What is eleven quarters as a mixed number?

What is five halves as a mixed number?

What is nine thirds as a mixed number?

What is one and one quarter as an improper fraction?

What is two and two fifths as an improper fraction?

What is four and five sixths as an improper fraction?

Improper fractions

﻿Hi everyone. It's Mr. Whitehead. Feeling ready for this lesson. Why am I feeling ready? Well I've just taken a lovely walk outdoors, alongside the river, a chance to get some fresh air, and to calm myself and ensure that I'm ready to be focused on learning on maths learning with you for the next 20 minutes. I really hope that you are feeling in a good place and ready for some learning as well. If you need to, please take yourself away from anything around you that's likely to cause a distraction. Just press pause and get yourself set up somewhere where you are able to focus on yourself and your maths for the next 20 minutes. Press pause while you get yourself sorted, and play again as soon as you are ready. In this lesson, we will be comparing and ordering decimals with up to three decimal places. We're going to start the lesson off with some skip counting, before we have a place value battle. After that, we will focus in on decimal place value, and it will leave you ready for your independent task. Things you're going to need, pen or pencil, a ruler, and some paper, pad, or a book, something to write onto. Press pause, go and collect those items. Come back as soon as you are ready. Let's start off with some skip counting from zero to four. I mean zero to three. Four's in my head for another reason. What do you notice about the space between each whole number? There are four equal parts, there's my four. So if a whole number has been divided into four equal parts, what is each equal part worth? One quarter. Let's start off counting in improper fractions from zero all the way to three. Should we say them at the same time? Ready? 0 1/4 2/4 3/4 4/4 5/4 6/4 7/4 8/4 Let's just pause. Which number are you looking at on the number line now? 2 8/4 is 2. Let's continue. 9/4 10/4 11/4 12/4 Where are you now? You're on the 3, good. Let's do the same again. But we're going to count in mixed numbers. On the screen now, you can see those improper fractions that we said. This time, let's count in mixed numbers. Let's alternate. I'll start with 0, then it's over to you. We'll go back and forth. Mixed numbers from 0 2/4 1 1 2/4 2 2 2/4 3 Good, let's go back. I'll start with, so no, you start with 3, and then we'll go back through me. Ready? 2 3/4 2 1/4 1 3/4 1 1/4 3/4 1/4 and we're at 0. That was tough going, to go backwards. I was thinking about what you were saying, and what I was saying, almost got in a muddle. But this should be what we just said. Let's, of course those 2/4's we could of course say as 1/2. 1 1/2, 2 1/2 Let's repeat the process, but this time in decimals. We'll go forwards, and we will alternate again in decimals from zero. My turn. 0 0.5 1 1.5 2 2.5 3 Fantastic. This is what we've just said there. Moving on after our quick skip counting warm up, thinking about improper fractions, mixed numbers, and decimals, I have a challenge for you. Do you see my pink numbers, the pink digits? I would like you to see how many numbers with three decimal places you are able to make using them. Press pause, use the place value columns as a guide. How many numbers can you come up with that have three decimal places using those digits by me? Come back when you're ready. How did you do? Hold your paper up, show me. Good, so I can see numbers with three digits, sorry with three decimal places. And I can see numbers that have five digits in total. So we've got some tens and ones, and then three decimal places filled. Here are some that I came up with. How do these compare? We probably haven't got the same, there are quite a few options. But these are four example numbers that I made. They all have three decimal places. Ah, which one. You're not so sure about the last one. You're right, we wouldn't typically record 35.120. We wouldn't include the zero in that final decimal place. We would include it if there were a fourth decimal place that had a one through to nine in it. But when we've reached that final decimal place, if there isn't any of it, we just leave it blank normally. So perhaps that final one don't agree with. I have some questions for you. How does the value of a digit change in different columns? Look at these digits I've coloured green. What's the same and what's different? What changes from the hundredths column to the tenths to the ones to the tens. What's the same and what's different? Fantastic, I can hear you talking about 10 times bigger. 10 times smaller. The three in the hundredths place is 10 times smaller than the three in the tenths place. The three in the ones place is ten times bigger than the three in the tenths place. What about the relationship between the tenths and the tens? When the columns, when there's a difference of two columns. The three in the tenths is 100 times smaller than the three in the tens. Finish my sentence. The three in the tens is 100 times bigger than the three in the tenths. Now I want us to describe the place value of some of these digits. Place value is so much more than the threes in the ones place. We can talk about it more deeply using the sentences underneath my video. So if I give you an example. The three is in the tens column. Sorry, the three is in the ones column. The three represents three ones. There are three ones. Can you have a go with some of the other digits using those sentences? Work through the three sentences, and I'll listen out for the numbers, the orders of the digits you're describing. Go. Sentence two. Good! Sentence three. Fantastic. Take a look at these numbers now. What's the same and what's different about them? Tell me some things that are the same. Yeah. They both have one 10 and five ones. Oh, one has five digits, one has four. One has three decimal places, one has two. Good. Which of those two numbers has the greatest value? Which one? Say it again. Oh, how do you know that has the greatest value? Okay. I'm going to show you something now to help support your explanations. Well, to help support you identify the greater or less value, add to support your support your explaining. I'm going to use place value counters to represent each of the parts of these two numbers. Pause. Have a go at drawing them yourself, then come back and check. Right now I'll show you. So, hold up your paper first of all. Let me have a look. Good drawings. I can see clearly the columns. I can see the number of counters representing. Fantastic, the digits on each of those column. Let's compare. One 10, one 10 in each. Five ones, five ones in each. Here's where things start getting different. Two tenths, zero tenths. Two hundredths, three hundredths. Three hundredths, zero hundredths. How does this help us to explain which has the largest value? Yeah 15.23 We've got two tenths. We haven't got any tenths in the other number. So 15.23 has to be larger. We've got 23 hundredths. We've got 230 thousandths, in this bottom number. The top one, we've got 23 thousandths. We can compare using that place value language, and identify and explain which of the numbers has that greater value. We're going to play a game now. I'm going to reveal five digits. As the digits appear, you need to decide in which column to place the digits. The target is the smallest number possible. By the end, you will have a five digit number. You want it to be as small as you can, so as the digits appear, think. Am I going to put that in the tens, the ones, the tenths, the hundredths, or the thousandths place? I'm going to play with you. I've got some paper, it's blank, and my pen. So as the numbers appear, let's both decide which column to pop them into, and at the end we can compare and see who achieved the target, who made the smallest number. So maybe, grab your pencil and a pen as well. I'm just writing down a T for tens, an O for ones, going to draw the fraction tenths, the fraction hundredths, the fraction for the thousandths. So my paper now looks like this. And underneath those headings I'm going to write down, choose where to put the digits as they appear. Are you ready? six Where are you putting your six? Now, you don't know which other digits will come up. Choose carefully. I'm putting mine here. Next digit, are you ready? two Oh, two, two, twos I'm going to put my two, okay done. Are you done? Next digit, oh zero Okay. Ready? Two digits to go. nine Where are you putting your nine? And final digit, a one. Oh, wow. Okay. Are you ready to compare? Now, I'll show you which number I created. Hold yours up to the screen, and I want you to tell me which of us has the smallest number. I've got 20.169, what did you get? So who's won? Who has the smallest? Okay. Let's play again. You ready? It's the same idea. This time the largest number possible as the digits appear. Which column are you placing the digits? And why? Why are you placing the digit in the column you've chosen? The aim is the largest number. Make really careful choices. Got a five first. Okay, put it there. Next one. Ready? seven Okay. picked Ready? Third digit, where's it going? Oh, eight Wish I waited. Fourth digit's a one. Ready for the final digit? three, oh wow Really close, mine was really close to being as large as it possibly could be, I think. Are you ready to hold up yours and compare? To look at my second number, 78.531, what was yours? Who has the largest number? Okay good work. Are you ready for another one? The smallest number possible, five digits are going to appear. Same rules again. One digit per place. Choose carefully as each appears. Make you sure you record before the second or third and each next digit appears. five Smallest number, where are you putting five? Next six Okay. Ready? nine, wow. Smallest number possible. All right, two digits left. seven final digit, a two, yes Okay ready to show? One, two, three, hold yours up. I've got 27.659, what did you get? Who has the smallest number? That was fun. Okay, keep those numbers safe. You could choose to use them later in your independent task. Let's have a look at these. The target was the largest number possible using the digits five, four, nine, one, and six. Who won? The person at the top had the lesser number. What's the number, how do you know? They have six hundredths, the other person only had one. They've got 961 thousandths, the other person only had 916 thousandths. They both had 54 ones. So the person at the bottom was closest to the target. Now, looking at the person at the top. What changes would you have made, so that they could, with those digits, have the largest? Press pause, and make those changes. Create the largest number possible to show them where you could have placed the digits to achieve the target. Are you ready? So, what did you get? Tell me the number you created, the largest possible. 96.541 Look at the pattern with those digits. From the largest value to the smallest to help us create that largest possible number. In the independent task you're going to have the opportunity to look at some numbers that we've made, and make some changes to them. If you want to, you could also do that with the numbers you created while we were playing the game together. The largest, the smallest, the largest What changes would you make so that the number you created achieves the target each time? That's an extra, definitely do it though, please, with the numbers I prepared for you. Come back when you're ready to check. Let's take a look. Hold up your paper, I want to see what you did with each of these numbers. How did you change them? You can see the targets, largest and smallest. Oh, let's compare now. Well done everyone, let's have a look. So, for the smallest, the first one 78.061, I've created this. Before I look at the next one, one possible change here. Some of you might not agree that 1.678 is the smallest because I haven't technically used all five digits. So perhaps if I would be fair by having 10.678, I've used all five digits, they're all used in the number. Whereas this, I'm not really the zero, am I? So actually, probably this is the smallest you can make. The largest over here, 87.431. The smallest, 23.569. And then the largest, I have 53.21. Again, you might not be happy because I haven't technically used the zero. So perhaps, 53.201 would be the largest you came up with. I hope you enjoyed this lesson. Looking at the size and value of different decimal numbers, playing that place value battle, who came up with the largest and smallest number using those digits. It's a really fun game to play, perhaps one that you can repeat. If you want to share any of your learning from this lesson, please ask your parents or carer to show your work on Twitter, tagging @OakNational and #LearnwithOak. Wow, you have worked incredibly hard this lesson. I'm not surprised, but I definitely am pleased. I am proud of all of you for all of your contributions, joining in, or calling out, and all of that brilliant learning. You have earned yourself a well deserved break between now and whatever else you have lined up for the day. I'm going to be taking a quick break, possibly another quick walk outdoors, depending on the weather. I look forward to seeing you again for some more maths learning. Until then, look after yourselves, and I will see you very soon. Bye!

Which is worth the most?

Which is worth the least?

Ordering decimals

In this lesson, we will compare and order numbers with up to 3 decimal places.

Maths

Y5 Maths

Key Stage 2

Year 5

Comparing and ordering

Fractions and decimals

Number

THEME

UNIT

What is a fraction?

Representing fractions

Equivalent fractions

Tenths and hundredths

Ordering fractions

Thousandths

Comparing fractions and decimals

Improper fractions (Part 1)

Improper fractions (Part 2)

Rounding Decimals (Part 1)

Rounding Decimals (Part 2)

Fractions and division (Part 1)

Fractions and division (Part 2)

A half can be represented by a shape divided into two parts.

Which fraction of the square is shaded pink?

What is six tenths as a decimal?

What is four eighths as a decimal?

If white is one half, what is black?

Round to the nearest whole number: 5.16

Are these in ascending or descending order?  One half, one third, one quarter, one sixth

What is one hundred and seventeen thousandths as a decimal?

Lesson overview:Comparing and ordering

Core Content

Fractions and decimals: