Intro Quiz: Estimating and rounding contexts

Video: Estimating and rounding contexts

﻿Hi, welcome to your maths lesson. My name is Mrs. Harris, and we're going to be looking at rounding and estimating in real life contexts, so when you'd actually use it. Here's what we're going to do. We're going to start our lesson by looking at real life contexts, then we'll move on to consider appropriate degrees of accuracy when we're estimating, then we'll actually make some estimates before you do your independent task. Now, you're going to need a few things. A pencil and a rubber, maybe a ruler, and something to write on, a piece of paper or a book. If you don't have these things, pause the video now, go and find them, and then come back to me. Okay, got everything you need? Let's get started then. Here, we're going to look at our real life contexts for estimating and rounding. Here are some reasons why we might need to round or estimate. If we took the number line, and I asked you to plot a number on it, you kind of have to estimate where it would go because you haven't got all the intervals on there. Likewise, with the jug, if you knew that that was one litre at that top mark, you could estimate the rest of the liquid and find out how much you need. With the cherries, you could estimate how many are in the box, how many bananas would you need. With the map of Dr. Livingtone's expedition, you can estimate the total length of his journey. When shopping, you could estimate how much it's costing you as you put each item in the basket, or you could estimate your weekly budget. You could estimate the number of bottles of water in the packet, or you could calculate quite quickly, and you could estimate how many marbles or sweets there are in a jar just by counting a few of them and estimating the space. What do we need to know to make an appropriate estimate? Well, we need to know the purpose of the estimate, and we need to know the magnitude of the number or quantity. Now, let's look at appropriate degrees of accuracy. These three scenarios, we've seen them before, the map, the shopping receipts, and the cherries. What would be an appropriate degree of accuracy if we were to estimate each of them? Would you round them to the same multiple each time? Would you round them to the nearest 100? Would you run them to the nearest 10? Let's imagine these children are doing a geography project. They want to compare the population of different capital cities in Europe. The girl says, "The population of Paris is 2,206,488." And she thinks, "We need to round it "so we can compare it easily to the population "of other capital cities." It would make it easier, wouldn't it? If we rounded it and some of the digits weren't there that we had to say or look at. It would make it a quicker comparison. So, the boy then says to her, "This is a seven-digit number "and is only going to be used for a rough comparison. "I think we could round it to the nearest multiple "of a million so that it would be 2 million." Hmm. There are probably quite a lot of cities with populations around 2 million, so our estimate may not be accurate enough. 200,000 is quite a lot of people to forget about. What about rounding it to the nearest multiple of 100,000? I think that sounds like a better idea. I get where she's coming from, and so does he. So a good estimate for the population of Paris is 2,200,000. They didn't round to the 10s, did they? Like we looked at a minute ago. And they didn't round to the 100s, or even the 1,000s, or even the 10s of 1,000s. But they reasoned why they were rounding to the 100,000th place. I've got a couple of problems for you, and as you look at them, I'd like you to consider what would a reasonable estimate be and why? Firstly, look at the Children in Need target problem. We can see how much they want to raise. We can see how much they've raised. We need to report how much they've raised, and how much they still need. Then, have a look at the problem with the bedroom wall. We know how long the bedroom wall is, its length. We need to know or estimate how much would we need to buy to make a shelf. So pause the video now and consider these problems. Welcome back. So let's take the Children in Need problem first. Their target is £50 million, and so far they've raised £7,598,912. Now, we could round that to 7,600,000, and that's how much we could report that they've raised. But when we consider that figure in terms of how much is still needed, I don't find it that helpful. So I would tell, if I had to report, I would say that they needed to still raise £42 million. Then, if we took the problem of the bedroom wall, we can see its length, but we wouldn't want to round it down at all, to 160, would we? Because then our shelf would be too small, too short. So we would round it up. Also because its decimal point is past the five. And so we would need to buy 161 centimetres of wood to make a shelf. Now, I've already made some estimates. I want you to think, are they appropriate? Why or why not? And what could a better estimate be? So take a look at these problems. Okay, let's look at the England game at Wembley. The actual attendance was 88,795 people, and a newspaper reported that as 89,000. I think that is an appropriate estimate. It's rounded it up and made it much easier for everybody to read. However, if we look at the other one with Dev's walk, he's walked 5.2 kilometres, and he's estimated that and said, "It's about 10 kilometres, I think." Well, no, he's rounded it up quite significantly, almost doubling the length he walked. That should be rounded down, and he should estimate that he walked five kilometres. That's quite a significant difference. Is that what you thought? So now, it's time for you to make some estimates of your own. Here, we have Dr. Livingstone's expedition again, but I'd like you just to take a second to have a look at each leg of his journey, which we can see is 636 miles, 427, 586, and 527 miles. That's being accurate. We haven't got the time to be accurate. I just want a quick estimate, a reasonable estimate, of the length of his expedition. Okay, if we rounded 636 down to 630, and we rounded 427 up to 430, 527 up to 530, and if we rounded the 586 up, we could get to 600 miles. Therefore, I can quite clearly see that the estimate, a reasonable estimate would be over 2,000 miles, and my estimate would be 2,150 miles. Answer a. Now, this one, we've got the cherries again. And we need to estimate how many boxes of cherries the teacher should buy to give as a snack for two classes? Well, there's a few variables here, isn't there? Well, we don't know how many children are in the class, but we know most classes are around 30. We don't know how many cherries are in the box, but we could estimate that there's about, ooh, what do you think? I think there's probably about 40 cherries in the box. How many cherries is she even going to give each student? I think, if she's going to give everybody at least two cherries, she's going to need to buy four boxes. Here, we have the shopping receipts again, and they're from one week's shopping. If we added them together, what would be a reasonable estimate for a weekly shopping budget? Now, we don't want to look really closely at each pence, and we don't want an accurate figure for what they spent this week. We need to round each figure up or down and then add them together. So if we had the first, one instead of £74.68, £75, the next one, we'll have as £66, and the last one, we'll have as £59. If we added them figures together quickly, the weekly shopping budget would be £210, and it didn't take us quite as long to add up. Now, Graeme wants to buy a shelving unit, and he needed to know if it would fit in his lounge. He only had a ruler instead of a tape measure, so he measured the width of one square. His measurement was 27.3 centimetres. I'd like you to sensibly estimate the height and width of the entire unit. Pause the video now and have a quick go at this. Okay, I had a go too. So that I could do it quickly, I didn't use the figure 27.3. I rounded it up to 30. I then had 30 times 4, 120, and 120 going up as well 'cause it's a square. So the width of my shelving unit, or Graeme's shelving unit, is 120 centimetres, and the height of it is 120 centimetres. And if we wanted to change that into metres, it would be 1.2 metres each way. Now, we've got a little problem with the money raised for Comic Relief. We'd like to know how much has been approximately raised altogether by these three comedians. What would be a sensible estimate of the total? Okay, the sensible estimate of the total would be 1,300,000. We should have a look at our figures and round them up or down appropriately, and then add them together. It's easiest if we don't worry about the 100s in this case, the 10s or the ones, and we added the other figures together. Now, it's time for you to do your independent learning. Let's take a look at the independent learning I want you to do. So you've got a problem. Bethany and George are each thinking of a whole number, an integer. Bethany rounds her integer to the nearest 100. George rounds his integer to the nearest 1,000. What are the smallest possible sum of the original integers? Remember, sum is the total when we're doing an addition equation. So pause the video, have a go at this, and then come back to me so we can discuss the answer. Welcome back. How did you get on with this? I thought I had the answer, but then when I thought a little bit harder, I didn't. So my original answer was 550. I thought Bethany's integer could be 50, and she could round it up to 100, the nearest 100. I thought George's integer could be 500, and he could round it up to the nearest 1,000. But when I thought about the problem a little more, I realised I'd forgotten about rounding down. If Bethany's number was one, she would round it down to the nearest 100, multiple of a 100, zero. And if George rounded his integer, which was also a one, down to the nearest 1,000, that would be zero as well. So I'm thinking that the smallest possible sum of their integers was two. Like to say a big thank you for all your hard work today. And if you'd like to share any of your work with me and everyone at Oak National, please ask your parent or carer to pop it on Twitter for us, tagging @OakNational. I'd love to see some of your work. Now, the only thing that's left for me to do is point you to the quiz that I'd like you to do and to say goodbye, bye.

Worksheet: Estimating and rounding contexts

Exit Quiz: Estimating and rounding contexts

Completed: Estimating and rounding contexts

The learning in this lesson supports pupils in developing number sense as well as applying the skills of rounding and estimating linked to everyday situations.

Maths

Estimating and rounding contexts

Introductory Quiz

Video

Worksheet

Final Quiz

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