Multiplying 3-digit numbers by 1-digit numbers

Key Stage 2

Maths

Multiplication and division

What is the missing number? 3 x ____ x  2 = 60

What is the missing number? 9 x ____ x 2 = 108

Select the correct equation for the representation.

﻿Hi, and welcome to the lesson. My name's Miss Thomas, and I'll be going through the lesson with you today. We've got some great maths coming up. We're learning how to multiply three-digit numbers by one-digit numbers using the short multiplication method, so I hope you've got your thinking caps on and you're ready to get stuck in. Off we go. In today's lesson agenda, first, we'll be solving multiplication problems, regrouping in one column. Then we'll go to the talk task where you can have a practise of your own. After that, we'll be solving multiplication problems where we regroup in more than one column. And finally, we'll finish with the end of lesson quiz where you can test yourself in the lesson's learning. The equipment you will need for the lesson is a pencil, paper and a ruler. Pause the video if you need to get your equipment. Here we have the big picture. It's a map of North America. Look closely at the picture. What can you see? Whisper your answer. Great job. I'm sure you saw a lot. We've got a question here, and it says, when might we need to use multiplication? Use the picture to answer your question. You might come up with some multiplication questions of your own using the picture. Pause the video now and have a go. Fantastic, I'm sure you got so many. I had a go at writing a few of my own. I said, how many times more people live in the USA than Alaska? Or how many times has the owl population increased from 2019 to 2020? I'm sure you've got some great ones too. We need to use multiplication so much in our daily lives. Okay, let's take a look at the first problem. I'm going to read it, you read along with me. In one month, 273 families camp in the Boreal Forest. The following month, three times as many families stay there. How many families stay that month? I've got two questions for you. First question says, what is known, what is unknown? And the second question says, what calculation is needed? Pause the video now and answer the two questions, explaining out loud your answer. Welcome back. You might've spotted that we know that there are 273 families that camp in the Boreal Forest in one month. You might've also known that three times as many families stayed there the next month. What we don't know is how many families stayed there that month, the next month where there was three times as many. So, what calculation is needed? Call out your answer. Great. 273 multiplied by three to find out how many families stayed that month. We've got our bar model here to represent it, so I've got one bar with the value 273, to represent the families that stayed in the Boreal Forest in the first month, and then we've got a bar underneath three times the size, because that's what we're trying to find out, how many families stayed there. Okay, we can use lots of different methods in multiplication. I'm going to show you a method now which is where we partition the number 273 and we multiply those parts by three separately. So, 273 could be distributed into 200, 70 and three. So, three times three is nine, 70 multiplied by three, well, I can derive that answer because I know seven times three is equal to 21, so 70, which is 10 times greater than seven, 70 times three, the product must be 10 times greater, so it's 210. Finally, I'm going to multiply the 200 by three. Again, I can derive if I know that two times three is six, 200 is 100 times greater than two, so I can derive that 200 times three is equal to 600, the product will be 100 times greater. The final step is to add all of the products, 600 plus 210 plus nine, which is equal to 819. So, I know that 273 multiplied by three is equal to 819. We're going to take a look now at how to use short multiplication to solve the same problem. Okay, so our task was 273 multiplied by three. I've got my place value chart here, and I'm going to use the counters to solve that multiplication equation, and I've drawn my place value chart here, because we're going to use short multiplication algorithm to solve it as well. Okay, so, let's start. We're going to multiply 273 by three. So, let's add one group of 273 to our place value chart first. So, let's go, start with our ones. So, we've got three, three ones, so one, two, three ones, I'm going to add that to mine, I'll draw a line to make it clear. Add that to my short multiplication, so three ones. Next, I'm going to go to my tens, so I've got seven tens. So, one, two, three, four, five, six, seven. So, we've got seven tens. And we've got, last one is our hundreds, we've got two hundreds. One hundred, two hundred. So, we know that one group or one times 273 is 273. But we weren't asked to find one group. How many groups were we asked to find? Call out your answer. Great, we were asked to find three groups. So, we've got one group. Now we need to times 273 by three. Let's go to our ones, then, we always start with our ones. So, we've got one group, so we need another group, one, two, three ones. And my third group, one, two, three ones. Now, we know our three times tables, so I know that three times three is equal to nine. Do I need to regroup nine ones? Hmm. If I've got nine ones in my ones column, I haven't got to 10 yet. Haven't got any tens there, I've only got nine ones, so I don't need to regroup. Let's have a look at our next column. I've got one group of 70 there, but I need three, so I need two more. Let's add another group of 70. One, two, three, four, five, six, seven tens. That's my next group of 70, I need another group of 70. One, two, three, four, five, six, seven. So, I've got three groups of 70 here. I can use my derived facts for this. If I know that three times seven is 21, I know that three times 70 is going to be 10 times greater, so I know that I've got 210 here. If I've got 210 in my tens column, do I need to regroup any to my hundreds? Call out your answer. You might've realised that yes, we do. Now, I need to regroup, because I've got 210 in my tens column. Two of those hundreds, 200, belong in my hundreds column. So, I need to take out and regroup 200 into my hundreds column. So, let's have a go. So, if I've got one group of 70 here, I can take that away. Another group of 70 will be 140. So, now I need to get to 200, so, 140, 150, 160, 170, 180, 190, 200. And I'm going to regroup them into hundreds counters, so I've put my 200 that I regrouped up here. Let's have a look what that looked like on here now. So, we had, draw a line to make it clear, we've got nine ones, and we have one 10 in here, and we regrouped the 200 up to the hundreds column, so I'll add that in. Now, we need to multiply our hundreds, so I've got a group of two, because we've got one group of two, but I need two more to have three groups of two. I'm going to leave these up here, because in multiplication, we add what we regroup, because these have already been multiplied by three in the tens column. So, let's have a go, we've got another group of two, and our third group of two. So, I've got one, two, three, four, five, six, seven, eight, I'm going to add those in, I've got 800 in my hundreds column. Do I need to regroup into my thousands column? Call out your answer. We don't need to regroup. Can you explain why we don't need to regroup? You might have said if we've got 800 in our hundreds column, we haven't equaled to 1000 yet, so our eight hundreds stay in our hundreds column. So, then I need my final point and I need to add in, we've got 800 in our hundreds column, is equal to nine ones, so we've got one 10 and 800. So, we've got 800 and 19. Let's see what we've got to do next. Okay, so we've already had a go at using the counters like these. Now we're going to have a go at using the pictorial counters that you can see on the screen. So, we're going to work together to solve 224 multiplied by four. I'm going to use the pictorial counters, and you're going to use the short multiplication algorithm that you can see under the word you. Now, I don't want you to solve it yet, but I do want you to write down 224 multiplied by four, just like it does on your screen, onto your paper. Now, pause the video and do that. Welcome back, okay, so, I'm going to need, I've got four ones in my one column, two tens in my tens column and two hundreds in my hundreds column to represent the number 224. I'm going to multiply it by four, I'm going to start with my ones, so I've got four ones, I need four groups, so I need another group. To have two groups, there groups, and four groups. Four multiplied by four is equal to 16. If I was to count all of those ones counters, it would be 16 counters. Now, if I've got the number 16 in my ones column, what do I need to do? Explain, whisper to your screen. Great, you might've said that you need to regroup one of those tens. In the number 16, there is one group of 10, which needs to be regrouped to the tens column. And we need six ones to stay in the ones columns. I'm going to do that now. So, we've got the number 16, we can't have one of 10 in our ones column, so we're going to regroup it to the tens column. So, now I've got six ones left in my ones column and I've regrouped one group of 10 to the tens column. Pause the video and show this on your short multiplication algorithm. Welcome back. Don't worry, we're going to go through yours at the end to make sure you've got it right. Okay, next we've got two tens. We need to have four groups of two tens. At the moment, we've got one, so we need another three. So, we've got one group of two tens, two groups of two tens, three groups of two tens, four groups of two tens. I don't need to multiply the one that we regrouped from the ones column, because it's already been multiplied. So, 20 times four, hm. If I know that two times four is eight, how will you solve 20 times four? Call out your answer. Great, you might've said from two times four is eight, you can derive that 20 times four, the product will be 10 times greater, so the product will be 80. Do I need to regroup 80 in the tens column? Do I need to regroup eight tens, what do you think? Great, I love it when you explain out loud to the screen. So, we don't need to regroup eight tens because that's equal to 80, and we haven't reached 100 yet, so we can put it there, but you might notice I've got nine in my tens. Why do I have nine and not eight in my tens column? Call out loud. Excellent, because in multiplication, we add what we regroup and we had our regrouped 10 counter, so now we've got nine tens. Can you pause the video now and write this into your written algorithm, please? Welcome back, okay, now we're onto the last column, we've got two hundreds and we need four groups of 200, so we've got one group of 200, two groups of 200, three groups of 200, four groups of 200. Hm, if I know that two times four is equal to eight, how could I solve 200 times four? I'd like you to use the phrase derived facts in your answer. Call out your answer. Great. If you know that two times four is eight, you can use your derived facts to work out that 200 is 100 times greater than two, so the product, the answer needs to be 100 times greater. So, 200 times four is equal to 800. Do I need to regroup if I've got 800 in my hundreds column? What do you think? Great, you might've said that 800 isn't equal to 1000 and it's not greater than 1000, and our next column is 1000, so, no, 800 can stay in the hundreds column. Pause the video now and add this to your written algorithm. Welcome back. Okay, let's take a look at the written algorithm together. So, first of all, we did four times four, which was equal to 16, we kept six ones and we needed to regroup the 10 into our tens column. Next, we did 20 times four, which was equal to 80, but we needed to add one group of 10, which gave us 90, so we have 90 is equal to nine groups of 10. Next, we did 200 times four. We know that two times four is eight, so we can derive that 200 times four is 800. 800 is not greater than 1000, so we don't need to regroup, so we have eight in our hundreds column. Well done for the talk task, let's see what we've got to do next. Here we have a word problem. One evening, 154 people camp. Each person has dinner at the Campfire Lodge at a cost of £6. How much money does the Lodge receive? I have three questions for you and I want you to explain your thinking out loud. The first question says, what is known and what is unknown? Pause the video and explain. Great, we know that there are 154 people and each person's dinner costs £6. We don't know how much money the Lodge receives for all of the dinners. The second question is, what will the equation be? Call out your answer. Great, the equation will be 154 multiplied by six. Now, you need to create a representation for the equation. Pause the video and represent on your paper. Welcome back. There are many representations you could've drawn. I chose a not-to-scale area model. I wonder what you chose. The last question says, will we need to regroup? So, when you solve 154 multiplied by six, will you need to regroup? Pause the video and explain. Remember, we regroup when the factors multiplied equal greater than the value of that column. Welcome back. So, we know that four multiplied by six is greater than 10, so we will regroup in the ones column. I know that 50 multiplied by six is greater than 100, so we will regroup in the tens column too. Let's have a look at solving our problem. So, I've got my counters showing my pictorial representations for 154 multiplied by six, and I've got my written algorithm for short multiplication. So, I've got in my counters, in my ones column, I've got four ones, in my tens column, I've got five tens, and in my hundreds column, I've got one hundred. I need six groups of four ones in my ones column, so I've already got one group of four ones, so I need to add another, two groups of four ones, three groups of four ones, four groups of four ones, five groups of four ones, and six groups of four ones. I know that six multiplied by four is equal to 24, and if I was to count all of my counters, I'd have 24 ones. But 24, just going to go back, 24 does not, we cannot have 24 in our ones column, because 24 has two groups of 10 in it, so we need to regroup two tens into the tens column. And I've left four ones in the ones column. So, I'm going to add that into my written algorithm, we've got four in the ones column and we've regrouped two tens into the tens column. Next, I've got five tens in my tens column and I need to multiply it by six, so we've already got one group of five tens, two groups of five tens, three groups of five tens, four groups of five tens, five groups of five tens, and six groups of five tens. If I know that five times six is 30, then I know that 50 times six is going to be 10 times greater, so I've got 300. But I've also regrouped two tens, so I've actually got to add what I regroup, so I've got 320. Do you think I need to regroup into my next column, which is my hundreds column if I've got 320 in my tens column? What do you think, call your answer out. Great, you might've said, yes, we need to regroup, because 320 has 300 in it. So, we're going to do that now, we're regrouping our three hundreds, and we're going to leave the two tens in the tens column. So, I'm going to show you that in my written algorithm, so we've got two tens, and we regroup our three hundreds into our hundreds column. Finally, I've got one hundred in my hundreds column, and I need to multiply it by six, so I've got 100, and then there's my six hundreds there now. So, I've got to add what I regroup, so if I had six hundreds, I also need to add the three hundreds I regrouped, so 600, 700, 800, 900. Hasn't reached 1000, so I don't need to regroup, so I've got 900 in my hundreds column, and I'm going to add that into my written algorithm. So, 154 multiplied by six is equal to 924. We're going to delve in deeper now. What's the same and what's different in the two calculations? You might need some thinking time here. Pause the video and decide. You might find a few things that are the same and a few things that are different. Welcome back. You might've spotted that 232 is the difference between the two products. You also might've noticed that one of the factors are the same, 232. What would happen if a factor increased or deceased by one? Have a look, call your answer out. Great, you would see that the whole would be one group greater or one group lesser. You're now ready for your independent task. Solve the multiplication calculations, explain each step out loud using our key vocabulary that's in the bold, black writing. The more you can explain out loud, the better you'll remember how to use the written algorithm for short multiplication. Pause the video and complete your independent task. Here are the answers to the equations. Well done for explaining it out loud using the key vocabulary. I've shown the regrouping in purple too, so you can tick them or correct them if they're wrong. Fantastic work this lesson. Head over now to the quiz to test yourself on the learning. And we've reached the end of the lesson. You've worked so, so hard today on your maths, well done, and what an achievement to have learned how to use the short multiplication method to times three-digit numbers by a one-digit number. Fantastic work. See you next time, have a great day.

Multiplying 3-digit numbers by 1-digit numbers

Multiplying 3-digit numbers by 1-digit numbers

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UnitMaths / Multiplication and division

Maths