Using mixed numbers

Key Stage 2

Maths

Fractions

Which of these sets of fractions are ordered from smallest to greatest?

Which of these sets of fractions are ordered greatest to smallest?

﻿Hi, welcome to your math lesson today with me Ms. Jones. How are you doing today? Hope you're feeling ready and have your thinking caps on, let's get cracking and see what we're doing today. In today's lesson, we're going to be using mixed numbers. Do you know what's a mixed number is? If not, don't worry. We'll be covering that later in the lesson. We're going to start with a starter that warms up our brains. Then as promised, we're going to think about what mixed numbers are and how we might represent them. You've got a task and finally, a quiz. You'll need today, a pencil and piece of paper to jot down your ideas. You might want to use a ruler just to help you with number lines or drawing on number rods. Before we get started properly, here's our starter today. You need to find the odd one out. Now as a hint, when finding the odd one out, there's not necessarily one right answer. The key is that you need to explain and justify how you know. Now what I would do is I would look for similarities and think about, in which case, is it a similarity for three of these fractions, but not the fourth. Okay. Pause the video now to have an explore. Okay. Hopefully you've had a go at that. Now, as I mentioned, there's not necessarily one right answer. You might have said that one half is the odd one out, because it's the only one with a numerator of one. It's the only unique fraction, but you might've equally said three quarters is the odd one out because it's the only one with a numerator of three. As long as you justify your answer, then it's okay. You might have explored several different answers. I wonder if you could make a case for each one of these, for being the odd one out. Okay. My question here asks how many circles are there? Can you say it out loud? How might you write that as a fraction? Pause the video now to write down your idea. Okay. Let's have a look if you've got the same thing as me. Here, I can see one whole circle, but I can't see two whole circles, this is half a circle. Now we might say that as one and a half, but how do we write that as a fraction? Well, we write it as a mixed number one hole, to representing here with the a one and the fraction one half, one and a half. Mixed numbers are numbers consisting of an integer, which is a whole number and a fractional part. Let's look at some more examples. How many circles are there? Let's look at this orange picture first. You can clearly see there are two whole circles and then a fractional part. This looks like it is one half. So I can say there are two and a half circles. Now as a mixed number, I could write that as two, and my fractional part is one half, two and a half. Let's look at this one on the right. We can clearly see how many wholes there are. And then we need to think about what's this fractional part. Can you have a go at saying that out loud? Okay. This looks like it represents one third. So altogether I've got three and a third, I can write that as a big number three, then my fractional parts here, three and one-third. Looking at this one here in the bottom left, can you have a go at saying that one out loud? Okay. You might've have seen that this is two and two thirds. We can write that as a mixed number two and two thirds. And finally this blue one at the bottom, have a go out loud. Okay. Hopefully you've said two and a quarter. Have a go at writing that one down for me. So you should have had two as your integer, your whole number and one quarter. So all together here, I've got a mixed number, an integer and a fractional part. That's now have a think about how we can show mixed numbers on a number line. So here I've got my number line and this number line goes beyond one so we can explore mixed numbers. So let's think about how this number line is split into parts. So we've got one, two, three, four parts between zero and one. So it's split into quarters. My denominator here would be four. This would be one quarter. So if this is one quarter, what would this point be? Okay, this should be one whole, and one more quarter, so we could say here would be one and a quarter. Here would be one and two quarters or one and a half, one and three quarters, two. What would this point be here? Have a think, see if you can say it out loud. Okay, let's count in quarters, we've got two, two and a quarter, two and two quarters, Or we could say that's two and a half. This would be two and three quarters. That's okay. A different number line now. Okay. This time let's have a think about what these intervals are representing. Can you count them and see what you think this point would be? Okay. There are one, two, three jumps between zero and one, which means this is split into thirds. This point would represent one third, so this represents one third. What would this point be? Well, this is one whole, this is one and one third. So this is one and two thirds. Okay. Let's have a go at one more. What would this point be? Well here we have three, so this is three and one third. Okay. It's time for you to have an explore. I'd like you to have a go at representing these mixed numbers. You can use a number line or you can use a diagram such as the circle diagram that we used earlier. If you want to, you can show the mix number using both. Whilst you're doing it, see if you can use some of these sentence stems that you can see on the screen. How many wholes are there? What's the fractional part? How might you need to split that fractional part? Okay. Pause the video now to have a go. Now for your main task today, we're going to be thinking about how we can represent mix numbers with number rods. Now you might've used number rods or sometimes called cuisenaire rods in school before or seen pictures of them. If you haven't, don't worry. I've got a picture here that can show you how to use them. For each number rod, the size increases by one unit. There are 10 number rods all together, so we can see that the pink one here is two units long. The green one is three units long. The purple one is four units. Long. Sometimes they might represent the numbers one to 10, but we can also have fun with them and get them to represent other numbers or in this instance, fractions. Let me show you an example to make sense of this. If the white rod represents one half, what would the pink rod represent? Now, the pink rod remember is two units. The white one is one unit, so the pink one is twice as long. So if the white one represents one half, the pink represents one whole. What would the green rod this third one represent? Well, we're cutting in half so, one half, one whole. This is one more unit. So this would represent one and a half. What would the purple board represent? We'll let you see if you can work that one out. Can you say it out loud? The purple one, we count in halves, this would be one half. This would be one whole one and a half would worth two wholes. All the same as four of these white rods. Let's have a go at a different example. This time I'm going to stick with the white rod and I'm going to assign it a value of one third and see if I can work out the value of some of the other rods. So if the white rod is one-third, what would the value be of the purple rod? Hmm. Well, we can either count into thirds. One third, two thirds, three thirds or one whole, one and a third. The purple one is worth one and a third. Is there any other way we could have worked it out? Well, we could have worked out the size of the pink rod, two-thirds and thought about what the pink rod was doubled. Hmm. I wonder if there are any other ways you could have worked it out. What about the green rod? See if you can have a go at this one. What if the white rod is one third? The pink one will be two thirds. The green one would be three thirds. Now we know if the numerator and denominator are the same three thirds, we can simply write that as one whole. What would the black rod be? Well, we know that green is one whole, so let's count on from that one and a third, one and two thirds, one and three thirds or two wholes. This would be two and a third. It's sometimes handy to think about where the whole numbers would be. I know here I'm working with thirds, every third rod would be another whole number one third, two thirds, one whole, one-on-one third one and two thirds, two wholes. Let's look at one more example. White rod has a value of one half, what's the value of the dark green rod. Hmm. Now let's use that strategy of thinking of where the wholes would be. So if this is a half, the pink would be one whole. Every second rod would be another whole number. So the pink would be one whole, one and a half, two, two and a half, three. The dark green rod is three. What would the value of the orange rod be? Hmm. So this is the 10th rod. Interestingly, you might've noticed that the dark green rod, which is the sixth rod, one, two, three, four, five, six, had a value of three. So let's use that information to help work out the value of the 10th rod. I can see that the number of the rod has been halved to get its value here. So the 10th rod, which is the orange road, would have a value of five. We can check that, so half, one, one and a half, two, two and a half, three, three and a half, four, four and a half, five. For your task today, I'd like you to assign a value to one of the rods and then use that to work out the value of the other rods. And you can start with any value you like, and you can explore. You might want to start with the white rod being a third and work them out. Well, why not start with the pink rod being a half and have to start with the white broad or with the purple rod being one whole. Those are just some examples, but you get to decide and explore. Good luck! Pause the video now to complete your task. How did you get on with your task today? Hopefully you had fun exploring with the number rods, if you'd like to share your work, please ask your parent or carer to do so. It's now time for the quiz. Thank you. Bye-bye.

Using mixed numbers

Using mixed numbers

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