﻿Hi everyone, Mrs. Sawyer again, I left you with this activity at the end of the last lesson, how did you get on? For the first two lines, the whole has been divided into six equal parts. One of the parts is highlighted. This part is 1/6 of the whole. Even though it's a different part highlighted on each, they still represent 1/6. The part highlighted on the bottom line, represents 1/5, and on the vertical line 1/4 is highlighted. Great work if you've got those right. Did you have a go at folding anymore strips of paper? I tried folding my strip into half, four times, and I found that the whole had been divided into 16 equal parts, with each part being 1/16, like this. In today's session, we're continuing to use the language part, whole, and fraction, but we will also be using volume and 3D or three-dimensional. Our stem sentences today are the whole has been divided into equal parts, one of these parts says, which is one of the whole. Today it would be great if you had, any construction blocks like Lego or cubes. It's very important though, that whatever you use are the same size. If you don't have anything to build with, then don't worry, you can draw instead. If you have crayons, then that will work just as well. Am going to be using yellow and blue cubes throughout the lesson, so if you do have those colours, that would be great. Finally, it's always good to have a pen and paper handy too. In today's lesson we're still going to use fractional notation and names, but we're going to use 3D representations. We could also call these volume models. To start with, I'd like to show you this tower of bricks that I made, can you see how many bricks I've used? I have used six bricks, each brick that I've used has an equal part. It might look like the yellow brick is larger because it's on top, but actually that all the same. I wonder if we could calculate what fraction of the tower is yellow. These stem sentences are familiar to you and may help. I will say the sentences first, and then see if you can repeat them back to me, filling in the blank spaces. The whole has been divided into equal parts. One of these parts says, which is one of the whole. You turn. How did you get on? Can we say them together? The whole has been divided into six equal parts. One of these parts is yellow, which is 1/6 of the whole. Well done if you've got that correct. Now have a look at these three models. What's the same and what's different. If you need to pause the video now to give you some thinking time, if possible, you could discuss this with someone else in the house too. When thinking about what's the same, you may have said all the models have six bricks, but the volume of models are all equal, but all the models have one yellow brick. And you may even say that the same fraction of 1/6 is yellow in each of the models. All of those things are true. When we're thinking about what is different, you may have said that the bricks have been laid out differently, that they're not tall in towers or but the one yellow brick is in a different position in each of the three models. This made me think back to the last lesson where we learned that if any equal part is highlighted and it represents the same fraction. Jane was asked to build a tower, which was 1/3 yellow, and this is what she built. Can you see the mistake that she has made and what would she need to do to correct it? Pause the video if you need to, and perhaps have a chat with someone else in your house. Did you work out Jane's error? Jane had used an additional three bricks, rather than including the yellow in the whole. In Jane's model, the whole had been divided into four equal parts. One of these parts is yellow, which is 1/4 of the whole. For her model to represent the yellow as 1/3, the whole needs to be divided into three equal parts. And so Jane needs to remove one of the blue brick. Brilliant work if you were able to spot Jane's mistake. I'd like to set you a challenge now. If I told you that my one yellow brick represents 1/4 of the whole, I wonder how many blue bricks I would need. I also wonder what my whole shape could look like, is it more than one answer, and if there is how many can you find? For this question if you have any Lego pieces or cubes that are equal in size you could use those. If not then just have a go at drawing the answers. Pause the video now. And come back when you're ready to continue. How did you get on? Did you find more than one answer, I had to go too. I wonder if we found any of the same models. For each of my models, I use one yellow brick and three blue bricks, because the denominator is four. Then I know there must be four equal parts or in this case for equal bricks. If one brick is yellow, then then must be three blue bricks. I started by building towers, but we learned in the last slide that the yellow brick can go in different positions, and so in these towers, it can go in four different places. Did you draw or build models like these? Did you find any others? I started thinking about how the bricks could be arranged differently and again, how the yellow brick could be in different positions. And I came up with these, although I know that there are many more I haven't built yet. I'm sure there are others that you created too. That's half one more go at a similar question. Again if you have equipment to build that's great, but if not, just throw your answers. This time my one yellow brick represents 1/5 of the whole. Do you think there will be more answers or fewer answers than when the yellow represented a 1/4. What could my whole look like this time? Perhaps you could start by thinking about how many different towers that could be first and then looking at different models. Pause the video now and come back when you finished your investigation. How did you get on this time? We needed five bricks in total, one yellow and four blue. Because we had more bricks there were more possible answers. Firstly how many towers did you find? If you found five, well done. Here are mine. I found that it helped me to follow a pattern, moving the yellow brick down one place each time. I found lots of other ways to build a model with five bricks too. Did you build or draw or any of these. I've laid mine down flat but they could also stand upright. And don't forget the yellow brick would move into different positions too. Wow that really are a lot of possibilities for what the whole could look like. Still thinking about three-dimensional models. I want to now think about the fraction of the whole space that is filled. Let me give you an example. You can see here that I have been Oxo cube box. All the brands are available. The full box holds 12 cubes. And so each queue represents 1/12 of the whole box. If I empty the box and put one cube back in, then we could say that 1/12 of the whole box is filled. Let's have a look at another example. I have a book that is filled with packs of paper. If the whole box is filled, then it will hold five packs of paper. Each pack that full represents 1/5 of the whole box. If I remove all of the paper. And put back in only one pack, then we can say that 1/5 of the whole is filled. These next questions continue to look at what fraction of the whole is filled. In this image, the box is the whole. Is it all filled? No, the pink section shows us that a part of the box is filled. We need to work out what fraction of the whole the pink part is. I wonder if we could work that out. Perhaps if we could work out how many of the pink parts would fill the whole box that would help us. This marker on the box is there to help. I think that one more pink parts might fit to the left of the marker and one to the right. How many pink parts would that be all together? Do you agree that there would be three? No, let's use our sentences to help us. We can see these together, filling in the answers as we go. The whole has been divided into three equal parts. One of these parts is pink, which is 1/3 of the whole. 1/3 of the whole is filled. We need to visualise again in this image. Once more the box is the whole, you can see that a part of the box is filled in green, but what fraction of the box is filled this time? Again there are some little markers to help us. Can you see that another green part would fit to the rate of the one that is shown. This would feel the back half of the box, but it would not fill the box. I know the two green parts would be needed in the front to fill to the whole box. We can use that information to fill in the blank sentence together. The whole has been divided into four equal parts. One of these parts is green, which is one quarter of the whole, 1/4 of the whole is filled, were you right? Well done. One final example, again the whole is the box and it's just not filled. The question is what fraction of the box is filled. Can you look closely at the picture and use this marker to support you. The sentences are there too if they are a help. Pause the video and come back when you think you have an answer. How did you do? Say the sentences with me. The whole has been divided into six equal parts. One of these parts is yellow, which is 1/6 of the whole, 1/6 of the whole is filled. Did you get that correct? Great work. Three of the yellow parts would fit along the bottom of the whole. And two of these layers would be needed to fill the whole box. You've done a great job thinking about 3D models today, and I'm going to leave you with this practise activity. It linked back to the work we completed with the yellow and blue bricks earlier in the session. I wonder if you could have a go at completing this table. We can do the first one together to make sure you understand. In the first example, we know that one third of the cubes are yellow. I know then that there must be three equal parts or three bricks. If one of the bricks is yellow, then how many will be blue? Well done if you said there will be two blue cubes. It then asks, what the whole could look like. You may like to build this again first and then throw a representation into the table. Mine looks like this. As long as your model has three equal parts, one in yellow and two in blue, then you are correct. If you wanted, you could investigate how many different representations you could find for each question. Well done everyone. Bye.

In this lesson, we will investigate how to determine the size of fractions in a 3D space. For example, we will determine what fraction of a stack of cubes is yellow.

In this lesson, we will investigate how to determine the size of fractions in a 3D space. For example, we will determine what fraction of a stack of cubes is yellow. Resources provided by NCETM (CC BY-NC-SA: https://creativecommons.org/licenses/by-nc-sa/4.0)

Maths

Y4 Maths

Key Stage 2

Year 4

Assign unit fraction names and notation to 3D representations

Working with fractions

UNIT

Divide and describe the same whole when divided into differing numbers of equal parts

Understand fraction notation to represent a relationship between part and whole

Begin to use and understand the terms 'Numerator' and 'Denominator'

Name unit fractions and match them with the fraction notation and a representation

Embed previous fraction work using a linear model

Assign unit fraction names and notation to equal parts of quantities

Recognise and reason about unit fractions in a variety of contexts

Understand that Equal Parts Can Look Different - Area

Understand that Equal Parts Can Look Different - Volume and Area Contexts

Compare unit fractions using a fraction wall

Reason about comparing unit fractions

Compare unit fractions in a measure's context

Can we compare unit fractions of different wholes?

Construct a whole from a part and identify the fraction it represents

Build and compare different wholes from the same unit fractions that represent the same length

Build and compare different wholes from the same unit fractions that represent different lengths

Build and compare different wholes from different unit fractions that represent the same quantity

Build and compare different wholes from different unit fractions that represent different quantities

Build and compare wholes when different unit fractions represent different amounts

Lesson overview:Assign unit fraction names and notation to 3D representations

Core Content

Working with fractions: