Okay welcome to our Math Kangaroo Set B webinars for level 3-4. This is the fourth of this webinar series. We'll meet every Sunday with the same Zoom address. If you have any questions as we are going along, you may put them in the chat. That is the way you can communicate any problems you have with me and also with Ishan. Ishan is our teaching assistant and we will introduce ourselves here in just a moment but we can both wave hello and like I said you can reach us both in the chat. Okay now this is a webinar. It is a large group format so we will keep your faces hidden. We are recording this. If you ever want to go back, if you miss a class or you didn't understand a problem and you want to come back and see it again, you can do that by looking at the recordings. Okay that will be the best way to catch up on something that you missed or if you needed to stop and go to the bathroom or whatever that happens to be, you can do that. We're going to have the students with their videos off please. Okay so today we are doing an introduction. We will go through several different types of problems. You'll notice there'll be a heading on each slide to tell you what strategy we are introducing with that slide. Okay so we will try to solve it first by the strategy listed but we recognize that there may be alternate ways to solve problems and you might be using a slightly different method and that is perfectly okay because these are contest questions and you should use the methods that feel the most comfortable for you. All right so we will have your cameras off and your microphone muted during the class. You should have the handout. You should have the links to print out the handouts each week. This week I don't think it's too complicated. You should be able to do it if you forgot to print it. It won't be too big a problem but definitely have paper and a pencil ready because you'll want to be taking notes and doing your work on paper as we go through. If you have questions go ahead and send them to Ishan the teaching assistant or to me and what else? We do have some polls so for most of the problems we have polls so you'll be able to choose from the multiple choice answers in the polls and we'll see how everyone does as a group. The polls are completely anonymous so if you make a mistake no one will know it was you and it's no big deal. The idea is to learn so you can make a mistake it doesn't matter. All right so we're gonna have some fun. We're gonna do some new math. Let's get going. My name is Dr. Sarah Segee. If you want to just like address me in the chat you can just use coach or coach Segee is fine or you'll just select where it says Sarah Segee and you don't have to say anything. You just ask me the questions. I am a biomedical scientist. That means I studied biology and I live in San Diego, California. I've been tutoring math and science for a very long time and I have four children of my own so I was the coach of their math club when they were in elementary school and I still go back to do some special lessons in the math club. I like to do Zumba and karate. I've taught swimming and I make soap from scratch. I guess that's one of my most unusual hobbies is that I make soap from scratch with natural vegetable oils and sodium hydroxide which is dangerous and you can't touch it. It will burn your skin so I have to wear goggles and glasses and look like I'm back in a chemistry lab. And I will give Ishan a minute to introduce himself. Hello, my name is Ishan Agredi. I'm currently in 11th grader who lives near Atlanta. I started participating in Math Kangaroo last year and I'll be participating this year too. But I've also been doing other math competitions since around third grade. Currently I go around helping the middle school and elementary schools math clubs within my county. But I'm an officer in my high school's math club. Other than math, I enjoy reading, playing chess and exercising. I'll probably spend the most time playing chess. And I'm very eager to be helping all of you. So if you have any questions, you can ask me or Dr. Ziggy in the chat. Okay. So hopefully that gives you a little bit. We're both human beings. So feel free to use that chat if you need to reach us. Again, we cannot do this is not one-on-one tutoring time. But if we see a lot of students asking the same question, that really helps us know that we need to explain that much, much better so that everyone understands. And if you put your correct answers in the chat, hopefully we can give you a thumbs up and give you some encouragement because we want everyone to feel like they're learning and doing well in this class. All right. These are the topics that we're going to cover over the next 10 weeks. So today's an introduction. But we'll be looking at patterns. We'll be looking at how pictures and diagrams can help you solve problems. We'll be looking at organized lists and tables. We'll be doing some guess and check and algebraic thinking, some logical reasoning, some logic puzzles. Those are always really fun. We'll learn how to use time, clocks and calendars. And we'll be doing a little bit of math problems. We'll learn how to use time, clocks and calendars for problems. And then we have geometry, which can be anywhere from points and lines to three-dimensional shapes. And then in our last lesson, we kind of put all these pieces together. We're calling it missing values. But it's how can you work with using all these tools to solve your problems together. Okay. So you're going to notice that math kangaroo problems are a little bit out of school. Math kangaroo problems are mostly word problems, although there are quite a few visual and spatial problems as well. And what you will find is that you will need to very carefully read and understand the problem. And you might have to read the problem more than once. Because there are going to be key little tricky words in there that you're going to need to see. Okay. So make sure that you have that going, that you have those key little tricky words. You're reading the problem very carefully. Figure out what it's asking. What does your answer need to be about? Sometimes it's going to put in, like, which of these is not possible, when all the other answers are possible. So if you just say, oh, that first one's got to be a good answer, but you didn't read that you need to know it's not possible, then you won't have it correct. Make a plan. How are you going to solve the problem? Use your pen and paper. Be very careful when you carry out your plan. So in this class, if I make any mistakes as I'm going along, I'm going to ask Ishan to help me out, because I'm not perfect. I'm human, just like the rest of you. And if you see that I've made a mistake, you can politely put that in the chat. If I write down the wrong number, let me know. Because I don't want to lead you incorrectly, okay? But I'm human, and I will make little typos, just like the rest of you sometimes make a mistake when you're working a problem. That's why we want to be careful and look back and check. Check our answers. Did our answer make sense, or did we make a mistake someplace? Can we solve it by another method? Because if we can solve it by another method, a lot of times we can make sure we have it correct. We use two different methods and get the same answer, then we can have pretty high confidence that we're correct in the answer. Okay. So we're going to start right off with our problems. Today we have 10 problems in the main lesson, and then we have some bonus problems. And I have polls for more than half of them. So we'll see how it goes. Remember, if you want to put your answers in the chat, you can do that. At noon, the minute hand of a clock is in the position shown in the picture on the right. What will the position of the minute hand be after 17 quarters of an hour pass? Okay, so some of you who put answers in the chat with me have noticed I might have given you a thumbs up. I can't respond to everybody on every question, but you can also try Ishan, see if he has a little more time. But I did have some questions about this, so let's go over it. Somebody asked me, what is a quarter? That's a good question. A quarter equals one-fourth. There are four quarters in an hour. So if I do some dotted lines with my out, my clock in it, there are, this is one quarter. If my hand gets down here, it's two quarters, three quarters, and four quarters. So there are four quarters in every, sorry, see, I told you I make mistakes, four quarters in every hour. So if we go through 17 quarters, well, one hour will be four quarters. Two hours will be eight quarters. Three hours will be 12 quarters. And four hours will be 16 quarters, right? And some of you may have done that by saying four times four equals 16. And that's a perfectly good way to do it. But if we have 17 quarters, every time we go a full hour, the minute hand, I'm going to switch colors, the minute hand is going to go all the way around and back up to the top in one hour. So if we go four times around, four times around is four hours. But it says that we go one more quarter. We go 17 quarters. So 17 minus 16 is one extra quarter. So we're going to end up going one more quarter of an hour, and our hand is going to look like A. You notice sometimes I like to get very colorful on my slides. Now, what do you do if you want to see this all over again? You'll be able to get the recording and see this all over again, okay? Number two. I do have a poll for this problem. So after I read it and give you a minute or two, then I will post the poll. Jack drew a point on a piece of paper. Next, he drew four different straight lines going through this point. Into how many pieces did these lines divide the paper? If you have the handout, you can work right on the handout. If not, you should have some paper and you can draw a rectangle with a dot in it. That's not so hard. And I'm having great answers so far. Hopefully you've all had enough time to read the problem and draw the rectangle, and I will start the poll. So for most of you, you'll notice that that pops up on your screen. If you don't see the answer you need, you might have to scroll up or down to find the correct answer, and then you just click on it and tap submit. All right, it looks like most of the students have answered the poll. You'll notice I don't have time to respond to every comment that you put in the chat. I'm sorry, but I just don't have enough fingers to handle that in between the problems. So here are the results of the poll. And you'll see that more than half of you think the answer is eight, but quite a few of you are saying four. So let's take a look and see what happens when we actually just follow the instructions on the problem this time. Kind of how I'm gonna solve it. It says that Jack drew a point in the middle and next he drew four straight lines and they're all different going through this point. So if I draw my first straight line going through the point, it'll look like this. That's line number one, line number two, line number three, and line number four. You notice it doesn't matter where I draw them as long as they all go through that very same point. Now, if I had drawn perfectly, they would all go through the exact same point because a point doesn't have any dimensions in the rectangle, right? So now all I have to do is count up the pieces. One, two, three, four, five, six, seven, eight pieces if I'm going through the center point, okay? All right, we will move on to our next problem. A three-digit code is needed. Oh, Ishan, you wanted to lead this one. I'm sorry, we're gonna let Ishan do this one. A three-digit code is needed to open a safe. How many possible codes are there if it is known that only three numbers, one, three, and five are used in this code and each of them is only used once? Dr. Sagi, do we have a poll for this one? Do we have a poll for this one? Yes, we do. After they have a minute to read the problem over, we can launch the poll. I launched the poll. You'll notice the problem is repeated in the top of the poll, so if it's popping up and it blocks your screen, you can still read the problem right there in the poll. Okay, Sean, it looks like almost everyone answered the poll question. I think we can solve it together. I'm not exactly sure how to annotate on this. So could you draw it out while I explain it? I'd be happy to be your note taker. No problem. Okay, so we know we're told what we have to solve for they want to know how many possible codes are there. If it's known that we only use three numbers, one, three and five, and this code and each of them is only used once. So, since there's only three numbers, and each of them is only used once we know that there would have to be a very small number of possible codes. So the first thing we can do is brute force this. So we can start with their first first code, one, three and five in order. And now we can switch around the five and the three and we have 153. And these are the only two codes, we can make where one is in the hundreds place. So now let's put three in the hundreds place, we can go 315. And then 351. And then 351. Now these are the only two options, or it's only two possible codes where three is in the hundreds place. So now we can start with five, so the 513. And then 531. And then we noticed that these are the only six possible codes. And there's two other ways to do this. So first, you notice that there's three open spaces for the code because these three digits make a three digit code of these, there's three possible numbers that can go into the first slot. So we can put three there. So we can put three there. And then in the second slot, there's two possible numbers because we know each number in this code is used twice. So for example, if we used one in the first slot, then in the second slot, there could only be three or five. In the first slide, if we use three in the second slot, there could be one or five, and so on and so forth. And then in the last slot, there's only one possible number that can go in there. As if we already used one and three in the hundreds and tens digit respectively, then the only number that can go in the third slot is five. So we know that there's three options for the first choice, two options for the second choice and three options for the third or slot of this code, we can multiply these together and we get six possible choices or six possible codes. And we can double check that with the six codes we got with brute forcing and that all makes sense. Thank you. You're welcome. And I want to share the results because the students did really, really well. You see that? Most of you, over 80% of you thought that the answer was six. And I'm sure now after seeing it solved in two different ways, but Yashan, all of you would say it's six possible choices. Okay. Thank you. Eva lives with her parents, her brother, one dog, two cats, two parrots and four fish. What is the total number of legs that they have all together? You'll notice the title on this slide is making a table. So I will solve it with a table, but you can solve it whichever way you prefer. As long as you stay organized and don't miss any legs. All right, I'll stop the poll. And this group is doing really well so far today. The correct answer is 24, which was overwhelmingly your first choice for this. Said I will show you how to do it with a table because that's the instructions for this particular slide. But if you made some sort of list or another organization, that's fine. Eva is a human and she has two legs. So she's only one person. So there's two legs and the total so far is only two. We're going to assume that Eva has two parents. Each one of them has two legs. So in that group of parents, there would be four more legs. And two plus four is six legs in total. Her brother should have two legs and there's only one brother because it's singular here. So we have to assume it's just two and now we have a total of eight. There's only one dog, but a dog has four legs. So four times one is four. And when we add that into the eight, we have 12. It says there are two cats. Each one has four legs. So now we're going to add eight legs for the group of cats. And that takes up to 20. We know that parrots are kind of bird and birds have two legs. With two parrots, that would be four more legs for a total of 24. And fish, I think was just in there to trick you. There's no legs on fish, just fins. So the total answer is going to be 24. It's pretty common that Math Kangaroo might try to trick you by giving you some extra information that you don't really need. So we didn't need to know about the fish. Adam spent five days preparing for a test. The first day he solved one problem and on each consecutive day, he solved twice as many problems as the day before. How many problems did Adam solve all together preparing for the test? Now, if I'm doing my steps, I need to read the important information here. We know he spent five days, that's important. We know he started with one problem and then he solved twice as many. Twice as many is going to be important. And then it's asking, how many problems did he solve all together? Not how many on the fourth day or the fifth day, but how many all together? So I've highlighted all together. So I've highlighted, underlined the words that I think are really important for this problem. Oh, this group is super speedy. I will launch the poll. Remember, the problems are rewritten in the poll. So I know some students have told me the poll blocks the problem, but it doesn't, because the problem is right there. Wow, these are some speedy solvers, Eshaan. I'm going to share the results of this poll. Look at, they solved it speedy and accurately. 31 is correct. So let's take a look together. I'm going to kind of do a little version of a table, but I'm not going to draw in all the lines. So I'm just going to have on the day. So day 1, 2, 3, 4, and 5. And then I'm going to do how many problems. So on the first day, he solved 1. On the second day, it's twice as many. Twice as many means multiply by 2. And then I'm going to have to multiply by 2. So that's what it means when it says find the pattern. The pattern here is times 2. But since they want all together, I now have to add them. 1 plus 2 plus 4 plus 8 plus 16. You can add it up kind of the easy way. 2 plus 8 is 10. 14 plus 16 is 20. 10 plus 20 is 30. And one more, 31 problems. 31 problems. So don't be afraid to add things out of order if it makes your life simpler. If you want to add them straight from left to right, that's also correct. Just depends on how you prefer. All right. So this question, I think, is a little bit interesting the way they presented it. Let's see if we can make sense about it. About the number 325, five boys said. So then it says Andy. This is what Andy says. Andy says, this is a three-digit number. Barry says, all the digits are different. Charlie says, the sum of the digits is 10. Danny says, the ones digit is 5. And he says, all the digits are odd. Which of the boys was wrong? That's important that we need to find the wrong boy. There's no poll here and I'm seeing such fantastic answers in the chat. Good. So if only one of the boys is wrong, then we're going to know that the other boys are correct. Right? This is a three digit number. That is correct. All the digits are different. That is correct. The sum of the digits is 10. 3 plus 2 is 5 plus 5 is 10. So that's correct. Danny says one of the digits is 5. The ones digit is 5. And he says all of the digits are odd. So if you remember, odd digits are the opposite of even digits. Right? And the odds are 1, 3, 5, 7, 9. And any digit that has those in the ones place and the evens are the 2, 4, 6, 8, and 0, like 10. Those are even. And we do see that 2 is an even number. So all the digits are odd is the wrong answer. Number 7. I do have a poll again. 13 children are playing hide and seek. One of them is the seeker, and the others hide. After a while, 9 children have been found. How many children are still hiding? You can think back to when you played hide and seek. I'm about to close the poll. Anybody else want to put an answer in there? OK. Once again, we're doing amazingly well. The answer is 3, and that's what most of you have said. So if 13 children are playing hide and seek, and we have to subtract the one seeker, that leaves 12 hiders. And then we have 9. So from the 12 hiders, 9 have been found. That means 3 hiders are left. OK. Very good. OK. Some birds were sitting on a telegraph wire. Then 5 of them flew away. And after some time, 3 birds came back. At that time, there were 12 birds sitting on the wire. How many birds were there at the very beginning? So this we call working backwards, because they give you the ending, but not the beginning. There is no poll, so you can put your answers in the chat for me or for Ishan. This group is very, very speedy, Sean. Yeah, so when we talk about working backwards problems, one way to solve them is to make a flow chart, and we'll have a lesson where we practice this. But when we work backwards, we basically need to do everything in reverse. So instead of three came back, we're gonna subtract three, and that's gonna get us nine. And instead of five flew away, we're gonna put those five back into the group, and we're gonna get 14. And the nice thing about working backwards problems, if we go forward again, we should get it correct. So 14 minus five is nine, and nine plus three is 12. So we know that the correct starting number was 14 birds. Now, could you think of this in another way? Could you say, okay, five flew away and three came back. So the difference between five and three is two. So we started with two more at the beginning than we have at the end, and 12 plus two is 14. Can you do that? Absolutely, it works just fine. So if that's how you thought about it, you're correct as well. I just like to show you that we might all have slightly different ways of thinking, and that's perfectly normal for not everybody to be exactly the same. One tour bus can seat no more than 55 people. What's the smallest number of buses needed to seat 160 people? I'm gonna launch the poll right away. Yeah, this group is amazing. I stopped the poll there because I'm getting all, almost all the same answers. Almost everybody says it's three buses that are needed. That is correct. Very good. Because on the first bus, on the first bus, all right, I have to do a couple of clicks in order to make the annotations work. On the first bus, I'm gonna be able to put 55 people. If I add another bus, I'm gonna be able to get 110 people. On my third bus, I would be able to put a hundred, oops. Little typo, can have them even when you're handwriting. You'll have 165 people and we only need 160. So I need those three buses so everyone has a seat. Okay. Out of how many blocks is this tower built? There's a very good question, which is, is it symmetrical? Yes, it is symmetrical. It's the same kind of stepping stairs in four directions. And that will make it faster to count. Very good. So if we look at that symmetry, we can see that this piece here is repeated. This piece here has one, two, three, four, five, six blocks, and there are four of these. So four times six equals 24. Then I need the centerpiece. The centerpiece is four stories high, basically, right? So this is four more pieces. So 24 plus four equals 28. So the correct answer is D. Excellent. All right. And I know we have a special request, and it's my favorite one of these as well. Ishan, would you lead us through this bonus that you had liked? Oh, sure. And once again, could you take notes for me? Okay. So it looks a little bit complicated, but it's probably one of the simplest questions on here. So we're given that four square tiles were arranged in the way shown in the picture. The lengths of the sides of two tiles are indicated. What is the length of the side of the largest tile? So just by looking at this picture, we know that the sum of the two smallest, or the sum of the side lengths of the two smallest squares must add up to 40, because that 40 is split into, or that side length of 40 on top is split into the side lengths of those two squares. And if we rotated it, we would see it's the same way with that 40 and that second smallest square. So we know that the side length of the second smallest square plus 40 must add up to the side length of the largest tile. So just looking at this, we know that since 40 plus 16, sorry, since 40 must equal a 16 plus the length of the second smallest tile, we can subtract 16 from both sides, and we get 40 minus 16 equals the length of that second smallest tile, which is 24. Now we know the length of the side of the second smallest tile plus the length of the side that's 40 must add up to the length of the side of the largest tile, or 24 plus 40 must add up to the length of the side of the largest tile, which is 64. So your answer is E, 64. Thank you, Ishan. That's going to bring us to the end of our first week of this webinar series. So I hope you have enjoyed these problems. So I just want to give a little reminder that you make sure you're following the steps. You look at what is the problem asking, come up with your plan of how to solve it, carry out the plan, and then look back and check your answers. So over the next few weeks, we'll be solving some number system problems, geometry, we talked about the different things, but these are kind of the ones that really appear a lot in math kangaroo problems. You'll notice that the method you use is going to be your personal choice, but we will focus on one method a week just to make sure you practiced all different ways of solving problems. And then when you face a whole contest, you can choose which ways are working well for you. Okay, I hope you enjoyed this week. Thank you very much, Ishan. And we will be back again at the same time next Sunday. Have a really good week. Bye-bye.

Math Kangaroo

problem-solving

mathematical competitions

interactive webinar

algebraic thinking

logical reasoning

Dr. Sarah Segee

student engagement