Rounding numbers using a number line

Key Stage 3

Maths

Accuracy and estimation

﻿Hello, and welcome to your first lesson with me, Ms. Oreyomi. Today's lesson is going to be on rounding numbers up or down. So for today's lesson, you're going to need a pen and a paper, or something you can write on or with. Also, if you could clear away any distractions and put yourself in a place where you're less likely to be disturbed for the rest of this lesson, that would be really great. So pause this video now, go get your equipment, if you have to, or go to a different room with less distractions if you have to as well. And when you're ready, press play to continue. Excellent, let's begin. Okay, so by the end of the lesson, you will be able to round numbers to the nearest integer. You'll be able to round numbers to the nearest 10, or to the nearest 100. And you will also be able to round numbers to a given decimal place. So we're going to come back to that in a moment. But before we proceed with the lesson, what do I mean by integer? Yes, exactly, integers are whole numbers. Okay, your first task is to see if you can place 53.7 on each of these number lines. So in your book, I would suggest you draw each one, and see if you can place 53.7 on each of them. So pause the video now, and attempt these tasks. Okay, so I'm trying to place 53.7 on the number line. For the first one I can see, or actually be able to tell, that each number is increasing by 0.1. So this is 53.1 to 53.2, point three, point four, point five, point six, point seven. So H is going to be where I place 53.7. so check your work and see if you've got that correct. For the next one, it's going up by one each time. So this will be 51, 52, 53, this will be 54. So I know that my number is between 53 and 54, and because it's 53.7, it's going to be closer to 54. So I'm going to write this here, roughly this is going to be 53.7. Now for the last one, for the last number line, it's going up by 10 each time. So 10, 20, 30, 40, 50, 60. I'm going to put it somewhere here. And I'm going to label this 53.7. So check your work and make sure that you have what I've got roughly in your book as well. Okay, so going on from the try this task, we are told to round 53.7 to the nearest integer. I remember from our introduction, our key word integer means whole number. So if I want to round 53.7 to the nearest integer, I am looking for the nearest whole number that 53.7 is close to. So if I write the number 53.7, which we've done before on my number line, is it closer to 53, or is it closer to 54? Exactly, 53.7 is closer to 54. So if I'm rounding this number up to the nearest integer, the answer is going to be 54. Secondly, we're told to round it up to the nearest 10, which means round 53.7 to the nearest multiple of 10. So, again, from the last task, we know that it is going up in increments. This is 51, 52, 53, 54. So it's going to be somewhere around here. So this is going to be 53.7. Now, is this closer to 50 or is it closer to 60? Exactly right, it is closer to 50. So 53.7 rounded to the nearest 10th, the nearest multiple of 10 is going to be 50. How about this one? I want to round 53.7 to the nearest hundred, which means the nearest multiple of a hundred. So, like I said it's going up in tens, so 10, 20, 30, 40, 50, 60. So it's going to be between F and G. So it's going to be somewhere around here. Is it going to be close to zero? Is it going to be close to 100? Yes, it's going to be closer to a hundred. Because it has gone past the halfway point of 50, It is going to be closer to 100. So rounding 53.7 to the nearest hundred is going to be 100. So now we want to try with the number 67.5, and we want to round that number up to the nearest integer/whole number. So, 67.5 is going to be bang on in the middle. Now, if a number is bang on in the middle of our two numbers, do we round up, or do we round down? Exactly, we should be rounding up, because if we look at this 0.5 over here, if a number is five and over, we round up. So although it is bang in the middle of our two numbers, if the number I'm looking up to decide whether to round up or down, which in this case is my five, here. Because this number is five and over, I am going to be rounding up to 68. So, just to recap that, if any number is in the middle, bang in the middle, of my two numbers, I should be rounding up. What of the second one? We want to round this to the nearest 10. 67.5 to the nearest 10. There are two ways of doing this. We could use our number line as we've already been doing. So it's 61, 62, 63, 64, 65, 66, 67, and it's going to be in the middle of H and I. So this is 67.5. Clearly, we can see that if I'm rounding this number to the nearest 10, it is closer to 70 that it is 60. So I'm going to round that to 70. Another way you could do this, which was what I touched on just earlier was, here's our rounding to the nearest 10. This is my tens column, and this is my ones. I can look at my one value and see that it is more than five, and because this seven is more than five, I'm going to increase this six by one, and round up to the next value, to next multiple of 10. So I'm just going to say that again. I can look at my number 67.5. I am trying to round to the nearest 10. So I am looking up my ones value. My ones value is seven. Seven is more than five, so I am going to increase it to the next multiple of 10. Using that same method, let's round this 67.5 to the nearest 100. So again, 10, 20, 30, 40, 50, 60, and 70. So it's going to be between there, 67.5. This is my tens, this is my ones. So I'm going to be looking at my 10th value. My tens value is six. Six is more than five, so I should be rounding up to the nearest multiple of 100, which is 100. Or, just look at your number line, 67.5 is closer to 100 than it is to zero, so I am going to round up to 100. In the next slide, you are going to have a chance to go through some questions yourself. So get your pen and paper ready to do this. Okay, so you have three questions on your screen right now that I want you to try. So I want you to pause the video, attempt these questions, and then come back and check your answers. Excellent, so for the first one, I want to round 56.4 to the nearest integer. So I am looking for the number, the closest whole number that 56.4 is closer to. Is it closer to 56 or is it closer to 57? If you're drawing your number line, you should've seen that 56.4 is indeed closer to, this is a rough sketch, is indeed closer to 56. So the answer here should have been 56. So well done, if you got that correctly. Let's look at the second one. We're rounding 48.2 to the nearest 10. So, this is my tens value and this is my ones value. I should be looking at my ones value. Since my ones value is bigger than five, is greater than five, I would be rounding this number up to the nearest multiple of 10, which is 50. So again, good job if you got the value 50. What of the last one? We want to round the number of 158 to the nearest 100. So, I would be looking at my tens value. So this is my hundreds value, this is my tens value, and this is my ones value. My tens value is five. Remember we said, if it's five and over, we round up. So I would be rounding to the nearest multiple of 100, which is two, just get that down, 200. Okay, now we're going to move on to rounding to a given decimal place. The question says, round 2.44 to one decimal place. When we're told to round to one decimal place, it means I need to have one number after my decimal point. Now I've already marked where 2.44 is on my number line, between 2.4 and 2.5. And, is it closer to 2.4 or is it closer to 2.5? Exactly, it is indeed closer to 2.4. So 2.44 rounded to one decimal place, My answer is going to be two point, and I only need one number after my decimal point. And that is 2.4. What if I have 2.46? Is it closer to 2.5 or is it closer to 2.4? Exactly, this time around, 2.46 is closer to 2.5. So 2.46 rounded up to one decimal place is going to give me 2.5. Let's try another example. This time around, I have to round 35.47 to one decimal place. Instead of using a number line, I could look at my second number after my decimal place. So, if you're asked to round to one decimal place, you're looking at the second number after the decimal place to determine whether to round up or down. So if your number is five, six, seven, eight, and nine, you round up, and if your number is less than five, then it stays the same. So, this time around 35.47, seven is greater than five. So rounding this number to one decimal place is going to be 35.5. What if, just here at this point, I tell you to round the number 35.43, and I tell you to round this to one decimal place. What's my answer going to be? I'm just going to give you five seconds for you to think about that. Round the number 35.43 to one decimal place. What's my answer going to be? So I will be looking at this number three. Three is less than five, so this four is just going to stay the same. So 35.4 to one decimal place, my answer is simply going to be 35.4. Okay, so if I tell you to round 67.499 to two decimal places, we know that we are looking at this third number, this third digit after a decimal place, to see whether to round our second digit up or down. This number is nine, nine is greater than five. So we are looking to round our nine in hundreds to 10 hundreds. So the second number is going to be zero. And I'm going to add a one to the four, so it's going to be five. So rounding 67.499 to two decimal places is going to make it 67.50. Our last example, we're rounding 78.234 to two decimal places. So I'll be looking at this third digit after my decimal point, which is a four. Now four is less than five. So I am going to be rounding, exactly. I'm going to be rounding down. Which means these two numbers after my decimal point stays the same. So 78.234 to two decimal places is going to be 78.23. I'm just going to rub that out and write it again. Rounding 78.234 to two decimal places is simply going to be 78.23. As you already guessed from this preview, the next activity is going to be your independent task. So I want you to pause the video, and when you are ready, I want you to proceed to your independent task, which is on the next slide view. Okay, first question. Using a number line or otherwise, round 67.2 to the nearest 10. So I want to round 67.2 to the nearest multiple of 10. I'm going to be looking at my one value, which is a seven, to determine whether to round this number up or down. Because seven is greater than five, I'll be rounding 6 up to the nearest multiple of 10. That is going to give me 70. Do the same for the second one. This time I am rounding to the nearest 100, which means the nearest multiple of hundred. This is my hundreds value, this is my tens value, which is what I'm going to be looking at to determine whether to round up or down. Again, because it is a seven, it is greater than five. So I am going to be rounding 672 to 700. So the nearest multiple of a hundred to 672 is 700. Now, I am going to use a number line to round this up, 'cause I find it easier to do. So I'm going to put my 67 here, and I'm going to put my 68 here. I'm going to roughly sketch where I think 67.2 is, which is somewhere around here. And I can clearly see that 67.2 is closer to the integer 67 than it is to 68. So I'm just going to write 67 here. Now, I want to round 67.24 to one decimal place. I will be looking at my second decimal place to determine whether to round up or down. 67.24, four less than five. So I'm going to be rounding this number down to 67.2. What of this one? 68.748 to two decimal places, first the small second decimal place. I'll be looking at my third decimal digit to determine whether to round it up or down. Now, eight is greater than five. So I'm going to be rounding my number. I'm going to be rounding four up to five. So it's going to be 68.75. So I looked at my third number after my decimal point to determine whether to round my second number after my decimal point up or down. Okay, the 2016 Olympic had an average attendance of 57,381 fans per event. The ticket cost an average of 43.50 pounds per game. Round the number 57,381 to the nearest 1000. So, this is my thousands of digits. So I'll be looking at my hundreds. Three is less than five, so I will be rounding this down to 57 thousands. So, if 57,381 to the nearest 1000 is 57,000, so that's a five. Now I want to round 43.50 to the nearest pound, should be 44 pounds We now have our explore task where your task is to find a counter example to each of these statements. The first statement reads, if a number rounds up to the nearest 10, it also rounds up to the nearest 100. Your job is to find an example that doesn't work for that first statement. And also a number that ends in a five rounds up. Again, find a statement, or find an example that doesn't work for that statement. Lastly, rounding a number to the nearest integer gets a different result to rounding to the nearest 100. Again, I want you to find an example that doesn't work with that statement. If you can find an example that doesn't work, one number that doesn't work with all three statements, that would be perfect. But if you can only find one number each that doesn't what for each statement, that is totally fine as well. So I want you to pause your video and attempt it. And if you've paused and you're really struggling, then carry on watching the video where I will provide you with some support. This student is thinking about the number 325, and she's wondering which statement this number 325 is a counter example of. So again, pause the video, and think about which number 325 is a counter example of. Okay, so, this student is thinking of the number 325. And, for the first one. Would it work, if your number rounds up to the nearest 10, it also rounds up to the nearest 100? So if I round the number 325 to the nearest 10, it's going to give me 330. If I round it up to the nearest 100, it's going to give me 300. So, exactly 325 is a counter example that doesn't work for the first one. What of the number 4,295? This is just my example. So you could have come up with something else that is perfectly fine. 4,295, if I round that, the second example is saying that a number that ends in a five rounds up. What if I rounded this to the nearest 1000? What is this going to round to? Exactly, it's going to round down to 4,000. So my number 4,295 is a counter example for number two. What of number three? Rounding a number to a nearest integer gets a different result to rounding to the nearest 100. So, I have thought of the number 400.2 if I round the number 400.2 to the nearest integer, I'm going to get, you guessed it, good, 400. If I then round 400.2 to the nearest 100, exactly, I am also going to get 400. So, the number 400.2 rounded up to the nearest integer and the nearest 100 gives me the same result. So this number is a counter example for statement number three. If you manage to get one example that is a counter example for all of these three statements, please send it to your teacher and let them know. Well, we've now reached the end of today's lesson. And well done.

Rounding numbers using a number line

Rounding numbers using a number line

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UnitMaths / Accuracy and estimation

Maths