The Rookery

Today in math I introduced an algorithm for multiplication that I had invented called, "Michelle's Crazy Algorithm." The exact procedure was not important — but I asked the students to decide if my method was valid or not.  I was surprised (and delighted) to find that they were confused by the question because, in their words, "You're basically just doing multiplication wrestling, just in a different way."  EXACTLY!  Once a child (or adult, for that matter) has a true understanding of an underlying concept, then all algorithms are quite obviously related.  It's only when we have only a procedural understanding of an algorithm that we see it as discreet or "the only" way to solve a problem.

It was wonderful to hear the gasps (yes, gasps) of recognition as students saw that each and every algorithm we had seen for multiplication had the exact same numbers in it.  They were really excited to discover the connections among them and to realize that the commutative property (the "FOIL" method for those of you who remember your algebra) is the underlying tool we use whenever we multiply large numbers.  We break apart the multiples into simpler numbers which are then multiplied by each of the other numbers with the partial products added together.  If you click on the image above, you'll be able to see the color coding we used to show the different parts of the problem across all of the algorithms.

I encouraged the children to spend a little extra time with "The Lattice Method" which is one of their favorites.  This method is often seen as a "trick" algorithm because it bares little resemblance to the traditional algorithm.  However, as the children saw today, it is really a modified traditional algorithm, with the vertical columns tilted on a diagonal.

In the next days, I'll be helping the kids gain confidence and competence in one or more of the algorithms we've briefly looked at in the past two days.  For a closer look yourself, you can visit a site that I wrote years ago when I was in Connecticut teaching — Cidersites Multiplication Algorithms.