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Solve multiplication problems using known facts

﻿Hi again, everyone and welcome to today's lesson. So today's lesson is going to be to find efficient strategies to multiply numbers, including decimals, and the thing we're going to focus on today is looking at the different strategies we could use and looking for the most efficient way of doing it. But before we get started, just want to start with today's joke. So, why was the Easter bunny really angry? Because he was having a bad hare day. Bad hair day? It's a good one. Okay, nevermind. Right, let's get on with the lesson, then. So in today's lesson, let's have a look at our agenda. The first thing we look at is we're going to look at some of those efficient strategies, short multiplication, then you'll think about how we go about checking someone's work and think about other strategies we can use in order to check people's work, we'll have a go at that. Then we'll have a look at some problems, including decimals. Then finally, we'll put that into practise, applying it in our independent tasks. Make sure as always, you've got that pencil and paper ready to engage with the learning. So let's go. I've got a problem here: in order to help customers get to their destination, Oak Travel are designing their new range of aeroplanes . Now for long distance journeys, these planes will need to carry food for customers. There are six storage boxes of food and each box can carry a maximum 312 portions. So how many portions of food could the plane carry in total? Now, before you pause the video, what I'm going to do is I'm going to walk through a model how I might go about solving this problem, then we're going to have a look at some, but if you do want to pause the video and have a go yourself first, by all means, do that now. So what I want to do is I first want to think, with all problems, what do I know? And what do I need to find out? And I think that's a really good way of approaching a problem and then think, well, how can I represent it or show this problem, which will easily demonstrate how I'm going to be able to solve it? So the first way I do that is I think, well, a bar model is a brilliant way of thinking, and it's a great tool for understanding. So I know that there are 312 portions in each storage box and there are six storage boxes, therefore I've represented it here in that format. Now that will tell me, I need to know how much it is in total. Now I could do repeated addition, but that's going to be quite cumbersome and quite slow. So actually, I think multiplication is the right way to go here. I need to do 312 multiplied by six. So, how would I go about solving this? Well, there are lots of different practises but the one I'm going to use first is perhaps the one we quite often jump to first and that's short multiplication. Now, along with my numbers that I've got on this side, I'm going to be using place value counters to give us that conceptual understanding of what's happening while we're doing it and the really knowledge further behind to make sure we have an understanding of it. So thinking about this first, then first thing I'm going to do is I'm going to do two multiplied by six. So multiply my ones first, so I can see that I've represented it there, and I've now got 12 ones in total. Now I need to do, because I've got 12 ones, I can regroup 10 of those ones and make myself two ones, and we've got one 10. We then multiply out our tens. So I've got one 10 and multiply that by six. But I can also see that once I multiply that, I've also got my other ten there. So you can see as I'm doing this, I'm also going to represent it with my numbers over here. So do keep an eye on that, as well. So now I've got seven tens in total and you can see I represented it there. I'll then go to my hundreds and three hundreds multiplied by six is 18 hundreds. Again, I already know that I can now do some regrouping so I could take 10 of those hundreds and regroup them for one thousands, okay. And the final bit I need to do, just complete my chart there. So I've now got 1,872, okay. Nice, efficient way of solving that problem, probably was quite an efficient way of doing it. Here's another problem then. One of the new planes is scheduled to fly between London and Lisbon which is in Portugal. The distance is 1,285 kilometres. In one weekend, that plane is going to complete this journey nine times. So in total, how far will that plane travel? Again, first thing I need to do think about what do we know and what do we need to find out? So maybe have a pause now, how could you represent this problem in order to help you to show how to solve it? Great. Hopefully we came up with a nice bar model to be able to help us represent it nice and clearly, and this is showing us, we want to know how much there is in total. We've got 1,285 in each journey and there are nine journeys in total, so we're going to use multiplication to help us. Over to you, then. What I want you to do is think about the faculties we just used. You can use those place value counters if you have some at home, or if you want to draw some to help you, that's fine, or if you just want to use that short multiplication, that's fine as well, but make sure you're clearly thinking about why you're doing each part, and you might want to just talk out loud to help you, okay? So pause the video now and have a go. Right with that now, so let's have a look how we should have done that. Now, rather than those place value counters, we're going all the way through it. I just want to double-check make sure we're happy with what we've done. So what you could have done or should have done may look a little bit like this. So first, we're going to do five multiplied by nine. And we should find that 45, so I can represent that here with my five in my ones column and then my tens, my four tens, just waiting for the next calculation. Now, our next calculation's eight multiplied by nine or eight tens multiplied by nine is equal to 72, then I add my four extra, so I'm then left with six and I've got seven which I'm going to make sure that I put into my hundreds column. Now I've then got two hundreds multiplied by nine, which I know is 18 hundreds, and then I can add my seven extra, so that's 25 in total. So, I can then put my five in that and then I can add my two extra, so one multiplied by nine, so I get 11 thousands in total. So my answer is 11,565. Well done if you did that. However, was it the most efficient way of doing it to solve it like this? Could we have done it more efficiently? Perhaps you looked at this problem and thought, "I can solve that far faster than short multiplication." Did you spot one? Well, I did. I thought to myself, "What do I know? What multiplication really supports me?" Well, I know that 1,285 multiplied by 10. That's really easy. If I want nine lots of a number I can just simply subtract one lot of 1,285 from that to give me that calculation. That's probably going to be a lot faster than going through all those stages of short multiplication. So this lesson is all about thinking about the most efficient strategy we use. In order to support this, now we're going to do a little bit of check my work. Here, I've got a calculation that I use to solve a problem. Now, looking at this, I want to think how many different ways can I try to prove that there's been a mistake here? Not, I don't want to know that there has been one, I want to know how many different ways could you use to prove it. So let's have a look. You may want to pause the video and see if you can find some different ways using your mental strategies. But I am going to show you some examples now to support you slightly. So different ways that we could come up with here. Well, actually an area model might be a great way of showing this. I can partition 305 really quickly into three hundreds and five using the distributed rule, then multiply both parts, so 300 multiplied by eight is equal to 2,400, that's really easy. And five multiplied by eight is really easy, that's forty. Add those two parts together, 2,440, that shows me 2,520 is not correct. Another structure I could have used is knowing that if you multiply by eight, you are doubling, doubling, and doubling. So if I double 305, I get to 610, double that, 1,220, and I double that again, we get to 2,440, which proves yet again that 2,520 is not correct. So you see what we're doing. We're trying to use other mental strategies to help us to prove some answers. Over to you. Here I've got two more examples. So what I want you to do is to use other strategies to help you to prove that there are errors here. Okay, now, because of all the different strategies you could pick, I'm not going to go through all the different examples with you that you could have. So do have a look at this and try and prove it in lots of different ways. So pause video if you need to, to have a go at those and then when you're ready, you're happy, we're going to move on to our next piece of learning. Okay, so pause the video when you're ready and then play again when you've done those different examples and you're happy. Okay, guys, let's move on then. Now we want to think about problems including decimals. Now, Oak planes want their seating to have more leg room. Now in order to have more leg room, currently each row of seating has got 56 centimetres of leg room, but MM and Oak Travel want to add 3.5 centimetres extra to every row. So how much extra space are they going to have to create in order to make sure that they've got that extra leg room? Again, think about that first question we always ask when we have these word problems, what do we know, what don't we know, what do we want to find out? And how could we go about representing or explaining it clearly? Okay, pause the video if you want to have a think about that, then we're going to have a look at the different strategies. So what did you come up with? Maybe, yeah, you could have had, I suppose, we could have used a bar model here, but a bar model slot might be slightly confusing and a bit clunky in that if you're going to have 32 different rows, each one with an extra 3.5, it could be a very big bar model. So instead of that, I've chosen instead to use an area model, knowing that the total amount of extra leg room I'm going to need is I've got 32 rows and I need an extra 3.5 centimetres in each one. That's going to give me my total. Again, that proves I need to use multiplication. Now, thinking about strategies for that, we could go back to our place value counters and our short multiplication here. So you can see that I partitioned 3.5 into 0.5 and three, and then we'll multiply it out to see how we do. So first thing I need to do is my two ones, I need to multiply by naught 0.5, and that will give me so two lots of naught 0.5 is equal to one, and then I need to multiply 30 by 0.5. So 30 lots of naught 0.5 is equal to 15, so I can represent that here. So then I've got my 16 in that part. So I could then put that into my short multiplication of what I've done there, then I need to do 32 multiplied by three. So, first off, two multiplied by three, nice and easy, and then I've got my tens over there. So adding them all up then, once I put that into here, I've got 96 and 16, then I need stay to go through and add those up to give me my total. We can say in total that we're going to need an extra 112. Okay, so hopefully we're happy with that. However, is there another strategy you could have used? Would one of these strategies have been slightly more efficient? Now, what we've done here, you can see, 16 multiplied by seven is almost using my number facts and manipulating those numbers to find something which is more efficient for me, okay? So hopefully you can see slightly what we've done there. So 16 multiplied by seven, we've taken half of 32 and then we've multiplied 3.5. We've doubled that. So we've just given ourselves a calculation that's going to get us the same answer, but perhaps is a little bit easier for us to be able to deal with, or we could go and make that even slightly easier. We could then halve 16 again and double sevens, give us eight multiplied by 14. So that may be easier for us, or we could do it all mentally. And we could use mental calculations to support it. Lots of different strategies we could use in order to solve these problems, and today's lesson is getting you thinking, that's why we did the checking work for getting you to think about possible strategies you could use, which aren't just the one that you always use, because using one strategy for one question may not be the most efficient strategy for another question. It depends on the numbers and it depends on how you can manipulate and use them, and we want to have that fluidity to be able to work with lots of different strategies. Okay, enough talking from me, it's time for you guys to have a go. So Oak Travel needs your help to choose the best seat manufacturer. They need to think about the total amount of space for leg room, because it has to not be over 210 centimetres. Then once you've kind of ruled someone out then, then you then need to look for the cheapest one. So we want to pick the cheapest of the options. So we're looking for something which isn't over 210 and then the cheapest, okay. So different ways of working on this. Think carefully about the strategy that you're going to use in order to help you to solve this problem most efficiently. It might be that you want to try a couple of different ways to get yourself the best way. Okay, so when you're ready, pause the video now, go to your worksheet, complete that, ask in lots of different ways, thinking about lots of strategies, and then when you're ready, we'll come and check the answers together. Okay. Right guys, let's have a look at some of those answers then. So we have our different chair companies, our chair manufacturers, so the first stage we should have gone through is we need to find out the total amount of leg room and we know that it needs to be under 210 centimetres, so it needs to fit. So what could we rule out from that then? Well, we can see that this one, if it's 46 multiplied by 4.5, we're going to have 207. Here we'd get 212.5 and here, we'd get 203 centimetres. Hopefully we can see that we need to rule out Safe Seats, so they're not going to be the one we use. We then need to work out of the two remaining options, which one is going to be the cheapest because that's the one we want to go for. So this time we're going to need to think about the cost of each seat and the amount of seats. So in this case would be 46, the amount of seats, multiplied by the cost of each seat, so 46 multiplied by 6.25, and that's going to give us 287.50, and over here, we can see that we'll do the total amount of seats and we'll multiply it by the cost of each seat. And we can see that that's 275 pounds 50. So the one we're going to go for, we should have gone for, hopefully, is Relax and Recline for 275 pounds 50. Right guys, that was quite a challenging task and I wonder how you did. Don't worry if you made some errors or little mistakes or hopefully going through it now has helped you to see where those were and we can go through. The purpose of today's lesson was really about thinking out those different strategies, not necessarily solving all those problems, okay? So just going through and getting more confident with lots of different strategies. That's what we're looking for. That's what great mathematicians are able to do. Now, that's all we've got time for today. What I want you to do is make sure that you, if you want to get your parents or your carers to share anything that you've done today on our Twitter page, and before you finish the lesson, make sure that you complete that end-of-lesson quiz to review and consolidate the learning. Great job today, guys, and I'll see you again soon.

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Use efficient strategies to multiply numbers, including decimals

In this lesson, we will evaluate what strategies are most efficient for various multiplication problems.

Maths

Y6 Maths

Key Stage 2

Year 6

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

Practise multiplication and division skills

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:Use efficient strategies to multiply numbers, including decimals

Core Content

Multiplication and division: