Multiplying 3-digit numbers by 1-digit numbers

Key Stage 2

Maths

Multiplication and division

What calculation is needed to solve the problem?

﻿- Hello and welcome to today's lesson. My name's Miss Thomas and I'll be going through the lesson with you today. We've got loads of exciting maths coming up where you are going to need to explain your thinking a lot out loud to your screen. So I hope you're ready for a very active lesson that will need lots of your participation. So bring your thinking caps and let's get stuck in. In today's lesson agenda, first, we'll be solving multiplication problems using place value counters. After that, we'll go to the talk task where you can have a go at correcting other people's mistakes. Then we'll look at solving multiplication problems using the short multiplication method. And finally, we'll finish off with the end-of-lesson quiz. For today's lesson, you will need a pencil, paper and a ruler. Pause the video now if you need to gather your equipment. Let's take a look at our first problem. Read along with me as I read. One night, 617 tents are pitched by Niagara Falls. Niagara Falls is a waterfall. Each tent can hold three people. What is the maximum number of people who could be camped there? I've got some questions for you that you need to answer. First question says what is known? What is unknown? And the second question says what calculation is needed? Pause the video and answer the questions, explaining out loud. Welcome back. You might have spotted that there are 617 tents. That's something we know. And that there are three people in each tent. That's how many people a tent can hold. What we don't know is what is the maximum number of people who could camp there. So what calculation is needed? We need to do 617 multiplied by 3 to find out the maximum number of people who could camp there. Here I've drawn a representation to show you this. I've got a part with the value of 617 and the bar underneath is three times greater than that 617 bar. The number that is missing is the value of 617 multiplied by three. Okay, we're going to learn a new star word. My turn, estimate. Your turn. Estimate means guess what the value might be. So before we come to solve 617 multiplied by 3, we're going to have an estimate at what the answer could be, what the product could be. So I know that 617, if I look at my number line, 617 is between 600 and 700. Point to where the value 617 is on my number line. Great, is it closer to 600 or closer to 700? Call out your answer. Great, it's closer to 600. We have rounded 617 down to the nearest 100, nearest multiple of 100 and the answer is 600. So now that I've rounded 617, it's easier to multiply by three because it's a multiple of 100. If I know that six times three is equal to 18, I know that 600 times 3 is going to be 100 times greater. It'll be 1,800. Okay, now we've estimated our answer, 1,800, we're going to use counters to solve the problem, 617 multiplied by 3. Let's go to the counters next. Hello, okay, let's have a go. I've just popped down here so I can say a quick hello before we begin. So our equation is 617 multiplied by 3. Over here I've drawn my place value chart so that we can show our short multiplication method on the paper whilst we use our concrete materials, our counters to show us pictorially. Okay, now I've drawn four columns in my place value chart even though I've only got a three-digit number. I estimated that I'm going to need to regroup into my thousands. So I've put my thousands column there. All right, let's put the number 617 into our place value chart. In multiplication, we always start with our ones. So I'm going to put out seven ones. One, two, three, four, five, six, seven. Let's pop that in actually. So I've got seven ones and I've got one 10. And I've got six hundreds. One, oh, sorry, wrong column. Hundreds, one, two, three, four, five, six. And we're multiplying 617 by three. Now, we know that one times 617 is 617. But we want three groups of 617. So multiplication, we'll start with our ones. So I've already got my first group. I need two more. So let's have a go with our second group. We're going to count seven ones. One, two, three, four, five, six, seven. That's my second group. We need three groups. One, two, three, four, five, six, seven. Now, I know that seven multiplied by three, I know my three times table, that's equal to 21. So if I counted up all of my counters here, I'd have 21 ones. What's the problem with leaving my 21 ones in my ones column? Call out your answer. Great. You might have said that we can't have 21 in the ones column because there are two groups of 10 in 21. We need to take our two groups of 10 and put it in the tens column. So I'm gonna take out my, I've got seven here. I need two groups of ten, so I can take those seven. So two groups of 10 is equal to 20. So I've taken away seven. I know that my second group will give me 14. So I've taken away 14. I need to get to 20. So 14, 15, 16, 17, 18, 19, 20. Taken away 20 ones so I'm left with one. I'm going to regroup to the next column. I took away 20 ones, how many tens counters am I going to need? Call out your answer. Then whisper it to the screen. Great, I'm going to need two tens. Now, I'm gonna pop them up here because these have already been multiplied by three. These are regrouped. In multiplication, we add what we regroup. So I'm gonna show you what that looks like here. So we did seven times three, that gave us 21. We've regrouped two. I'm gonna pop that here, a little two to show I'm regrouping. Two into the tens column. And we have one, I'll draw a line here to make it clear. One in our ones column. Next, we need to do one group of 10 multiplied by three. So I've got one group of 10 already. I need two more. One, two. So I've got my three groups of 10. Remember, I'm not going to multiply what I regrouped because they were already multiplied when they were in my ones column. Okay. Let's count and see if I need to regroup. One, two, three, four, five groups of 10 is equal to 50. Do I need to regroup? Shout out your answer. I don't need to regroup. Why don't I need to regroup? Shout out your answer. We don't need to regroup because we haven't reached 100. We've got five groups of 10, which is equal to 50. So we can leave them there. So we had three groups of 10 plus the two we regrouped, gave us 50. I'm gonna write that down. Let's see if I can do an upside down five. There we go. And then finally, we're onto our hundreds columns where we had six, we didn't regroup so we've just got six. One, two, three, four five, six hundreds. And I'm going to need three more groups of six hundreds. So we've already got one, so another 100, 200, 300, 400, 500, 600. And we're timesing by three, so I need my third group. 100, 200, 300, 400, 500, 600. Okay, if I know that six times three is equal to 18, I know that 100 times three is going to be, sorry, I know that 600 times 3 is going to be 100 times great. So it's going to be 1,800. If I've got 1,800 in this column, am I going to need to regroup? Call out your answer. Great, can you explain why we're going to need to regroup? Explain, whisper it to your screen. Fabulous. We're going to need to regroup because 1,800 has 1,000 in it. We need to take out that 1,000 and regroup it to our thousand column. So let's count out 1,000. 100, 200, count with me. 300, 400, 500, 600, 700, 800, 900, 1,000. So I'm going to take out my hundreds column and I'm gonna add in my regrouped 1,000. Okay, how many have I got left? 100, 200, 300, 400, 500, 600, 700, 800. So we have 800 left. We regrouped into the thousands and remember, we add what we regroup, so I'll bring it straight down. So 617 is equal to 1,851. Excuse my bunched up writing there. Well done, give yourself a pat on the back. Okay, we've reached the talk task. Here we have equations that have been completed incorrectly. You need to use the star words to explain out loud what the mistakes are and how they've been made. You can then correct them. So let's have a look at the first one. The equation says 635 multiplied by 4. Now, there's a mistake here, so I'm going to try and find it. In multiplication, start with the ones. So we need to solve five multiplied by four. Five multiplied by four, I'll use my known facts and I know it's equal to 20. If it's equal to 20, 20 has two 10s in it, so I need to regroup two 10s. Looks like this person didn't regroup the two 10s 'cause we know five times four is equal to 20 and not two. Let's have a go at correcting it this time. Five times four is equal to 20. So I regroup my two tens into my tens column and I leave my zero to hold my place value of zero ones. Next, I need to do three tens multiplied by four. I know that's equal to 12 tens or 120. Plus the two tens, it's equal to 14 tens. So I put my four in my tens column and I regroup my 100 into my hundreds column. I'm using lots of my star words here. Then I need to do six hundreds times by four, which is equal to 24 hundreds, plus the one is equal to 25 hundreds or 2,500. If I've got 2,500, that's two thousands in my hundreds column. So I need to regroup. I'm going to leave my 500s in my hundreds column and regroup my two thousands. I could add it straight in because we don't need to multiply it. We add what we regroup. Now it's your turn to complete your talk task. Pause the video and have a go. Let's take a look at the next problem. I'm going to read it out loud, you can follow along when I read. For a weeknight ice hockey match, the stadium sells 709 tickets. The weekend match sells three times more tickets than the weeknight match. How many tickets are sold at the weekend match? I'm going to ask you some questions now and you can pause the video and explain out loud your thinking. The first question is what is known? What is unknown? Pause the video and explain. Welcome back. You might have found that we know that there are 709 tickets sold at the weeknight match, and that the weekend match sells three times as many. What we don't know is is how many tickets are sold at the weekend match. So my second question is what will the equation be? Pause your video and explain. Welcome back. The equation will be 709 multiplied by 3 to find how many tickets were sold at the weekend match. We're going to go through that calculation together now using our short multiplication with counters. So we've got 709 multiplied by 3. I'm gonna add one group of 709 into my place value chart first and then we're going to need to find three groups. But let's start with the first group. So we've got seven hundreds. Oh, I've got a zero in my tens column. Do I need to put any counters in my tens column? What do you think? No, we don't, we've got zero but we still need to write the number zero in our number 709 because it holds our place value. So let's go to the next column, and we've got nine ones. Okay. Just going back to that zero now in the tens column. If I multiply zero by anything, what's the answer? Whisper your answer. Great, we know it's going to be zero. Okay, so let's go to the ones. I've got my first group of nine ones, my second group of nine ones and my third group of nine ones. Nine times three is equal to? Great, 27. If I've got 27 in my ones column, do I need to regroup? Call out your answer? We do need to regroup. Can you explain why? We need to regroup because in the number 27, there are two tens. So we need to take our two tens and regroup them into the tens column and we'll leave seven ones in our ones column. I'm going to do that now. So we've left our seven ones and we've regrouped our two tens. Now I've got tens in the tens column. Do I need to multiply them by three? Call out your answer. No, they've been regrouped. They've already been multiplied by three in the ones column. So we're going to add them in at the end. So we're gonna leave them there. They don't need to be multiplied by three again. Now we go to our hundreds column. I've got seven hundreds in my hundreds column but I've only got one group. I need two more 'cause I'm going to need three groups of 700. So I've got my first group, my second group of 700s and my third group of 700s. So if we've got 700s multiplied by three, if I know that seven times three is 21, how can you use your derived facts to tell you what 700 multiplied by 3 is? Pause the video and explain. Great, you might have explained that you know that seven times three is 21. So 700 times 3 is going to be 100 times great. It's 2,100. If you've got 2,100 in your hundreds column, do you need to regroup? Call out your answer? Yes, we do need to regroup. Can you explain why? Excellent, the number 2,100, you might have said has two thousands in it. Thousands belong in the thousands column, so we need to regroup two thousands to our thousands column and leave our 100 behind. So we've left our 100 from 2,100 and we're going to regroup our two thousands. Now, I don't need to multiply those two thousands because they've already been multiplied in the hundreds column. So we're just going to add them in. So we know that 709 multiplied by 3 is equal to 2,127. Okay, we've got another problem here. This time we're going to go through it with the counters but also in the short multiplication algorithm in the column that you can see on the screen. Okay, I'm going to read the problem. Read along with me. A three-night stay in a luxury house by Niagara Falls costs 319 pounds per person. Imran stays with his seven family members. How much do they pay for the house? So what's known and what's unknown? Pause the video and decide. Welcome back. You might have found that we know that there's a three-night stay in a luxury house and it costs 319 pounds per person. There's actually eight family members. We want to know how much it costs all together, so our equation is 319 multiplied by 8. All right, let's have a go then. So first, we want to put 319 in counters in our place value chart. So I've got nine ones here. I'm going to multiply my nine ones by, what are we multiplying by? By eight. Nine times eight is equal to? Call out your answer? 72. So in the number 72, do I regroup or do I leave 72 ones in my ones column? Call out your answer. Great, I'm going to regroup. I'm going to regroup because 72 has seven tens in it, okay? So let's leave two ones, so we're going to regroup seven tens. There we go. Now I've got seven tens regrouped in my tens column. Do I multiply my regrouped tens? Call out your answer. No, they've already been multiplied. But I do need to add three groups of my one 10 that haven't been multiplied. Let's go to our written algorithm. So we've put in the ones column and we've regrouped our seven. I'm just writing that up as well because you'll need to do that in your independent task in just a moment. Let's go back to our tens then now. So we've got one group of 10 multiplied by eight. That will give us eight ones. Now, because we've regrouped seven, we need to add the eight ones and the seven. So eight ones plus seven ones is equal to 15 tens. Also, that's 150. If I've got 150, I need to regroup one of my hundreds to the hundreds column and leave my five tens in the tens column. Have a look now at my written method. I'm going to show you what that looks like. So we added our seven tens to our eight tens. That gave us 15. So we wrote the five 'cause we had five tens in the tens column. And we regrouped our 100 to the hundreds column. Now we've got our hundreds in our hundreds column. We regroup. We're not going to multiply that but we do need our three groups of eight in the hundreds column. Let's do that now. So here we've got our three groups of eight. Three times eight is equal to? Call out your answer. Great, three times eight is 24. Plus the one is 25. Now, if you can derive the, 'cause you now that eight times three is 24, what's 800 times 3? Brilliant, 2,400. You can derive that. Plus the 100 is 2,500. Have a look at my written algorithm now to see how I write it in. So I've regrouped them over. And now we've got 500 in our hundreds column. I regroup my two thousands and I've written that in. And then I've added it straight in 'cause we don't need to multiply. It's already been multiplied by three in the hundreds column, and we know that it's 2,552. Great work, you're now ready for your independent task. You're going to use short multiplication to solve each of the word problems. Pause the video to complete your independent task. Okay, let's take a look at the answers. You should have used the short multiplication method to solve the word problems. I've included the answers on the screen in purple. Go through and check. If you made a mistake, don't worry, just go back and spend a few moments finding where you made the mistake and correcting it. Here are the second lot of answers. Fantastic work in today's lesson. Well done. You're now ready to complete your quiz. Fabulous work today in our lesson. Well done. I hope to see you again. Have a fantastic rest of your day. Well done for all your hard work.

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