Area models for division12/7/2023 ![]() 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. 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. And we're done.Like most people working in education today, I was a student before Common Core standards came around. ![]() And you can see, when you take 20 and divide it into four equal groups, then you get one, two, three,įour, five circles per group. What we're talking about, or what we started talking about. We have divided it into four equal groups, and so that's exactly Two, three, four, five, and we have, one, two, Now, but what about this one? So let's see, we have one, So this is 25 divided byįive, not 20 divided by four. So this looks like 25 circles divided into groups of five, or divided into five equals groups, which is, of course, equal to five. Like we have one, two, three, four, five groups of one, two, three, four, five. ![]() Now, what about this one? Let's see, here, it looks So this one over here, it's really representingġ6 divided by four, not 20 divided by four. Into groups of four, or we could actually also view it as divided into four equal groups, because both of those are true. 16 circles divided into, we could do it as divided So how many total circlesĭo we have in this picture right over here? Let's see, we have one, two, three, four, and then we have four groups of four. And, actually, let's think about what each of them could represent. ![]() Represent 20 divided by four? Pause this video and see ![]() Different pictures here, and my question to get us warmed up is which of these could ![]()
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