Which is greatest?  One half or one quarter

Which is greatest?  One third or one fifth

Which is worth less?  Two fifths or two sixths

Which is worth less?  Two quarters or two sixths

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

Are these in ascending or descending order?  Two eighths, two fifths, two quarters, two thirds

Comparing fractions

﻿Hi everyone, it's Mr. Whitehead here ready for your math lesson. And I'm feeling really ready for this lesson. Earlier on I took a walk outside, breathed in some fresh air. I live close to a river, so I took a walk along the river and it really lifted my spirits. So I'm feeling, as I said, really really ready for this lesson. All that we need to do now is check that you are in a distraction free zone. Do you have any siblings around you that you need to send off somewhere else? If you haven't got any siblings, perfect. But is there a television to turn off or some notifications to turn to silent on any type of technology. Take a moment, please by pressing pause to get yourself sorted and ready for the lesson to start, press play again once you're ready. In this lesson, we will be reading and writing decimal numbers as fractions. We're going to start off with a number line activity. Before we spend time looking at tenths and hundredths, what they are, what they look like, how to record them. Then we're going to look at some common fractions as decimals. All of this is going to set you up for the independent task for the end of the lesson. Things that you're going to need a pen or pencil, some paper or pad or book from school and a ruler, press pause, collect the items, then come back and we will start. So the fractions on a number line activity, here's a number line, I've already marked it. I'd like you to think of and record some other fractions along the line. Press pause, copy the number line down. See which other fractions you can include. Come back when you're ready, hold your number lines up. Let me have a look, how did you get on? Keep them steady, there we go. Fantastic. Compare to the choices that I made. When I looked at the number line one half, three quarters, I used my skills and knowledge of equivalent fractions to get me started. One half is the same as two quarters. Okay, sit between two quarters and three quarters what could I represent? Well, there's only a difference of one quarter. So let me make some changes again. Let me think about those quarters as eighths, four eighths, three quarters is six eighths, brilliant. Now I can represent the eighth that falls between four eighths and six eighths, five eighths. Halfway between the two I could have stopped, but I continued using my skills of equivalent fractions this time thinking about sixteenths. Did you see that change? Four-eighths, eight-sixteenths, six-eighths, 12-sixteenths. So now I've got some sixteenths that I can mark between eight and 12. Nine, eight, sorry, nine sixteenths falls between eight sixteenths and five eighths, five eighths, 10 sixteenths, nine sixteenths halfway between the two. So between 10 sixteenths and 12 sixteenths again, halfway 11 sixteenths. How did that compare to yours? Were you able to follow my train of thinking? My mathematical thinking, as I explained to these connections to equivalent fractions, that helped me to fit in some other fractions on the line could have continued I chose to stop there. Okay, moving on then thinking about tenths and hundredths, looking at these four shapes, what do you know about them? When are you used to seeing them? What can you tell me? Tell me something about the orange cube and the blue flat, the blue flat shape. How about the green stick? And what's about the yellow cube. So we've got a big cube, a small cube. I've got a flat and a stick, so great. Yes, we're used to seeing the orange cube, the largest cube representing a 1000 the blue flats are representing a 100 the green stick representing 10 and the yellow small cube representing one. These pieces of mathematical equipment, really helpful. They're called dienes really helpful for representing these numbers because of the relationships in size between each of them and the numbers they're representing. What if the orange cube that normally represents a thousand represented one? What would that mean for the other shapes? Pause and have a think if you'd like to or keep going with me, if you're ready to call some things out. So if the orange cube is one, what is the blue flat shape? It's one tenth. It's one tenth the size of one. It's one divided into 10 equal parts. And that's one of them. 10 of those blue flats would make one orange cube. It's one tenth. The stick the green stick compared to the orange one. The green stick would be one hundredth, because one hundredths would make one orange cube. One orange cube divided into 100 equal parts. That is one of them. One of the hundred equal parts, one hundredth, the yellow cube. We will be coming to in a future lesson. But you might already have come up with an idea for that. I'm sure. Okay, then how would we represent this in our place value chart with which digits we would represent this with a and where would that digit be? Brilliant a one in the ones place. Nice and simple. How about this one? So it's one tenth, a one in the tenths place. One tenth. How about this one? How would... Read out the whole decimal? What the decimal would be and say, it's a fraction. Fantastic, it's one hundredth. It's a one in the hundredths place, one hundredth. Okay, what if we've got more than one of some of these shapes? Here are flats. One flat represents one tenth. What are we representing here? Four tenths, so as a decimal, 0.4, a four in the tenth place this time, what do we have? We've got hundredths. How many of them did you notice the pattern? Five and two, set five in the top row and then two, we've got five and two, seven. So it really helps you to see it quickly without counting seven sticks, seven hundredths as a decimal 0.7, 0.07 as seven in the hundredths place. Seven hundredths well done. And this time fantastic. There are 13 of them, 10 and three, 13 hundredths like this, now what would you change? Why there is a rule you're right. When it comes to place value, we can only have one digit per place. What's the largest digit we could have in any place nine and the smallest zero representing that there isn't anything of that column. Of that place of that thing. Nine is the largest digit after that. What do we do? We start to regroup to the next largest column. So if we had 13 hundredths, that's the same as one tenth and three hundreds. We regroup 10 of the hundredths for one tenth, recording like this 0.13, 13 hundredths. Fractions as decimals, here's a fraction. How would we represent that as a decimal? Hmm, pause and have a think. Write some things down or if you're ready, start telling me what would this be a it decimal? 3.5, 0.35, no tenths and hundredths, three fifths, tenths, three fifths is equal to six tenths, six tenths, 0.6. And it would look like this. How about this one, one quarter. Ooh you might be quick at recalling this. You might want to make some connections to tenths or hundredths pause if you need to carry on if you're ready one quarter, hmm. Can't make a relationship to tenths I can to hundredths four multiplied by fantastic four multiplied by 25, 25, four times is 100. 25 one time is 25, one quarter equal to 25 hundredths, 0.25, which would look like this. Wow, 25 hundredths. But we know we can't have a two and five in the hundreds place. We regroup 20 of the hundredths for two tenths. Here I would like you to pause record as decimal numbers and with drawing of Dienes now you haven't got Dienes at home to show me I doubt. I haven't TIVA to show me those fractions decimals and with dienes. So use some drawings instead, the flats, the blue flats, you can draw a square. The green sticks to draw a line. There are three fractions there represent them as decimals. Use some equivalence work, make connections to tenths and hundredths represent as a decimal, any equivalent fraction, and a drawing of those flats and sticks. Come back when you're ready. Okay, hold up your paper, let me have a look. Three fractions, some equivalents okay, good. Some decimals and the drawings fantastic. Compare to mine please. So three quarters starting with, while we've just looked at one quarter, haven't we 0.25, 25 hundredths. So we could either use that or make some connections or recall it. But three quarters, how many hundredths? Fantastic 25 three times, 75 hundredths as a decimal 0.75. Now the drawing we would use here, seven flats for seven tenths, 70 hundreths. That's what is equivalent to and five hundredths, five sticks, 0.75. Next oh, an easy 21-hundredths. We can straight away record that as a decimal 0.21, two tenths, one hundredths 20 hundredths and one hundredths, the 20 hundreds equal to two tenths, two flats and one stick. Four-fifths hmm, some connections two tenth yes four fifths. How many tenths? Eight tenths, well done. Eight tenths as a decimal, 0.8 as a drawing eight flats. 80 hundredths equal to eight tenths, eight flats. Well done. How is this written as a fraction five hundredths. Notice as you say 0.05, as you say what it is five hundredths, you hear it as a fraction, five hundredths, five hundredths. I wonder if that can be simplified. Is there any connection between one hundred and five, one hundred and five,? Is there a connection? Yes, of 20 five twenties is a hundred, 100 divided by five is 20. Five divided by five is, is one. One 20th is a simplified version of five hundredths. It's five hundredths in its simplest form. Next how would we say this one? How would we write this one as a fraction? 12 hundredths. We're saying what we can see in the place value grids, 12 hundredths. Is there a simplified version of 12 hundredths relationships between 12 and a hundred? We're thinking about factors there. We're thinking about the Highest Common Factor of 12 and a hundred. We're thinking about numbers we can divide 12 by and divide a hundred by and the highest one that we can choose. Four, 12 divided by four, 100 divided by four. How many fours in 100, how many fours in 12? Excellent. Three twenty-fifth, three twenty-fifth is a simplified version of 12-hundredths. Their equivalent we can write 0.12 as 12 hundredths or as three twenty-fifths. All three of those are equivalent. It's time for your task. Press pause, go and complete the activity. Then come back when you're ready to share, how did you get on? So we were matching. Wow, look at all of these representations we were matching fractions, decimals, and the flats and sticks. They're all blue, this time and still they're representing the same idea, a flat a tenth a stick, a hundredth. There's a lot of matching here happened. I wonder how you laid it out though. Hold your paper up so I can see how you got on. I see, nice. Well done. Now how I'm going to show you the solutions is using some colour. So I'm going to bring some colour on to some of the images. These are all equivalent. These are all ways of representing in this case, 0.24. You ready for the next colour. These are ways of representing two tenths, 0.2 all the purple dots. Next I've got blue against everything that is a representation of tell me. Two-hundredths 0.02, well done. And then I've got green for everything representing 0.42. I know I went through that quickly. So just before I show you them all on one page. Here we've got 35-hundredths. all the ways of showing 35 hundredths. In turquoise, we've got all of the ways of showing 53-hundredths. And I think we're ready for all of them on one page. As I was saying, I've gone through them quickly. I didn't want to show you this page at the beginning because wow, there's a bit of an overload. So we've slowed it down. If you need to rewind, pause for each of the colours to check them off or pause on this page now and check that you've got them correctly matched, then do that now. Wow, what a busy lesson. I would really love to see some of your learning on Twitter, particularly that last activity. So I can see clearly how you have laid it out and structured your thinking. If you would like to share it with OAK National, please ask your parents or carer to share your work on Twitter, tagging us @OakNational and using the #LearnwithOak. Thank you so much for joining me, everyone. I told you at the beginning that I was in a particularly good mood and you have helped keep me there with all of your participation and fantastic learning over the last 20 minutes. Now the walk coupled with this math lesson has left me ready for a break. I think I could do with a snack from the fridge. So I'm going to head over there and see what I can find. What are you up to next? Whatever it is. I hope that it's with a big smile on your face and you have a well deserved break before you start it. I look forward to seeing you again soon for some more math lessons, bye for now.

Lesson overview:Fractions and decimals

Core Content

Fractions and decimals: