Venn diagrams

Key Stage 3

Maths

Sets and Venn Diagrams

﻿Hello, and welcome to this lesson on Venn diagrams with me Miss Oreyomi. For today's lesson, you'll been needing your paper and your pen, or something that you could write on and with. Should you need to pause the video at any point during this lesson, just to understand further what I've just said, or should you wish to rewind the video, then please by all means do so. Also, I would suggest you put your phone on silent, just to avoid distraction. If you can also get into a space of less noise and distractions, that would be great for your learning as well. So, if you need to pause the video to do those things, pause it now, and then press play to resume with the lesson. Let's think about our try this task. All the students in the class were asked, what they wanted to eat and drink with school dinner, the results are shown in the Venn diagram below. Can you take a moment, pause the video, can you explain the Venn diagram if someone gives you this, how would you go about explaining this Venn diagram? So, pause the video now and attempt this task and press resume when you're ready to carry on. Okay, hopefully you are able to have a go at trying to explain this Venn diagram. If I ask you then how many students preferred stuffed peppers? Hopefully, you've said eight and 10. So, 18 students preferred stuffed peppers. What if I asked you how many students did not want either stuffed peppers or orange juice? Hopefully, you've said six, six students, they don't like stuffed peppers or oranges with school dinner. What of students who just wanted orange juice? Simply they only wanted to drink orange juice with the school dinner. Hopefully, you've said, so this is not orange juice. Hopefully, you've said for oranges 15 students. What if I said shouldn't have preferred orange juice in general? Yeah, so that again would be 25, orange juice in general will be 15 and 10. This is going to be what we're learning in today's lesson, how to use Venn Diagrams to represent data. So, let's take a look at this then. Venn diagram is the visual way of showing like a survey result. For example, what do people prefer? And when we're drawing our Venn diagrams, we have this symbol here at the top it means the data set that we're interested in. So, for this question, the data set I'm interested in, is one, two, three, numbers from one to 16. Also, when we're drawing our Venn diagram, we draw one circle that represents our sets. This squiggly line here means set. We're going to talk about what set means later on in this unit, but just know that this squiggly line here means set. So, we're going to draw one circle to represent A, so I'm just going to write A here, and then another circle to represent B. As we saw from our try this task, we have this overlap B, which means the data represents both A and B. Yeah, and then A just meant to represent A, B just meant to represent B, and we always draw our triangle around our circles because it means if we have a data that doesn't fit into A and B, then it goes outside our circles into the rectangles. So, if I want to complete this Venn diagram there with the data set we've been given, I would start by writing the multiples of three, from the data set given to us. So, that's meant to be a squiggly line. I want to write the multiples of three. Well, I've got three, six, nine, 12, and 15. Haven't I? What of B? I want to write this data set for the multiples of four. Well, that's going to be four, eight, 12, and 16. Now, I want to go and fill in my Venn diagram. I always start from the middle. What can I fill in? What is the same for both A and B? Well, if we're looking at our set for A and B, what's the same? The number 12, isn't it? So, I'm going to put the number 12 here. And then I could go ahead and fill in A. I've got here three, six, nine, and 15. And for B I've got four, eight and 16. But I'm not quite done yet, 'cause I haven't put in all the data that I've been given into my Venn diagram. So, I've got one here, for example, that doesn't fit into A or B. So, I'm going to write one outside of my circle. I'm going to write five here, I'm going to write five, six, not six going to write seven, nine, 10, 11, 13, 14. So, these numbers one, five, seven, nine, 10, 11, 13, 14, they don't fit into either A or B. So, I'm going to write it in the rectangle. Let's look at this example, I want to draw a Venn diagram to represent the relationship between these three sets. Set X, set Y, and set Z. So, I've got three-way Venn diagram. That means when I draw my Venn diagram, I would be having three circles. But before I can draw my Venn diagram, I want to know information that would go in the middle of my Venn diagram. So, what information is the same? Do they overlap? So, let's start with information that fits both X, Y, and Z. Which numbers are both in X, Y, and Z. Five and six, isn't it? So, five is here, five is here, five is here, six is here, six is here, six is here. What of information that fit X and Y? Hopefully you've said one. So, the number one is in X and the number one is in Y. Do we have any others? Yeah, what others do we have? We have Y and Z, don't we? What information fit both Y and Z only. We have three, three and what else? We have eight, don't we? What other ones are common between my sets? I've got X and Z, isn't it? What number fit in both X and Z? Hopefully, you've noticed the number seven. So, that will be seven. So, now I can go ahead and draw my Venn diagram. So, I am going to start with one circle here, another circle here, and then a third circle overlapping all of them. So, this is going to be for set X, this is going to be for set Y, and this is going to be for set Z. But I'm not done. I need to draw my rectangle over here. So, I always start by filling in the middle of my sections. So, where am I looking for X, Y, and Z? The circle I am looking for X that fits both X, Y, and Z, would be this one right here, because X is here, Y is here and Z is here. So, I'm going to write the numbers five and six over here. Hopefully, you can see that. I'm going to write the numbers five and six, 'cause I did that again. Okay, what of X and Y? The intersection for X and Y would be this one here. Let's see if I could change the colour. Let's go with blue. So, over here, I'm just going to write one. What of for Y and Z, the intersection for Y and Z? Well, that's this intersection here, isn't it? So, I'm going to write the numbers, three and eight. What are the for X and Z? Let's go with yellow. Hopefully, you could see it. For X and Z the intersection is going to be right here, number seven. No, it's not. It's going to be right here, number seven. The intersection between X and Z. Right, now, I can go ahead and fill in the rest of my information in my circles. So, for Y, I am going to put, for X rather, I am going to put number two, I'm going to put number two and number nine. 'cause I haven't filled in two and nine. For Y, I am going to put in four. And for Z, I am going to put the number 10. I don't have any other numbers to put outside my circles I have to put in my rectangle 'cause I've already filled in all the data set I've been given into my circles. So, I could see the numbers that represent or the numbers that is in all sets, all three sets are numbers five and number six. The numbers in the set Y and Z are numbers three and number eight and so on and so forth. Okay, your turn then, pause the video now, can you draw a Venn diagram that represents the relationship between the sets A and B, and your universal data is this information here. So, for number one to number 10, draw a Venn diagram that represents the sets A and B. So, pause the video now and attempt this task. Okay, hopefully you started by writing out the set that would fit in for A. So, I want the multiples of 10, between the numbers one and 10. Multiples of two rather between the numbers one and 10. So, that's two, four, six, and eight. And for B, I want the multiples of three between the numbers one and 10. So, again, that will be three, six and nine. Right, which one would fit in the middle of my intersection for A and B? Which one would fit in the intersection for A and B? Well, six is common for both, isn't it? Now that I know that information, I could go and draw my Venn diagram. So, I only have two sets. So, I would draw in two circles like so, I am going to draw my rectangle and then I'm going to label this A, and I'm going to label this B. I know the six is common for both. So, I'm going to put six in the middle, which one fits just A then? Well, it's going to be the numbers two, four, and eight. And for B? Three and nine. I need to fill in the other information that haven't been filled in and put those in the rectangles because they do not fit into sets A or B. So, I'm going to have one here, I'm going to have five here, I'm going to have seven here, and I'm going to have, oh 10 should be here, shouldn't it? And 10 is going to go in set two, 'cause it is a multiple of 10. So, I'm just going to check that I actually have 10 numbers in my Venn diagram, 'cause sometimes it's very easy to miss out numbers, as I almost just did now. So, I'm going to have one, two, three, four, five, six, seven, eight, nine, 10, perfect. Another go your turn again, pause the video. Can you draw a Venn diagram that represents the relationship between the three sets? So, now you have three sets, and your data set you've been given the data you're working with are numbers between one to 15. So, pause the video now and attempt this task. Okay, hopefully this was a bit easier because they've given you the information that you need. So, I am going to see which ones are the same for A, B and C. Well, for A I've got the number four and four. So, that is for A and B, number four is the same for A and B. Two is the same for A and B, notice how I'm not putting it in order. It doesn't really matter as I just want to know which informations are the same. I've got six is the same for A, B and C, for B and C the numbers 12, is the same here and here. The numbers three is the same for A and C. So, just check in numbers off as I go along, I've got the number six, got the number six, got the number six, 12 is the same for B and C. I've got that there. And am I missing any other? I don't think so. And I've got two for A and B. Okay, let's see if we can draw a Venn diagram, if we're missing any other, we can go back and fill it in. So, I've got three circles, one, two, and three, making sure that they overlap. If there's information that's in the intersection of my sets. So, I'm going to label this A, I'm going to label this B and I'm going to label this C. So, starting with the middle then, which one is the same for A, B and C, is the number six, isn't it? So, I have forgotten to draw my rectangle, It's the number six. So, six is going to go here as this fit into A, B and C. Going to change my colour again. So, it's easier for you to see what I'm doing. For A and B which is there. I am going to write the numbers two and the numbers four. And four, let's go with green, for B and C which is just that intersection there. I am going to write the number 12, number 12. And then for A and C, I am going to write the number three, 'cause it's the same. So, A and C that's going to be the number three. I don't think I'm missing any other information. So, I'm going to go and fill in the rest of my Venn diagram. So, A have got the number one and have got the number five. So, I've got one, two, three, four, five, and six. So, I'm doing quite well for that one. So, for B, I've got two, four, six. I'm going to fill in eight, I've got 12 already, and then I'm going to fill in 14. For C, I've got three, six going to fill in nine. I've got 12, and then I'm going to fill in 15. What numbers haven't been put into my Venn diagram? Well, I've got one, two, three, four, five, six. I don't have seven. So, I'm going to write seven here. I have eight, I have nine. I don't have 10. So, I'm going to write 10 here. I don't have 11, so I'm going to put 11 here. I have 12, I don't have 13, I have 14 and I've 15. And this is how you fill in your Venn diagram. Okay, it's now time for your independent task. You have two main questions. First one, is copy and complete this Venn diagram on your right. And then the other question as well. So, pause your video now, attempt both questions and then press resume. and we'll go over the answers together. So, pause your video and attempt your independent task. So, I hope you're able to have copy and completed this Venn diagram. So, if I write out the factors of 24, if I write up at this point I've got one and 24, two and 12, three and eight, six and four. And if I write out the factors of 18, it's going to bring this down a bit, got six and I'll go four. For 18, I have one and 18, two and nine, three and six. And I believe that's all. Right, what is the same between 18 and 24, between the factors of 18 and the factors of 24. Well, if I change the colour, I've got one is the same, I've got two is the same, I've got three is the same and I've got six is the same. So, in the middle here, I am going to write one, two, three, and six, and then I'm going to fill in the rest of my Venn diagram. So, over here I have 18, I have nine, that would be here. And for 24, I would have 24. I would have 12 and I would have eight and four. Okay? Now, can you fill in the blank? So, each section has at least one number in it. I wrote the factors of 10, 12, and 15. I wonder what you got, did you manage to get those three? This was after a lot of trial and error, by the way. So, if I write out the factors of 10, 12, and 15, this would be one and 10 and two and five. This would be one and 12, two and six and three and four. This would be one and 15 and three and five. For 10 and 12 over here, what would be the same for the intersection of 10 and 12, which would be here. Well, I know that one is the same for all of it. So, blank in the middle here, I am going to write the number one and I don't think there's any other, which is the same for all of it. Number two is the same for 10 and 12. So, I'm going to write number two there. Number three is the same for 12 and 15. So, over here I'm going to write number three. And number five is the same for 10 and 15. So, here I am going to write five. Then I'm going to fill in the rest. So, for 10, I have 10, for 12, I have six and four, and for 15, I have 15. So, checking my numbers I've got one, two, three, four. So, I've got one, two, three, four, five, six. I should have 12 somewhere, 12 yeah. So, I think there. That's how I would have filled in my Venn diagram. So, fill in the blank so that each section has at least one number in it. The three numbers I chose was the factors of 10, 12, and 15, and then filling it in like so. So, each section has at least one number in it, okay, It's now time for your explore task. You've got this image on your screen. Cala asks every student in her class three questions. First question, do you own a dog? Second question, do you have black hair? Third question, are you a vegetarian? 10 students own a dog, 15 students have black hair, and 18 students are vegetarian. At the bottom of your screen, you have the cards five, two, and eight. How many different ways can you put this cards in the boxes and complete the Venn diagram? So, it's about exploration. How many different ways can I put my cards five, two and eight into my Venn diagram, so that it fits the sets that I have, which is 10 student own a dog, 15 students have black hair and 18 students are vegetarian. So, pause your video now and attempt to explore task, and press resume when you're done with that task. You have now reached the end of this lesson, a very big well done for sticking through and completing all your task. Don't forget to complete the quiz before you go, just to consolidate your knowledge on a new unit, a Venn diagram, and I'll see you at the next lesson, goodbye.

Venn diagrams

Venn diagrams

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UnitMaths / Sets and Venn Diagrams

Maths