Overlapping circles (Part 2)

Key Stage 3

Maths

Sets and Venn Diagrams

Which of the following is a subset of  V? V = {r, a, r, e}

Which of the following statements is true?

Which of the following is NOT a subset of set P? P= { 2, 3, 5, 7, 11}

How many subsets will the set below have? J = {Teacher, Students, Nurses, Engineer, Lawyer}

If D = { whole numbers < 6} and E = { 5, 4, 3, 2, 1 0}, then which of the following statements is true?

﻿Hello, and welcome to the second part of overlapping circles with me, Miss Oreyomi. For today's lesson, you'll be needing a paper and a pen or something that you can write on and with. Should you need to put your phone on silent to avoid distraction, please do that now. Also, if you need to get into a space with less noise, also please do so. If at any point during the lesson you wish to pause the video, or go back to listen to something I said previously, then by all means do so. And, when I tell you to pause the video and attempt the task, it would really help if you do that, as it would aid your understanding even better. So now, pause the video if you need to go get your pens or your equipment, or if you need to go into a space with less noise and distractions. And, resume when you're ready to proceed with the lesson. Okay. For your try this task, you've got six circles on your screen, and they represent different sets of numbers from numbers one to 10. Your job is to fill in the number of frames and these are the number of frames here, using these cards at the bottom of your screen. How many different values of x can you find? So for example, I could say A intersection B has, I don't know. How many elements does A intersection B you got? You don't have to use this example we're giving you, this is just an example. So your job is to fill in the number frames, so that you can have different values for x. So pause the video now, attempt your try this task, and then click resume when you're ready to proceed with the lesson. Okay. So I don't want to do A intersection B, and I want to do something else. And I wonder how you got on with it. How many different values of x did you find? So the first example I want to do, 'cause it's quite an interesting one, is E and C. Well, if I look at my elements in E, it's got four, five, eight, nine. And if I look here as well, it's got exactly four, five, eight, nine. So I know, from previous lesson, that is E a subset of C. So, if I have my E set here and I have four, five, nine, and eight, and this is E, I could have two, three, four here, no. I could have two and three just here and this would be C. So, over here I could write well, E is a subset, remember this symbol from last lesson of C and it's got one, two, three, four, five, six. It's got six elements. So that's one example. Let's do another one. I am then, I want to do A and D next. So if I draw my Venn diagram for A and D, A has got one. One is the same for A and D, three is the same for A and D, and four is the same for A and D right there. Then A, D. I have five, six, and nine, and I just have the number two here. So, over here my number frame, I could say A intersection D has three elements. Just one, two, three. I could change , I could say A union D has got one, two, three, four, five, six, seven elements. And so on and so forth. So I hope you were able to do that. Right. Let's think about this Venn diagram then. We've got Venn diagram, we've set A over here, and we've said to B over here. Write down the numbers that are in set B. So we're just looking for the numbers that are in set B. What would my numbers be? Well, the numbers in set B are six, five, and nine, isn't it? Because this whole circle over here covers all of B. So over here, I am going to write five, six, and nine. Next then, write the numbers that, write down the numbers that are in set A union B, remembering that A union B means the whole circle, including the overlap and the intersection. So I'm looking for all the numbers in set A, and I'm looking for all the numbers in set B. So that is one, four, five, six, and nine. Right. Look, write down the numbers are set A compliment. Remember what we mean by A compliment? It means the numbers that are not in A, right? Well, that means I don't want, I don't want any of these numbers here. Don't want them. So, what numbers am I left with? Six, six is not in A, 11 is not in A, and seven is not in A, so I am going to write six, seven and 11. Right. Here's a Venn diagram. I need to fill in my datas. I need to fill in my set A with multiples of six up until I get to number 60, and then I need to fill in my set B with factors of six. So let's go about that. Multiples of six, I've got six, 12. I don't need that comma over there. I should probably write this out first actually. I've got six, 12, 18, 24, 30, 36, 48, 54 and 60. And then factors, here I've got one, two, three, six, right. Let's fill our data. What is the same for both? It's just six, isn't it? So six is going to go in the middle, and then for B, I'm just going to have one, two, and three, and then for A, I'm going to have 12, 18, 24, 30, 36, 48, 54 and 60. Write down the numbers that are in the set not A. So, what would be my numbers that are in the set not A? Well, it would just be one, two and three. What of A and B, write down the number in the set A intersection B. Remembering that this A is A intersection B. So the only number I'm writing down is six. Okay. The last one, I want to find the numbers that are not in A union B. So not in A union B, that means I can still count this six as my B, because it is a union. That means all the data set in A and B. However, I'm not going to include my data set in A but six also counts as B. So I am going to write one, two, three, six. If however, they said, write down the sets of numbers that are A compliment and be your intersection B. Then I can't include the six, because the six is part of that A, and I'm looking for not, all the values that are in A, that are not in A rather, intersecting B. So I'm just going to have one, two and three over there. Your turn then. On a Venn diagram, there are three sets. Set A is multiples of three, set B is square numbers, and set C are odd numbers. Over here, I'm just going to add, that I want the first seven multiples. The same for this as well, the first seven square numbers, fine. And over here as well, first seven odd numbers. Totally fine, okay. Represent this information on a Venn diagram, and then answer the questions below. Write down the number that are in the sets, so on. So pause the video now, attempt this task and then resume, we'll go over the answers together. Okay. I always write the values in my set, the element of my set as that really helps me to see what I need to include in my Venn diagram. So the first one, multiples of three first, seven mutiples of three. I've got three, six, nine, 12, 15, 18, and 21. B square numbers, I've got one, four, nine, 16, 25, 36 and 49, for C, I've got one, three, five, seven, nine, 11, and 13. Now, I want to represent this information in a Venn diagram. So I've got that, cause I've got three sets, I would have three circles. So this is A, this is B and this is C, and I'm going to draw my rectangle in case I have any data, any element that doesn't fit into A, B or C. So let's try to populate our data. What value is the same for A, B and C? It is the number nine. So I am going to put the nine here to show that it is common, it is the same for A, B and C. What of B and C? Well, one is the same for B and C. So I'm just going to put that one here. Three is the same for A and C. So I am going to put three over there. Just going to check it off to make sure I don't repeat myself. And I think, these are all the values that are the same. So for A, I am going to write six, I'm going to write 12, I'm going to write 15, 18 and 21. For B, I am going to write four, 16, 25, 36 and 49. And for C, I am going to write five, seven, 11, and 13. Write down the numbers that are in the set A union B. Well, all these numbers here. Let's see if I can get a different colour. All the numbers in this circle, and in this circle, would fit over here. So I am going to write the number six. I'm going to write 12. I'm going to write 15, 18, 21, three, nine, four, 16, 49, one, 25 and 36, and 49, I've got that already. Yeah, so they're all the numbers in A, and all the numbers in B. Now for C, I want not in A, and C. So not in A intersection C. So, all the numbers that are not in A, well would be that circle over there, isn't it? And I can't have three and nine, because it is part of A. 'Cause I'm looking for not in A intersection C. So I can't have three and nine. So my values for this one, I'm going to use a different colour. My values for not in A intersection C, would just be these values over here. So was going to be five, seven, 11, and 13. Now, next one. Not in B, values that are not in B. If you notice, this one is in B, So I can't have it. This nine is in B, so I can't write it. So my values that are not in B would be my A, without B, and my C without B. So, that is going to be six, 12, 15, 18, 21, three, three is in A and C, so that counts. Five, seven, 11, and 13. Last one then, B union C. So, that is everything in this circle over here and everything in this circle over here. So, that is going to be three, nine, five, seven, 11, 13, one, four, 16, 49, 25 and 36. I hope that make sense. If you need to pause the video to think about it some more, please do so. Right. It is now time for your independent task. I want you to pause the video now and attempt all the questions on your worksheet. And then once you're done, press resume, and we'll go over the answers together. So, pause your screen now and attempt the questions on your worksheet. Okay, how did you get on? I hope you are able to answer as many questions as you could, so let's go over the answers now. So A intersection B, write down the numbers that are in set A intersection B. I've got nine and four. A union B I've got 25, 16, 36, nine, four, and five. Not in A, I've got five, 40 and 17. This two are also not in A, and not in B, I've got 25, 16, 36, 40 and 70. Yup, let's look at number two. Write down the numbers that are in set not A. Well not A means everything here. So, numbers that are in set not A is eight, 11, 10, and 12. For not B, well, it will be four and 12 because not B is everything here. Not there. Everything in this region here is not B. So this is going to be four and 12. A and not B, well, it's in A and it is not in B, so that would be four and 12. We want a number, well numbers that are not in A and not in B. Well, that's just 12, isn't it? Cause 12 is not in A and not in B. So that would be 12. Okay. This was quite interesting 'cause you needed to, you needed to rewritten this sentences using union and intersections. So, how many people enjoy all three sports? How can we say this? How could we have written this using union or intersection. Well, it would have been B intersection C intersection S . So baseball, swim and cricket. How many people enjoy all three sports? Well it would be 31 here? How many people enjoy baseball and cricket, but not swimming? So we want B and C, and then we want not swimming. That means intersection S compliment. So, baseball and swimming, but not cricket. Baseball and cricket rather, my apologies and not swimming. So that would be 14. Last one then, how many people enjoy baseball and swimming, but not cricket? Well would be the other way. So it'd be B and S but not C. So baseball, swimming, not cricket, and that is 17. How did you get all those? Okay. For your explore task, using the numbers one to 37, that means in each of these empty boxes, the numbers one to 37, would be filled in these. And you can only use each number once. So for example, if you fill the space here with 18, you can't use 18 again for another one, okay. So, using numbers one to 37, fill in the boxes with numbers that would be in this region. So if I'm looking for multiples of two and three, I can write up my multiples of two and three until I find two numbers that are in the overlap, that are in the intersection of two and three, and then write those two numbers down. And then do the same for square numbers and odd numbers and so on and so forth. So remembering that the numbers one to 37 can only be used once. So, pause your video now and have a go at this. And then once you're done, press play, and there will be an answer on your screen. So pause your video and attempt to explore task. Okay. I hope you are able to have a go at that. That was quite an interesting task to have completed actually, because you see that, for example, the even numbers and the odd numbers, and the even numbers and not square numbers. There are lots of different options you could have gotten. And I was able, were able to fill in each box with the number one to 37 without repeating ourselves. So I wonder how you got on with this task. Okay. A very big well done to you for getting to the end of today's lesson. I hope you are able to learn more about Venn diagrams, how to read off, how to read values off Venn diagrams. Don't forget to complete the quiz before you go. Just so you know what you learned from today's lesson, and I will see you at the next lesson. Bye bye.

Overlapping circles (Part 2)

Overlapping circles (Part 2)

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Starter quiz

5 Questions

Exit quiz

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UnitMaths / Sets and Venn Diagrams

Maths