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Area models for division12/10/2023 Students also seems to grasp a better understanding of how partial-quotients can add up to a quotient with a remainder. This method brings more meaning to why the division process works. I just played school and figured that it wasn’t worth trying to find meaning, but instead just pass the class and move on.įor the past ten years I have been introducing the partial-quotients method to students. It didn’t make sense to me why I was dropping zeros or setting up the problem in a certain structure. I was always encouraged to use the traditional division algorithm. During my K-12 math experience I never questioned what was introduced. You might be a fan of this method if you’ve ever wanted to know why the traditional division algorithm works. One of the more interesting parts of the unit delved into the use of the partial-quotients method. They spent a great deal of time exploring division and what that means in the context of a variety of situations. 1 plus 3 is 4.My fourth grade group just finished up a unit on division. And so we added it allįinding the combined area- the area of this plus theĪrea of that the area. The 6, we carried this 1 into the hundreds place. Multiplied the 2 times the 16, we just calculated Just doing that we justĬalculated that right over there. But notice we're really thinkingĪbout 20 times 60 is 120. So we're used to carrying theĢ down here and carrying the 1. So if you multiply 2 timesĪnd carry the 1. Said, oh, you know, I just throw a 0 down there. Into the tens place you've probably always So 7 times the 10 or theħ0, plus 7 times 6, the 42. So 112, what you justįigured out right over here, is this area Right over here. Sum of both of these things, because you're multiplying 7 The 7 times the 1, you really multiplyingĬarry it when you add this carried 4, and But right when youĭid that 7 times 6, we essentially calculated The 4 in the tens place because it's a 40. With the 7 in the ones place and you do 7 times 6 is 42. Hey, Sal, why did we go through all of this business? I've seen before Did I add that up right? Let's see, this will be 11. Tens is 9 tens, plus 4 tens, is 13 tens, which is the same Let's see, in the ones place, you get a 2. Going to be 200 plus 120 plus 70 plus 42. So what's the area of thisĮntire thing going to be? Well, it's going to be theĢ00 plus the 120 plus- let me do it this way- it's So it's going to be 7 timesĦ or 42 square units of area. And then finally, what's theĪrea of this little section right over here? It's 7 high and it's 6 wide. This purple, and I'll thrown some blue in there, too. Section right over here? Well, it's 7 high Now what's 20 times 6? Well 2 times 6 is 12, In there from the 20 to make it clear that this Not the color I wanted to use- let me use In your head 20 times 10 is just going to be. You could think of as 2 timesġ, and you have two 0's there. So we could figure out theĪreas of each of these sections, and then the area ofīe this product, is going to be the area of all Up by parts, because it'll be easier to compute, and weĬan see what part of the area those differentĬan think about what 10- so let me separate Is going to be 16 times 27, the area of thisĮntire rectangle. Right over here- and then the height of my rectangle, The product 16 times 27, what gives you the area ofĪ 16 by 27 rectangle. Point right over here, this line right over The 2 in the 10s place is representing 20. Which I want to do in that green color, the sixth, I've gone 10 slashes, or I'm representing 10 What's going on in the multiplication process.
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