Which of the numbers below is not prime?

What is 0.075 ÷ 10?

If I buy 10 cupcakes that cost 75p each, how much change will I get from a £20 note?

I save £35 a month to buy a bike, how much will I have saved after 20 months?

Which of the numbers below is not a factor of 27?

Practise multiplication and division skills.

﻿Op, hi everyone. Just turning my notifications off because first of all my name is Mr. Whitehead. And second of all, I'm here to teach your maths lesson. I need to be distraction free. That's why I was turning my notifications off. If you are not yet in a quiet space, I need you to press pause in a moment, go and find somewhere quiet, where you are able to focus on your learning with me for the next 20 minutes, free of any distractions. If you need to do that, press pause and do it now. Otherwise keep watching and we'll get started with the lesson. In this lesson, we will be using formal written methods for multiplication. We're going to start off with a sorting activity. Then we're going to look at solving multiplication equations in two different ways. First of all, using our skills of making numbers 10 times bigger and 10 times smaller. Then we will look at those four more written methods. After that, you should be set for your independent task. There are a few things that you need for the lesson, a pen, or pencil, a ruler, and then something to write on some paper, a pad, a book. Press pause, get those items collected then come back and we'll start. So a sorting activity to kick things off, here is a list of multiples. How could you sort those multiples? Press pause, have a go at finding different ways to sort and organise them. Then come back and we'll share. So how did you get on? Can you hold up your paper so I can take a look at the different ways that you have, hold the paper still the different ways that you have been sorting and organising, looking good, quite a few different ways that put your paper down. Now we can't go through all of the ways, so let me share with you the way I sorted. Can you spot the rule I used for my sorting? So I made a group here, so I made a group here. How have I grouped or why have I selected those two multiples for that group? What do you notice about them? Take a look, call out when you've noticed anything. Say it again. So I have grouped these because they are multiples of three. How about this are they still from the same list as you. How about these multiples? Take a look. What might my title be? Call out when you've noticed. Say that one again? Yes, so I have grouped these because they are multiples of three and six. So what about those three multiples I haven't grouped? What can I do with them? What title could I give to those? Not multiples of three or six, yea. Good, and actually 13 I suppose, could have its own title. What's special about 13? it's a prime number, it's only factors are one and itself. Based on the way I've sorted and thank you for spotting those titles. I wonder if you can help me here. A multiple of six is always sometimes never a multiple of three and a multiple of three is always, sometimes never a multiple of six. First sentence, Which of those three words would you choose? Always, sometimes or never? Multiple of six or to put a six is, what would you say? Excellent, always a multiple of three. And how about the second sentence, a multiple of three is? Good, sometimes a multiple of six. Well done. So let's start things off of a problem, could you take a read of it? Read it with me If you'd like to. Oak Travel have got a problem. They want to put up some posters in their office window advertising their latest offers, but they don't know how much space they will take up. There are six per, sorry. There are six posters in total and each poster has a width of 25.7 centimetres. How much space do they need to put all the posters up? I'd like you to pause and have a go at answering the three questions I've given you. What do I know? What do I not to know? What knowledge and skills do I have that I can use with this problem? Take a moment to think about those three questions and then come back. Okay, so what do I know? What do we know from reading this problem? We know there are six posters, did you get that? Good. Is there anything else that we know ? Of course, we know the width of each poster, 25.7 centimetres. And what do we not know? Good. We do not know how much space they will take up. And when you look at the last sentence, that last sentence is the question for us. How much space do they need to put all the posters up? What knowledge and skills do we have that we can use here? Now you may have started to make some connections as you were reading through the problems paragraph, but I wonder if the representation of the information from this problem could help us with that final question in black, help us to make connections to our knowledge and skills. In a moment, I'm going to show you a bar model of the information from this problem. If you would like to pause now and have a go at drawing one of your own first, press pause then come back and you'll be ready for me to go through one on the screen. Okay, let's take a look then at a bar model using what we know and what we don't know, and then making connections. So we know there are six posters and that each poster has a width of 25.7 centimetres. What we don't know is, how much space they will need to put up all the posters, looking at the bar module now, what knowledge and skills do we have that we can use here to solve the problem? Excellent, we could use addition repeated addition 25.7 six times. But of course, multiplication is going to be a more efficient calculation to use 25.7, six times. 25.7 times six, six lots of 25.7. How could we solve this then ? Again, take a moment, pause. Think about the skills that you have when it comes to multiplication and how you might approach solving this equation. Press pause and come back when you're ready. Set, now, I wonder if you thought about calculating it mentally using written multiplication or using any of your skills with making numbers 10 times bigger then calculating and making the product 10 times smaller. That option on the left caught my attention because we're working with decimals 25.7. So it could help to make that decimal 10 times bigger, then calculate and make the product 10 times smaller. Because there are decimals, I'm thinking that calculating mentally probably won't be the most efficient methods. So we've got two strategies to try. let's look at each of them. First of all making numbers 10 times bigger and 10 times smaller. So there's a decimal here and we know that if we increase the numbers size 10 times in this case, we'll be working with a whole number. See what you can see, how many ones? Good. So far, what number do we have? 25 and now say it again, 25.7. Good. We can make it 10 times bigger. Each part of 25.7 increases in size 10 times, just look at that again. So our two tens, become two hundreds. Our five ones, become five tens and our seven tenths, become seven ones. And we now have the number? Good. 257, which we can multiply by six. And we might use a written method for that part, 257 multiplied by six, six sevens. Tell me? Good, 42. 42 ones. Five sixes will help us with five tens, multiplied by six or six lots of five tens, six lots of five, 30. So six lots of five tens, 30 tens 300. We need to include the regrouped four, 34 tens recorded in our grid as you can see. Finally, six multiplied by two, six lots of two ones, 12 ones. So six lots of two hundreds, 12 hundreds. Don't forget the three hundreds already there. Read the product with me. 1,542. Is that the solution to the problem? No, it's 10 times too big. So let's make that product 10 times smaller, see what you can see one thousands, five hundreds, four tens, two ones as a number 1,542. which we can make 10 times smaller by using which operation, not subtracting, dividing by 10. Divided by 10, make your number 10 times smaller. Did you notice it? Watch again, each part is made 10 times smaller. This is our final product then. Read this number to me? Good. 154.2. So when we think back to that original problem, how much space do they need to put the posters up, 154.2 centimetres. Let's take her look at that same calculation without making any of the parts 10 times bigger than 10 times smaller. Let's just calculate with that as a decimal multiplied by six. So we can use some short multiplication. If you'd like to press pause and have a go on your own first, please press pause now, then come back in time to join me as I go through it. So, we're looking then at six lots of seven tenths or six sevens, six of seven ones 42. So six lots of seven tenths, 42 tenths, 4.2. Next six lots of five ones. Good. 30 including the four ones from the 42 tenths, 34 ones. Finally, six lots of two hundreds, six lots of two. Oh six lots of two hundreds, six lots of two tens. Six lots of two ones, 12 ones. So six lots of two tens, 12 tens. Plus the three tens, 15 tens. How do we say 15 tens, 150. Just look back at the place value counters, that six lots of two tens, 12 tens. Read the final product to me. 154.2. So same solution, we've still solved the problem and worked out how much space is needed for the posters, but we've taken two different approaches. Making 10 times bigger, calculating, making the product 10 times smaller or using written multiplication. Which of those two did you prefer for this problem? 25.7 multiplied by six press pause while you think about your preference and your reasons why. Let's have a read of this problem, Erhun is planning a hike in the Atacama desert over 26 days. He will need to drink at least 2.7 litres of water each day. He can carry up to 50 kilogrammes of luggage. How much water will he need over the trek? Press pause and have a go at answering those three questions. What do you know? What do you not know? And what knowledge or skills do you have that you could bring to this problem to help solve it? Press pause. Let's take a look shall we? So things that we know, things that we don't know, we know that he'll be travelling, he'll be hiking for 26 days. He'll need 2.7 litres of water each day, he can carry up to 50 kilogrammes. We don't know how much water he will need for the whole trek. Now show me on a scale of zero to five, five being I've got lots zero, not very much yet. What ideas, how many ideas do you have or how confident are you in the ideas you have for the knowledge and skills that you could bring to solving this problem? So not really sure yet, a couple of ideas. Yeah, I think I can see all the connections. Let's see now then if a bar model will help to confirm those ideas or to give you some, if you haven't got them yet. Again, if you'd like to press pause and draw the bar model first, please do that now. And come back when you're ready to look at the bar model alongside mine. So using what we know, we know that he will be needing 2.7 litres of water each day and that there will be 26 days in total. What we don't know is how much water he'll need for the whole track. Looking at the bar model, can you now see the maths that's needed the knowledge and skills that you'll need to bring to solve the problem? 2.7, how many lots of 2.7? 26 lots of 2.7. How would we say that as a multiplication? Super, 26 multiplied by 2.7 or 2.7 multiplied by 26. How might you approach solving this problem? Press pause as you have a quick think about strategies, you may or may not use come back when you're ready. So what's you thinking, call out to me a strategy you might use? Yeah, so I'm thinking calculate mentally written multiplication, make 10 times bigger and then make the product after calculating 10 times smaller calculate mentally again, I'm working with decimals here, I want to be accurate. And if I work mentally with these numbers, I'm not sure that I will be as accurate as they could be, if I use a written multiplication or might making 10 times bigger, 10 times smaller approach. I'd like us just to think about the written multiplication. Before we do, can you think of an estimate for the product, for the size of the product after calculating? So looking at the numbers as they are, what changes could you make to them to help you estimate? Have a quick think, have a go. What changes are you making? Are you using some rounding, 2.7 to the nearest whole number 26 to the nearest 10, 30 multiplied by three 90. So an estimate of 90 litres for the whole trip. Let's take a look at the multiplication. Now, technically this will be a long multiplication because we're multiplying by a two digit number, not with tens and ones, but with ones and tenths. So there's going to be a longer approach than there was with our short multiplication where we were just multiplying by a single digit. So let's have a look then, first part we're looking at the seven tenths and we've got six lots of seven tenths, six lots of seven tenths, 42 tenths, 4.2. Two lots of seven tenths 20 in fact, if two lots of seven tens is 14 tenths, 20 lots of seven tenths, 14 ones, plus the four ones 18 ones, 18. Now we're thinking about the two from 2.7, two lots of six or six lots of two either way round. What is it? Good, 12 and then two lots of 20 lots of two, two lots of two is four, 20 lots of two is? 40 plus two one, 50, Five tens. Is the problem solved at this point? No, we need to now combine we've multiplied 26 by seven tenths and we've multiplied it by two, let's now combine those parts total them. So two tents. We haven't got anything from the second part of the calculation. Eight ones and two ones, 10 ones. One tens plus five tens, plus the regrouped ten, seven tens. Can you read the product with me? 70.2. So how much water will he need over the trek? We had an estimate of 90 and we've got the product of 70.2 litres. Good. So we've explored making changes to numbers in a calculation, making them 10 times bigger and 10 times smaller to solve the problem. And we've looked at using both short and long multiplication. This is the problem I'd like you to work on for your independent task. Let's have a read of it. Sarah is on holiday even in Italy, while the Naples, she goes to an old cafe to learn to cook Italian pasta. The pasta chef there, Valentina has a special machine to help her create the perfect sheets of pasta for her world famous lasagna. It has two dials. The first dial controls the length of the pasta and we've got those three numbers, those three different lengths. Then we've got the second dial, which controls the width of the pasta and we've got three different widths. The best sheets of pasta are the ones closest to a multiple of 50. Help Sarah find out the settings on the pasta machine to get the best pasta. On your worksheet there's a getting started example in this activity you're going to use your multiplication skills. There won't be a need for long multiplication because in the multiplications that you work on, there will be a single digit number that you multiplied by, but there will be a choice of making a number 10 times bigger calculating and then 10 times smaller, or just using the numbers as they are in your short multiplication. Press pause and go and work on the activity, come back when you're ready to look at the solutions. Okay, so how did you get on, can you hold up your paper and let me see how you've been recording? Oh, there's a lot of multiplication going on there. Isn't there? Fantastic. And we were looking for the best pasta, We were looking for those products that were closest to a multiple of 50. So this grid shows all of those multiplications you were just holding up all of the options. We could have multiplied each of the lengths, 42.3, 58.7 and 61.4 by each of the widths. Each of those lengths multiplied by each of those widths to create nine different multiplications. But which of them would result in the perfect pasta? It's the products closest to multiple of 50. Did you remember to do that part? If you didn't, quickly pause and do that now, because I'm about to show you, which of those products are closest to multiples of 50 and therefore the best pasta. Ready? It is these ones with a smiley face next to them, they're closest out of them all to a multiple of 50. So we had four options for the perfect pasta. Which strategies were you using? Now you've held them up and I could see most- well everyone's used at some short multiplication, but I couldn't see, clearly enough whether you've had used any of the making 10 times bigger and 10 times smaller before the short multiplication. So just give you a paper a wave, if you were using the numbers as they were. And give me a thumbs up, if you made any of the numbers 10 times bigger, and then the products 10 times smaller. So a bit of a mixture. Which units of measurement do you think the machine might be using? If we're making pasta and we've numbers, we've got links of 42.3 and width of six. What units might we be working in? Possibly in centimetres, so visualise a 30 centimetre ruler, 42.3. So it's a bit more than that as a length of pasta. and if it were millimetres 42 points, that's four centimetres. Maybe versus six centimetres. My estimation is a bit off between my hands. I suppose it depends on the size of pasta that you want. For larger pasta those units or centimetres, the smaller pasta those units are millimetres. And I wonder if you can make any final connections, based on what you were doing there with the multiplication, multiplying lengths by widths, what other measurement connections are there within this work that you've been doing? You were calculating area, the area of the pasta. So we were making pasta that's rectangular in shape, perfect for lasagna. I wonder if that influences your decision on the units that apply. Would we be measuring those sheets in centimetres, 42 centimetres by six or millimetres? I hope you've enjoyed this session, it's busy and really busy session. Lots to think about, lots of connections to make. If you would like to share any of your learning with Oak National, please ask your parents or carer to share your work on Twitter, tagging @OakNational and #LearnwithOak. Thank you so much for joining me for this lesson. I hope you enjoy it. There's another feeling that I've got now, as well as enjoying the lesson am being really proud of each and every one of you. I am feeling hungry, all of that talk about pasta and world famous lasagna. I am feeling rather package right now, but it's not quite time for me to get something to eat. With whatever you have lined up for the rest of the day. I hope that you enjoy it and I look forward to seeing you again soon for some more maths. Bye.

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Short Multiplication

In this lesson, we will apply short and long multiplication skills to calculations involving decimals.

Maths

Y6 Maths

Key Stage 2

Year 6

Use formal written methods for short multiplication including multiplying decimals

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

Use efficient strategies to multiply numbers, including decimals

Practise multiplication and division skills

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 formal written methods for short multiplication including multiplying decimals

Core Content

Multiplication and division: