To recognise the inverse relationship between multiplication and division

Key Stage 1

Maths

Multiplication and division: 3 and 4

Which of the equations below does this array show?

Which array below matches this equation: 5 x 2 = 10 ?

Which of these sets of equations is incorrect?

﻿Hello, everyone, I'm Mrs. Crane. And welcome to today's session. Today, we're going to be looking at part of a unit called multiplication and division. And our objective today is going to be to recognise the inverse relationship between multiplication and division. For this lesson, you will need a pencil and some paper, please pause the video now to go and get these things, if you haven't got them already. Okay then. Thought I'd start off today with a little hello, and a bit of a fact question. Why do dogs curl up to go to sleep? And for those of you that know and have watched any of my lessons before you will know that this dog here is my dog, he's called Arlo, And he loves to curl up, particularly on comfy chairs that really aren't for him. So, why do dogs curl up to go to sleep? It's actually an age old instinct that they have that allows them to keep themselves warm and to protect all of their vital organs whilst they're asleep. So it makes them more protected basically. Let's have a look then at today's lesson. So our agenda for today, we're going to be learning how to recognise the inverse relationship between multiplication and division. So we'll start off with a quiz to test your knowledge. Then we'll have a look at today's star words. Then we're going to look at how we can use arrays and part-whole models to solve division and multiplication equations. Then it will be time for you to do your talk task. Then we're going to develop our understanding of how we use the inverse to answer missing number equations. And finally, there'll be a quiz to see what you've remembered from today. Please pause the video to complete your starter quiz. Okay then, let's get started. We'll start with our star words today and we'll do them using my turn, your turn. So, inverse. Multiplication. Division Product. Whole. Part. Groups. Okay, let's have a look then at today's new learning. So we've got an equation here. It says four multiplied by something is equal to 24. How can we find the missing number? So I've got some questions here that are going to help us. What do we know that will help us find this missing number? Can we use the word product and part to help us explain? Going give you five seconds thinking time to think about how we could find out this missing number, not what the missing number is, I don't want to know that at the moment. I just want us to have a think about how we go about finding it out, how do we answer this question? Okay, let's think then, we've got the word product here and the word part here. Now I know the product is the result of two numbers or more being multiplied together. So I know my product here is the number 24. And I know that one of those parts that's being multiplied together is four. I don't know that missing number. Here the word from our star words, inverse, comes in really, really handy. We're going to use the inverse to help us today to work out what this missing number is. So let's see how we're going to use that. We're going to use it by looking at a part-whole model firstly. So, we know the whole is 24 and we know that the parts, there's four of them. One, two, three, four. At the moment, we don't know how many is in each part. So we've divided 24 into one, two, three, four. To do that effectively, we actually have to split 24. So we might use counters in a moment, into these boxes to work out what this missing number is. So, here we go, here we have our counters here. We know we're going to 24 and we're going to divide it into four, because we know 24 is our whole and four are one of our parts, we just don't know the other part yet. So we've got 24 in our whole. We've got one, two, three, four parts, and we've got 24 counters here counted out. Now I'm going to split these counters into these boxes, and I'm going to count up until I get to 24. Then I'm going to see how many is in each box to be able to answer my equation. So you can count with me. So I've got one, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 20, 21, 22, 23, 24, and I have to stop there. If I keep going, I've gone past my 24, I just have 24 counters, so I've split them into my four boxes. Now, in order to work out this answer I need to know how many counters are in each box. So let's take one box and let's count them. One, two, three, four, five, six. Now, because I split them equally, I know that I haven't put extra counters in any of the other boxes. So I know in each box there is six counters. So my answer is going to be six. So 24 divided by four is equal to six. Now I have to go back to that original equation, otherwise I haven't actually answered it. I've used the inverse to help me, but I must put that number back in that missing number box. So I know that four times by six is going to equal 24. Because I have four, one, two, three, four boxes. And in each box I have six equally split, which it gives me 24 as my whole. Have a look there, and what's the same and what's different between this picture here of an array and this part-whole model here? I would like you to have a look and pause the video now. Give yourself five seconds thinking time at what you think is the same and what's different, and then we'll discuss it. Okay. Let's have a look at the array firstly. So here's our array. We've got one, two, three, four, and we've got four, one, two, three, four, five, six times. So our array shows four multiplied by six is equal to 24, or it shows 24 being split into groups of four, six times. So 24 divided by four is equal to six. Again, similarly, it shows it again here, but it's showing it with 24 in writing as numbers, rather than as our counters. And it's shown to be actually physically split into those four groups with each of them showing six. You might have a preference for which way you prefer to show it. You can show it in either way, or you can show it in both ways. Okay, we're going to look at another equation then. How can we find the missing number here? Three multiplied by something is equal to 21. Going to give you three seconds thinking time. How will we find the missing number? Okay. Well done to those of you who thought and thought that word from our star words today was the word inverse. So we're going to do 21 because we know that is our product, it's our whole. And we know we have three as one of the parts of that. We just don't know at the moment, what that other part is. We've got our part-whole model here. We've got 21 in our whole and we've got three parts. I've then got myself 21 counters here that I need to split into these three boxes equally. Really important that I do it equally. If I put all of them into one box, not going to help me, because I haven't grouped them into three groups. So we've got our division equation here at inverse. We know that 21 is our product, which is our whole, we've got 21 and we're going to divide it into groups, into three groups 'cause we've got one of our parts we know is three. We'll work out what that answer is going to be, and it's going to give us our answer here. So, let's take our counters and let's put them into our part-whole model. You're going to count with me again, okay? One, two, three, four, five, six, seven, eight, nine, 10, 11, 12. 13, 14, 15, 16, 17, 18, 19, 20, 21. Again, I've got to stop, I've used 21 counters up. I've shared them equally because I've worked systematically through each part here. Now to work out what this missing number is here, and what the answer is here, I need to count how many counters are in each box. So let's count together. One, two, three, four, five, six, seven. Do I need to count every box? No I don't because I've shared them equally. So I know my answer is going to be 21 divided by three is equal to seven. Now, again, I cannot forget here, I must put my seven in here, so I can show three times by seven, so here I've got three groups, one, two, three, and seven in each, is equal to 21. Again, I want you to consider what you think is the same and what is different between this array and this part-whole model. You've got three seconds thinking time. Okay, so we've already looked at our part-whole model. We know we've got our whole and we've got our groups of three, and in each group we've got seven. Here, we've also got our groups of three and we've got one, two, three, four, five, six, seven of them. So, it represents the same thing, it's just done differently. So differently, we don't have any numbers written here, we'd have to split count in our threes until we get to 21 to work out our answer. Here, we have already got 21 written down and we've got it already split into our three groups and then we've worked out that there's seven in each group. Okay, it's now time for today's talk. Today, for your talk task, I would like you to draw an array to represent the following problem. I'll read the problems out to you, and then I'll read the say it out loud. I multiplied a number by three, and my answer was 12, what was my number? Part two, I divided a number by four and my answer was three, what was my number? I'd like you to have a go at using this today? I will make an array of, with, in each part. The whole is. Pause the video now to have a go at today's talk task. Okay, welcome back, everyone. We're going to have a look at an example from the talk task together. So we've taken, I've taken the first example, which is I multiplied a number by three and my answer was 12, what was my number? So I'm going to have a go at drawing an array to represent the following problem. Now, before I draw my array, I need to know what the problem is actually asking. So I've put a square here because this is the number that I've multiplied by three and my answer was 12, so my product is 12. I don't know what this number was, so I need to work out how I'm going to work it out. So I know that I've got my whole, which is my product. And I've got one of my parts, which is three. So using my inverse, I'm going to do 12 divided by three is equal to, to be able to work that out. So, now here, I'm going to do my array. So I'm going to do an array in threes, and I'm going to keep going until I get to? 12, well done. One, two, three, four, five, six, seven, eight, nine, 10, 11, 12. Stop, I've got to 12. How many groups did I have of three then, I had one, two, three, four, so my answer would be four. So I have four here and my groups are in threes. So here I can go back to my original question, and I know that my number was four. Right then, we're going to use these today to help us with our develop learning. So my question, I multiplied a number by four and my answer was 32, what was my number? So firstly, I put in here a box, 'cause I know that there's a number here, but I don't know that number at the moment. But I do know that that number was times by four and that the answer, the product was 32. So I'm going to use the inverse to help me work it out. So I'm going to take my 32, 'cause I know it's my whole. And I know one of my parts is four, so I'm going to divide it by four. And I'm going to work out what that missing number was by working it out. So, here's my array. I'm going to draw out four and keep counting until I get to 32. So I do four, eight, 12, 16, 20, 24, 28, 32. I've counted out 32, now I need to see how many times I drew four in my array to get to 32. So I drew it one, two, three, four, five, six, seven, eight times. So my missing number has got to be eight. There's another way I can show it though, 'cause I can show my whole here is 32, so I know that's for my product here. And I know it's been split. I need to split it into four groups to work out how many is in each one. So I can split them into groups, into four groups. Again, I have one, two, three, four five, six, seven, eight, and I have that in each group. So I know 32 divided by four is equal to eight. So I can put that in here. And I know that that fills out my missing number here. Let's have a look at another example, this time I divided a number by three and my answer was six, what was my number? So I have a number here. It's being divided by three and it's equal to six. So six is my product, but my product's already been split into groups of three. So, here I'm going to do three times by six to work out that answer. Again, I'm using the inverse. I'm going to do three times by six to get to, Sorry, to get me to that answer. So, here's my array. Here are my groups of three and I've done them one, two, three, four, five, six times. So in order to work out our answer, I can either count them all individually or I could count in my threes, six times. So together with me, I'm going to start counting out three, three, six, nine, 12, 15, 18, so my answer would be 18 here. We can also show it in my part-whole model. Now this time, I know I've got one, two, three groups. And I know I've got one, two, three, four, five, six, in each of them, I don't know my whole, I don't know my product here. So I have to do three times by six. So this time I can count in my sixes three times, so I could say, six, 12, 18. So I know that my whole would be 18. My product would be 18. So I know here, the whole was 18 and it had been split into groups of three to give me six, or here, I have three times by six to give me 18. Okay then, I think it's time for our independent task today. Using arrays or part-whole models, answer the following questions. So you've got three questions here. Read them really carefully. I've also given you some of the example, the equations from those questions for you to use using the inverse. You've then got three more questions here. Again, I've given you the equations from the question using the inverse. Please pause the video now to complete your task. Okay, welcome back. Let's have a look then, we're going to go through the answers together. So I multiplied a number by three and my answer was 18, what was my number? So, three times by something is equal to 18. So I could do 18 divided by three is equal to something, to give me my answer. I know three times by six is equal to 18 because I can work it out from doing 18 divided by three is equal to six. Next then, I multiplied a number by three, and my answer was 21, what was my number? So I had three, I multiplied a number by it, and my answer was 21. So I'm going to do 21 divided by three is equal to something. So using an array or a part-whole model, I could work out that my number would be seven. So three times seven is equal to 21, or 21 divided by three is equal to seven. I multiplied a number by three and my answer was 24, what was my number? So three multiplied by something is equal to 24. So I'm going to do 24 divided by three, to get me my answer, and I know that if I divide it by three, I get it eight times. Next then, these questions are slightly different because my number's been divided each time. Let's start at the top, I divided a number by four and my answer was seven. What was my number? So something divided by four is equal to seven. So here I'm going to do seven and I'm going to times it by four to get my answer. Again, I'm using the inverse 'cause multiplication and divide are inverse operations. So seven times by four is going to give me 28. So my answer would be 28 divided by four is equal to seven. Then I divided a number by four and my answer was six. What was my number? So something has been divided by four and it's answer was six. So I'm going to do six multiplied by four, so I've got one of my parts and the other part here to work out my whole. So I'm going to do six times by four, which gives me 24. So I know my whole here has to be 24 divide by four is equal to six. And last question is, I divided a number by four and my answer was five, what was my number? So something divided by four is equal to five. So here I've got my two parts. I'm going to do five times by four to give me 20, so I know 20 divided by four is equal to five. Well done for working really, really hard today, everybody, I've been really impressed. Please pause the video now to have a go at the final quiz and answer the last few questions. Thank you, and hopefully see you again soon. Bye bye.

To recognise the inverse relationship between multiplication and division

To recognise the inverse relationship between multiplication and division

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UnitMaths / Multiplication and division: 3 and 4

Maths