Building our Understanding

Over the past few weeks, I have been using a new instructional approach to help my students understand multiplication and division.  This approach is called Concrete Representational Abstract (CRA). Concrete refers to the stage in which students are working with hands-on manipulatives.  The representational stage uses images or models to show how to solve a problem.  The final stage, abstract, is when students use only numbers and symbols to solve a problem.  This is the stage that most adults are used to, as this is the way we were most likely taught in school.

While students have been learning this way, or in a comparable way, what I have found most successful, is showing all three of the stages simultaneously.  It allows for all of my students' different learning styles to be met.  It also allows for my students to choose a strategy that works best for them at any given time.

To show multiplication and division concretely, the students used place value disks.  This helped them understand what happens to each place value when multiplying and dividing.

                    

          


The ultimate goal is for students to have a deep understanding of multiplication and division.  I can say that from what I have observed, and what the students have shown me, they are well on their way!