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Short Division

﻿And that, is the TV off. Believe me when I say, that for this session, you need to be distraction-free. What we are about to tackle needs your 100% attention, your eyes, your ears, your brains focused and engaged. So please, take a moment to make sure you are free of all distractions in a quiet space where you will be able to focus on your learning for the next 20 minutes. Press pause, get yourself sorted, and then come back. And you are in for a treat with this lesson's focus. In this lesson, we are using the formal written methods for long division. We're going to start off with a grouping activity, before we have a look at estimating and long division. Both really important skills that you'll need for the independent task. Things that you're going to need to help you today, pen or pencil, ruler, and some paper, pads or a book, if your school has provided you with one. Press pause and collect the items, then come back and we'll start. So kicking off then, with a grouping activity, I have identified using colour, three groups. I wonder if you can pause and spot how and why these colours have been used to group some of the numbers together. Press pause, come back when you're ready to share. So what have you noticed? Let me remove some of them, focusing just on these three. What is it that's the same about these three numbers? Good, they are all prime. They all have factors of one and themselves, that's it. Just two factors each. How about these three? Good, they're all multiples of 10. And finally, excellent, factors of 36. Moving on to our division focus. Can you remind me, each of these numbers in a division equation have a name, what are their names? 23 is the, good, the dividend. Which of the numbers is the quotient? And the divisor, therefore, is eight. Let's switch these two around, dividend, divisor, quotient. If you're able to remember those words, and use those words, it will help to improve your explanations. As you're explaining your mathematical thinking, talking about division, if you can use these words instead of just numbers, then you're able to speak with more clarity. Here's a problem for us. Let's give it to read together. Football fans are travelling to Dortmund for a champions league match. And Oak Travel, has arranged for coaches to take them to the ground from the airport. Each coach can take 47 passengers. If there are 611 fans, how many coaches are needed? Press pause, have a go at answering those three questions, come back when you're ready. So from the problem, what do you know? Tell me, good. What do you not know? Fantastic, now the third question, you might be making some connections, pause that thought, let's just draw out what we know. Each coach can take 47 passengers. There are 611 fans. We don't yet know how many coaches will be needed. I'd like you to pause again, to have a go at drawing a bar model, to represent the maths within the problem. This is going to help with that third question, and that sentence stem I can use. What knowledge or skills do you have that will help you solve the problem? Prove it using the bar model, or reveal it using the bar model. Pause, come back and we can compare in a minute. Okay, show me your bar models. Hold them still, looking good. Here's mine, using what we know. There are 611 fans. We also know that each coach can hold 47 fans. How many coaches are needed? Well, that's another 47. So we're looking at how many 47s, how many equal groups of 47, we can make from 611. So what maths is going to be connected and used here to solve the problem. We could look at repeated subtraction. It might take a while, but of course, repeated subtraction is division. So we can divide the whole into 47 equal groups. Thinking about how we can approach this division. When we're working mentally, we've got these strategies on offer. Will any of them apply to this equation, to the expression that we're going to complete as an equation. Division using factors, oh 47 is prime. We can't use that. Division using multiples, could take a while, if we're thinking about what one group of 47 is two groups of 47, three to, and so on. Not so efficient. Related facts for me, there aren't any related facts that are calling out to me from 611 divided by 47. How about an equivalent division? There's no equivalent division that's going to help us here. So instead, because mental strategies aren't appropriate for the numbers that we're working with, it's going to be a written division. And because we're dividing by two-digit number, we're going to use a long division to help us. Before we look at that, it's important to start off by estimating the size of the quotient. This is what these four children are thinking they could do or use to help them find their estimates. Press pause, and evaluate each of their thoughts, come back when you're ready to share how you think, which of the children perhaps, how do you think we could estimate the size of the quotient? What do you think, which of the children top left, bottom right, middle? I'm thinking, that the most appropriate and efficient approach to estimating will be using his approach. And let's look at how this works. So he's rounded 611 to 647 to 50 really nice numbers to work with. We know how many fives are in 60, 12. Now because 50 divided by 600, and five divided by 60, because they are equivalent divisions, because the horizontal relationship and the vertical relationship is maintained across both fractions across both divisions, they're equivalent. And if we know how many fives are in 60, then we also know how many 50s are in 60. So 12 is our estimate. We've used a related fact and equivalent division to help us there. Read the sentence at the bottom for me. So the quotient will be approximately 12. A quick practise for you, use this approach to estimate the size of the quotient for these three divisions. Press pause, work through them, come back and we'll check. Are you ready? So a quick check then, now this is dependent on how you've rounded. You may not have rounded the same way I have. Let's see, I've rounded to 920 and separately, 20. Nice numbers, multiples of 10, multiple of 100s that we can work with. Then 900 divided by 20, I'm thinking 90 divided by two, 45. Because the horizontal and vertical relationships between the fractions is preserved. I know that there will be 45 twenties in 900. Next, 2020, again, nice numbers to work with. Be kind to yourself when you're choosing how to round thinking about how many twos are in 200, 100, I then know how many twenties are in 2000. The same quotient because of what's happened to 2000 to become 200, and 20 to become two. They've both been divided by 10. The question remains the same. Finally, 8,100 and 90, wonderful connection between eight, sorry, between nine and 81 and therefore nine and 810. And the relationship is preserved because 90 is 10 times bigger than nine, 8,100 is 10 times bigger than 810. Can you read the sentence at the bottom out for me for the middle division? One, two, three, so the quotient will be approximately 100. Good, and say it for the top, one, two, three. And so the quotient will be approximately 45. And say for the bottom, one, two, three. So the quotient will be approximately 90, really good. So, we're set with our estimation. We're expecting a quotient around the size 12. Here, we're going to use long division. This is really exciting. I'm going to use place value counters, and show you alongside that, the long division. If you need to pause and rewatch, please do. I need your focus though. I really need your attention looking carefully at what's happening with the counters and with the grid and my digits. So I'm dividing 611 by 47. I'm asking how many 47s, how many groups of 47 can I make from, first of all, here's the number, 611 is that right? Yes, so back on track. How many 47s, how many groups of 47 can I make from six? None, so look at those 600s, I need to exchange them for 10s. 100, 10-tens, 600, 60-tens. There they are. Now I can ask myself how many 47s, how many groups of 47, can I make from 61-tens? How many? I can make one group. I can make one group of 47. I can remove that one group of 47, there it goes. One group, one group of 47 has been removed from the 61-tens 47-tens have been taken away from 61-tens. How many 10s are left? 14-tens. Did you see that, and how it appeared within my long division as well? So let me just take you back. So here we had our 61-tens. I'm making one group of 47, one group of 47. And now look in my grid. There's my one group of 47 recorded. I'm removing those 47-tens from my 61-tens. I've got 14-tens left. How many groups of 47 can I make from 14-tens? So I'm going to exchange my 14-tens for ones. And there's a lot of ones, 141-ones. In fact, look at them go, and then another three. Wow, let me just take you back because I want you to see as what in the grid where that one appears. So we asked how many groups of 47 from 14-tens? I'm going to exchange those tens for ones. Now look on my grids. As the one comes down from 611, and then I'm exchanging to show what's happened there. My tens have been exchanged for ones. And once they're all there, I'm going to ask how many groups of 47 can I make from 141-ones? And there they are. So how many groups of 47 from 141? I don't know about you, but I do not know my 47 times table. So look to the left. This table is going to increase. I know one group of 47 is 47, two groups of 47. That's two, lots of 47. I can double that, 94. But I've got 141. So I'm going to see if I can make another group. Three groups of 47. Let me add 94 and 47. 141, fantastic. So how many groups of 47 can I make from 141-ones? I can make three groups. So I can remove all of those ones. Let me go back. I've made three groups of 47 that all used. I record my three at the top of my grid. I used all full, 141-ones. I haven't got anything left. My long division is complete. What is the quotient? 13 and our estimate was 12. Fantastic, how close they are. Looking back at the original problem then. So the solution is 13. What does that mean? 13 coaches are needed. Here's another long division, this time without the place value counters. Let's just focus on the use of the grid. So estimating first of all. Why have I estimated do you think using 8,100 and 90? Why have I made those changes? Tell me, tell me. Yeah, I can see a lovely connection between nine and 81. I can easily mentally estimate there. How many nines are in 81- Nine? So how many nines are in 810, 90. And the relationship's preserved here, multiplying nine by 10, 810 by 10. So the quotient will also be 90 for 8,100 divided by 90. Let's go. How many 89s. Oh, actually, if you want to pause now and work ahead independently, you can. If you want to work with me, copying down the digits as we go, then do that. But please don't just sit back and watch unless you're going to rewatch and work on at the same time, but you need to be active at some point. 89, how many groups of 89 can we make from eight? How about from 82? Almost, how about from 827? 89 times table needed? Let's work out some of them one group of 89 is 89, two groups doubled 89, double 90 subtract two, 178, not big enough. Let's get bigger. What about 10- 89s? 890, oh, so I'm thinking it's one less than 10 groups. Nine groups of 89s subtract 89 from 890 or subtract 90 and add one, 801. So we can make nine groups using 801-tens of the 827-tens leaving us with 26-tens, bringing down the seven. We can ask how many 89s are in 267 ones, because we haven't been able to make a group of 89 from the 26. We know that already. So we're going to now work with ones, 267. Looking back at the grid bottom left. Two lots of 87 of 89 sorry, is 178, three lots, 267. So I've added that very quickly, of course, 178 add 89, 267. So from 267, we can make three groups of 89. We've used all 267. The long division is complete. The quotient is 93. Our estimate was 90 again, really close. So it's a good indication that we've been successful. It's time for you to practise. And I'm so excited for you. Long division is a challenge. It is a challenge, but with practise and thinking and rewatching these videos, if you need, you can definitely achieve it. Even if it's not something that you can give a big tick for in this session, with practised over time. You definitely will get there. Press pause have a go at your long division questions. Come back afterwards and we'll look at the solutions. Ready to have a check. First of all, I need to see it, hold up your paper. Let me see. I want to see big smiles on those faces at the same time. Fantastic, so much determination, really, really good to see that you're having a go, that you're taking those first steps to achieving your long division skills. Really, really proud of you. Well done everyone. Let me show you the solutions. So question one, if you want to pause on these pages to compare to yours, please do, but I can see I'm showing you here. The estimate on the left, you've got the useful table on the rights of groups of 17, and you've got the long division through the middle. So quotient there 54. Seconds one we've got 42, really close to the estimate. And the groups of 19 over there on the right. Pause if you need to. Question three, estimate 40. Quotient of 41 long division down the middle, quick check it off against yours. Pause if you need to. Question four, six away from the estimate. Quotient of 86. And five quotient of 96, compared to an estimate of 100. Before we finish, I want you to have a look at these questions, these divisions. Sometimes it's more appropriate to work mentally than using a written methods. And mental approach for some of these will work. Sow our written approach, but you're going to be saving some time and you're going to be working more efficiently for some of these divisions, If you choose to work mentally, rather than using a long division. Which of them do you think you could work on mentally? And which do you think you could use a written method for? How many of them do you think would work mentally? And is it these ones? Absolutely, we'd be able to use some related facts, maybe some equivalent divisions. And we certainly could solve these with a mental strategy. Whereas these ones would be more appropriate with a written method, a long division, where we're dividing by two-digit numbers. Thank you so much for joining me. I would love to see on Twitter, any of your work that you're willing to share, please ask a parent or carer first though, you should be really proud of your work learning from this session. Please ask your parents or carer. If you'd like to share your learning with OAK National. Ask them to share it on Twitter, tagging @OakNational, and #LearnwithOak. Wow, you all deserve a huge pat on the back for that session. Long division is certainly a challenge. There's so much to think about and focus on. So thank you for your attention and your engagement and your practise. Keep it going, practise it every so often. And it will soon really stick. And I hope with that real true understanding of what's happening when you're doing it as well. For now, a well-deserved break awaits. Takes some time between now and whatever else you have lined up for the day. And I look forward to seeing you again soon for some more maths. Bye.

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Long Division

In this lesson, we will use long division to complete equations.

Maths

Y6 Maths

Key Stage 2

Year 6

Use the formal written method of long division to solve appropriate calculations

Multiplication and division

Number

THEME

UNIT

Represent decimal numbers in a variety of ways

Place Value to 3 Decimal Places

Multiply and divide by 10, 100 and 1000 involving decimals

Multiply and divide by 10, 100 and 1000 with in context

Understand the terms 'common factor' and 'common multiple' as properties of a number

Identify properties of numbers

Multiply a decimal number by a whole number

Solve multiplication problems using known and derived facts

Use efficient strategies to multiply numbers, including decimals

Practise multiplication and division skills

Use formal written methods for short multiplication including multiplying decimals

Multiply by a two-digit number using long multiplication

Use formal written methods, including long multiplication, to solve a range of problems

Explore efficient mental strategies for division

Use the formal written method for short division

Solve problems involving division with remainders (Part 1)

Solve problems involving division with remainders (Part 2)

Represent remainders in different ways depending on the context of the problem (Part 1)

Represent remainders in different ways depending on the context of the problem (Part 2)

Lesson overview:Use the formal written method of long division to solve appropriate calculations

Core Content

Multiplication and division: