![]() ![]() I might say, “Gina found partial quotients to solve 46 ÷ 2. While the original model was terrible, the question wasn’t bad at all. Does someone think interpreting bad models is a sign of rigorous math instruction? I don’t. And there’s still the problem of there being two numbers side-by-side along the length. I get that a student solving 46 ÷ 2 might think about and possibly even jot down potential options for partial quotients, but there is no reason this needs to be shown to children on their homework. So the first problem my friend shared wasn’t great, but of course there was a second problem. I think it’s important to distinguish between those two things: features of the model itself and recording strategies a person might use as they build the model. Now, if a student were building the area model while using the partial quotients strategy, then the subtraction might be a useful recording strategy, but that’s not the same as being part of the model itself. The repeated subtraction underneath isn’t terrible, but it’s unnecessary if you just want to know what multiplication or division sentence this model represents. Our students don’t need more confusion in their lives. Putting them along the top edge creates confusion about their meaning. For example, what is the purpose of writing the dimensions along the top as “10|70” and “3|21”? Knowing how an area model works, the only place 70 and 21 appropriately appear are inside the rectangle to show they represent area. I don’t need all the “noise” included in the original model. This area model represents 91 ÷ 7 using the partial quotients of 70 ÷ 7 and 21 ÷ 7.Īll that from this one model. If I look at this model in terms of division, I know I can divide the area (91) by the width (7) to find the length (13). This area model represents 7 × 13 using the partial products of 7 × 10 and 7 × 3. If I look at this model in terms of multiplication, I know I can multiply the length (7) times the width (13) to find the area (91). If you understand the components of the model, you should be able to write equations related to the model using both operations. ![]() ![]() Here’s a cleaned up version of the model.Īny (good) area model should simultaneously represent multiplication and division. The first is because this model is too bloated and trying to show competing ideas. There are two reasons for this, the second of which I’ll get to later in this post. “Sorry to hit you up for math help but I can’t find any like this on the internet.” Last night, my friend messaged me again about some different models. Help your 4th graders build a solid sense of “why” and “how” of division in this engaging and interactive lesson.In my last post, I shared some abominable strip diagrams. ![]() Have fun reviewing and applying division to real life applications. “Area Model Division” Answer Key (1 copy for display)ĬCSS: 4.NBT.6, MP2, MP4, MP6 Lesson Plan Description.“Area Model Division” (1 copy for display).“Area Model Division” (1 copy per student).Complete an exit slip to help you determine next instructional steps.Use area models with division problems in order to formulate a conventional way in which to divide whole numbers.Practice different strategies based on place value, the properties of operations, and/or the relationship between multiplication and division.Determine whole-number quotients and remainders with up to four-digit dividends and one-digit divisors.Construct viable arguments and critique the reasoning of others.Collaborate with peers to practice the "language" of fractions and attend to precision.Subject: Math, Numbers and Operations Fractions ![]()
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