One and one third is equivalent to....

Three and two fifths is equivalent to,,,

How else could I write two and two fifths

How else could I write five halves?

Which is greater?

Converting Mixed Numbers into Improper Fractions

﻿Hi, welcome to today's maths lesson with me, Miss Jones. How are you doing today? Hope you're feeling okay and raring to go. Let's see what we're up to today. In today's lesson, we're going to be adding fractions up to one whole. We're going to start off by looking at some fraction problems and thinking about how we can represent those with bar models. Then we're going to look at some more abstract problems, and look at some fraction calculations. Then you've got your independent task, a challenge question and finally a quiz. You'll need today something to write with and something to write on. If you haven't got what you need, go and get it. A pencil and a piece of paper should do just fine. Okay, if you've got everything, let's begin. Here we've got a problem. A pizza, oh I'm so happy this is about pizza, my favourite. A pizza has eight equal slices. Lisa eats one slice, and then eats a further two slices. What fraction of the pizza did she eat? Now, in order to make sense of this problem and what I need to do, I'm going to use a bar model to represent it. Now when we're using our bar models, we need to think about what do we know and what is unknown? What do we want to find out? Okay, so looking at this problem, I know that the pizza was divided into eight equal slices. And the question is asking me to give my answer as a fraction. So we could represent those eight equal slices as eight eighths. We know that Lisa ate one slice and then another two and we need to find out how much she ate all together but write it as a fraction. Here's my bar model. You can see here I've got eight equal parts to represent my pizza. Now we don't really need to worry about these parts because it's not asking us about how much pizza is left. It's asking us how much she ate all together. So we need to find out what this amount is. So I've put that with a question mark, that's our unknown. But we do know that she ate one eighth, that's one part, and then she ate two eighths. So looking at the bar model, how much, as a fraction, did she eat all together? Well, we can see here that all together there are three eighths. One eighth added to two eighths is equal to three eighths. Now we can also represent this as an equation. One eighth added to two eighths is equal to three eighths. Lisa ate three eighths of her pizza. Now, I want you to have a look at that equation and think about what you notice about the numerator and what you notice about the denominator. Now, looking at this closely, we can see that our numerators have been added. So one eighth added to two eighths would get us to three eighths. But our denominator has stayed the same. It's always eight. This is because it's a common unit. There are always eight parts of the pizza. Let's look at a second problem. Leah walks two sevenths of a mile to the post office, and then walks a further three sevenths of a mile to the corner shop. How far does she walk in total? I'd like you to have a look at this problem and see if you can draw your own bar model to represent it. And then think about how you might represent it as an equation. Use your pencil and piece of paper, pause the video now and have a go. Okay, let's look at this together. So, what do we know and what is unknown? Well, we know she walks two sevenths and then a further three sevenths. We know we're working with seven equal parts and we need to find out how much she has walked. Here's my bar model. Now you can see my parts here are divided into seven parts. We're not finding out how much she's got left, so we're working out on this part. So this is my unknown. I need to add two sevenths to three sevenths. Now if I was representing that as an equation, I could represent it as my denominator is two. Two sevenths added to three sevenths. And I need to find the total. Well you can see from my bar model that all together this is five sevenths. My numerators have been added and my denominators have stayed the same because throughout the problem, I'm working in sevenths. My denominator doesn't change. When adding fractions, we can use our known facts to help us. This is something that we've always done. We know that two and three is equal to five. Therefore, we know that two tens add three tens is equal to five tens. We know that two hundreds add three hundreds is equal to five hundreds. And we can apply this when adding fractions with the same denominator. Two sevenths added to three sevenths is equal to five sevenths. It makes sense, doesn't it? It's time for you to have a go at a let's explore task. I want you to look at these three bar models and think about what the unknown is. What's the missing fraction? How would you represent each problem with an addition equation? And, if you can, have a think about a word problem that could represent that bar model. Okay, pause the video now, and then I'll go over the equations and the unknowns with you. Okay, hopefully you've had a go at that by now. Let's have a look. Here are the bar models. Let's see if we can work out the unknowns. So here we have two sixths added to one sixth. The total would be three sixths. Now if you wanted to, you could have used your knowledge of equivalent fractions to say that three sixths is also equivalent to one half. This one, we've got three sixths added to one sixth. And the answer would be four sixths. My numerators have been added. My denominator has stayed the same. Now again, if you wanted to, you could use your knowledge of equivalent fractions to also write this as two thirds. Now, there's one at the bottom. One sixth added to four sixths would be equal to five sixths. Again, my numerators have been added, my denominators have stayed the same. We're still working in sixths. How did you do? Hopefully you also had a go at creating some word problems for these. Okay, now that you've had a go at your let's explore task, it's time to do your independent task. This time, I've got some abstract calculations. You need to work out what the total of each pair of fractions is. Okay, pause the video and have a go. Now that you've finished your task, let's have a look at the answers together. Three eighths added to three eighths is equal to six eighths. If I wanted to write an equivalent fraction here, I could have also thought of this as three quarters. But either answer is correct. You get a point for six eighths, maybe a bonus if you've thought of an equivalent fraction. Perhaps, if you haven't thought of the equivalent fractions, you could go around and do that afterwards. One sixth added to two sixths is equal to three sixths. I wonder if you could find an equivalent fraction for that one. One third added to one third is equal to two thirds. Two fifths added to one fifth is equal to three fifths. Five ninths added to three ninths is equal to eight ninths. And one third, sorry one fifth added to three fifths is equal to four fifths. And for these, hopefully, you had a go at using your known facts. I know that one add three is equal to four. So one fifth added to three fifths is equal to four fifths. To finish the lesson, we're going to have a look at your challenge question. Now, hopefully you've already had a go at this, but if not, you can always pause the video now and have a quick go. Let's go over this together. Three fractions add together to make nine twelfths. What could the three fractions be? Now there might be more than one right answer here. My question's asking me what could they be? So, my answers might not be the same as your answers. But let's have a think about what we need to do. We know that when we're adding our fractions, our denominator stays the same. So I'm going to put twelfths in all of my denominators. Here. Now, my numerators, however, need to make a total of nine. So I could do this in many different ways. If I was to start with one twelfth and then added another one twelfth, what would this numerator be? Well, I need to make a total of nine. So far I've got two twelfths, so this would need to be seven twelfths in order to make a total of nine. What else could my numerators have been? Well, let's have a think about it. What we could have done here is started with something different. We could have said three twelfths added to five twelfths. How many have I got all together? Eight twelfths added to one twelfth. As long as your numerators made a total of nine and your denominator stayed the same, it will work for you. Okay, it's time to now go off and complete your quiz. Thanks everyone. Take care.

What is the total?

What is the sum of the two fractions below?

Calculate:

Adding Fractions (Up to One Whole)

In this lesson, we will use bar models to support our understanding of adding fractions where the total does not exceed one.

Maths

Y4 Maths

Key Stage 2

Year 4

Miss

Adding fractions (up to one whole)

Fractions

Number

THEME

UNIT

Recognising fractions as different representations

Calculating unit fractions of quantities

Recognising  equivalent fractions

Recognising equivalent fractions (2)

Calculating non-unit fractions of quantities

Equivalent fractions

Fractions and division

Comparing fractions

Ordering fractions

Using mixed numbers

Using improper fractions

Converting mixed numbers into improper fractions

Subtracting fractions

Adding fractions (with a total greater than one)

Subtracting fractions (2)

Comparing non-unit fractions of quantities

Reasoning with fractions

Which representation shows three quarters?

What does the denominator tell us?

What does the numerator tell us?

What is the sum of the fractions?

What mixed number is being represented?

What improper fraction has been represented?

A packet of paper has 261 sheets. Two thirds of the packet has been used. How much paper is left?

Lesson overview:Adding fractions (up to one whole)

Core Content

Fractions: