Solving correspondence problems

Key Stage 2

Maths

Multiplication and division

What is the inverse calculation for 12 ÷ 2 = 6

What calculation could this bar-model show?

27 glue-sticks were shared equally between 3 classes. How many glue-sticks did each class get?

﻿Hello there, I'm Miss Brinkworth. I'm going to be going through this math lesson with you today. Let's look at the learning objectives together before we get started. So today's lesson is going to be structured a bit differently to ones that you might've done in the past, either in your classroom or on Oak National. So what we're going to be doing today is we're going to be solving correspondence problems. So we're going to be working systematically, and we're going to be making sure that we've looked for every single possibility. So let's go through what our agenda looks like. So this is related to our three and four times tables. And so we're just going to have a recap of that three and four times table knowledge. We are then going to consider what correspondence problems are all about. So we're going to have a practise together or I'm going to show you how I would do one. We're going to have a practise of one together, and then you'll have your independent work. Well, we're going to talk about working systematically, and then there'll be a chance for some independent work. There won't actually be an exit quiz on today's lesson just because this is more of an investigation than a series of questions today. So before we get started, please just make sure you've got a pen or pencil and some paper. That is absolutely crucial for today's lesson. You will be working out your own way of recording your results. So really important you've got a pen or a paper, pen and paper, or pencil's absolutely fine. And make sure you've got that really can-do attitude 'cause like I say, today's going to be a bit of a different lesson. So pause the video and get what you need. Wonderful, let's get started. So we're going to have a bit of a recap on some times table knowledge before we get started. Our times table knowledge is really going to be pulled into these questions today. So as you can see, you need to fill in the gaps on these. There are some multiplication and some division questions. Just remember that you can use your multiplication knowledge to help with all division questions. And if you're stuck on any where the missing number is appearing in a part of the question you're not used to, like at the start of the question or in the middle of the question, just think about what number could go there. Think about those fact families. So for example, if you've got number two and seven, what number do you think might be missing in that problem? So pause the video here and take as long as you need to answer those questions. Great, well done, everybody. I'm really hoping you had a very good go at those questions. I'm sure some will have seemed easier than others. So as we go through them, I will talk through what I would do to answer each question. Your thought process may be different, and as long as you get the right answer, that's absolutely fine. So if we look at this first question, we've got three times something equals 12. Three times something equals 12. Where does 12 appear in my three times table is what that question is asking me. So let me have a think. Three, six, nine, 12. Oh, four threes are 12, so it must be four that's missing from that question. So, well done if you've got that. The next question is always about my three times tables. So I got to four threes are 12. And then if I carry on counting in my threes I get 15, 18. So six threes are 18. So there's the answer to the next one. The third question there is a more of a sort of more traditional question where we have our two parts and we're being asked to find the whole from multiplication. So if we have two lots of five, what's the answer? And I'm sure most of you found that one quite easy. And 10 times something is 60. What have I done to 10 to get to 60? Where does 60 appear in my 10 times table? Well, well done if you saw that that was 60. Okay, below I've got four times five. Now I might want to think of that as my four times table or my five times table, whichever one I feel most confident with. If I go in my fives, for example, I can go five, 10, 15, 20. That might seem quite a simple, straightforward calculation to do. Okay, seven times something is 21. So I could just count in my sevens until I get to 21. So I can go seven, 14, 21. So seven times three is 21. Nine times something is 45. Well, I recognise 45 from my five times table. So nine times five is 45. Four times 12, well for that one I think I would double. I'd do two times 12 is 24. And then I doubled 24 to get me 48. On to the division questions here which some people sometimes find trickier than their multiplication, but really it's all the same facts. So 70 and 10, what have I done? What happens if I divide 70 by 10? My number's going to get smaller, so I've got seven there. Something divided by seven is two. What's the missing number? What's going to be the whole if I've ended up with seven and two? Well, the missing fact number there in that fact family is 14. 12 divided by something is four. And again, if you've got that confidence with your three and four times tables, straightaway you should be thinking ah, the missing number is three there, well done. 16 divided by something gives me eight. So I could count in my eighths till I get to 16 or I could count... Yeah, I could count in my eights till I get to 16, and I know that there are two eights in 16. So that doesn't take me very long. Same with the next one. I can count to my fives. How many fives are there in 15? Five, 10, 15. So 15 divided by five is three. Something divided by three is three. I've got two threes. So I've split something into three and I've got three. Three times by three is the fact that's going to help me answer that question which is nine. My three times table again here. How many threes are there in 30? It's 10. And 32 divided by something gives me four. So where does 32 appear in my four times table? It's eight times four. Well done if you got all of those questions right. You're really feeling quite confident with those times tables, which is brilliant. If there was some that you did struggle with, sometimes it's some that you found harder or which maybe you didn't get right, that's absolutely fine. But maybe just make a note of them and think hmm, yeah, I need a little bit more practise with my threes, for example. Or when I have a number with a seven or an eight in it, that's when I get a little bit stuck. So just have a think about the ones that might need a little bit more work. Okay, this is another little warm-up which is going to help us with today's lesson. So we've, hopefully you've talked about factors and products before. So factors are the numbers that you multiply together and the product is the answer. So all you need to do for this question is link together which answer do those factors give you, which product do those factors give you. So where is the line going to join to connect the factors with the product? So for example, two times five, two and five are the factors. And the product of that, what's made out of two times five is 10. So pause the video here and have it go thinking where those lines are going to appear to match the factors and products. Well done, let's see how you got on then. So three times five is 15. So well done if you found that correct product. Eight times four, well, eight times two is 16. So I can double 16, gives me 32. Seven times three, I can count in my sevens or my threes depending on which way round I feel most confident. Oh, sorry, I've missed that one out. I'm coming back to it. Eight times 10 or 10 times eight is 80, and 12 times two is 24. And then back to seven times three is 21, just in a bit of a different order there. So these are factors and products, and that's what we're going to look at in our first investigation today. So what we're going to be doing is investigating. We are going to look for all possibilities. We're going to work systematically. We're going to find a system which means we can say very confidently that we found all possible outcomes. And in today's lesson, the working out is more important than the answer. So I would love for you, I'll share the information at the end, but if you could share your working out with us if you ask your parents or carer, that would be wonderful because it will be really fascinating to see what working out you've done for today's lesson. And how you record today's working out is completely up to you. So I've said this lesson is little bit different. This isn't a set of questions for you to answer today. There's an investigation for you to go away and record how you wish and get to hopefully get to an answer. But like I say, the working out is super important today. Okay, so what am I talking about? An investigation, here's one for us. I want to find all the possible ways of multiplying two numbers to find 12. We know that the correct vocabulary for that means that what I'm doing is I'm looking for all the factor pairs to find the product 12. How many different ways can I find 12 by multiplying? So I've drawn out a grid here to help me work systematically. Working systematically means that I'm going to have a clear system. I'm starting at one and I'm going through my times tables from there to see whether I can make 12. I've then drawn out this grid. So I've got my first factor in the first column. I've got my second factor in second column. And then I'm checking that and making the product 12. If you would like to think about recording this differently, that's fine. Maybe you would just like to write out the pairs, for example. That's absolutely fine. This is how I like to record it. It keeps it nice and clear, it keeps it neat, and it allows me to see that I've tried every possibility. So I'm looking for all the ways of multiplying two numbers together to get 12. So I've started at one. I can do one times 12 is 12. So there's my first factor pair. And now I'm going to try two. Can I multiply two to get 12? Yes, I can. I can multiply two by six and I get 12. So there's another factor pair. I'm now going to move on to three. Is there anything I can do to three? Can I multiply three by a number to get 12? Yes, I can. I can multiply three by four to get 12. I've done this one already, but here's it in the other order. I can multiply four by three to get 12. Is there anything I can do to five to get 12? 12 doesn't appear in the five times table, but I've put it down and I'm going to check it anyway. But I know that 12 doesn't appear in the five times table. The sixes is as well, this has appeared already because I've done my twos, but six times two makes 12. Now I'm going to stop there. I know that I can stop there because six times two is 12. So I can't multiply seven by anything to get 12. It's too big. I know that if I multiply seven by two, I'm going to get a number bigger than 12. So any number after six is not going to allow me to multiply it to get 12,. I can stop there. So I've worked systematically. I've got one, two, three, four, five, and I haven't missed any of my numbers out. I've stopped when I'm sure I found everything I could possibly find. And as a result of that, I found all the factor pairs for 12: one and 12, two and three, sorry, two and six, three and four. And those are all my factor pairs that I can find for 12. So I've investigated, I've written it out however I wish, but I've written it out in a clear, systematic way that means I'm sure I found all the possibilities. So let's have a go at another one and we're going to try this together. Here's a different kind of investigation, but we're going to record it in a really similar way. How many different combinations of lunch are there if there are two main options available, chicken and pasta, and two dessert option available? So it's useful when we see this written down to get that picture in our head. Maybe you can see your school canteen. I can see mine. What's available today? Right, you can either have chicken or pasta. And then for dessert, you can either have fruit or cake. So how many different combinations can we make from those two main options and two dessert options? So again, I'm going to work systematically. I'm going to pick one of my mains to start with, and I'm going to put both desserts with it. So I'm going to start with chicken. It doesn't matter what order you started it in. It's completely up to you. So I'm going to start with chicken. So option one is I can have chicken with fruit. And this time I'm just going to write down what each combination. So I've got chicken and fruit, but I could also have chicken and cake. There's no other option available for me with chicken. So I've done both of my main options. That one's finished. So now I can move on to the next main, pasta. And my options are pasta with fruit or pasta with cake. Now, can I be sure that I have got all of the combinations? I've used both my mains with both my desserts and then the I've used two mains with two desserts. So those are all the possible combinations, I'm sure of it. And then I can check how many combinations there were. So for two mains and two desserts, there are a total of four combinations I could have. I could have chicken and fruit or chicken and cake, or I could have pasta or fruit or pasta and cake, four options. So now it's your turn. You've got a different investigation. Let me talk to you about it. So you've got Robin Hood and you're sorting out his wardrobe for him. He's got three hats and he's got four tops, and they've come in different colours. I would like you to work out how many different outfits he can make. How many different combinations of hat and top can Robin Hood make from his three hats and his four tops? I've drawn you out a grid here that you can use to help you if you want to, but don't feel that you have to. If you would rather record that in a different way, that's completely up to you. The next part moves on to Robin Hood having a different combination of, sorry, a different number of hats and tops, so for you to think if you can see any patterns. So take as long as you need, record the results however you wish, and come back for some of our thoughts afterwards. Okay, I'm not going to go through how you recorded it 'cause like I say, that's completely up to you. But if we go onto this one here, can you see any patterns? Well, I'm hoping that you saw that for that original question where he had three hats and four tops, there are 12 possible combinations. If you then moved on to the second part, which I'm really hoping you did where he had four hats and four tops, it went on to 16 combinations, 16 different ways of dressing from just four hats and four tops. That seems like a lot, doesn't it? And then really well done if you moved on to that final one. Five hats and four tops gives a combination of 20. So what pattern can you notice there? Can you see a formula? A formula means a way of working out every possibility without having to write them all out. Well, what's the relationship between three and four if I get 12? What's the relationship between four and four if I've got 16? Can you see that you multiply each of them together? Three times four is 12, four times four is 16, five times four is 20. And why do you think that might be? Well, that's because we multiply them together to give us those combinations. Fantastic if you found that pattern. That is really, really some fantastic work. You have understood your times table knowledge really well and you've applied it to a brand new situation. That's really impressive work. Like I mentioned at the beginning of the lesson, it would be fascinating to see your working out from today's lesson. If you would like to, please ask a parent or carer to share your work with us either on Instagram, Facebook, or Twitter tagging @OakNational and hashtag #LearnwithOak. Some amazing work today, everybody, well done. Enjoy the rest of your learning today, bye-bye.

Solving correspondence problems

Solving correspondence problems

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UnitMaths / Multiplication and division

Maths