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Find the product of 4.5 and 16

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Oak travel are giving out refreshments to their guests on their plane, each guest receives 0.75 litres of water. There are 105 guests. How much water will they need?

Use efficient strategies to multiply numbers, including decimals

﻿Hi again everyone, and welcome back. Today's lesson, we're going to look at practising multiplication and division skills. So we're going to be reviewing lots of some of the key skills that we need in terms of multiplication and division. If there's anything during this lesson that you're a little unsure of or you want more practise of, then do go and seek out the previous lessons, 'cause we will be reviewing everything from other lessons within this unit. Okay, now before we get started with the lesson, I have, of course, got a bit of a joke for you. Why did the banana go to the doctors? 'Cause it wasn't peeling very well. Get it? The peel. Okay. Right. Anyway, let's get started, guys. So, first things first, let's have a look at that lesson agenda. So we're going to look at a few different things today. We're going to look at representing and identifying the value of decimal numbers and we're going to use Dienes for that as our representation. We're going to look at multiplying and dividing by 10, 100, and 1000, and we're also going to look at common factors and common multiples. Then we're going to have a bit of time for you to be able to apply that yourselves in your own learning. In making sure, of course, you'll need your pencil and paper today. So do pause the video if you haven't got those already. A bit of a warmup for you, then. What I'd like you to see. You might want to draw this out yourselves on your piece of paper and complete it, is pause the video and complete all of this and then come back when you have finished. Right, let's have a look at those answers then. So three, two, one. Okay. So my recommendation, I'm not going to wait on this or go through them all is to pause the video, double check all of your answers, tick them all off. If you've got any errors there, then do double check them and try and work out how that occurred. When you're ready, we'll continue. So, some of the things they can look at safe. First thing we look at is representing, and I did find the value of decimal numbers. Now to do that, in order to try and represent decimal numbers well, we use these. Now, to do this successfully, what we've done here is the normal way of looking at Dienes. You might think of this as a thousand, or we might think of this as 110 and a walk, but what we've done is we reassign the value of the Dienes. So we say that this is now our whole. This is our 10ths. This is our hundredths and this is our thousandth. Okay? So now that we've got that, what I want you to think about is what can you then say about the relationship between the Dienes? For example, what's the relationship between our thousand and our a hundredth here? So what are the relationship between these, what would the relationship between the thousand and the whole beat? Okay? So pause the video and have a bit of think. Maybe jot, write some down, and then we'll come back together. So, what we should be thinking about is looking at the relationship in terms of using our Dienes to help us. So we can see that from our thousandth here, we know that there are going to be 10 of them, which make up this hundredth. So we can say that the relationship between these is this hundred, it's 10 times greater than my thousandth or the other way around, that this thousand is 10 times smaller than my hundredth. And likewise, our thousandth, the reason we call it a thousandth, is it's 'cause it is thousands of them, which would make up my whole. So again, the relationship between them would be that this is a thousand times smaller than my whole, and my whole is a thousand times greater than my thousand. Okay? There's lots of difficult words there. And lots of words that sound like other words. So it's well worth practising that out loud. Just speaking through, picking a couple of examples and getting really confident with those relationships. Now, let's take what we've done there. And when we use that, using those values that we talked about before, what number we represented in the Dienes below? Have a bit of a think, just jot down on your paper. What number are you representing in the Dienes here? Okay, when you've got it, let's have a look. Well, we've got one whole for one, and then we're going into our decimals, 'cause we've then got tenths and hundredths. So, that's our decimal point. We then got two tenths here and then we've got three hundredths. So the number we represent is 1.23. Okay? Got the hang of it? Same thing, then. Can you tell me what numbers are being represented by the Dienes below? So pause the video and get your answers, and when you're ready, play the video again. Okay. How did we do you guys? Safe? That's one. Hopefully we got 1.331. We've got one whole. We've got three tenths, three hundredths and one thousandth. Second one's slightly tricky. Hopefully you've got 2.016. Now that zero is really important. Now we've got our two wholes, we've got no tenths. So we need to make sure we represent that. We've got one hundredth, and we've got six thousandths. Okay, well done if we did that, guys. So that kind of rounds up our review of this part. Let's move on, then. Multiplying and dividing by 10, a hundred and a thousand. Now just remembering our rules. So if they are multiplying something by 10, a hundred, or a thousand, if we multiply by 10, then we are making all of the digits 10 times greater. Okay. That means they're going to move up one place to the left on our place value chart, because they're going from 10 to a hundred because our place value chart represents that kind of relationship, and every time it's 10 times greater. Okay? So if we multiply by 10, for example, we're going to move one place to the left. So let's have a go about. So we would have four tenths becomes 400, and then three ones becomes three 10s, and our seven tenth becomes seven one. So our number now, if we multiply it by ten, is 437. Then go back to our original number, if we multiply it by a hundred, so we multiply by 10, a hundred, then that's two places on our place value chart to the left. So this time, we're going to end up with 4,370, remembering our placeholder there to make sure that that number has got its proper place value. Okay? And then, as we know, if we multiplied by a thousand, it's going to be three places to the left 'cause you multiplied by 10, a hundred, a thousands. Okay? So three places to the left. Let's have a look from our original number. We should end up with 43,700. Okay? So quick review there of multiplying by 10, a hundred and a thousand. You know what's coming next. Dividing by 10, a hundred and a thousand. Now when we divide by 10, a hundred and a thousand, we're going to be moving up that digits, all our digits are going to become 10 times smaller. So they're going to move, if we divide by 10, one place to the right, because of our place value chart, and all has got a relationship of 10 times smaller from column to column. Okay? So taking our original number, if we divide it by 10, then each digit is going to become 10 times smaller, so we end up with 4,343. Okay, so if we then divide by a hundred, we're going to be moving at an hundred times smaller, so each digit is going to become a hundred times smaller, moving two places to the right. So from our original number, we're then going to end up with, instead of 40,000, you're going to end up with 400 from 3000, so our three, here, it's going to become 30. And so we end up with 434, and then we've got our decimal place, and we've got three tenths. Okay? Then lastly, providing by a thousand, we're going to be moving all our digits because we're getting a thousand times smaller. So each digit is going to become a thousand times smaller. Now remember, 10, a hundred, a thousand times smaller is going to mean that it's going to move three places in our place value chart, so each digit becomes a thousand times smaller. So we're going to end up with 43 points. Four, three. Okay, well done. If you press pause, are you doing that as I was doing it. Great job. But now we're going to give you some time to be able to practise this yourself. So, got some examples here, remembering our rules, remembering what we practised, have a look at these and try and solve them. And then when you're ready, play the video again and we'll go through the answers. So pause now. Let's go through those answers, then. So number one, 2.4 multiplied by 100 equals 240. Number two, 1035. Remembering that zero as that placeholder. Number three, 4.509. Number four, 0.012. We divide 0.12, divide it by a 10. So everything's are going to become 10 times smaller. And number five, 4,566. And number six, if we multiply it by 10, we get 2.95. Well done. If you've gone through all of those and you're feeling really confident with that, that's great. Let's move on. Defining common factors and common multiples. Now just a bit of a review and a reminder, a factor is a number that divides into another number exactly without leaving a remainder. So, for example, if I have the number 24, some of the factors of 24 are going to be the numbers that multiply together to make 24 to equal 24. So three multiply by eight, is equal to 24, so three and eight are a factor pair of 24. They are both factors of 24. So top tip is always to work systematically. Now we're using factor books. The reason we use these is they help us to give a clear representation of our factors and creating our factor pairs and helping us to work systematically as we work through. Now, the top antenna of our factor bug will always be one and the number itself, 'cause they will always have antenna factors. So first off, we have one and 36. They will always be our antenna. If we have prime numbers, that's numbers, there's only half the factors, one in themselves. They won't have any other legs. So they are fat as slugs. Okay. Let's have a look at the other factors here, working systematically. I want to work round. So we've gone from one, and then is it an even number well, then it's going to have a factor two, then. And so two multiplied by 18 is equal 36, then I think, does it have three as a factor? Well yes, it does, three multiplied by 12 is equal to 36. Then I move on to four, four multiplied by nine. Yep. Great. Well done. And then five, is it a factor of five? Five? No, 35 and then 40. No. So it's not. And then working through six is our last factor because six multiplied by six is equal to 36. Now that factor we've got here. So the six is really important because six multiplied by six is meaning it's a square number and square numbers have an odd number of factors. So they get a special stinger on their factor bugs, as we can see here. Hopefully we're feeling happy with that. So what I'd like you to do now is to create your own fat bug for the number 48. And then can you look at the common factors? So factors which are in both 36 and 48 and find me the greatest, the highest, the biggest common factor of both 36 and 48. Pause the video now and then play when you're ready and we'll go through the answers. How do we do? Finished? Brilliant. Let's have a look, then. So 48. We've got one and 48, of course. It is an even number, so we've got two and 24. We've got three and 16. We've got four and 12. Any others? We've got six and eight. Okay? Hopefully you've got all of those factors. You then find what the greatest common factor is there with the highest number, which is a factor of both this. Yep. You got it. So it's 12. So our highest, our greatest common factor of 36 and 48 is 12. Great job guys. So that's common factors. Hopefully we're feeling confident, now. Let's have a think about multiples, then. So a multiple is the result of multiplying a number by an integer. So as we do it in a multiplied by an integer, then we'd go up in different multiples. Now, if you know your times tables, I'm afraid you already know multiples. But let me give you some examples, then. Hopefully this isn't too challenging for us. So multiples of five, you've got there. They are the multiples of five, but they are not exhaustive. They can keep on going up, but I haven't got space on my page. So if those are multiples of five, then, what I'd like you to do is find the first 12 or only go to the first 12, multiples of three and then find the common multiples of both three and five. So which are multiples of both three and five. Perhaps you can see a pattern in them as well. Right, now pause the video now and have a go at that, then play when you're ready. Let's have a look at those answers, then. So multiples of three, here's what we should have had up to 12, okay? So there's what we should have had looking at that. Where are those common multiples of both three and five, or 15, 30, anymore? So 15 and 30 are our common multiples. Well done. If we spotted those and identified them, if you did go further then great, good job. So what did you notice? Any patterns there? Yeah? So possibly you notice some parts as being identified. So it's the fifth going up in fifteens, perhaps? Yeah? So I suppose the next one that I thought might be coming up with 45 might be in there as well, but all of this, because we've only gone to 12 multiplied by three, I was kind of half expecting it. You might have been too, but obviously you've only got to 12 multiplied by three, so it isn't there. Okay? Good job guys. Right. It is now time for you to go and complete your task. So you've got your worksheet. So go pause the video, complete those worksheets, then come back and we'll have a look at the answers and check them together. Great job guys. Okay. Hopefully we are finished. So let's have a look at some of those answers, then. Question one, you have to identify the value of the underlying digits. So the digit, which was underlined what's now, what is its value, to give us an understanding of those decimal numbers? So in A is seven hundredths. In B, well, it's two, two ones. In C, three thousandths. It's difficult to say. In D is six tenths. E, it was 30, three tens, And in F, it was six thousandths. Well done if you've got all of those. Number two, you have to arrange it, make the greatest possible number, and then the smallest possible decimal number. Hopefully you got a little bit creative with this, and what did you come up with? You should have found the greatest number that you could find would be, obviously we want the most value out of our largest numbers, so we want that right up here, and then we should be going in a descending order. Okay? So a bit of a strategy in there. So we should have got 7.651. Likewise, with the smallest number. We want to use that smallest number in our collection, in the place, which has the greatest place value. So in this case, we should have 1.567. So we can see that pattern being established there. In question three, we found that the ticket for a charity concert and there are 306 being sold, and how much is raised in total? Yes, it was quite simple. So each one is worth 10 pounds. Therefore 306 multiplied by 10 is 3060 pounds raised in total. Number four, slightly more challenging. There's two steps for this. A bakery makes cupcakes, and there are 2,600 cupcakes in a week. The cupcakes are placed into boxes of 10, and each box of cupcakes is sold for three pounds. Well first, we need to know how many boxes there are. So to do that, cause they're in boxes of 10, we need to divide by 10. So that leaves us 260 boxes. Then we need to say that each box is then sold for three pounds. So we need to multiply that number by three. So that, therefore, will leave us 780 pounds in total. And question four. So we gave you a list of numbers and we wanted you to circle any which are a factor of 24, and underline any that are a multiple of three, just practising our factors, our multiples. So the factors of 24, that circle those, should have had four, six, eight, and 12, right? We've made it slightly more confusing 'cause we weren't asking you for the factor pairs, there, so we're getting to think a little bit more, but hopefully you drew out your factor bug and you could see and easily identify them, that's the nicest way to sort it. Now, underlining any numbers that are multiple of three. Nice and easy job, if you know your three times table. So three, six, nine isn't there, 12. Okay? Sorted, brilliant job guys. Hopefully we're being a lot more confident now with all those things to do with multiplication and division. It's nice to have that review and consolidation regularly just to keep everything on the boil, keep everything ticking over in our brains. Too, if you feel like you want to, then please ask your parent or your character, share your work on Twitter, using the hashtags that you can see on the screen. Thank you very much for your hard work today. It has been great working with you, and make sure, before you go anywhere, to go and consolidate your learning through that end of lesson quiz, hopefully we'll see you again soon. Have a great day guys.

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Practise multiplication and division skills.

In this lesson, we will revise multiplication and division skills and apply them to problems.

Maths

Y6 Maths

Key Stage 2

Year 6

Practise multiplication and division skills

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 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

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

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:Practise multiplication and division skills

Core Content

Multiplication and division: