Which pair of equivalent fractions are represented here?

Which fraction is equivalent to two thirds?

Which fraction is equivalent to one fifth?

Which of these is incorrect?

True or False: The numerator and denominator can be multiplied by the same number to find an equivalent fraction.

Equivalent Fractions

﻿Hello, and . Hope you're ready for today's maths lesson with me, Miss Jones. Today, I am particularly excited, because we're going to be looking at problems all about pizza. So what do you think it could be about? Let's have a look. In today's lesson, we're going to look at fractions and division and explore how they're connected to one another. We'll start off by doing a little bit of division, just to get our brains warmed up, then we'll look at the connection between fractions and division. You've got a task and to finish off a quiz. You'll need today a pencil and something to write on, such as a piece of paper, you'll also need some paper circles to help with our exploration, and these can be downloaded or you can just draw them yourself. But be aware, if you're drawing them yourself, you might need some extra time for today's lesson. Okay, if you need to, pause the video and go and get what you need, then we'll carry on. Let's get started. As promised, here's our division starter. I want you to spend a few minutes having a go at these. Whilst you're doing it, think about what do you notice? Okay, hopefully you've had time to have a go at some of these and think about what patterns you spotted too. Let's go through them quickly together. So four divided into two will give us a quotient of two. My parts are two and two multiplied together will get me my whole which is four. This time, we've got a missing part. Eight divided by mm is equal to two. This needs to be four. I know that four times two make a whole of eight. Eight divided by four is equal to two. This time, I got something divided by six is equal to two. Let's have a think. This time, we've got our two parts. Let's multiply them together to get a whole. 12 divided by six is equal to two. 16 divided by eight, I know is equal to two as well. Already, I've noticed the pattern that we've got all the same quotients here, all the same answer. Okay, looking at this column, we've got mm divided by eight is equal to three. We're missing our whole, so if we multiply these together, we should be able to find it. It was 24 divided by eight is equal to three. 12 divided by four is equal to three. Okay, I wonder if all of these are going to have the same quotient too. Let's check. Six divided by two is also equal to three. And I know that three multiplied by two would get me my whole of six. Three divided by mm is equal to three. Hmm, if one part is three, what's our other part? Three multiplied by one would get us three. Three divided by one is equal to three. What did you notice? We've already discovered that our quotients are the same throughout this column and then throughout this column too. Did you notice anything with the other parts of the equation? You might have noticed how the relationship here between our two numbers relate to each each. We know that two here is half of four. Four is half of eight. Six is half of 12. And each time we've ended up with two. Interesting. Here, we've got eight I know is 1/3 of 24. Four is 1/3 of 12. We ended up with a quotient of three. I wonder if we could come back to this sort of thinking later on when looking at fractions. Okay, time for a true or false question. One divided by three is the same as or equivalent to 1/3. Is that true or is that false. Take a moment now to think about that. What did you think? Let's investigate this a little bit further. I wonder if the same is true for non-unit fractions where our numerator is more than one. Here we've got another problem. If three pizzas are divided equally between four people, how much does each person get? Will the answer be 3/4? True or false? Well, let's investigate. Now, you can do this by using a circle or a piece of paper or a drawn circle and divide it into four equal parts. You can cut them up and move them around. I have used colour coordination, so you can see how I've moved my pizzas around. Here I've got my three pizzas and I'm sharing them between four people. Now, I could share them out one by one. So one piece of pizza goes to this person, to this person, to this person, to this person. And I've got my four greens and I've shared them out. And then my four blues and I've shared them out. And you can see, after sharing, each person got 3/4 of a pizza each. The other way you could do it is by doing it in blocks. So instead of sharing them 1/4 by 1/4, I've given half to this person and then half to this person. My green pizza, I've given half to this person, and then half to this person. And then, when I got to my blue, I knew that I couldn't just give half to this person and this person, because that would mean that this person wouldn't have an equal amount. So then I split it into quarters. But again, they ended up with 3/4 of a pizza each. Now I'd like you to have a go at doing something similar. Let's try sharing four pizzas between six people. Now, for this, you're going to need four circles divided into six parts. Now, if you haven't got those already, you can draw them. I want you to have a go at sharing them out and see how much or how many slices do those people get. Okay. Hopefully you've managed to share those out and you found that, actually, people get four slices of pizza. We could say that's 4/6 of a whole. And remember, our problem was four pizzas divided by six people. These are equivalent. Four divided by six is equivalent to 4/6. And again, our numerator is the same as our dividend and our denominator is the same as our divider. Okay, let's apply this to a problem. Would you rather share three pizzas between four people or four pizzas between six people? Now, we've already looked at both of these situations and we know that three pizzas shared between four people is equal to 3/4. And four pizzas shared between six people is equal to 4/6. Hmm, which group would you rather be in? I know that I'd rather be in the group that gets the most pizza. So which fraction here is greater, or rather, equal to each other, equivalent? Hmm, well, we can think about our representations to help us. We've already looked at both of these and we can see that 3/4 is slightly bigger than 4/6. So I would prefer to have 3/4, because 3/4 is greater than 4/6. Let's look at another one. Would you rather share four pizzas between six people or two pizzas between three people? Hmm. Are these fractions equivalent or is one greater than the other? 2/3, is it greater than, less than, or equal to 4/6? Have a think about that now. If you need to draw some representations to show your thinking, please do. Pause the video now and then we'll have a look together. Okay, what did you notice when you were exploring? Here, I've used a similar representation to earlier. I've used paper circles. And you can see I divided my paper circles into six parts here, and each person got 4/6, which looks like this. I then divided them into thirds, shared them out. Each person got 2/3. What I notice is actually 2/3 is exactly the same size as 4/6. Each person gets twice as many parts here, but the parts are actually half the size of here. I know that 2/3 is equal to or equivalent to 4/6, and that makes sense, because look at our numerators and denominators. Two has been multiplied by two to get to four and three has been multiplied by two to get to six. Hmm, I wonder, what other division equations and fractions are equivalent to 2/3? What if I wanted to share the pizzas between nine people, but I still wanted them to have the equivalent to 2/3 each? What about 12 people? Now, do you remember our starter in the beginning when we were looking for patterns in division? Well, we can apply the same thing here. If we look at the relationship between our dividends and our divisor, we can spot a pattern. Two is 2/3 of three. Four is 2/3 of six. Look at the pattern here. Hmm. Let's follow the same pattern here. Two, four, six. Six is 2/3 of nine. Six divided by nine should be equal to 6/9, which is equivalent to 2/3 or 4/6. Let's look at this pattern again. Now, if we wanted, this time, our divider to be 12, we would need to make sure the same relationship is happening with our dividend. Two, four, six, eight. Eight divided by 12 would give us 8/12, which is equivalent to 2/3, or 4/6, or 6/9. Eight pizzas shared between 12 people would give is 8/12, which is equivalent to 2/3. For your independent task today, I'd like you to think about what equivalent fractions you can represent in the context of division as sharing? Here's some examples. One pizza shared between three people. Can you represent that with a picture? What fraction would they get each? What about two pizzas shared between mm people? You can decide how many people we share the pizzas between. How about three pizza? How many people are you going to share those with and what is the fraction that you're representing that each person gets? Have a look for patterns as you're exploring and make sure you're showing your answers with circular representations. Have fun exploring. If you finished, if you want to share your work and your representations, ask your parent or carer. Now it's time to complete your quiz. Bye-bye.

If you share 1 cake between 4 people, how much does each person get?

How else could we write one third?

2 ÷ 3 is the same as....

If you share 5 pizzas between 6 people equally, how much would each person get?

Which of these division equations are equivalent to 4 ÷ 5

Fractions and division

In this lesson, we will use pizza problems to explore the connection between fractions and division.

Maths

Y4 Maths

Key Stage 2

Year 4

Miss

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

Comparing fractions

Ordering fractions

Using mixed numbers

Using improper fractions

Converting mixed numbers into improper fractions

Adding fractions (up to one whole)

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?

How else could I write five halves?

What is the sum of the fractions?

Which is greater?

What mixed number is being represented?

Calculate:

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:Fractions and division

Core Content

Fractions: