Connecting the Area Model to the Standard Algorithm

By Cassandra Hatfield, RME Assessment Coordinator

Using the area model for multiplication and using the standard algorithm for multiplication are often put in two separate and unrelated categories. Often times textbooks spend very little time developing the conceptual understanding and focus on the procedure of the standard algorithm.

However, “as much time as necessary should be devoted to the conceptual development of the algorithm with the recording or written part coming later.” (Van De Walle, Karp, Bay-Williams, 2013). Students are more successful when they can relate their prior knowledge with a new concept. Designing lessons that connect the area model and partial products can then lead to the understanding of the standard algorithm. This powerful transition allows students to visually see the why behind the standard algorithm.

The model below uses color to amplify the connection between the area model, the partial products strategy and the standard algorithm with 2-digit multipliers. Notice that the area model was drawn proportionally, not as a “window pane.” The importance of drawing area models proportionally was discussed in one of my previous posts, It's Not a Window Pane... It's an Area Model.

It is important to consider the value of the digits rather than the digits themselves when using partial products or the standard algorithm. For example, when multiplying 20 x 20, use the base 10 language 2 tens times 2 tens is 4 hundreds or 20 times 20 is 400. Try to avoid “two times two.”

Students can use the partial products strategy just as effectively as the standard algorithm. In fact, it is of utmost importance to give students the opportunity to explore, explain, and demonstrating their understanding of the value of the digits over the digits themselves.

Van De Walle, J.A., Karp, K.S., & Bay-Williams, J.M. (2013). Elementary and middle school mathematics: Teaching developmentally, 8th edition. Boston: Pearson.