Intro Quiz: Using multiples to divide

Video: Using multiples to divide

﻿Hey everybody, great to see you. Thank you for joining me once again, on Oak National Academy. My name is Mr Ward and today is lesson 12 in the unit of multiplication and division. We're going to be focusing today on how we can use our knowledge of multiples, to divide confidently and efficiently. Now it's important that you can focus on your learning so I ask that you are free of distraction and try and find a quiet spot for your learning. When you've got everything you need and you're happy to begin, continue the video into the main part of the lesson. See you in a few moments. But before I make a start on the main lesson, there is of course, time for the mathematical joke of the day to put a smile on your face, and hopefully get you cracking up as much as I have been over my own jokes. Why do people never ask for help from obtuse angles? It's because they're never right. I hope you enjoyed that one. I thought was a pretty good one actually for today. Here is how the lesson's going to look, no more jokes I promise. The new learning will introduce dividing using multiples and then you're going to have a go at a talk task in which you explain and demonstrate how you're using multiples to divide. And I'm going to introduce some Cuisenaire rods to visualise and demonstrate how we can use them to help identify multiples to help with division. And then it's over to you. We're going to give you a task to do in which you have to hunt for multiples, before you end the lesson by having a go at the Oak National Academy end of lesson quiz, where hopefully you'll find yourself confident and familiar with the content within the quiz. As always, to maximise your learning experience, it's important you've got the right equipment to allow you to do your jottings, to do your working out, and to complete the tasks. So you need to have something to write down with, a pencil is ideal. You can rub out if you need to although a rubber is optional, drawing a line through your work is perfectly acceptable and actually a really good way of showing that you've identified a mistake and you corrected it. Have a ruler to help with any presentation you might need, also some help for your basic multiplication and addition. It's a really good practical calculator, really. Then you'll need something to jot your ideas down. So paper, ideally grid paper, but if you haven't gotten any and you've got plain paper or lined paper or the back of a cereal box, that's absolutely fine but you may have a book that's been provided from your school. And of course, use that. If you happen to have nothing at the moment or you're lacking something, please pause the video, go and get exactly what you need and then come back when you're ready to resume the video and make a start on the main learning. See you in a few moments. Our first task during this lesson is to get ourselves warmed up by introducing speedy multiples. And you can time yourself if you like the extra challenge but don't worry if you don't like the pressure of time. You have four grids there. I'd like you to complete those grids as well as you can with as much information that you can. There's an example on the screen about how you can double numbers and double again, double again to help identify all of the multiples of the numbers. So you've got to find multiples of 15, 24, 32 and 45. Pause the video now, spend as long as you need and then resume the video when you want to share your answers. Okay. There are all the answers from the multiples that you need. Now if you haven't got all of them, there's gaps, pause the video now and fill those tables 'cause you're going to need these for other parts of the lesson later on. So it's important that you have those grids with you, they're going to help with the activity later in the lesson. So fill out the information, make sure it's correct so if you have made any misconceptions or put the wrong multiples in, that's perfectly fine. Okay, you can see where you've gone wrong but make sure you got correct grids to allow you to complete the independent task later in the lesson. And we're going to make a start on our learning by using multiples to divide. Read the question on the screen. Eight athletes in each race and 112 athletes compete in total. How many races were there? So I'm going to demonstrate it using an area model. Now abstractly, that is our calculation. 112 divided by 8. I'm going to introduce the idea of partitioning by using rods during the lesson but thought I can demonstrate it as a bit of an inverted area model. So, 8 goes into 112 how many times? Now I'm going to break 112 into partitions, so to say. Not break, I'm going to partition 112 into 80 and 32. Now I'm doing this, and I'm going to demonstrate on my area model here because 18 and 32 are both factors of 8. I know my eight times table, and I know that 8 goes into 80 ten times and I know that 8 lots of 4 makes 32. So because 8 is a factor of both 32 and 80, it allows me to partition 112 into two parts. You see, 8 goes into 80 ten times, 8 goes into 32 four times, 80 and 32 also make 112 as we've demonstrated, but it also means that 10 and 4 together makes 14 which gives us our answer of 14. 14 lots of 8 makes 112, 112 divided by 8 equals 14. But I have also used this information to say that 112 divided by 14 equals to 8. I might present it in other representations. So you can see I've used an empty number line to demonstrate the steps taken in that calculation. I've used distributive law to represent how the partition took place. So I broke 112 into 80, and divided by 8 to get 10 and 32 divided by 8 to give 4, and then I added those two together to make 14. Of course you may also recognise it as being an inverse operation. So not only does 8 go into 112, 14 times. We can say that 14 lots of 8 or 8 lots of 14 makes 112. So I can go either way using my area model and using my abstract number sentence I can demonstrate distributive law. So 10 lots of 8 and 4 lots of 8, makes 80 and 32, together makes 112. And you can see, although written differently, it's a perfect demonstration of the inverse operations of multiplication and division. Right, I'm just going to quickly show you how to use partitioning and the area model to break this calculation into even quicker chunks to speed through mentally. So I would look at that and I think, well, I know 60, 10 lots of 6 is 60. So I know that I can put that into 60, take 60 away from there. I'm going to have 1,200, aren't I? 1,200. So I then, 1,200. So I'm going to use an area model. I'm just going to quickly sketch that. So I've broken that into... And there. So now I can find, if I put 6 there. So 6 goes into 1,200, how many times? And 6 goes in 60, how many times? So with my area model now, I can break it into two parts and I've done that by partitioning with my derived facts. I can now demonstrate the calculation in multiple ways. We can now see different representations of this problem. We know that 6 goes into 12 twice, so therefore 6 must go into 1,200, 200 times because it is 100 times greater than 12. Likewise, we know that 6 was going to 60 ten times because 6 goes into 6 once and 60 is 10 times greater than 6, therefore 6 into 60 must be 10 times. When we add those together, you get an answer of 210. Again, I can demonstrate using an empty number line, starting on zero, the steps I took. So I did 6 lots of 200 to make 1,200, again because I know 6 lots of 2 makes 12, and it's 100 times greater. And then from 1,200, I did 6 lots of 10, so 60, to get to the answer of 1,260. So collectively I did 210, so 210 steps. So therefore we can say there are 210 apartments as an answer to our question. And if I was to set it out using distributive law in number sentences, you will see that I broke it into 1,200 and I broke it into 60. And there we have the different stages when I write it abstractly. So now I'm going to pass it over to you to do a little bit of independent work, a talk task. We usually do this in school in small pairs, or groups, or even a whole class, and we discuss our work and we talk about and demonstrate as we're going through the task. If you're on your own, not to worry, you can still do this task on your own. Complete the task, complete the work needed, reflect on the information that's there. So here's your task. You're going to use multiples to divide. I'd like to represent each problem with an area model and then partition and calculate each part. Record the steps of the strategy on an empty number line. There are three problems in total. So an area model, you need to partition, calculate and record your steps on an empty number line. Pause the video now. So as long as you need on the task, read the questions very carefully. And then when you're ready to share your answers and resume the lesson, press play. Speak to you all in a few moments. Welcome back. We'll do, very quickly, show our answers. There's one example on the board, the first one. You can see I represented 252 divided by 6. So I partitioned it into 240 because I know 6 lots of 4 makes 24, so it's 10 times greater. And I partitioned it into 240 and 12. So 6, 240 divided by 6 plus 12 divided by 6, which gave me a total of 42. And I did that on my number line. I showed that there were 40 steps or 6 lots of 40 or 40 lots of six. And there was 2 lots of 6. So in total there was 42 lots of 6 went into 252. So there was 42 races. Number two, there were a total of 18 races. I partitioned 162 into 90 and 72. And for number three, I partitioned 1,920 into 1,800 and 120. I did that because of my derived facts of six. I know that 6 goes into 18 three times. Therefore 60 must be a multiple of 1,800, that made it easy for me so that I could do 30 lots of 60 makes 1,800. And I could do 60 into 120 went twice. Collectively, the answer was 32 floors. Okay, we're going to continue developing our learning now by introducing some strategies for hunting our multiples. Very important you focus on these strategies because you're going to have to replicate these and demonstrate these during an independent task. We know multiplication is the inverse of division, but how can we work out different multiples? Is there more than one strategy we could use? Now, for the first part of this demonstration, I'm using what we call Cuiseniere rods. You may have seen these in the classroom and we can set these out for different values on a progressive scale. And here we're going to use them to find out and help us identify the missing multiples of 24. So, as you can see, I've got some of my multiples in but I'm missing some. I can use these Cuisenaire rods to really help me find things out. So I know, for instance, that 3 lots of 24 must be equal to 1 lot of 24 plus 2 lots of 24, put those together, you will see. And if 1 lot of 24 and 2 lots of 24 is 48, 48 plus 24 equals 72. So I know that 3 lots of 24 is 72, because 2 lots of 24 is 48, plus one lot is 24. I then know that I can work out that 3, or, 6 lots of 24 is double 3 lots of 24, because when I take 3 lots of 24, you'll see if I put it on top. You'll see it's exactly half of my multiple. So what I'm saying is if I have 6, 3 lots of 24, I double that, 2 lots of 72 is 144. Okay. Or, I could say that 144 divided by 2 is 72, because 3 is half of 6. Let's look at five. I don't know 5 lots of 24. However, I do know 10 lots of 24 is 240. Now, if I, half of 24, 24 divided by two is 12. Therefore 240 divided by two must be 120. And just to demonstrate it, I've got my 5 lots of 24 here, each block represents 24. Two of those would add up to 240. So I know five lots of 24 is 120. I can find out what 7 lots of 24 is because I know what 5 lots of 24 is and what 2 lots of 24 is. So again, I'm just going to demonstrate, if I have five lots and two lots, I have seven lots in total. This should be the same length. It is. So 5 lots of 24 is 120 and 2 lots of 24 is 48. 120 plus 148 is 168. So therefore 168 divided by 7 equals 24, 168 divided by 24 equals 7. I can also find out what 9 lots of 24 is because I know what 8 lots of 24 is. And I could add that to 1 lot of 24, or I know what 3 lots are, and I can multiply that by 3, because 3 lots of 3 make 9. But this way I got 192, I'm going to add it to 1 lot of 24 which is 24, 24 added to 192, well 4 and 2 make 6 and 19 tens and 2 tens make 21 tens. 216. So I can say, I found out that 216 divided by 9 equals 24 or 216 divided by 24 equals to 9. So I'm using my multiple knowledge and I've used some halving and doubling to help me identify those missing multiples, but I can use my multiples to identify the factors by dividing or I can use my factors to help me identify the total. So 24 and 9 are both factors of 216, for instance, 24 and 10 of both factors of 240, but of course, half of 10 is 5. So therefore 5 is also a factor of 240, 120 is also a factor 240. All of these are interrelated using our inverse knowledge. I can also use my inverse of operations to identify division by using derived facts that I know. I know 96 is divisible by 24 because 4 lots of 24 makes 96. I know 160 is a multiple of 32 because 32 lots of 5 is 160. I know 45 is a factor of 360 because 45 times 8 equals 360. Likewise, I know that 360 divided by 8 will give me the answer of 45. I know 210 is divisible by 35 because 210 divided by 70 equals 3. Likewise, 3 lots of 7 makes 21. So 3 multiplied by 70 equals 210. I'm going to give two problems now to have a go at. I want you to pause the video and try and spend a minute or two either discussing with a partner or on your own, trying to work out whether it's true or not using the factors and multiples that we know. Now, I want you to introduce the multiple grids that we had to go at at the start of the lesson. This one is on the multiples of 50. Using the grid, can you work out whether it is true or false? This statement. 675 is divisible by 15. Is that a true or false statement? And can you use your multiplication grid on the screen to help you identify whether that statement is true or false? Pause the video, have a little think about that. Right, let's share what you've come up with. Hopefully you have identified 10 lots of 40, or rather, 10 lots of 15 is 150. And 4 lots of 150 is 600. So 40 times 15 must be 600 and that would leave 75. And if you know that 10 lots of 15 is 150, therefore half of that, 5 lots of 15 is 75. So with the steps of 40 lots of 15 and 5 lots of 15, you would get to 675. So we can say this statement is true. 675 is divisible by 15. Let's try a second true or false statement. Thirteen hundred, or one thousand three hundred, is a multiple of 24. That statement, true or false? Pause the video, use the grid on your screen. Spend a couple of minutes trying to identify whether that is a true or false statement and having some mathematical reasoning to support your answer. Okay. Let's see how you got on and what you identified. Did you think it was true or false? Well, now using our derived facts, we know that 5 lots of 24 is 120, therefore 50 lots of 24 would be 1,200 and that would leave a hundred left. We also know that 4 lots of 24 is 96, which is not exactly equal to a hundred. So therefore 50 lots of 24 and 4 lots of 24 will get us the answer of 1,296, with 4 left. Therefore we can be confident that this statement is false. 1,300 is not a multiple of 24. So after all those examples and strategies used together now over to you to see if you can put that into practise by completing the independent task. The task is called "Hunt for multiples". You can see nine numbers on your screen. Your task is to try and sort those numbers and identify which of those numbers are multiples of 15, 24, 32 or 45. Now you may use the multiple grids from earlier in the lesson to help with this task. You need to also generate some statements to support your mathematical reasoning, to help you identify which numbers belong to which multiples. I've given you some sentence stems. And I want you to use the language of "divisible", "factor" and "multiple" which has been the vocabulary that we've used regularly during today's lesson, for instance, an example, 900 is divisible by 15 because 90 is divisible by 15. You could say 900 is a multiple of 15 because 90 is a multiple of 15. Here are your grids to help. Pause the video, spend as long as you need on this task, and when you're ready to resume and share your answers and end the lesson, please press play. Enjoy the task. I'll speak to you all very, very soon. I'm going to go through very briefly. Here are some of the answers, you can see on your screen, just check that you have the right ones and you identified the correct numbers associated with the correct multiples. For those that are not quite ready to finish today's lesson I've got a challenge slide for you to have a go at. Look at the example statements generated using the facts found within the tables. What other numbers can you generate statements about? You see there under the four grid? There is an example statement that you can make. What are the statements can you generate using the information that exists within those tables? Pause the video and take as long as you need on the challenge slide. And if you're working in pairs or groups, this is a fantastic opportunity to get into further dialogue about your mathematical reasoning. So almost at the end of the lesson, just time now for you to have a go at the customary end of lesson quiz here at Oak National Academy, I want you to remember the key about inverse. Inverse has been at the heart of a lot of our lessons within the unit of multiplication and division. And if you can go fluently between multiples and factors, between multiplication and division, you will become far more efficient with your calculations. Good luck with the quiz, read the questions very carefully, and then when you finish, come back and finish the final few slides as we share the final messages at the end of today's lesson. Good luck, everybody. Just a reminder. We would love to see the work that you're producing across the country here at Oak National Academy. So if you would like to share your work or your mathematical jokes with us, please ask your parent or carer to share your work on Twitter, tag it @OakNational and #LearnwithOak. Well everybody, time has beaten us once again. And that brings us to the end of today's lesson. I hope you enjoyed the learning experience and you found it very useful, especially the models of area models, and the use of Cuisenaire rods to show how you can demonstrate your knowledge of multiples to help with your division. Now inverse was the focal point of today's lesson, and I hope that you are confident moving forward, using your knowledge of multiples and factors, when multiplying and dividing. Thank you for your hard work. You deserve a pat on the back. Very proud of the effort that you are continuing to put into our Oak National Academy lessons. I look forward to seeing you all very, very soon as we continue our unit on multiplication and division, but for me, Mr Ward, it's bye for now and I hope to see you very soon. Have a great day guys.

Worksheet: Using multiples to divide

Exit Quiz: Using multiples to divide

Completed: Using multiples to divide

Today we will explore dividing numbers by partitioning into multiples and dividing the parts. We will start with calculations that involve dividing by a single digit making links to the multiplication calculations in the last lesson. We will then find multiples of 2-digit numbers and use these to divide by partitioning into multiples in order to divide each part.

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Using multiples to divide

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