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Video transcript

I'm going to multiply 78 times 65 and a little less than standard way but hopefully it'll make some sense and you'll realize that there's multiple ways that you can multiply and this is actually the way that I multiply numbers in my head so 78 times 65 and then we're actually going to think about what the different parts of this process represent on this area model so 78 times 60 65 so I'm going to start just the way we normally start when we multiply I'm going to start with this five in this ones place and I'm going to say five times eight is 40 and instead of just writing a zero and carrying a four right over here I'm just going to write the number 40 so this was the five times the eight now I'm going to multiply the 5 times the 7 and we have to be a little bit careful here because 5 times this isn't just any 7 this is a 70 so what is 5 times 70 well 5 times 7 would be 35 so 5 times 70 is 350 so I'll write that down 350 so this does review 5 times 8 is 40 5 times 7 is 350 if you add these two together this is going to be 5 times 78 now let's go over to the 6 so let's multiply the 6 times the 8 now we have to be careful again this 6 is not just a regular 6 it's in the tens place this is a 60 60 times 8 well 6 times 8 is 48 so 60 times 8 is going to be 480 480 so it's going to be 480 and then 6 times 7 well that would be 42 but we have to be careful this is 60 times 70 so we're going to have two zeros at the end this is 4,200 not just 42 so 6 times 7 is 42 hundred 4,200 and now we can add everything together and this is a very similar process to what we do when we do the traditional method of multiplying I just made a little bit more explicit what parts are from what are from what multiplying which digits but we can add everything together in the ones place we have 0 in the tens place we have 4 plus 5 is not 9 9 plus 8 is 17 and now we can carry a 1 1 plus 3 is 4 4 plus 4 is 8 8 plus 2 is 10 carry 1 say regroup a 1 even and you have a 5 right over there so you get 5070 now I want to think about I want to visualize what was going on here using this area model so once again we had 78 so I'm going to make this vertical length represent 78 so this distance right over here this distance right over here represents the 70 that's the 70 and then we'll make this distance right over here represent the 8 let me make that a little bit cleaner so you see what I'm talking about so this distance right over here represents the 8 and we're going to multiply that times 65 so this distance right over here I it's not drawn perfectly to scale but it gives the idea this is 60 and then this distance right over here this distance right over here is the 5 so this whole distance is 65 this entire distance is 78 so when you multiply a 6 if you add a rectangle that's 68 you or 65 units wide and you multiplied it and it had a height of 78 units then its area is going to be 78 times 65 its area is going to be 5070 now each of these parts we can map to one part of this of this area model right over here when we multiplied the 5 times the 8 and got the 40 that was that was this section right over here 5 times 8 is equal to 40 when we multiplied 5 times 70 and got 350 that's this right over here 5 times 70 and we got 350 when we multiplied 60 the 6 and the tens place 60 times 8 and got 480 that's this right over here this is 60 times 8 is equal to 480 and then finally when we multiplied 60 times 70 and got 4,200 that's this area right over here this area is 60 wide detalle so this is sixty times 70 which is equal to 4200 and then when we added everything up to get 5070 we were essentially just adding up the areas of each of these tiles this big one is 4,200 that makes up most of the area then we get 480 from this magenta one then 350 from this kind of greenish yellow one and then 40 from this greenish blue one to get 5,000 70 so the area of this entire thing is 5070 square units

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Multiplying with area model: 78 x 65 (video) | Khan Academy

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Watch the video on how to multiply on a number line

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- [Instructor] What we're going to do in this video is think about different ways to represent multiplication. And especially connect it to the notions of skip counting and the number line. So if we were to think about what four times two means, we've already seen in other videos, you could view this as four groups of two. So we could have four groups, so one group, two groups, three groups, and four groups, and each of them have two of something. I'll just put two little circles here. So you have two there, you have two there, you have two there, and you have two there, and you could also view that as four twos, or four twos added together. So we could view it as two plus two plus two plus two. And this, of course, is going to be two plus two is four, four plus two is six, six plus two is eight. We see that over here, we could even skip count. Two, four, six, eight. Four times two is equal to eight. We can also think about that on a number line. So I'm gonna make a little bit of a number line here. And so we could imagine four times two being, all right. So this is one times two, two times two, three times two, and four times two. So we started at zero, and we took four hops of two along the number line to end up at eight. We went from zero to two, four, six, eight. We just skip counted our way to eight. So if I were to ask a similar question, actually, let me draw a little series of hops, and I want you to think about it the other way. What multiplication does that represent? So let's say I start here and then I'm going to hop like this. So I'm gonna go there and then I'm gonna go there. I'm taking equal jumps every time. Then I'm gonna go there. Then I'm gonna go there. Then I'm going to go over there. So what would that represent, if we used the same type of ideas that we just thought about? Well I went from zero to four, eight, 12, 16, 20. I'm skip counting by four. So you could imagine this is probably something times four. Now how many hops did I take? I took one, two, three, four, five hops of four. So this is five times four. And we can see that we ended up at 20. We could also view this as being the same thing as five fours or four plus four plus four plus four plus four, and you see that over here. You have, we're starting at zero, we're adding four, then another four, then another four, then another four, and another four. We have five fours here. Let's do one more. So I'm gonna have a number line here and think about what it would mean to say, do something like seven times three, times three. Well, we could view that as seven hops of three starting at zero, seven equal hops. So one, two, three, four, five, six, and seven. We end up at 21, so this is equal to 21. You could also view this as we took seven threes and added them together. And you could also view it as skip counting. You went from zero to three, six, nine, 12, 15, 18, and 21. Now just out of interest, what if we went the other way around? What if we were to take three hops of seven? What would that be? Well, we would start here and so we would take our first hop of seven right over there. Get to seven, then if we take another hop of seven, we get to 14, and then if we take another hop of seven, we get to 21, interesting. At least for this situation, whether we took seven hops of three or three hops of seven, we got to the exact same value. I encourage you to think about whether that's always going to be the case. I'll see you in a future video.

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Multiplication on the number line (video) | Khan Academy

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Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

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Multiplication on a Number Line Practice

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Multiplication on a Number Line Practice

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AFTER watching the video, complete practice questions

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Practice skip counting to find a number on a number line with only two tick marks labeled.

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After watching the video, complete the practice questions

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Multiply with arrays (practice) | Khan Academy

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Practice multiplying 1-digit numbers using arrays.

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This video explains what arrarys are.

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Grade 3 Math  3.5, Model Multiplication with Arrays

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You will watch the running problem and then complete the practice questions.

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Abe went running 4 days this past week. He ran 9 kilometers on each day. In that same week, Beth ran 15 fewer kilometers than Abe. How many kilometers did Beth run that week? So I encourage you to pause this video and to try this on your own, try to figure out, how many kilometers did Beth run that week? So there's a couple of ways to think about it or a couple of ways to visualize it. The first thing we might want to do-- in fact, the first thing we definitely want to do-- is to figure out, well, how far did Abe run in that week? Well, he went 4 days, and each day, he went 9 kilometers. So we could say that he went-- let me do that blue color-- 4 days times 9 kilometers per day. And we could visualize that. So this is how much he went in one day. This is how much he went in two days. This is how much he'd go in three days. This is how much he would go in four days. So what is this? What is 4 times 9 kilometers? Well, this is essentially 9 plus 9 plus 9 plus 9. So we could just add up the 9's. 9 plus 9 is 18, plus 9 is 27, plus 9 is 36. So he ran a total of 36 kilometers. Now, that's not what they're asking us for. They're asking us for the number of kilometers Beth ran that week. And they tell us that she ran 15 fewer kilometers than Abe. So this right over here, Abe's total distance-- if we start from here, and we were to go all the way over the week, all the way to here, he ran 36 total kilometers. Beth ran 15 fewer kilometers than Abe. So let's go back 15 kilometers. So Beth ran 15 fewer kilometers than Abe. So that's 15 fewer kilometers. And so the number of kilometers that Beth ran would be this distance. It would be this distance right over here. So this is kilometers Beth ran. Let me write it like this-- Beth's distance in the week. Beth's distance would be this distance right over here. So how do we figure that out? Well, if we say Beth's distance-- let's just use the letter B for shorthand. So Beth's distance plus 15 kilometers is going to be equal to Abe's distance, is going to be equal to 36 kilometers. Or another way of thinking about it-- Beth's distance is going to be equal to Abe's distance, so 36 kilometers, minus 15. So what is Beth's distance going to be equal to? Well, 36 minus 15-- 6 minus 5 is 1. 30 minus 10 is 20. So it's going to be 21. So Beth's distance is 21 kilometers.

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2-step word problem: running (video) | Khan Academy

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Abe went running 4 days this past week. He ran 9 kilometers on each day. In that same week, Beth ran 15 fewer kilometers than Abe. How many kilometers did Beth run that week? So I encourage you to pause this video and to try this on your own, try to figure out, how many kilometers did Beth run that week?

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Complete practice questions. Only allows 10 so if you finish early go back and complete practice questions with video

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IXL | Estimate differences | 3rd grade math

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Improve your math knowledge with free questions in "Estimate differences" and thousands of other math skills.

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Watch the video first and then complete practice questions

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- [Instructor] What we're going to do in this video is get some practice estimating adding and subtracting three digit numbers and so here it says 398 plus 251 is, and this squiggly equal sign means we just need to make an estimate. We wanna know what is this roughly equal to? So normally I say pause the video but here I want you to work it out in your head. So I'm just gonna pause. I'm just gonna stop talking for like a second and see if you can come up with what this is or maybe I'll give you three seconds 'cause the whole point here is to estimate, not get the exact right answer. Okay, so I'm assuming you've had a go at it. Now, I'll tell you how I think about it. We of course could maybe take out some paper or you might even be able to get the exact answer in your head but in everyday life, if you're at the supermarket and you're like, okay, I guess it would be an expensive supermarket, something is $398, something else is $251. Roughly how much would I be spending if I bought both of them? Well, my head would say, alright, 398, I would round to nearest 10 at least, maybe the nearest 100. So let's round to the nearest 10. In the case of 398, the nearest 10 is the nearest 100. And so we would get to, this is approximately 400. And then this is, 251 is approximately 250. So if you were to add these two things up, you're going to get something that is approximately equal to 650. And lucky for us, that is one of the choices and what I'm about to do is not estimate but just see how far off we were. So if we were to just actually do it, 398 plus 251. Eight plus one is nine. Nine plus five is 14. This is 14 10s. We put four 10s here, and the other 10 10s we regroup as 100 and then one plus three plus 200 is 600. So in this case, in this particular case, we got awfully close with our estimation and if you don't need to get the exact number, well, that'll be fine. Let's do another example. In here, we are going to do a little bit of subtraction. So once again, pause this video or try to do it as quickly as you can. Try to estimate what this difference is going to be. 678 minus 273. Alright, let's do it together. So there's a couple of ways to tackle it. You could round to the nearest 10 and you could say, well, this is approximately 600, let's see, to round to the nearest 10, you would round up right over here so you'd say this is 680 minus you could say 270 which is going to give you and here you're still gonna have to do some mental math. This would be what? 600 minus 200 is 400 and 80 minus 70 is 10. So that's one way to do it or you could do it even rougher. You could just do to the nearest 100. So you could say, look, 678, the nearest 100 is 700 and then minus 273, the nearest 100 there is 300 and so this is even rougher but it gets us actually still similar answers and either way we estimated, either the kind of rougher way or the slightly less rough way, we got to something around 400. So you could feel good that this is your choice. The reason why we even have to make multiple choice questions for estimation is not everyone is gonna get the exact same estimate but the correct choice should be the one that any reasonable estimate would be closest to.

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Estimating adding and subtracting 3-digit numbers (video) | Khan Academy

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Instructor] What we're going to do in this video is get some practice estimating adding and subtracting three digit numbers and so here it says 398 plus 251 is, and this squiggly equal sign means we just need to make an estimate. We wanna know what is this roughly equal to?

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Complete the 7 questions and then review your feedback

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Subtraction With Regrouping: StudyJams! Math | Scholastic.com

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When a subtraction problem calls for regrouping, have no fear! With these easy steps, students will become subtracting sensations.

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You should have watched the video first.

Complete practice questions

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IXL | Rounding - nearest ten or hundred only | 3rd grade math

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Improve your math knowledge with free questions in "Rounding - nearest ten or hundred only" and thousands of other math skills.

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Watch this video first and then complete the IXL practice questions

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- [Narrator] Let's say that you have a jar of jelly beans, and you know that there are exactly 282 jelly beans in that jar of jelly beans. And then the next day you come and you see there are fewer and you say, what happened, and let's say someone who lives with you or your friend says, oh yeah, I counted exactly and I ate 59 of those jelly beans. So you started with 282, 59 are taken out, and you don't need to know exactly how many jelly beans are left, but you wanna estimate roughly how many jelly beans are left, and that's why, as this title of the video says, we're going to estimate when subtracting large numbers. And we can debate how large is large, but these are reasonably large. So let's do that, let's see if we can estimate what 282 minus 59 is. And sometimes when we're estimating, we will use this squiggly equal sign. This means approximately, which is another, just a fancy way of saying roughly what is this equal to. So the way that I would approach this, I would say hey, are these close to numbers that are easier to subtract with. So for example, 282, I'd say, you know what, maybe I can round to the nearest 10 here, and so I could round it down to 280, if I round down to the nearest 10. If I rounded up, it would be 290, but 282 is closer to 280 than it is to 290. So I would round this, when I'm estimating to 280. And then what about 59? If I were to round to the nearest 10, what would I round that to? Pause the video and think about that. Well, 59 if I round down to the nearest 10, it would be 50, and if I round up to the nearest 10, it would be 60, and 59 is definitely closer to 60. So I would say that this is roughly, if I'm rounding, I could say, hey I'm gonna round that to 60. So I could say the 282 minus 59 is roughly going to be 280 minus 60. And now what is this? You might be able to do this in your head. You could view this as 28 tens minus six tens, and so if you have 28 of something minus six of it, you're going to be left with 22 of that something. And so you could say that this is going to be 22 tens. 22 tens, or another way to think about it. You have two 100s and then 8 tens, and then you're gonna take six tens away from it, so then you'll be left with two 100s and two tens. Just like we have here. So the whole point here, this is not, this is actually not exactly what 282 minus 59 is, but if you just said, hey ballpark do I, I wanna know, do I have roughly how many jelly beans do I have, well this could be useful. And you'll see later in life this is actually a very, very usefully skill where you might have these numbers that get a lot larger than this, but you'll round to the nearest 10, or you'll round to other places, so that you can do that computation in your head.

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Estimating when subtracting large numbers

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Narrator] Let's say that you have a jar of jelly beans, and you know that there are exactly 282 jelly beans in that jar of jelly beans. And then the next day you come and you see there are fewer and you say, what happened, and let's say someone who lives with you or your friend says, oh yeah, I counted exactly and I ate 59 of those jelly beans.

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1.Watch the Video FIRST
2.Complete the practice questions

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Rounding Numbers Song | 3rd Grade - 4th Grade

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Click on the link to watch the video.
Then complete the practice questions afterwards

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We've got four numbers here. What I want to do is try to round each of these to the nearest 10 and to the nearest hundred. So I encourage you to pause the video and try that right now. So let's make two columns. Let's make one first for the nearest 10 and then make another column for the nearest 100. And let's start with 154. So 154, what is the multiple of 10 above 154? Well, it's 160. And the multiple of 10 below 154 is 150. So we're going to round up to 160 or down to 150. Well, when we're rounding to the nearest 10, we need to look at the ones place. One place to the right of the place that we're rounding. So we look at this 4 in the ones place. Since 4 is less than 5, we round down to 150. Now, let's think about that same number, rounding to the nearest hundred, so 154 to the nearest hundred. So now we need to think about if we were to round up, what's the multiple of 100 above 154? 160 isn't the multiple of 100 The multiple of 100 above 154 is 200. What's the multiple of 100 below 154? Well, that's going to be 100. So if we're going to round to the nearest hundred-- so we look at the hundreds place. We'll look one place to the right of that, which is the tens place. If that place is 5 or greater, we round up. If it's less than 5, we round down. Well, this is clearly 5 or greater so we round up. So this is interesting. When we rounded to the nearest 10, since we had a 4 in the ones place, we rounded down. But when rounded to the nearest hundreds, since we had a 5 in the tens place, we rounded up to 200. Let's do some more of these. This is fun. So 4,674. The multiple of 10 above that is 4,680. The multiple of 10 below that, 4,670. Remember, we're concerned only with the multiple of 10. So do we round up or down? Well, we're thinking about rounding the tens place. So that's why it's either going to be an 8 if we round up, or a 7 if we round down. To figure that out, we look at the ones place. If the ones place is 5 or greater, we round up. If it's less than 5, we round down. It's, once again, less than 5, so we round down to 4,670. Now let's round the same number to the nearest hundred. What's the multiple of 100 below this? Well, the multiple of 100 below this is 4,600. The multiple of 100 above this is 4,700. If we're trying to think about rounding to the nearest hundred, we want to look at the tens place. The tens place is 5 or greater, so we round up to 4,700. Now let's tackle 9,995. And once again, always try to pause these, if you haven't done so already, to try to do this on your own. So 9,995. What is the multiple of 10 below this. Well the multiples of 10 below this is 9,990. And what's the multiple of 10 above this? Well, if you increase this by 10, you actually get to 10,000. So you might say, hey, well isn't this a multiple of 100, and actually this is a multiple of a thousand-- it's also a multiple of 10,000. It's all of those, but the multiple of 10 right above 9,995 is 10,000. You just have to add a little bit to this to get to 10,000. Or the multiple of 10 below it is clearly 9,990. 10 more than that gets you to 10,000. So how do we around this? Well, once again, if we're rounding to the nearest 10, we want to look at the ones place. The ones place is 5 or greater so we round up to 10,000. Now, let's round to the nearest hundreds. You should be getting used to this now. To the nearest hundreds, what is the hundreds below this? Well, it's 9,900. What is 100 above this, the next multiple of 100 above this? Well, if you add 100 to 9,900 you once again get 10,000. So how do we decide whether to round up or down? Well, we don't look at the ones place anymore. We're now rounding to the nearest hundred. So we want to round to the nearest hundred. To do that, we look one place to the right, which is the tens place. If this is 5 or greater, we round up. If it's less than 5, we round down. It is 5 or greater so once again we round up to 10,000. Now we have one more, 8,346. The multiple of 10 below it is 8,340. Multiple of 10 above that is 8,350. If we're going to round to the nearest 10, we need to look at the ones place. The ones place is 5 or greater, so we round up. Now, let's round to the nearest hundred. 8,346, the multiple of 100 above this is 8,400. The multiple of 100 below this is 8,300. Notice we're rounding to the nearest hundreds. If we were to round up, the hundreds place becomes a 4. If we round down, the hundreds place stays at 3, but it's followed by zeroes. If we want to round to the nearest hundreds, we need to look at the tens place. The tens place here is less than 5, so we round down to 8,300. Notice, again, when we round to the nearest tens, we rounded up to 8,350. When we round to the nearest hundreds, we rounded down to 8,300.

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Rounding to nearest 10 and 100 (video) | Khan Academy

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Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

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The video will go over material but also give practice problems. You can make the video Full Screen.

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Rounding Whole Numbers Part 1: To the Nearest Ten

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Look at the examples and then complete the practice questions

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Estimating Differences Lesson & Worksheet - My Schoolhouse - Online Learning

You can estimate to find out "about how many" when subtracting as well as when adding. This is also called rounding.

You can estimate the differences of two-digit and three-digit numbers.

Look at the examples below.

77

Rounds to

80

31

Rounds to
- 30

50

The estimated difference of 77 - 31 is 50.

459

Rounds to

500

287

Rounds to
- 300

200

The estimated difference of 495 - 287 is 200.

Practice estimating the difference with two-digit and three-digit numbers.

- 32
Rounds to
- 26
Rounds to

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Estimating Differences Lesson & Worksheet - My Schoolhouse - Online Learning You can estimate to find out "about how many" when subtracting as well as when adding. This is also called rounding. You can estimate the differences of two-digit and three-digit numbers. Look at the examples below.