Quiz involving calculating intervals across zero.

Which of the below gives an answer of -1?

Which of the calculations below has the smallest answer?

A school football team scored a total of 3 goals in their recent games but let in 5. What is their goal difference?

I am in an elevator (lift) and I'm currently on level 6 but I need to get to -2. How many floors away is -2 from me?

The Olympic golf course in Rio has a par of 71 (expected number of strokes needed), if David scores 65, 70 and 66 on his 3 rounds, what is his total score?

Calculating intervals across zero

﻿Hi there, my name is Miss Darwish. And for our maths lesson today, we are going to be solving some problems involving division with remainders. But before we get started on our division lesson today, if I can just ask you to take yourself away from any distractions to a nice quiet place, just so you're ready for the lesson. Okay, so first of all, we're going to start the lesson just by looking at some quick division. And then we'll look at some division with remainders. And then we'll start explaining remainders, seeing what they mean within worded problems. Okay, at the end of course, there will be a quiz for you to do on today's lesson. So, for this lesson, if I could just ask you to get yourself a pencil or a pen, a sheet of paper or a notebook is fine, and a ruler. If you want to grab those things then we can start. Okay, if you're ready, then I've just got three very quick, hopefully, questions for you to do. So if you just want to quickly jot down the answers, I am going to give you 10 seconds. And pencils or pens down! Okay, should we go through them together? So 16 divided by four of course is equal to four, four times four is 16. 12 divided by three is equal to four, four times three or three times four is 12. 20 divided by five is equal to four, four times five is equal to 20 and five times four is equal to 20, so well done if you said that. So three different questions, but they all give the answer four. Okay. Which other division calculation gives an answer of four? Can you write something down for me, quickly? A different one. Okay, and then tell me, what is it? So there are lots of different options you might have had. You might have had 44 divided by 11 is equal to four, you might have had... So the way I do it is I've done four times four, four times three, four times five, you could have four times six, which would be 24. So 24 divided by six is equal to four. There are lots of different options you could have had. Okay. So, 40 divided by 10, 28 divided by seven, some more options. Okay, here's a division problem. So 14 divided by four is equal to? I'll give you some thinking time. What's it equal to, and why? Or can you give a rough estimate to what the number might be? Okay, let's have a look. So, 14 divided by four. We have got 14 pieces of fruit, can you see them? Okay. We've got 14 pieces of fruit and we have four children. So we've got 14 pieces of fruit shared between four children. What we want to do is say, I want to share 14 pieces of fruit amongst these four children, and they all want fruit. But, they don't want more or less than someone else. Everything has to be equal when you are sharing or dividing, okay? So, so that it's fair, every single child has three pieces of fruit. Can you see that? Now, they have noticed, that there are two pieces of fruit left. So each child has three pieces of fruit, okay? And three times four is 12. But then we've got another two pieces of fruit 13, 14. And that brings our total to 14 pieces of fruit, like the question says. Now, some of us might say the answer to 14 divided by four is three remainder two. Because each child has three pieces of fruit, and there are two pieces of fruit left for no one. Now, what's going to happen to these two pieces of fruit? Are we going to leave them to rot? What a waste! Now, all four children, don't know if you notice those who are looking to the side. They're looking at those extra two pieces of fruit. They're looking at that remainder. What's going to happen with that remainder? Is it going to be left to rot? So, 14 divided by four is equal to three remainder two, as we said, and that is the remainder two down there, can you see it? Now, obviously we want to share these as well. Just like we shared the other pieces of fruit, why not share these two pieces of fruit as well? So, now that each child has got its three pieces of fruit, that's theirs to keep, they've put them away, they've kept them in a safe place. We've now got two pieces of fruit to share between four children. So, how do we share two between four children? Two divided by four. So, each pair can get one fruit to share. Does that make sense? There are four children and just two pieces of fruit, so these two children can share that piece of fruit, and these two children can share that piece of fruit. So each child will not only have their bag of fruit they've left on the side, but they can also have half an apple! So, each child has 3½ pieces of fruit. And do you know what the brilliant ease is? There are no apples left to rot anywhere. We don't have a remainder anymore. Everything has been shared equally. So 14 divided by four is equal to 3.5. Or we can say, 3½. 14 divided by four is equal to 3.5 or 3½. Each person gets 3½ apples. If we have 14 pieces of fruit shared between four children, each child would have 3½ so it's fair. Okay, let's have a look this division problem. Nine divided by four. So, this time we have donuts, yum! I love donuts, what about you? Okay, we've still got four, just the same four children, they're very hungry children, mind you. Okay. They've had their healthy snack, they've had their fruits. So now is they're allowed a bit of a treat. So they've got some donuts. And again, we don't want some donuts left on the side, rotting. Okay, nine divided by four. We've got nine donuts, shared equally between four children. So, so it's fair, each child can have two donuts each. And again, you see their eyes wandering to the side of that extra donut, that remainder one. What are we going to do with that remainder one? Me and you can't eat it, I know what you're thinking. No, we can't eat it. It has to be shared between these four children. So, hmm, what are we going to do with that extra donut? Of course we have to share it between four, okay? So, nine divided by four is 2¼ or 2.25. So each child will have their two donuts, and they get a quarter of the donuts, okay? So it's fair because we don't want to leave that one remainder. Do you see what the difference is between a remainder and then a decimal? Remainder means I'm just going to leave it to the side, sort of, this is what's left that's extra. But when we convert it to a decimal, everything's being shared, can you see that? Everything's being shared? This donut is now being shared, we're not leaving it to the side for now. It's not a remainder one anymore, no! It's also shared between those four children, they all get ¼, each. 2¼ So nine divided by four is equal to 2¼ or 2.25. Okay. Now, let's have a look at another division question. So from now on, we're not going to be talking about remainders anymore, okay? Because remainders doesn't exactly mean we've shared everything. We want to share everything, okay? We want to see a decimal if it needs a decimal. So, read this question out for me. 661 divided by five. So, if we had 661 objects, shared between five people let's say, each person would receive what? So basically, what we're saying is how many groups of five in 661? So if I split 661 in five groups, how much would there be in each group? So in one group, how much would there be? And that will be our answer to 661 divided by five. Should we have another look? Okay. So I've laid it out over there, can you see how we lay it out? 661 divided by five. Okay. So, can you see those counters? How many 100 counters have I got? I've got six, the blue ones. And what about the 10 counters? I've also got six. And the one counter? One, so that there represents 661. Can you see that? Okay. Now, here, you can see my rectangle. I've got five boxes, these are my five groups. I'm going to be sharing those counters into five equal groups. Are we ready? So, let's have a look. So first of all, I'm going to look at the 100s, and then I'm going to look at the 10s, and then I'm going to look up the ones, does that make sense? So 661, I'm going to do some partitioning. 661 is the same as 600, add 60, add one. You with me? So, first we're going to do 600 shared into five groups, and then we're going to do 60 shared into five groups. And then we're going to do one shared into five groups, and then we're going to see what we get in each group. And that will be our answer. So, first of all, we're focusing on the 100s, so 600. If I was to share it in each group, so first I share 600 amongst five, what would that be? Let's have a look. So I have 100 guys in that group, another 100 guys in that group, another 100 guys in that group, 100 guys in that group, 100 guys in that group. Remainder, I've got a remainder, but we don't want remainders. Where am I going to put that extra 100? Hmm! So, I've been fair so far in each group, there is 100, okay? Or 100 counter. But, now I've got a problem, I've got one left! Okay. Do you know what we're going to do? I have an idea, do you know? Well, first of all, I'm going to say, I'm going to look at my formal written method there, and I'm going to say, "In each group, I've been able to put in 100 counter." How many counters are in each group? One. One group of 100 in that group. So I've put it over there, I've written it there, okay? Now let's come back to that remainder that we've got left. That 100 we've got left. We need to regroup. So, instead of the 100, I'm going to exchange it, for 10 10s. So 10, 20, 30, 40, 50, 60, 70, 80, 90, 100. That's the same as 100. 10 10s is the same as 100. So what I'm going to do, is instead of that 100 there, I'm going to exchange it for 10 10s, okay? So there's the 100, can you see that remainder? I've put in 10 10s now, okay? I've gotten rid of it. So, first of all, we shared the 500, now we're going to look at the 10's, okay? So, we have now got 60 shared amongst five, but it's not 60 anymore, is it? Because we have to exchange that 100. It's 60 add 100 shared amongst five. So actually it's 160 shared amongst five, but we'll say it's 60, the original 60 we had, plus 100 shared amongst five. Should we start sharing out our 10's now? Let's have a look. Get one there, another one there, put three there. Just put another three there. Just put another three in that group. Oh no! What have we got now? So, I have been able to share three 10's, three 10 counters in each group, can you see that? And what have we got left? We've got another remainder! So, first of all, before we deal with that remainder, what am I going to write? How many 10's was I able to share in each group? Three, well I don't know if you said three. Now let's deal with that remainder. What am I going to do? I've got something leftover. I'm going to have to regroup. Well done if you said regroup. So, instead of a 10, I'm going to exchange it for 10 ones. That's one, two, three, four, five, six, seven, eight, nine, 10. I'm going to exchange it for 10 ones. Right. There's my 10, it's now going to disappear, and it's going to be swapped or exchanged with 10 ones. Right. So we've done 600 shared amongst the five, we've done the 100s, we've done the 10s. Now we're going to look at the ones, okay? So I've got my original 10 that I had. So my original one that I had, plus extra 10 ones from my other remainder. And now we're going to do the same thing. What we're going to do? We're going to share it in five groups. Let's make those boxes a bit bigger. One two, three four, five six, seven eight, nine... Not again! How many ones did I fit in each group? Two ones. And again, I've got something left! Oh, deary me! Right, before we deal with what's left the remainder, how many ones did I fit, in each group? Two, sorry, two ones. So I'm going to write that over there. Now, what are we going to do? Well done if you said exchange, we're going to need to regroup. Instead of one, I'm going to have 0.1 10, lots of 0.1. So 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1. That was same as one, 10 lots of 0.1 is the same as one. Now we need to regroup again. Okay, sorry. That one remainder that we've got over there, I'm going to exchange it, I've made my boxes bigger, I don't know if you noticed, for 0.1's. Now, let's see how many would I put in each box, or in each group? Two in there, two in there, two counters in there, two counters in there, ooh! Guess what? We've got nothing left over! Okay, happy day. So I've got 0.1 and 0.1, I've got 0.2. So I've got two, 0.1 counters in there, haven't I? And I've got nothing left over. So what am I going to say I've got in each group, or in each box? Point two. So we're just seeing in one group, we've split everything into groups of five. In one group, what do we have? We have 130, three 10s, 2.2, can you count that for me? Just in one group? Okay, well done. 132.2 is our answer. So 661 divided by five is equal to 132.2. Okay. Right, now it's time for you to pause the video, to complete your task. Once you've finished and you checked for your answers, come back and we will check them together. Okay, welcome back. How did you find that? Let's have a look together. Okay, so the task that I left you with said solve the two calculations. Can you think of word problems to go with the calculations? We have 36 divided by five, and 538 divided by four. So, let's see what you did. 36 divided by five, is equal to 7.2. Well I don't know if you said that. And, what could you have had? Maybe we had £36. shared amongst five children, and each child got £7.20. Maybe we had, so we could have had a money problem maybe it was a weight problem, 36 kilogrammes of weight. Maybe they're going on holidays, divide it by five adults, and each adult only carried 7.2 kilogrammes. It's very light, cause I carry a lot. Okay let's have a look at the second one. 538 divided by four is equal to 134.5 or 134½. And again, maybe it could have been a money problem. £538, divided amongst maybe four charities, each charity would get £134.50. Okay, lots of different options you could have had for word problems. So well done if you got them both answers correct. So 36 divided by five is equal to 7.2, and 538 divided by four is equal to 134.5. Okay. If you would like to share your work with us here at Oak National, then please do ask your parent or carer to share your work for you on Twitter, tagging @OakNational and to use the #LearnwithOak. Now, I just want to say well done on all the brilliant learning that you have achieved today. Now I'm just going to leave you to go and complete the quiz, and I'll say good luck.

Quiz involving division with remainders and decimals.

Which of the below gives the answer for 8 ÷ 5 ?

Which of the calculations below does not have any remainders or decimals?

Which of the below is the answer to 613 ÷ 4 ?

Solving problems involving division with remainders

In this lesson, we will investigate and model division problems, and we will interpret remainders.

Maths

Y5 Maths

Key Stage 2

Year 5

Miss

Solving problems involving division with remainders (Part 1)

Problem solving with whole numbers and decimals

Number

THEME

UNIT

Solving problems involving division with remainders (Part 2)

Calculating and interpreting the mean as an average

Developing strategies to plan and solve problems

Adding 2 or more numbers mentally

Calculating across zero

Investigating properties of number

Exploring properties of palindromic numbers

Exploring properties of number

From the set of numbers below which does not have a mean of 8?

Tickets to the cinema cost £8 each. Five friends go and each friend has the following amount of money: £9,£11,£6,£7,£6 Do they have enough money between them to pay for 5 tickets?

What is the answer to 87 - 88 + 89

Which of the following numbers is not a multiple of 11?

Which of the following numbers is not a multiple of 9?

Lesson overview:Solving problems involving division with remainders (Part 1)

Core Content

Problem solving with whole numbers and decimals: