical term. They're not just following a procedure; they're representing what they already discovered concretely. Finally, in the ABSTRACT stage, we'd connect the drawings to numerical algorithms.
Students would see that finding a common denominator is precisely what they did when they redrew their models. The equation now makes concrete sense because it has been physically built and visually represented. The scaffold serves as a constant reference throughout this journey, reminding students of the conceptual path from physical ½+¼ ½ ¼ ½+¼=¾ ½ ½ ¼ ½+¼=2/4+1/4=3/4 manipulation to symbolic representation, ensuring deep, lasting understanding rather than rote memorization of a procedure they don't understand.
