Okay, right now 10 o'clock and 180 students have joined. So without further ado, I am going to start. All right, welcome again. Welcome to the Mask and Glue webinar level three and four. Today we are going to work on specific or the strategy making an organizer list. Now what we are going to do, let's quickly that we just go through quick, you know, we have to do things we're going to go through housekeeping, let's go to the next slide. So your microphone should be muted during the session, you will not be able to turn it on. I'm sorry, but again, you can leave the questions. Now you'll be able to ask some questions via the chat dialog box. Now the host and co-host, Maya, read these questions and please keep them about the topic being discussed. I'm sorry, but we are not going to answer much about how the logistic or how I can help you to practice for the exam. Mainly we are focused on questions about today's lesson. All right, we cannot answer every question, I'm sorry. However, the team is going to respond to you. Can you be a little bit patient and then we can respond to the next couple of days. Also, as I said, you're going to participate this webinar very actively. How? You can do by poll. So please check the setting for polls. And these polls are all anonymous. Don't worry about the question, you may make a mistake, but it's okay. So you're just going to pick the right questions that you think that this is the answer and I am going to see how you are doing and that's fun part, right? All right, so then next part. So again, this is a one hour long webinar and also next four Saturdays, coming Saturday, we are going to have a whole another series of webinar. So make sure that please do not lose this opportunity and register. And another thing is a handout, okay. I need a handout. All right. So then we are going to go next things. Hi, everyone. Again, I am going to the spotlight. Okay, I'm going to switch to stop share. All right. Hi, everybody. My name is Mrs. Sharif. I am today's webinar's lecturer and I am the California schools public school teachers. I love math kangaroo because that trained my class students to be problem solver and critical thinker, which is a boss we needed for going through next coming future, which we have a lot of, you know, that anticipating some problems like climate change or whatever we need to solve. You need to use this math. If you become want to become an engineer, you are definitely major math, is that right? So that is my goal for the math kangaroo. And also I like to enjoy even you are new to the math kangaroo or you are a little bit younger than third grader, you can join us with today's, you know, help of the handout. You can go get that great, great scores. All right. So I am looking forward that you are enjoying and understand what I teach you today. So please follow me with that handout. Now I'm going to introduce my very special contributor, Maya. I'm going to give you Maya's spotlight. All right, Maya, go ahead. Hi, I'm Maya. I'm in 10th grade and I've been participating in math kangaroo for a few years since fourth grade. And I will be helping today. So if you have any questions, you can message the host and panelists in the chat and I'll reply. All right. Thank you, Maya. Maya, you just mentioned about the gold medal. How did you get the gold medal? So I got the gold medal by getting a perfect score on the math kangaroo, which I did by doing a lot of practice problems for math kangaroo and learning different problem solving strategies like the ones that you're going to learn today. Oh, thank you so much. Some students ask how I can become like Maya. So the secret is doing many practice problem. Is that right? All right. Thank you so much, Maya, for helping me today. Okay. Then we are going to start. Let's start with today's lesson. So I am going to start with two warm up questions. Oops. I'm going to go one page. All right. I hope everybody can see my warm up page. Maya, can you see me? Can you see my warm up page? Thank you so much. Yes. Can you be my eyes? Okay. All right. Then other students. Now let's start warm up. Okay. It's not so difficult, but you have to wear the thinking cap and you have to see very carefully. You have to read a sentence carefully. Okay. Sometimes math kangaroo's language, the words, is a little bit difficult. So I am going to navigate you today. Now you have to get today's handout ready and we are going to work together. So I'm going to read a question. Number one, warm up. Which one of the figures on the bottom of the picture can you make using only the shapes shown in the picture number one? So I'm going to see picture number one here, two circle, and looks like a small and middle size large and middle size three triangle, and also one long rectangle. Now I'd like to ask you to just check everything. Now I'm going to start seeing some extra shapes. For example, there is a rectangle, I mean square. That is not the one. So I am going to say, okay, this is not. And also I am going to see extra things, one small circle. This is not. Now next part is a little bit difficult. Now you're going to take a look of the three, that's the triangle shape. You must take a look of the first size. So now this is a small, this is a large. Also, this triangle's name is a right triangle and also right triangle. This looks like a three side same. For me, it looks like an equilateral. So now with that size, okay, this is not because these two right angle is the same size. So now we are going to narrow down two of them. Now using your good eyes, now you're going to see how the size and how the angle. And you're going to choose one of them. Maya, then can you start the poll? Okay so I am going to go very quickly so then right now many people are now voting for E and I just want to say a couple people only seven people or so is now right now choosing other questions mainly almost everybody is choosing that E. Let's see all right so then oops I'm going to end the poll okay thank you so much all right then I like to ask you oops I'm going to choose this all right so everybody take a look of that some people choose D now take a look of this equilateral triangle it's the same size but we don't have a two equilateral see so that's why answer is E so 98 students got it thank you okay that's awesome now you feel better right everyone oops I'm going to go back okay sorry go back next warm-up questions oh before we go I just want to check because you guys are going to take a state test right so now triangle based on size remember the name that each size of difference we call scaling now two sides are same triangle we call isosceles and today we saw this one three sides are same equilateral equilateral now angle triangle is interesting by size and angle so 90 degrees are right angle smaller than 90 degree it's called acute so this green one and also larger than 90 degree we call obtuse so these are the words you have to memorize all right okay then let's go to the next warm-up okay how many three digit numbers can you create using that digit three zero seven three digit right and also it says only once what kind of list I have to make it what is the best way I will not miss anything so what is a good thing everybody think about this 10 seconds some of the students raising hands I'm sorry but I cannot pick your hands I would love to but today we have so many students so the six students put your hands down thank you no more hand please thank you so then let's use something I'm going to tell you three diagram everybody repeat after me three diagram can you say to yourself three diagram like a trees we are going to make three diagram so first of all we are going to start thinking three and zero and seven okay what is a number could be in the hundreds place place value hundred can I put the zero no so what you have is only two option three and seven right and after that if I choose the three what the two choices I have maybe we can put zero or seven if I use three and zero logically I only have one only one seven if I choose three and seven I have logically have zero so this is called tree diagram you are not going to miss any number or any possibility but you have to logically think what is a number I can use now it is your time you are going to use the number seven in a hundred place you are going to start and maya please show the poll and this time 30 seconds question is asking how many ways we can make this number okay so we are going to count how many number you are going to make it with the three and zero but zero cannot be in hundred All right, looks like a poll stopped. So then let's check. Looks like a C is majority. And let's check the share result. Oops. All right. This is a result and 86% students answered that option is four ways. Okay, let me check the answers. So then I'm continue this diagram. Okay, now after seven, you have two options. Zero or three. Is that right? And after that, there is no other way. This is all combination possible because zero cannot be in the hundredth place value. Good? Everybody, if you put zero in a hundred, it's become a two-digit number. So which does not satisfy our problems. All right, thank you so much. Everybody did a great job. Now you have to a little bit warm up and you're going to go the next one. Then other students, we are going to start using your handout. So everybody pick up your handout and pencil. And just before we go start the question, we are now working on making an organized list. This is one of the strategies Masa Kangaroo is using that studying. Okay, I think I'm going to stop Paul. Maya, Paul comes back a couple of times. I don't know why. Okay, all right. And I like to ask you, making an organized list. And next four webinar, we are going to cover different strategies. So please come back, okay? Now, what's a making organized list and why we have to making list? That is the things I'm going to explain. So sometimes in a question, okay, there are lots of data numbers you have to analyze and then you have to understand, but too many. And I cannot remember how much I've made a progress. So that is a good way that this strategy works. Make some type of a list to keep track of the progress. Hmm, right now we use a tree diagram. I make sure I use the seven and the other number three in the hundreds number. That way you keep tracking. I am doing that every possibility. I don't miss anything. So that's important part of the strategies, okay? So every possible scenario, we are going to come up with. We are going to waiting one challenge problem, which is the last question. You have to come up with all possible scenarios or cases. So we call this casework, okay? Everyone, casework. Can you repeat? Casework, good. So then casework is a process of splitting problem into a limited number of cases. So you're going to use all these given cases, going to find something pattern or something hidden questions. So it's not straight. You're going to solve one time and then you reach to the next real question. So we are going to use this casework and solve this. Casework is used nearly all area of the mathematics. Now we will look back later in examples and keep track of solving your process. All right. Okay, then come back to our problem. First questions. The pages of the book are numbered. One, two, three, four, five, and so on. That's correct. I don't see page number zero, right? The digit five appears exactly 16 times. This book has some number of the pages. I don't know. But they say the number five comes back 16 times. But they don't ask you what is a page you are going to find a 16 times. Instead, question is this. What is that maximum number of the book could be? Now everybody start thinking how I can solve this problem. Sorry. My throat is so dry. I'm sorry. Okay, then let's start. So you're going to pick up your organizer. Sorry, I'm going to go back here. So organizer looks like this. Question, how I can organize this list? So I go organize by the page number. So I don't know what's a page. So I'm just going to randomly start page number one to 10. Everybody pick up your pencil, write it down. Okay. No raising hands instead of writing down. Still raising hands. Okay, everybody please write it down. Maybe page one to 10. I'm going to count one, two, three, four, five, six, seven, eight, nine, 10. So I have one page, the page number five here, right? This is a one time. Everybody good? So next one, 11 to 20. Now everybody, you find a pattern already. 11, 12, 30, 40, 15. So I'm going to write it down, 15. This is the second time. Good. Next one. Nobody wants to do count up anymore. I know. Next one is a 25. Go ahead. And so on. You can continue. 31, to 40. And this is a 35. Uh-oh, Mrs. Sharif, I have to little bit move this one. Just a moment. Okay. Okay, next one is 41 to 50. Everybody write it. Mrs. Sharif, this help helping. So you are going to do on your own. So 41 to 50, you can find out how many. Now, this one is actually, there is a difference. Look at this. This is a tens number. Tens number is now, I have five. So this is not only 45. This is actually 45 and 50. Now everybody, I am going to first go ahead and continue the table. And then you're going to finish to find out what is a page. Actually, you're going to find out the five, 16 times exactly. But that's not the answer. So first finish your work, okay? And then find out which page you are going to find. 16 times exactly, you can find the number five. Maya, just a moment, okay? I am going to finalize the last question part. Now everybody's working 51 to 60. Now that part, you have lots of five. So you have to go risk, make sure do not miss. Now, check tens and ones number, okay? Each time you find a number five, count as one. All right, now, hopefully you can find out 16 times which page you can find the five, but that's not the answer. What is a maximum number of the pages this book could have? Now, what? So what does it mean, maximum? I found out the answer, this is a page. Yes, but think about this. Maximum number is just before the next time you're going to see the number five. So what is the next page you're going to see the number five? And what is not including that page, not include that page? What is a maximum page of the book could be possible? All right, Maya, thank you so much, but let's go. This question, I am going to give you 40 seconds. I give you lots of hints, so 40 seconds. Everybody, let's go. One more time, the answer is not asking which page number you're going to find the five, 16 times. Everybody good? Think one more steps. 17 times, when is the 17 times come? What's a number could be possible? Okay, 76% participant has answered. I'm going to wait a little bit more. Right now, 300 students are in and 80%. Okay, wow, this is interesting. Everybody has pretty much the different answers you chose. Okay, then I am going to close the poll, five. Everybody, if you want to push the right now, pick one, four, three, two, one, and zero. I'm going to end poll and share result. Am I sharing result? Oops, not sharing result. Okay, sorry, all right. Okay, hmm, this is not maybe a little bit difficult. I don't know, but the very different way that people answer. So then I am going to go one time, very completely follow through, let's see. So then other students, take a look. So we talk about each page we are going to, I'm sorry, one more time. I'm going to go all the possible page number, okay? So page number one to 10. So you are going to find one, this is five, page number five, right? And next one, next one is page number 11 to 20. Now you are going to find out the answer is 15, good. And next one, you are going to find page 21 to 30. Now you are going to find out only one. Now this is the easy part, okay? Just following only one's number, but more getting harder. Okay, now 21, 31. So you are going to go check all possible, all possible five number appears, page number. Okay, now next one is going to be change. So now I have two number, 45 and 50, everybody good? This count twice, good? And next one, ooh, we have a big number, 51 to 60. So now I'm going to count everybody, 51, five intense place, 51. 52, everybody good? This is all counted as one count number five, okay? So 53, 54, 55, whoops. Okay, Mrs. Shreve, this has a two 55, two five number show up. So this count as twice, good? So now, oh, this is a two five. That's how we can read it. 56, 57, 58, 59. So up to here, how many I have? Let's count it. I can see five, one, two, three, four, five, six, seven, eight, nine, 10. Now this count twice, 11, 12, 13, 14, 15, 16. Okay, so this is a page, the 16th times I see five. Now question is not these answers. Question is, then what is a maximum number that this book should have? So next one, yes, you have already know. Next one is a 65, is a 17th time five show up, right? But we cannot have the 17th. So the answer is one page before 64 is the maximum. All right? Okay, everybody, let's go to the next questions. Okay, Joseph has four toys and one is a car, airplane, ball, and ship. Now he wants to put them all in a row on a shelf. Now the both, both means both, okay? Not only both, the ship and airplane have to be next to the car. One more time. This has you have to read carefully. That you have a ship right next to the car and airplane, same, right next to the car. Now, how many ways can he arrange the toys so that this condition is fulfilled? Now this part is a difficult. What is the meaning of fulfilled? Maskanguru ask you because, you know, they are more using the mask language. Fulfilled means you are going to use the rules. Then how many way you can do? So you have to follow the rules. What is the rules here? You have to put, I'm sorry, car and airplane and ball. Yeah, sorry, ship. One more time. Car, airplane, and ship. Because they are all the something that you can ride and travel. So that's why I think Joseph wants to put together, right? One group. Three are together and car is center. Now you're going to start making this list. Now, what is a loner of these groups? Who cannot become a three groups? That's a ball. The ball is going to be away. So far right and far left is going to be ball. So now you're going to go, you can start thinking. Now you're going to switch the location. Center is always cars, okay? Everybody there. Ball is going to go. One minute. One minute. Take, really think about. Don't just pick. You have to think carefully. I still see many people just jumping and not thinking well. Make a list. I'm gonna warn you. Some people are not making list. You just pick something, whatever. It's not difficult. This is a easy, more like a easy, easy four points. All right? Okay, math kangaroos question is one to 24. The first eight is easy. And next eight is medium difficult. And last one is very difficult. My point is that this type of the question is, you have to get this. Because to get a good score, this is a possibility you can get without any mistake. Okay? All right. Okay, so I am going to ask you, end poll. I think I didn't wait one minute. I feel sorry for you, so I can wait a little bit. But, okay, everybody, thank you. But you don't have to raise your hands. You are just going to take poll. Now I'm going to a little bit help people who is actually jumping on and did not think about carefully. So this is a car in the center. Now you're going to put a ball. This is a loaner. You cannot, he cannot be in the group. The ball could be far right, or ball could be far left. So now everybody, can you think about? What is a combination you can do? Some people say two, some people say four. Okay, they stop. All right, then I'm going to share. Right now, 81% students is now telling that answer is a four. So let's find out. And some people two, some people five, six, eight. Okay, so then stop sharing. All right. So again, I think, you know, ball can never be together. So we have to put far away. Now what you can do is, you can just make a combination of ship, airplane, and car. That's the only thing. So I'm going to do, car is center, right? So I'm going to put the airplane here, and car, and ship. Now I'm going to switch airplane and ship positions. Okay, these are two ways. More ways, yes. Now I'm going to move this car's position to here. And first, airplane, car, and ship. I'm going to switch ship, car, and airplane. Good, so answer is four ways. Thank you. Okay, then let's go to the next questions. Yeah. All right. So then next question is, oops, sorry. Next questions. Oh, this is a math kangaroo's favorite one. We are going to call the cube. In three dimensions, we are going to use a spatial thinking, okay? Jack built cube using the 27 small cubes, which are colored either gray or white. So color is only two, okay? No two of the small cubes, which are the same color, okay, have a common face. One more time. No two of the small cubes, which are same color, for example, gray and gray, they are not going to share a same face. That means not touching each other, right? The cube, how many faces? Six faces. Now six faces will never gray and gray are touching any faces and sharing, okay? That's a meaning. So that means gray, white, gray, white, whatever they are, different kinds of the two colors are put together. No one of them is going to be put gray, gray or white, white, any faces, okay? So then let's go. How I can solve this problem? Not missing anything, but covered, check all possibilities. So I'm going to use, I'm going to get using the layers, bi-layer and second layer and third layer. Now, everybody take a look very carefully. I think, you know, first layer and bottom layer looks like exactly same. So I don't have to do twice, but middle one is a little bit different. And I cannot see in the center of the middle layer. That is a difficult part. But I can just make a, just, you know, three dimensions, making to the second two dimensions in a picture. So I am going to start doing like this. So I say first one is, okay, top layer. This one is a white, white, white, white, right? So I'm going to just write it down. Second middle here, white. Oops, I can't write. Okay, white, and this is a white, and this is a white, this is a white. Again, top and bottom is same. White, white, white. I'm looking for white cube, okay? Mini cube of white cubes, not gray, white cubes. Now, middle layer, how you are going to making all possible way. Now, this is a hint, great hint. Look, the corner is white. So this is here. I'm going to give here, and everybody starts working on, and we are giving one minute. Go. How many white cubes, mini cubes in total? It's not the second layer. In all, how many white cubes? Remember, top and bottom is the same. So what is the middle layers and center part? How do they look like? White and gray cannot touch each other. So that's why we have to follow the rules. Okay, now 12 and 13, many people are choosing that part. Okay, I'm going to wait. All right. See, 85% participation. Everybody pick your finger, push one of them. Okay, that's okay. If you make a mistake, that's fine. Participation is very important. You know why? Because you do more, you can get smarter. Even to make mistake is okay, okay? You have a growth mindset. It's okay to make a mistake. Okay, now 92%. Okay, then I'm going to stop here. All right, then everybody check. The poll is, oops, doesn't check. Okay, poll is right now, like this. So 50% students said 13. And next most, the majority is at 12. So let's check the answers then. All right, so this is, I think we are covering. Okay, now corner here is a white. Okay, I write it down, white. Sorry, I come back again. So, okay, white. And the other side of the corner, you see this corner is going to be white again. And the other side, white. And you can see this one. Okay, this part is going to be this corner. You see the corner, right? This is a corner, corner, corner. And I cannot see it, but there is a corner, white. Now, I'm done because I don't see center. But wait, you can think about the middle part. How does look like here is a gray and white? That is how you have to think. And then remember our condition is not one single same color cube touching each other. Look, it's right now, this color is a gray, gray, gray. So it cannot be possible. If this is a gray, then you have to make this one white. So some students choose 12. I think this is you missed it. But you have to read the conditions and you have to find out, ooh, guessing work. 12 is actually not, answer is 13. Okay, let's go to the next questions. Okay, another same type of the cube questions. We made a big cube using 64 small white cubes. Now, number is 64. And then we painted five of the size of the big cube. One more time, it's a big cube. We are not talking about small white cube. Now, you made a structure, okay, the big cube, and you painted five of the sides. So we have a cube has a six sides and the five sides are painted, one left as a white. Ooh, lucky, I saw here, everybody take a look. Now, top of the face is actually white. So logically you have to conclude. Although I don't see anything, but the other side is green, right, everyone? So then another one, this side, I don't see at all, but I assume that's again green, right? So then this is the one thing you have to guessing. Also, wait, the bottom, right, bottom is also green. So I am going to ask you, you have a good imagination. And also you cannot see it, but you are going to, as if you can see it and you can count it, okay? So then let's go to that. A little bit more help, I'm going to show. Now, I am going to go with layer again, right? So layer means we are going to use that each layers check. And we can conclude, I concluded everything I check, okay? So this is a green. So first one, so this is a two, one, two. So this is a one box, right? This is a green, this is a green, okay? Everybody, two faces are green. Now, next two one is only one side because they have only showing this face toward outside. I cannot paint anyway. So this corner, the same logic. This corner is two side green, check. Hmm, you have a good eye to think. This corner is also green. I cannot see it, but the corner is showing two faces out, out, right? You have to, you can paint on the outside. So this is also two. This side and the other side is green. Everybody's good up to here, okay? So now, good news. One layer, second layer, third layer, up to here is exactly same structure. So you are going to check all the corners, good? But last one, the bottom layer is a little bit, you need a little bit of attention because the bottom one is, the bottom, you don't see the bottom of the big cube. That is green, good? So that means the corner one is, I'm gonna count one, two, and then bottom is a green. So this is no longer, it's not counted as a two-sided paint. Everybody's good? Then which part is a green? Think about how it looked like from the bottom. Okay, now I can see this side and the bottom, how many faces are green? Now, everybody, let's go, 40 seconds. Sorry, I am going to go very quick. 40 seconds, the pole, you have to think logically and check everyone. Wow, everybody's so good. Now, it's a, okay, good. You are going to count up, add up, all of the two painted, the tubes, okay? Not the last one, the bottom one, all of them, you have to add up. It's very easy, top is a four, right? If you're listening carefully, I don't know why the people choosing smaller number, but top layer, you have already four corners, is that right? Second layer, you have another four corners. You have to see and guess, you are going to see how does it look like the other side of that? Okay, okay, a little bit more people, 81% participated. Okay, then I am going to stop one minute. All right, thank you so much for your participating. And I am going to share the results. Okay, so right now, many people is going to choose a lot of things. Okay, thank you, but I appreciate that you're trying to. Now I'm going to continue. Okay, where did I go? So stop sharing. Okay, so again, the bottom one layer only. Let's take a look. Bottom layer is that the bottom mini cube is painted. So now this is a one painted. I'm going to change the color. Okay, so this is a one painted. Doesn't show. Okay, one, two, and this side, three, four. And the other side, there is a bottom layer, five, six. And this side, the bottom, there is a bottom, seven, eight. I'm sorry, I'm writing here, but this is not the top layer. Bottom layer, okay? So that means you are going to 12 plus eight. And 20 is the answer. So right now, 37% students, you got the answer correct. But let's keep going, okay? Thank you. All right, so then let's move on. Okay. All right, and let's go to the next question. Oh, okay, next question. We are going to start solving this question. In the botanical garden, shown in the picture, it looks like a map. And visitors walk only on the marked path. In how many different ways people can go from greenhouse A to greenhouse B? If this is the condition, only walk on given path once. You cannot go here and back and go walk around and come back. That's not acceptable, okay? Only one path, and you cannot come back, or double lines, okay? So choose one of them, four, six, eight, and 12. But what is a good, you know, the strategies? So definitely we are going to make a tree diagram. But before that, I'm going to give you a good hint. Use some labels for making a list. So I like to ask you to go, instead of writing the lines like this. Okay, I am going to go here and here. Or I can go to this way. Okay, I can go to this way and here. Wait, wait, wait, I don't know how many I did. This is going to happen, right? So instead of doing that, you are going to make using the letter to make a list, okay? So first one is the shortest lines, shortest path. So we are going to go shortest path, okay? So then it's easy. A, everybody think about this. Shortest path, C. And we'll walk that long path and come back to E and B. Oh, that's easy, right? This is one. So now we go down the bottom path. And next one is A, B. What's next? F and B. Okay, there's a shortest path. Now there is another one. Now medium length. Medium length. So in a quiet middle path, you have, for example, instead of going to A, I don't know the question I'm showing or not. I'm going to write it down one time. Instead of going to A, C, this way, we can go to A, B, C, okay? So this length you can add it. So this side and this side you can add it. This is going to be another way. A lot of ways, to be honest. And longest one, we are going to go. Oh, this is a hard one. I am going to share only one. Now, rest of them, we are going to think about this. So longest one, yes. Oops, I made a mistake. Okay, I am going to share the longest possible way is this. Now you're going to think. This is the other way you can do. You're going to go A, C, D, right? And then go here. And then instead of going to here, to the B, I go to the up and come back. So that means you counted this side twice. This is the longest way you can do. So how many ways you can come up with. Let's go to the one-minute question. Ready, set, go. Thank you so much. You can come up with all the way. You follow the letters, A to C and C to D, so that you will not miss that possible, possible way. So you have to exhaust every possible way you have to come up with. Okay, one minute passed, and not many people are going to answer. So that means it looks like a little bit difficult. All right, then let's stop here. Okay, so then, how did it go? Right now, right now, majority of people say six or eight, and I think that's a great guessing, actually. Also, even not the correct answer, that was really great. So let's continue. Middle length, yes, this is a four-way, and you can later on try to follow these letters, but this is only one time you count sideways. And longest one, as I said, from A, C, D, F, E, B, I'm going to write it. This is the longest pass. Okay, A, C, D, F, E, B. And the other way around, one more way, A, D, C, E, F, B. Good, so actually, one, two, shortest way, one, two, three, four, one extra sideways, and longest pass is both sides between the C, D, E, F that counted two times. I think it became hard to hear you again. Oh, okay. Now it's better. Okay, thank you. All right. All right, so then let's go to the last question. This is a challenge problem. So I am going to, one time, to go back to the, okay, last question. Oops, sorry. Challenging problem. Everybody, congratulate yourself. This is the last question. In three soccer games, the zero-backs team scored three goals and lost one. Now, when you say lost one, that does not mean lost the game, okay? Lost one goal. So lost one goal means the opponent team is scored to your goal. So when you play the soccer, the other people score to your goal. That means that, you know, we call the score against your team, okay? For every game won, the team gets three points. And for tie, one point. And the game lost, you get zero points. But this is the general rule. But it never say they actually lost how many games or how many wins. There is no written in this question. For sure, the number of points the team earned in those three games was not equal to which of the following numbers. What does it mean not equal? That means you are going to first solve the problem and find out not the choice of the answers. So you are going to choose not number, okay? Could be seven, could be one of them. But you are going to find out. So then everybody gets the handout, okay? And we are going to work with this. All right. So look like I am a little bit running behind three minutes or so. So I am going to, but, you know, stay with me unless you have something. So I'm going to change to, oops, thank you. And go to the camera. Okay. So I hope that I am going to pin myself. Everybody, can you see my things? Okay. So let's read one more time. So now question is this. All what I know is the boy named Zio Bax, they three scores and one lost goal. That's the only thing. It doesn't say how many games they won out of the three games. And then how many games lost in the three games. So that's the part we are going to come up with casework. Remember the word I told you? Casework, okay? So first things, pick up your pencil, I mean, or paper, anything. And then you are going to write it down. Ask yourself. Okay. He said his team, the goal, three times, three goals. When did he do that? Did they score three goals in one game? Or two games? Or one, one, one, each three games, one score? And also, you have to think about when their opponent team scored against them. We lost one goal, right? So where are you going to put? All right. So first of all, we are going to find out, assume, okay? Scenario. We are going to put the first game. This team scored three goals in one game. Okay. That's good. So there is no goal second time. And there is no goal for the third game. So this is a GGG. That's a meaning. One goal, two goals, three goals. But wait, I have to write it down somewhere. Opponent team scored against this team. So I'm going to first write it down. Okay. This happened the first game. Good. Then what is that team's outcome? I'm going to think. You go three times, lost goals one time. LG stands for lost goal. Then still you have two more goals. So I think this is the first game is win. Right? But the second game, third game, nobody scores. So that means this is a tie. Game outcome is a win and tie and tie. Remember, if you win, you're going to get three points. And tie, one point. Three plus, one plus one. This scenario, this case, is now possible outcome point is a five. So we are going to go next one. Wait. How about if the opponent is actually going to that goal against this team second time? Is it possible if it is a third? Yes, it's all possible. So you're going to figure out, is this a win? Yes. Is this a lost? Yes. He lost it. And is this no goal, nothing? It's a tie. So again, win. Next one, lost. L denotes lost. And tie. So this one is a three plus zero plus one. Four points. Good. Now we are going to go another one. Now, how about what if these team, first team, first game, two goals. Second game, one goal. Yeah, that's possible. Now, where did I put the opponent team goals? Maybe first game. Or maybe second game. Whatever. So we are going to start thinking. And first game, they lost a goal. And not instead of second game, they got one more time third game. Or the game, two game, two goal for the first goal, first game. And next one, second. But we lost one goal. Or the third game, you go one more time and lost one more. Last one. So this one is a one goal, one loss, one goal, one. These are both ties. And another one. Goal. Goal. Lost. Lost goal. Lost goal. Or goal, lost goal, and goal. Now, by this chart, you can come up with all the scenario that you are going to come up with. What kind of outcome you are going to have. So you are going to say, goal, two goals, and lost one goal. That means still that this team has one goal above. So it's a win. And goal, win. And no goal for any team. So tie. Three plus three point, three point plus one point. So this is a seven point like that. All right. So then it's already 11. So I am going to ask you, all the students, one minute. Try to think about. And let's answer the questions in there. Can you please show the Maya poll, please? This is a tough one and you have to use all possible scenarios. Is this second game or third game? And third game, second game, sometimes the result is the same. So you have to find a pattern too. Pattern could be you can more eliminate extra work. All right, they stop. Okay, this one looks like a little bit hard. All right, then I am going to stop and share result. Okay, everybody take a look. Everybody is going to be separated. So I am going to share all the... Okay, I hope that this is going to be, you can take a look. Everybody take a look. So this is an all possible scenario. Okay, so you are going to find a pattern. So when you lose, the other team is going to shoot against you. Does not really matter. You have to find out possible combination of the game outcome. Not that goal, but now important things is win or loss or tie. So possible game scenario is that only six way. Five points, four points, seven points and 5.67. So with that result, we are going back to the questions. Our question is not that what kind of points they can make it. But instead we are going to find out what is not possible. So the answer is E. And E is not possible because E is a three points. Actually, the D is actually winning. So it cannot be possible. Okay, well, thank you so much. 47 students, you did a great job. I'm going to applause you. Okay, thank you. All right, then I am going to go to the next part. Now, today's review. What we learned today? What is a restriction or a rule in this problem scenario? And you are going to draw a quick list or table to make possible combination or scenarios described in a problem. And sometimes it's useful to put some labels on the map. Or break a large information into the manageable size by making a group or cubes layer. These are helpful. Okay, then I just want to quick check. I'm going to, because of the time, I'm going to pass the exit tickets. But I go back to Maya. Maya, can you please just share with us what problem looks very difficult? What kind of question they are most frequently asked you? I think one of the questions that was most frequently asked was, I think for question one, some people were asking me why the answer wasn't 74 or 80. And then for question five also, some people asked me why it wasn't 20. Okay, all right. So the question is, actually, the shape is a shape. Okay, do you want to explain or not? You want to share? Sure. Just quickly. I think that one can be solved easily, yes. The question one about the pages, right? Oh, pages. Okay, yes, that's a tricky one. Maybe can you please go through one quickly? Everybody stay with me another two minutes, okay? Can you share the screen or should I share? Yes, I can share. Okay, go ahead, Maya. So here is the question about the pages. And you can make a table. I think why the two questions that, the two answers that people were getting a lot were not right. Okay. So for, as Ms. Sharif showed you, from pages one to ten, there was one possible answer. And then from pages 11 to 20, there was one five and also one five. And then from pages 21 to 30, there was one five. And from 31 to 40, sorry, there was one five. But then from pages 41 to 50, there's two fives. And I think the first thing here that's confusing is that here we have to remember that for 55, there are two fives there. So we can't just count 55 once. And so that's why the 16th five is 59 and not 65. And so the answer is 64 and not 74. Another thing that I'll clarify is that the question wants to know about the number of times the digit five appears, not the number of numbers that are divisible by five. So it doesn't want like five, 10, 15, 20, in which case you would get 80 because five times 16 is 80, wants to know how many times the digit five appears. So, yeah. Okay, well, thank you so much, Maya. All right. You are so smoothly explaining it. I'm so proud of you. You are really gold medalist. Everybody, you're going to be like this exam. You're going to get that perfect score. Then you're going to get award for gold award, gold medal award. So, okay, then I am going to finally wrap up and we are going to ask you, some students and parents ask you, ask about us webinars recording. That is going to be sent to your account automatically in a couple of days later. So can you please wait for us? And then I'm not going to send email by individually, but you have to check your Zoom account later on. And another thing, when you finish this Zoom, I close the Zoom, then you're going to see pop-up window and you're going to say survey. You are going to be asked in the survey. Can you please take the survey? Because it helps to make you more better program and I can serve you better. Okay, so whatever the option comment and you feel that how I want to change, you have to leave it for me. And I think that's all I covered. Maya, do I miss anything that I have to say anything? I don't think so, no. It's okay. And then I think again, yeah, chat people have questions. I am going to follow up and mask kangaroos. Awesome, awesome. Team is going to come back and then follow you up. All right, then. Thank you so much for participating. I'm sorry seven minutes late, but I hope you enjoyed it and learned and use these strategies for the coming exam. Have a great time. Bye-bye.

Math Kangaroo

problem-solving strategies

organized lists

tree diagrams

casework analysis

mathematical problems

webinar session

student engagement

problem interpretation

competition preparation