#AREA MODELS FOR DIVISION HOW TO#

…then add the products together, combining like terms… We’ve got 2 terms in each factor, so we set up a 2×2 area model like this… Let’s try that first expansion with an area model: The Area Model Method of Expanding Polynomials (A.K.A. Plus, it organizes the information for us without the requirement of memorizing an acronym. Still, the area model is much more inclusive, working with literally every type of polynomial expansion you can imagine. Granted, binomial pairs show up a lot in quadratics, and many students do understand the underlying principle behind FOIL which they can then adapt to different polynomials. What do you do if I throw a trinomial in the mix?!?!įor really anything other than binomial pairs, FOIL is useless. But, whereas PEMDAS reminds us of something as essential and broadly applicable as Order of Operations, FOIL has one and only one hyper-specific application. The adults reading this may not remember much from high school math but I would bet they remember FOIL, or PEMDAS. Either way I get it, acronyms are a powerful thing. It could also be LO-FI, which would be cooler.

The products are added together, combining like terms, and voila!įirst of all, the order really doesn’t matter here. …and finally, (quite fittingly) the last terms… It tells us the order in which we should multiply terms when expanding an expression such as… FOIL is an acronym that stands for First, Outside, Inside, Last. For the expansion, the favored method is known simply as FOIL.

#AREA MODELS FOR DIVISION HOW TO#

Quadratic expressions can be written as factored binomial pairs, and we spend a great deal of time learning how to factor and expand quadratics, over and over and over. Most students are introduced to polynomial expansion during their algebra unit on quadratics. It’s much more important to develop number sense, learn how to deconstruct numbers, and use creative reasoning to solve problems. But multiplying quickly by hand is not a skill of significant value beyond elementary school. It’s the way I was taught and still favored by many teachers and students today. For the pros out there, it’s the faster method when it comes to multiplying by hand. You may be more familiar with vertical multiplication. …and then adding up the interior pieces for our solution: We might put it into an area model like this:

Students today are usually introduced to area models in elementary school as a way of deconstructing large numbers for multiplication. While it is by no means new to the world, it was a revelation to me. This one actually came to me from a student. Inspired by the simplicity and versatility of the area model, I started looking for more applications. Or, in Algebra, you might use area models during polynomial division.Īll of these applications pre-date the Common Core, but the new standards introduced the area model much earlier and actually named it for what it is, a simple visual tool for deconstructing multiplication or division. In statistics, you might use area models when solving compound probabilities. For the science nerds out there, the Punnet Square used to breakdown and predict genotypes from cross breeding is a type of area model. You may not know it by that name, but area models have countless applications in STEM. It’s been rough seas for these not-so-new-anymore standards in the 10 years since, but I want to celebrate an undeniable gem of Common Core Math: the humble area model. In fact, I graduated high school the same year they were introduced, just missing the boat. Like most people working in education today, I was a student before Common Core standards came around.

Area models for division