Intro Quiz: Investigating multiplication patterns

Video: Investigating multiplication patterns

﻿Hello everyone. My name is Mr. Ward. Thank you for joining me today here on Oak National Academy. If you're new to Oak National Academy, you're very much welcome. Great to see you. And if you are returning once again, it's lovely that you can join me today. We're going to continue our unit on securing multiplication facts, by further investigations of multiplication patterns during today's session. Wherever you are in the country, I hope you're well, and I hope you're just as eager as I am to get on with our mathematical learning. Before we start, let's just make sure that we're in the right frame of mind and in the right environment to get the most out of our learning. So let me ask you now, can you be free of distraction, if possible, find a quiet space to work, and make sure you've got everything you need for the next half an hour or so as we go through the content of today's lesson. If you've got everything you're ready to start. Excellent. So am I, let's make a start and shall we see you in a few moments. Before we make a start on our main mathematical learning, I love to start every lesson with a joke, to put a smile on your face and get you enthusiastic about the lesson ahead. This one's an absolute cracker. I have been tickled pink by this, and whether you agree or not fingers crossed, I think you do, I think you will find it funny. I know I have. I'm chuckling to myself even now. Here we go. Did you hear about the maths teacher who was terrified of negative numbers? He would stop at nothing to avoid them. Put your hands up if you liked that joke. Well, I hope you enjoyed it anyway. I liked it. It's got me chuckling to myself. If it isn't for you. That's okay. We'll focus on the main learning from now on. You can see we're going to introduce adaptive multiplication grids, and then we'll go talk task, so that you have an opportunity to reflect on some mixed up multiplication grids, and then we'll develop our learning a bit further by looking at some mystery grids, using some of the artefacts that we already know. And then I'm going to hand the responsibility to you and ask you to have a go at an independent task in which you know it's by some patterns, before having a go with the customary end of Oak National Academy Lesson Quiz, in which you have a chance to try and embed some of that learning from today's lesson. A little ways to maximise our learning from the session. It's important we've got the right equipment if possible, so if you could get yourself a pencil or pen or something to jot down your ideas, a ruler will be useful. Some paper, good papers like the knurling mass, but if you've got plain paper, lined paper, just some cardboard, even white board or chalk board, that would be absolutely fine. Anything you can put your jottings and drawings down on. You also see I've got the hundred square there. If you've got one to hand, fantastic. If you would like to use one, you can print one off that's part of our worksheets slides, or you can draw your own or just have the hundred square on your screen. Does it matter if you've got, or does it matter if any of this equipment is missing? However, if you know, you've got it, please pause the video, go and get exactly what you need and then resume the video when you're ready to begin the lesson. Our first activity this morning is a warmup to get operating, firing on all cylinders ahead of the main learning. The activities, missing values. Can you complete the calculations below filling in the missing values to make those number sentences correct? They're both multiplication and division facts because of course using inverse is a really good strategy to allow us to find missing values. Pause the video if you need a little bit longer, and when you're ready to resume and check your answers, press play. Right quickly. Friends, your answers with the answers on the page. If you have gone wrong anywhere, just double check, why you may have gone wrong? Have you put in the wrong value? Did you misread the question or do you just have a little bit of a weakness in that timetables? You need a bit more practise on it. Absolutely fine. Whatever you may do. I hope you did okay. And I hope that's got you in the mood for some multiplication work today. We're going to start the lesson by looking at multiplication grids. We'll ask you to be a little bit flexible today. If you haven't looked at multiplication grids from a different perspective before, because we've got to be introduced to some of our known facts into different forms, representations over the course of this unit. First of all, I like to look at the grid on your screen. What do you notice about this grid? Which multiplication table made this grid? If I put multiplications of the grid onto a more familiar ten by ten grid or a hundred square the one we were shown. Does it become more obvious what multiplication table this represents? Of course, it shows us the multiplications of three, and on our ten by ten grid, we can see the intervals of three, six, nine, 12. Now the adapt to multiplication grid came in six columns. And so it looks a little bit different. And therefore, when we shaded it, it does look different. It's a way of adapting a multiplication grid. It still shows as we can still use it to identify the intervals between multiples and identify different multiples. But it's just been represented in a slightly different way. What do you notice about this grid? Which multiplication table made this grid? Hmm. Hopefully you've identified that these are the two times tables. Multiplication for twos. Now this was, I think, a bit more straightforward because the intervals between numbers was one blank square between two shaded squares. So therefore it's going in blocks of two, could be no mistake or a misunderstanding because there's only one possible multiplication table with eight interval of one between two multiples. As you can see on my traditional ten by ten, this is what I would normally look like multiples of two. And that obviously here, we've got five by five. So it's a square five rows, five columns. It's a nice check design, actually. I'd like to see that in my Roman Villa, if I was having my tiles done, very nice colours as well. How about this multiplication grid? Again, this has been adapted. What do you notice about the grid? Which multiplication table made this grid? Hopefully you recognise it as being the seven times table. We can know this because the intervals, again, there were six by squares before the seventh was shaded. One, two, three, four, five, six, and the seventh was shading. On our adapted grid, the pattern is diagonal. And although it is diagonal here, it's not quite as it's sort of steeper. And there are gaps between the shaded rows. Could this have been anything else? Well, no, it couldn't have been anything else. When there was definitely six blank squares between the different multiple, you have to be the seven times table as this was a complete grid. What do you notice about this grid? And which multiplication table made this grid? Think about strategies we just use to identify the correct multiplication grid. Hopefully you identified it as being in the five times table, because there were four blank squares between each multiple. This is our traditional ten by ten, where we would have five, 15, 25, 35, 45, and so on and so forth. And because five is half of ten, ten, 20, 30, 45 is overall the tens are also multiples of five and tens. Now that we've looked at multiplication grids being adapted and looking slightly different to what we've used before, but the maths still being the same and the number facts still being the same. The talk task for you. This task is called Mixed up grids. Now, if you haven't been working on your own, that's absolutely fine. You can still talk about the maths by jotting down some ideas and completing the task. But if we are all lucky enough to have somebody nearby that you can talk to and share ideas, please do, because this is a really good opportunity to talk about the maths you see, to explain your reasoning and use some of the key vocabulary that we have been using in today's lesson and the unit as a whole so far. So please look carefully at the grids shown, identifying the scuffs, which multiplication grids they represent. Can you create your own examples? Remember the two key questions we did look at together. What multiplication table does each good show? Why does it look different? Pause the video spend as long as you need on this task and then resume the video when you want feedback with your answer. I've included some blank grids that you may print off and use, or you can replicate and jot these down and draw these into your sheets of paper or your book. Enjoy the task and zoom the video when you're ready to continue, speak to you very soon. Okay. Well, come back briefly. Here are the answers and the patterns. First was part of the three times table. We know that because there was two blank squares. So there was an interval of two squares then the multiple. The yellow was the four timetables, there were three blank squares. Then the multiple, three blank squares, then the multiple. The two times table, as we already identified is a lovely check colour. The six times table for the orange, because it was a grid that had six columns. Therefore there was five blank squares, and number six was the multiple. Here's an example that I created as additional task that you could create your own grids for either a partner, which is to demonstrate that you could adapt more production goods. Here's my example on the boards. Just take a moment to look at my example, and also my well handsome face underneath the grid. What multiplication grid do you think this is part of? It is called the seven timetables. And you could identify that because there were seven, those six columns, rather sixth columns, which means the seventh square would start on the new row. And there were six blank squares before the multiple. So an interval of six blank squares and then the multiple. So therefore it became part of the seven timetables. If that represents seven, and this must represent 14, this would represent 21, and this would represent 28, and this will be 35. Well done if you got that right, but I'd like to take our learning a bit further, we're flying through today's lesson, but it's all about investigating and spotting patterns, but also being flexible without understanding your multiplication grid. Let's explore our knowledge of times tables. This time I want you to imagine that these grids have been taken from within a grid. They're not necessarily the end of a grid or complete grid. They are part of a grid. What timetables might it be from? On what size grid could it be from? Remember, it's not a complete grid. This is part of the grid. This means it could be more than one answer, but not necessarily. Take a moment to think and answer those questions. But we could say that it could be a grid with six columns. Showing the seven times table, the six columns, meaning there are six blank squares, then the multiple, because we know multiples of seven have intervals of six blank squares. The language I'm using could be replicated where you have a go at the independent task. So remember some of the key vocabulary such as columns, intervals, multiples, grid, timetables. We could also say an example could be a grid with seven columns showing the eight times table. Now we know this because multiples of eight have intervals of seven blank squares. So by counting those seven columns, the eighth square along must be the multiple. So that's two possible answers that that part of the grid could have belonged to. However, we can also use the process of elimination when using our timetable knowledge. So we know we can't represent the one, two, three, four, five or six times table because all of those times tables will require at least six blank squares between multiples. So one, for instance, multiples was one. It will be no blank squares. Two and also multiples of two would require one blank square between the two so forth, so on. So by process of elimination, I can eliminate all the possible multiplication grids. I try that again and using some of our written vocabulary to help with our explanations. Let me ask you, take a moment, look at the part grid again. What times table might it be? What size grid could it be from? Think about on knowledge of intervals again, is there more than one answer? And can you explain your answer and give your reasoning? Let's begin the other way this time and eliminate some possibilities. Looking at the part of the grid. We can look at the intervals. And this allows us to say with confidence, the following statement, I know it can't represent the five, six, seven, eight, nine or ten times tables because they require at least four blank squares between multiples. And as we can see, there are only three blank squares between the multiples. Therefore it must be a grid with four times tables, because we know multiples of four have intervals of exactly three blank squares. And when I show the ten by ten grid shaded with multiples of four, we can see that there are intervals of four that exist. Now that we used some great explanation of reasoning. I'm going to ask you to demonstrate the same task on your own today. I'd like to identify multiplication patterns. Here's some parts of various grids. This time you cannot see the edges. Can you identify what tables on what grids could have been used? There might be more than one answer or there might not be, so there's no single answer or no answer that can be given without mathematical reason. So look at the four parts, Which multiplication tables are these grids taken from. Pause the video now. Spend as long as you need, either print off some blank grids or create your own with your jottings to help, take as long as you need, and then we'll briefly share our ideas and answers afterwards. Speak to you in a few minutes. Welcome back. And we'll briefly share. I wonder if you found the same things that I did. So the first part grid could have been taken from the eight, nine or ten times table. The second grid could have been taken from the four or the five timetable that's because of the minimum number of intervals that existed. So if we imagine that it was taken as part, half way through a grid, there are a minimum of three intervals here. And we could imagine there may be a few other columns or rows here. So there could be four or five. The green tiles have to be only one answer because there was clearly a marked three intervals or three blank squares between multiples only to the before. And the same with this blue square here, there was clearly only two blank squares, therefore intervals of two, then the multiple. So the bottom two only had one answer and the top two had multiple answers. Tricky activity, and I hope you were able to identify some of them, if not all of them by using your multiplication grid and imagining what would happen if we changed those grids or move them around. But the key here, regardless of getting the right answers, but it was looking at more applications from a different perspective and focusing very heavily on the intervals and how they can allow us to predict future multiples or identify existing multiples within our hundred squares and beyond. I know there's some of you at home who are on an absolute roll and not quite ready to put where your equipment just yet. So fear not, I have an additional challenge, slide for you to have a go at. So you continue your mathematics learning today. How many different ways can you complete the equations shown below? Feel free to use your inverse, and also your other multiplication division facts, to generate different number sentences, to get to the same answers. Pause the video and spend as long as you need on this challenge slide. And I hope you enjoy the task. It's almost time for us to say goodbye, but not quite because it is time for the quiz, which is a custom here at Oak National Academy. The key reflection I wanted to take away was knowing the intervals between multiples helps us to be more efficient with our timetables. They also allow us to predict future multiples or identify sequences. Hopefully you feel confident and you enjoy looking at multiplication tables from a different perspective and how they were adapted. But now time to see how much of that information has been embedded. So please go find the quiz, take your time. And when you've completed the quiz, please come back. For the final few messages on today's lesson. We'd love to see some of the work, or mathematical jokes being used and produced all across the country. So if you'd like to share your work or your mathematical jokes with us here at Oak National Academy. Please ask your parent or carer to share your work and jokes on Twitter, tagging Oak National and hashtag learn with Oak. I'm looking forward to seeing some of the fabulous works, be produced by you all across the country. Right everybody as much fun as we're having, that is the end of today's lesson. Thank you for your hard work. It is now time for a break. Thank you for those that laughed at my joke early today. I know this guy here did, and I hope that you also enjoyed looking at multiplication tables from a different perspective, because I really enjoyed investigating what we already know, but looking at it from a different light. Now I hope to see some of you again, here on Oak National Academy as we continue our mathematical journey, but for now from me, Mr. Ward, have a great rest of the day. Hopefully I'll speak to you soon. Bye for now.

Worksheet: Investigating multiplication patterns

Exit Quiz: Investigating multiplication patterns

Completed: Investigating multiplication patterns

Today we will continue to look at different sized grids which are shaded with different multiplication tables. We can then investigate different pieces of multiplication grids, considering what grid it could be a part of, and what multiplication table it could show.

Maths

Investigating multiplication patterns

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