Which is greater?

Which is worth the least?

Which is worth more: three fifths or four tenths?

Which is worth more: two fifths or five twentieths?

Comparing fractions and decimals

﻿Hi everyone, it is Mr. Whitehead here for your maths lesson. Are you in a quiet space free of distractions? If the answer is yes, then carry on watching and we'll get started. If the answer is no, please press pause. It's so important that you're able to focus and give me your undivided attention. So if you need to move away from any distractions, whether that's siblings or the television, please press pause and do that now, finding yourself somewhere quiet where you're able to focus. Then you can press play again and continue with the lesson. In this lesson, we are recognising mixed numbers and improper fractions. We'll start off with a skip counting activity. Then we're going to separately look at improper fractions and mixed numbers. That will leave you set up for the independent task to end the session. Things you're going to need, so press pause in a moment while you collect a pen or pencil, some paper, a pad or a book, and a ruler. Go and get those things now. Come back and we'll get started. Okay, so some skip counting first of all. Here is the number stick. Divided into how many equal parts? Into 10 equal parts, but the whole of that stick represents how many tenths? It just represents 1/10, the space between, the difference between 2/10 and 3/10. So to help with our skip counting, I've included the equivalent hundredths. 20/100 and 30/100, giving us some numbers to actually skip count in. Let's start off in fractions. From 20/100, my turn, your turn. 20/100, 22/100, 24/100. 26/100, 28/100, 30/100. Let's go back, your turn, then my turn. Back from 30 100ths. 29/100, 27/100. 25/100, 23/100. 21/100, fantastic. What would be the number that you would say next? The one that would come before 20/100? 19/100, well done. Let's do this again but this time in decimals. So here we've got the decimal equivalents of 2/10, 3/10. 30 and 20/100. Let's count in decimals. Let's go back from 0.3, back from 30/100. My turn, your turn. 0.29, 0.27, 0.25. 0.23, 0.21. Really good, well done. Okay, moving on. This session is going to focus, as I said, on mixed numbers and improper fractions. And it will use these rods throughout. Let's make use of these rods to start off with with whole numbers. So from this selection, the white rod is worth one. So if the white rod is worth one, then the red rod is worth, the green rod is worth. Let's focus on what each of those other colours are worth. So if the white rod is one, you tell me what the red rod is worth. Good, and the next one? Next. Next. Now is the next one six? Who thinks it is? Anyone think it's not? Why not? Yes, look at the yellow rod compared to the pink rod. Look at the difference in size. Then look at the difference in size between the yellow and black. It's two lots of the previous difference. So if the previous difference is one, it's now two lots of one, it's two white rods. So the next number? Good. Same again or one more? Fantastic, nine. So watch out for those changes in the difference between consecutive rods. Is the difference one or more than one? In this case, two. Same again, but now the white rod is worth 10. So tell me the length or what, sorry, yeah the length and what the red rod is worth. Good, green? Pink? Yellow? Black and blue? Well done for spotting that increase, that difference of 20 between the yellow and black. Between 50 and 70. The difference, tell me, the difference between the green and the pink? Just 10, just one white rod. How about now? The white rod is worth two. So the red rod, then the red rod is worth four, good. Green? Pink? Yellow? Black? Well done. Why is there an increase of four between yellow and black? Really good, so we know that each white rod is worth two. The difference between red and green is white. It's one white rod, it's two. But the difference between yellow and black, it's two white rods. It's one red rod, a difference of four. What's the blue rod worth? Good, same again. It's that difference of four. A red and a black is equal to a blue. Or a black and two white, good, is equal to a blue. Let's now change things up. The white rod is now worth half. What are the other rods going to be worth? We're going to look at this in a number of different ways. First of all, in words, just how we would say it. If you'd like to pause and work out what each of those other rods would be worth, do that now. Otherwise, if you think you can join in as we go, keep watching. So tell me, if the white rod is worth half, then the red rod is worth, good, one. Green, 1 1/2. Good, green is red and white. One red, one white. It's 1 1/2. Pink, good. Yellow? Now black, what's it going to be? Three? 3 1/2. There's space for two whites, for two halves. And that's one. How about the next one, blue? Good, it's also one more, one whole more. One red more. Two whites more, two halves more. Good, so if that's how we say these as words, now how would we write them as decimal numbers? Again, if you want to pause and work ahead, do that now. Otherwise, say the decimals as we work through. If the white rod is worth half, 0.5, then the red rod is worth one. Green? Good. Pink? Yellow? Black? Good spot, 3.5. Blue? Same again, an increase of one. An increase of two white rods. 4.5 well done. Still a half, so we've looked at it in words, in decimals, now as mixed numbers. There's a really nice link here to how we say them. If the white rod is worth half, we'll work through the others. Pause again if you'd like to. Write them down them come and join us or say them as we go, ready? What's the red worth as a mixed number? One, it's just a whole one. Green? 1 1/2. And that's how we write it as a mixed number. 1.5 as a decimal, 1 1/2 in words. One and the fraction 1/2 as a mixed number. Pink? Two. Yellow? 2 1/2, good. Black? Good spot, 3 1/2. Blue? 4 1/2, really good. Final way to look at it, improper fractions. For this, we need to keep in mind how many halves each of the rods are equal to. How may halves is the white rod equal to? One, 1/2. The red rod? 2/2. The green? Good, there we have our improper fractions. What do you notice about them? The numerator is a larger number than the number that is the denominator. That is an improper fraction. Pink? Good. Yellow? Now what about for black? Two more halves, 7/2. And blue? 9/2. Now look, we can see the halves that are making up each of the rods. It's quick, but do you notice them? We can see the seven, the 9/2. That's why we can use that improper fraction to describe the length of that rod compared to the white rod that is 1/2. Let's think about that again. Same process, but for a different fraction. This time the white rod is worth 1/4. Can you, if you would like to, press pause now and work through the size of each of the other rods just in words. If you're ready to join me, let's say them together now. So if the white rod is worth 1/4, then the red rod is worth? Good, 2/4. Green, 3/4. Pink, one. We know 4/4 is one, we would say this in words as one. Yellow? Fantastic. Black? Really good. It's an increase of 2/4, two white rods. And the same again for the blue. So what will that make that length? Yes, 2 1/4, 2/4 more than 1 3/4. 1/4 more would be two, another 1/4 more, 2 1/4. Good. How about as decimal numbers? So again, you know the drill. Pause if you'd like to. Record the decimals, then come back and join us as we say them. If the white rod is worth 0.25, then the red rod is worth, good, 0.5. Green? Well done. Pink? I was going to say blue. I mean yellow. Super, what's going to happen here? Fantastic, 1.75. And then 2.25. Really good, decimal representation of the length of those rods and number of quarters. How about as mixed numbers? There's a link to how we say them, remember. Again, pause if you want to or let's work through them now. If the white rod is worth 1/4, then the red rod is worth 1/2. We could say 2/4, but we would likely simplify that to 1/2. Green? Good, 3/4. Pink? Yeah, one. Yellow? Well done. Black? Really good, 1 3/4. And blue? 2 1/4. You know what's coming, improper fractions. How many quarters are each of the rods? Pause if you'd like to. Make the list of improper fractions. Otherwise, say them as we go. Ready? If the white rod is worth 1/4, then the red rod is worth 2/4, good. Yellow? Pink? I said yellow, didn't I? What colour is this, silly Mr. Whitehead? Green, 3/4. Pink? Fantastic. Now we can have yellow, well done. Black, yes two more quarters. And blue, another two, so 9/4. Well done. Notice again, the number of quarters in each of the rods. You can see the quarters that are making up the length of the rods and why we can say them in this improper fraction form. I'd like you to pause now and go and complete your activity. You're more than ready for it. Come back when you're ready to check the solutions. How did you get on? Hold up your paper. Let me see how you've represented it. Keep that paper still. Uh-huh, looking good. Is there anything on the back? No that's fine, yes there is, okay, super. Super well done, okay, paper down. Let's compare, let me just go through the solutions. So in this case, we're told the length of the yellow rod and from that, we have to reason the length of the other rods. You should, if you're comparing that yellow perhaps with a white to start off with, then we should spot that the yellow is worth 5/5 or one. Because the white is representing. Or we would use five of the white to make one yellow. We would need more than five for the black and the blue. More than 5/5, we would need fewer than 5/5 for the two greens. Oh sorry, for one of the greens. The darker green we would need just 1/5 more, 6/5. I asked you to record as an improper fraction. That's this. I also asked you to record as a mixed number. And as a decimal number. Decimals wise, 10ths, 100ths, 1/5. 2/10, 0.2. And then multiples of 0.2. Steps of 0.2 to help us increase by 1/5 at a time for the other rods. Check those off. Pause on this page if you're still checking because I'm going to the next page. This time the red is worth one, so then we're looking at the green. Hmm, a bit more. How much more than a red is a green? We should have spotted that it's 1/2 more. That the red is 2/2, that the green is 3/2. There are the rest of the improper fractions as mixed numbers, we're looking at this. And as decimals, decimals. 1/2 as a decimal 0.5. So we've got one, then 1.5, 2.5, 4.5. Again, if you need to still check anything, press pause on this page. Final one, we are told the white rod is worth 1/3. Comparing the white rod to the yellow rod, we can spot that the yellow rod is made up of 5/3. And from there we can work out the length of the remaining rods. There are your mixed, sorry your improper fractions. Here we've got our mixed numbers. And finishing up with our decimals. Something we haven't talked about is how to represent 1/3 as a decimal. All I'm going to say at this point is that as a decimal we would record 1/3 as 0.333. 2/3 as 0.666, therefore 4/3, 1.333. 5/3, 1.666. If you would like to share any of your fantastic learning from this lesson, please ask your parent or carer to show your work on twitter, tagging @OakNational and #LearnWithOak. That was absolutely fantastic. Thank you so much for joining me, for contributing, and working so so hard on your learning over the last 20 minutes. You've left me in a really really good mood and I hope that you are feeling just the same. If you've got more learning lined up for the day, then I hope you approach that in exactly the same way as you have this maths lesson. Do take a break first though. I look forward to seeing you again soon for some more maths. Until then, look after yourselves and I will see you soon, bye!

Use this image to answer the questions

If white is one half, what is red?

If white is one half, what is yellow?

If white is one half, what is black?

If white is one quarter, what is green?

If white is one quarter, what is pink?

If white is one quarter, what is blue?

Improper fractions

In this lesson, we will recognise and name improper fractions and mixed numbers.

Maths

Y5 Maths

Key Stage 2

Year 5

Improper fractions (Part 1)

Fractions and decimals

Number

THEME

UNIT

What is a fraction?

Representing fractions

Equivalent fractions

Tenths and hundredths

Ordering fractions

Thousandths

Improper fractions (Part 2)

Comparing and ordering

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?

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?

Which is worth the most?

Lesson overview:Improper fractions (Part 1)

Core Content

Fractions and decimals: