Good morning everyone and from California and people who are from East Coast, good afternoon. I hope that we are going to have a little bit warm weather, but we are going to start the last session of Maskanguru webinar series. Today's strategy is experimenting and acting out strategies. All right, I'm wearing a Maskanguru shirt. Yes, Austin, me too. I love this color. I have many more, but I like this one best. All right, so then let's start. I'm going to close the chat box. Please follow up. Okay, welcome Maskanguru webinars. Now your microphone should be muted at all times. That means that you cannot actually talk and raise hands. Today you are going to write it down. Whatever you have a question, please write it in chat box. Good. And then Artem is going to check the chat box, you know, the question. And if it is necessary, he's going to respond. But mostly you have to focus on what we are learning. So don't chat, say hi, hi, hi, hi in a chat box all the time. Okay, now there is sometimes we are going to use pause. That means I am going to ask you, what do you think your answer is? So this is a completely anonymous. That means nobody knows. So you don't have to worry about that. You just participate. If you participate, you are going to learn more. Okay. So, and we are talking about many times handout. Now it is not too late. You have to open chat box, print out and get the scissors and come back here. Today we are going to use that handout to make the models. All right. Suara, I'm sorry I cannot answer the question. Chat box, okay. Welcome, welcome, everybody. I am going to introduce my awesome contributor. And also my name is Keiko Sharif. I'm a teacher at San Jose, California. I hope that you can visit someday. It's a beautiful city and lots of sunshine. But I love Math Kangaroo because not only the students who excelled already. I'm so good at math. But at the same time, I just learned how to work with this problem solving. And I like to support you. So, everybody, math is fun. And it's all math. It's one of the subjects that help you really go further in the future. So, everybody, welcome to here. And now I am going to introduce my really awesome collaborator. I'm really thankful. Artem, please unmute and introduce yourself. Sure, so my name is Artem Terbarth. And I've been a silver medalist for like the past two years. And I've been doing Math Kangaroo for a long time in my life. And I've been doing it ever since first grade. And so, in general, I'm a junior at Wayne Hills High School. That means I'm in 11th grade. And some of my interests include competition math, robotics, as well as I program and I do fencing outside of school. Wow, your life looks so busy, isn't it? Yeah, okay. Well, then, let's go. So, we are going to use a poll. So, we have to ask you for practice. Now, it's easy questions. So, I'd like to ask you, Artem, can you pull out the first practice one? All right. Okay, everybody. Let's go. Quick question. Now, why do you join? Why did you join the Math Kangaroos? All right. I know many people love math. But at the same time, probably you have a different reason. I'd like to know. So, during this poll time, this window shows up in the center, right? Oh, I cannot see it. What is behind it? So, everybody, practice. Grab the corner of this poll window. And can you pull or down so you can see behind it, my presentation? Because you need to see the questions, right? So, everybody, can you grab it and move around? And this is the best place that I'm going to put. Okay. All right. Then I think I'm going to end poll. And I'm going to share. This is what you got. Wow. Look at this. Many people, I love math, right? I think that's awesome. But at the same time, here, I just started new challenge. The Math Kangaroo is really new. There is 15% students. And interestingly, 30% almost says something else. What is something else? We'll see. Okay. Then let's continue that math content. Oops. I'm sorry. I have to close it. Stop sharing. Okay. Then let's go to today's topic. So, before we go to today's strategies, this is a four-step strategic math practice. Math practice means how you solve the math question. One, read the question carefully. Understand the problem. Ask yourself what they're asking. Especially the last line of the word problem is you have to pay attention. Two, plan how to solve the problem. So, each day, each week, each webinar, we taught you what is a strategy that you are going to use. So, you have to use this. Don't just randomly start. Now, number three, carry out plan. During this time, you have to carefully calculate or organize the thoughts and steps one by one. Right? And lastly, if you got the answer, look back and check. Is it really the right answer that they're asking? Or maybe I need to go one more step? You have to think about this. Okay? All right. So, warm-up questions. So, then, this is a warm-up. So, Aten, can you please read a question for me, please? Anne has four gray pieces shown in picture two. She needs to completely cover the white shape shown in picture three. Where does she need to place the T-shaped piece shown in picture one so that he can use the other three pieces to cover the rest of the shape? All right. So, then, other students, let's use your handout. And can you start working on that? And Mr. Shriff is also going to show. I'm going to switch the video. It's a kind of small. I know my window is not big enough. But I think I'm going to show something that what you're going to do. So, first, you need this, right? And then you're going to start. Pick up this, you know, something like this shape, right? You're going to try A. If I put it here. So, what's going to happen? Can I fit in all of these? Maybe like this? Can you try it? Let's experiment. Oh, now, Mr. Shriff has now realized that this piece is one, two, three rows it takes. So, this is a big piece that you have to pay attention to. Maybe around here? Because there's no other way to put that three pieces like this, three rows. Now, take a look. Hmm. This does not fit. So, A does not work like that. Okay? So, then, everybody, can you just try? I'm going to give you, let's see, another 30 seconds. Is that good? 30 seconds? Suara, I'm sorry, but we cannot pick you. We have a question in the chat box, please. All right, everybody, just move around a couple of pieces and figure out. Okay, then let's stop here. So, the answer is, actually, can you please then add them from, take from here? Take over from here. Yeah, sure. So, C is the right answer. And there's also another way to do this without just like cutting out the pieces because that might not always be time efficient during the competition. So, like, one of the things you can do is actually you can, is if you look at the answer choices, you can go through each one. And if you look at the, if you look at the picture too, right, do you see the one that's four long? Since that's so big, it takes up most of the answer. And so, basically, there's only so many places it can go for each scenario. So, for example, for A, if you try to place it in the two places it can go, three places it can go, you'll see that none of the other ones, pieces will fit so you can immediately find out that this will not work. And you can do the same thing for B. And then for C, you'll find out that it does work. And since you already, since you found something that works, you don't need to check any of the other ones because only one can be the answer. Okay. So, Mrs. Schrift's suggestion is, if you do not have time to cut like this, who can do this during the test time, right? So, that time, I suggest, first of all, write it down like the lines in the missing part. And you're going to figure out, okay, so I took this part, and how many more how you can just, you know, moving around. And then, first thing, the item says, this figure picture two, for me, this, and also, they are taking this two, three columns. This one is actually, you have to pay attention to this one. See? So, you cannot put it in one, two, three rows. It takes a lot of time. Okay. So, I agree with the item. You have to pay attention. What is the biggest, you know, that taking space, biggest one. So, you have to pay, put the prioritize on that. All right? All right. Then, let's go to the next questions. Next question is, we are doing this, number six, experimenting, acting out. So, then, Adam, can you read this one, please? Sure. So, problems involving geometric configurations or spatial relationships are sometimes solved by experimenting with a physical model in which concrete objects may be manipulated. Okay. So, then, let's go to the first questions. Now, you can see the picture of the domino, okay, from your screen in my tiny windows. You see this. Domino has two pieces of square attached. But, now, I suggest, first of all, you have to check very carefully the pictures. The first one is a one. Next one is a three. How this figure is, that number three is arranged. So, from the top left to the right bottom. Also, same thing. The number one is the center. Second number, two, is from the top left to the bottom. So, if you have luxury to have this, you can try this way, that way. But, you know, you can figure out twisting around. However, we are going to check, everybody, check the direction of the second piece of the number, number two, number three, how they are arranged, okay? Ready? 30 seconds. Ready, set, go. Which one is, actually, which two cannot make the pictures in the bottom here, shown? So, this is the poll questions. So, I'm going to ask the author. Please pick up the poll. Yes, we are going to give you 20 seconds, all right? Everybody is now working on that. That's wonderful, wonderful. And right now, okay, pay attention to, as I said, how the dominoes are arranged. So, second number, right now, and then let's share. All right. It's interesting, many people, it's divided, like third, 20, one-fourth, one-fourth. Okay, it's interesting. And I'm going to slow down one time, and I am going to actually do this work together then. How about this, all right? First of all, A, I'm going to switch this. I cannot show it. Everybody, can you take a look at my small window, okay? So, definitely, you picked the A students. No, white is not. Yes, it's easy to make it. Top is one, and bottom three. Top is one, bottom two. This is A, it's a definite. Probably, my guessing, you did not read the question. It says, cannot be made, all right? So, B, this side is okay. Now, I'm going to flip back up, right? So, then, one is here, the second number. That's two, is left, two, right? So, this we can do. B is correct. B is, you can make it. So, you shouldn't choose it. Now, C. Now, next one is, we are going to make dominoes this way. Oops, this one. And second one, C. Yes, you can do it. So, this is not you're supposed to pick, all right? Next one, D. Yes, I can do that. So, the answer is actually E. But, Aten, can you please tell us how we can do more efficiently? Sure. So, on the day of the test, actually. So, for many of these, you can simply just visualize them. And right away, you can. So, any ones that work, you right away know that they aren't going to be the answer. So, that way you can go through and see which ones you can make work. And then, right away, you can cross them out until you have a final answer. Okay. Which would be E in this case. Okay. Why is it easy to figure out? Very quickly, you can figure out. This is not. Because you cannot do this, this part. Right, everyone, take a look. The second number is left to right, down. But this one is, look, right up, left down. So to be honest, none of the work, you don't have to do it. You just see the O, E, because I'm looking for cannot. Everybody's good? So don't necessarily, you need to take this in a experimenting strategies. So that's how we can go, all right, everybody. And be smart, smart, smart out, okay? Let's go next questions, oops. Here. Okay, Atem, thank you so much. Please read it for us. Sure, so Nisa has three different types of cards in a game, apple, cherry, and grape. They can be arranged in sets of five. In each set, Nisa can choose just two cards and swap their places. She wants to arrange the cards so that all the cards with the same fruit are next to each other. For which set is this not possible? All right, so if you have a card, we are going to start working on that. So then take a look of the picture A. There is first apples, apples, and cherry, grape, apple, and grape. I want you to put the grape and grape together, and I want you to put somehow an apple and apple together. If it is not possible, then that's the answer, okay? Let's go then, this is apple time. I say one minute, ready? Okay, one minute work. Ready, we are going to start. One minute work, okay? Atem, can you please show the ball, please? All right. So one more time, question is not asking which one can do, which one cannot. It's impossible. How you can switch it, the card, it doesn't make the same kind of that. Fruits cannot be side by side. That is what you're looking for. I heard that many times I notice many students are not reading question carefully. So this is a skill that you are going to use any test in a school or math kangaroo, whatever, you have to read carefully. It says it is impossible. It's not possible, okay? All right, almost everybody's done. Ready, set. Okay, let's end ball and share. Oops, I'm sorry, end ball. So many people chose actually A. So I think I'm going to show why A is impossible, okay? So I hope that everybody can see. So first of all, it's a apple. And next one is cherry. Next one, grape. Next one, apple. And next one, grape, okay? So I'm going to switch one time. Stop sharing. I'm going to switch the videos to here. Oh, stop sharing. Stop sharing, all right. So this is A, actually this is the answer. Why we cannot do this? I'm gonna try it. I want to put this and this together, right? And I want to put this one and this one together. So I try, I'm gonna switch. Hey, now this is good. Because now I have two, the grapes are next to each other. But how about this? You cannot, you only can one time two cuts. So, okay, then I'm gonna back again here. So then I'm going to maybe switch this one, this and this. Hmm, doesn't work. Because these two are now together, but this one is not. So the answer is actually A. So I think, you know, everybody got these questions. Let's go to the next one, okay? So I'm going to share, back and share. All right, next number 11. Now 11 is, we are going to use the picture of these polygons, right? Everybody, which of the three of the five jigsaw pieces shown below can be joined together to form a square? All right, everybody, if you have already cut it out, you can try this, experimenting. If you have not done, you need a good guessing and we are going to figure out using a good reasoning. And we are going to figure out which three pieces making a square, okay? So this one is also pause. I say I'm going to use then one minute, okay? One minute pause, ready? Everybody's go. We are going to moving around. Piece one, three, five. So piece one, it's a kind of, we have a two sides same. This is a scaling, no, actually this is a isosceles. And one, three, three is this one, huge one, okay. Oh, I can make this one to fit nicely, this one, this one. You can just move in the round. And number five. Hmm, this looks like a good combination. That's what I'm thinking, okay? But how about this everyone? Take a look of the piece number four. This looks like a really does not fit any place, right? Even that this one, one and four. We can make a house, but we cannot make a square. So rectangle one, everybody, this good reasoning. This toss it out, all right, all right. Oh, Paul is not here, I'm sorry. Did I show Paul in or not? Oh, jigsaw piece. Okay, everybody starts. And right now, oh, many people has almost done. So let's see, 40, 80, 50. Okay, everybody push the button. All right, 63%, a little bit more. 80% people can answer the question. And I'm going to stop it, all right. We have right now, 180 students are here. And actually, oops, where's my things go? Okay, stop. And I'm going to share result. Many people says, hey, one, three, five, that's awesome. Now, I like to show you something that how they make a combination to make actual things. So I'm going to stop sharing. So first of all, this, I think it's a good shape because you look at this, see, it's almost like a square. Missing part is this. You want to put somewhere something well. So as I said, this does not work. I'm going to toss it, okay. Now, next one, this doesn't work either, right? How I can put this one? So now I'm going to do. So best way is to, this look like an equilateral and this is a, anyway, you're going to go here like this. Doesn't look like, oh, yeah, look at this. You're going to make the other side with number one upside down. And number five, go like this, all right. So this is how you can make a square. Demi, is there anything to add on? No, but if you can't really cut them out during the competition day, you can have a similar thought process, but instead just draw it instead. That's right. Drawing picture is enough to solve this problem. Thank you so much. All right, then let's go to the next questions. Okay, next question is acting out problem. So acting out is sometimes when your teacher says, oh, you're acting out, that's not so good. But point is this one is you are going to take step by step as if you are going to do these actions right there. So then that will help you. What kind of, you know, situations and sometimes it help you to use that something representing people or object, right? All right, so then let's go. Now, next one is dice. And if you have already made it some items, which is you need to make from the, see, net. Mr. Shariff yesterday I made it, but this is a luxury in a real exam test, but let's do try one time. And I am going to, and also Artem is going to chime in. How to do this one without making model? So everybody, this doesn't have a pole. So everybody going to start, if you have already done. Question is, standard die has seven as a sum of the dots on opposite faces. Okay, now I'm going to start examining. Okay, now this is a dice one, right? One, and the other side is a six. Oh yeah, that's right. One plus six is seven, okay? Next one, let's check more. Three in the bottom, you flip it. Oh yeah, seven, that's true. Five, flip it, the other side is two. So actually what he said is truth. The standard die has a seven, oops, sorry. Seven, I clicked the wrong place. Seven as the sum, right? And it's opposite faces, sum is a seven. Now the die is put on the first square as shown, and then roll towards that right, one direction. You are not going to left and right, stay on this path. When the die gets the last square, what is the total number of dots of the three faces? Now everybody, only three faces, okay? So the three faces are here, here, and here. You are going to figure out what's the number on this side, and you are going to add up what is the total. All right, let's go everybody. So I am going to experimenting, acting out with this. So this is a something, I put it two, facing towards me. So wait, this one, facing towards me. Now everybody, be sure the top is a one, and right side facing towards yourself is a two. All right, two and one. So then we are going to roll it one time, two time. How many times I roll? How many times I roll? Ah, 10. You roll five times. Five times, okay. And this is the third times, fourth times, and five times. Five times, one. I have noticed this all this time that the face towards me is always two, okay? When I rolling starts from here, and go roll, roll, roll, roll, roll, and back to here, five space I move, but just two is always here, right? Looks two, and then here, two is always here. So now everybody, what is actually best way to find these questions? I like to ask somebody something more use, effectively, can you find that? Because how can, who can make this in the during the test time, right? So let's focus on something that best way right now, okay? So then Aten, please go ahead. What is the best way you suggest? So it's very important, right, to notice that seven is the sum of the opposite faces, of course, because that means the face opposite the two will be a five, right? And the face opposite of one will be a six, the face opposite of three would be a four. And so one of the things you can do, of course, you can notice that two and five, they never change their position. That's right. Yeah, so you know that two will be one of the faces right away. So you can just put like, you can just write a two there and then find the other two that are missing. Now, one of the things you can do is sort of like each step of the way you can write which one, which one's on top. Oh, okay. So for example, so we know that one, three, five and four are all on this sort of like dice and they're all rolling through. So you can do, so yeah, so you can find out that one, so the one after the one, if you imagine it sort of flipping, you can imagine that the three will be on the bottom now and the face opposite the three is a four. So you know that there's a four on top. Four here, huh? Okay, and what's the next one? Four, and then the next one would be a six. One, two, three, four, five, six. Okay, and? And then it would be a three and then a one. One, two, three, and again, one. Oh, you know what, Artem? I realized that. When you roll one, two, three, four times, they came back to the same one, isn't it? Yes, because there's only four on the dice that are rolling through. Okay, so I don't have to worry about one, two, three steps. I just start from here, four to five. So what is the face is going to be look like on when you roll the five times? Yes, so now this would be, this is much easier to visualize, and if you imagine it, you can see that it will be a four on top and then the one would roll into being on the right. Okay, so four is on top, and then sideways towards me is always two, right? Yeah. And what's this side? This would be a one because the one used to be on top, and then when it rolled, it went to the right. Oh, yeah, 90 degree, 90 degree, you're going to turn one roll. So then top is a one before, and then going to this one is a sideways. Yeah, that's right. So then answer is four and one and two. You're going to add up. So what is the answer? Four plus two plus one is a seven? Yes. Okay, answer is a seven. Everybody, if you got it, you are so good at visualizing. So if you don't have a time in exam test, well, who can have a dice? No, there's no such time. So you're going to visualize, use a logical sense. The sideways is already set. What you look the most concerned is, Artem said, what is a top number? And you're going to see. And also, if you roll the four times the dice, you came back the same. Good, all right. So these are very good, efficient time strategies. All right, then let's go to the next one. So next question is, okay. Artem, can you read it for me, please? Yeah, Nora is playing with three cups on the kitchen table. In each move, she takes the cup on the left, flips it over, and puts it to the right of the other cups. The picture shows the first move. What did the cups look like after 10 moves? All right, thank you. So the question is this, after 10 move, right? 10 times you have to flip them, top and down, up and down, up and down, right? So you have to move the two cups next to, jump two cups, and you put it the next one. But you have to decide, you have to put the cups down. So first of all, everybody must understand what is that they are asking, and what is that they ask you to do action. One more time, you are going to put the three cups. Now you pick the left one, and pick, and you're going to move to the next, jump two cups, and put it downwards, all right? So now you pick the next one, the right now, far most left, you pick, jump, jump, and going to be down. So then with that, let's go then pour. We are going to find out what is that 10th move. What did the cups look like? All right, and this is that one minute job, go. Maybe I don't need a one minute, people. Just be patient with us, okay? All right. Okay. Okay. Okay, I think many people has already answered. Yeah. Okay. Right now, 65% students found it. I'm going to wait a little bit more. When I hit that 80, I'm going to stop it. Okay, come on. Three more, 3% students. All right, let's stop. Okay, now, can you please see? Many people says down, down, up. Oops. So down, down, up is actually, the picture is like this, down, down, up. So answer is a B, most people said that. Okay, so then answer is actually B, that's correct. But is there any way that I don't have these papers, right? I don't have cutting the cups. Oh, mom, let's get the three cups from the kitchen. I think, you know, maybe it's not so good idea. So is there any better way, time efficient way at them? Sure, I mean, one way without physical objects is you can actually do the same idea, but instead just make a table and draw each position of the cup for that. Okay, so you're talking about using something like, let's see, down. Is it okay to write it down like this, easy? Yeah, definitely. So then when you do 10 times means we are going to repeat three cups and three times first, right? Three times three equal nine. So you repeat that, this action, three sets. And plus one more. So I'm going to write it down. How you go? The down one, next one down, right? This one going to be down and next one down. So this is a one set. Next one, you're going to pick one and going to be up. Next one, up. Next one, up. Then this is a six times. Go down one times, two times and three times. Now this is a nine times. So what is the next move? So you pick that left side and bring it here and they are going to be up. So this is a tense number. So that means you don't need this cup, good? I think, you know, you have to think really more quickly, all right? Everybody understands, right? You are representing cups by arrows. That is a really easy way. All right, let's go. Next question. Okay, everybody, we are cruising very good pace, but next one is actually maybe it's going to be beneficial. So if you don't have anything, just go get that sticky notes. One sticky notes. I know for sure somewhere your mom has and go get it and you can follow this in our directions, okay? Adam, can you, are you okay, Adam? Can you please read these questions? Yeah, Ella folded a square piece of paper twice and so made a square with each of its sides as long as half of the original piece of paper. She then cut off all the four corners from the square she made. Which of the pictures below will show the piece of paper after unfolding? Thank you. So then, what is the action you are going to act out these days? So first of all, you are going to fold in half. Each one is as long as a half of the original piece of papers. And you are going to fold twice, okay? I'm going to show everybody pick up this paper. And first of all, you are going to be fold up one time. And one more, two times. Now, everybody take a look. This square is exactly half size of original length, right? And the other side same. So now, this is what you get. Now take a look of this before you cut. Now this is a corner, which is, ooh, that's a really good, you know, you see that center. If you cut here, they are going to have holes in the center. But you know, D, choice D does not have it. That's definitely not, right? You have to make sense. Now, you have to get the scissors and you're going to cut it four corners. Everybody following the actions. First of all, I'm going to cut the center. This is going to be the hole in the center. Next, next, next. Now, I know before you fold up. No, fold them. I'm sorry, add them. This one is going to pass the pole. You're going to figure out, oh, the cut here is going to be sideways. And I think that this corner is original four big papers. Corner, four corners. So then each time you cut it, how this part is locating with original B in the papers. Original in this square, sticky notes. You're going to visualize, okay? So then, let's go. Oh, how come the students picked the B? I don't understand that. You didn't cut the four corners. Okay, all right. Then I am going to, waiting for the students. Oops, again, I'm going to clear, clear, and change to mouse, right? Okay, so then let's go. This is your result. Many people said E, yay. Obviously, I think people who did not fold up correctly, it may be a wrong one. But if you fold up twice, if you cut this corner, it's going to be a center. Look, right? Center. Now, take a look. If you cut this corner, this is going to be, this is going to be just in between here, in between. If you cut this side, right? See? And then if you cut this side, the corner is going to be, this corner is going to be, put the mark on here, together here, these two. So something like this. So Mrs. Schrift says, if it is, you know, you have actually, go get the sticky notes. This is possible even during the test time. But if you can use good imagination, you are going to do, draw a line like this. See? If you cut this, if you fold up like this, this corner, four corner is, you are correct it four corner in one place, right? You just cut it one time. Then you are going to make this in a small, tiny triangle, folded. You check this one. What is that you cut it off? And another corner, if you cut it, there is two corners making in between. This is a one corner. This is another corner. And lastly, I said that the one corner is going to make a hole in the center. Good. Anything to add? Aten. No, that was actually better than my strategy because what I would do was I just like tear a piece of scrap paper. You know what Aten? And this allows you to visualize it better. Thank you so much. I'm so happy that you said that. Okay. Well then everybody, I hope that, you know, you can do this visualizing is important. We need a good imagination to solve the math. That's true. Okay. So then let's go to the next questions. Next question is, there you go. Challenging practice problem one. Okay, then Aten, can you please read it for us? We have three transparent sheets with the pattern shown. We can rotate the sheets, but not turn them over. Then we put all three sheets, exactly one on top of the other. What is the maximum possible number of black squares seen in the square obtained in this way if we look at it from above? Okay. So everyone, there is one restriction. You cannot flip it. Good. You cannot flip, but you can just, you know, rotate. Okay. Rotate means if you have this sheet, you can rotate like this, but you cannot flip. Right? Okay. So then one more time. This is a way how they are set up. Now, everybody use something that, something like a good logic thinking. Just not randomly do it. So first things, I want to make this, you know, overlap and make it, you know, all the face of the nine, nine, the cells into the, could be possible to make it everything black squares. That is what I'm looking for. Okay. One more time. You are going to visualize this and this, how you can turn around and to make into all nine, nine boxes into the all black one. Or we cannot make all of them. How many is a maximum you can do? So I'm going to give you a little bit thinking. So one minute. Okay, everybody. There is no poll. So I think I'm going to wait one minute. And during this time, when we are waiting for students, is there any better way to solve this in a kind of a strategic problem solving? I think the best way would be just to visualize it and maybe try it. If you can actually have it physically in front of you. Okay. So visualize. So when, where to visualize, where to pay attention to it? Okay. So I think you would just, if you draw it just like a grid of three by three, you can actually overlap the squares pretty easily. And then you could try it onto that and see what's the maximum you can get. Oh, that's a great idea. So then I am going to write it down one time. Okay. And then that made me giving me some idea. Okay then. If you do not have it actually, I think maybe we can start this way. So first one, then I'm going to actually transfer, transfer these two and these two here. Okay. So bottom two, this is black, this is black. Okay. Now middle rows, I mean columns, this and this. So from here, what do you suggest, Artem? Everybody actually watch this one. This might be a little bit better than actually that you're cutting papers. Okay. So- So from here, yeah. So from here, you would take the second image and you would just go down the line and you'd see which second image, how can you maximize the amount of holes there are? Okay. And so, I mean, for the second one, you can sort of like rotate it and then you can get three squares that you fill up. Okay. So this one is already here, right? This corner, right side of the bottom. So I think this doesn't work. How about these two? Does it work? These two are work or not? Should I put it here? Yeah. Okay. Then let's try one time. So I'm going to move these two to here. Okay. And then last one, what do you think? Yeah. You can, two of them will work and I, yeah. This one is I'm going to transfer here. All right. And how about this corner? Oops. I didn't draw the big one. Okay. There is a top right corner up. This one, I can move to here, right? Yeah. All right. So I think I got out of nine boxes. I think eight are possible if you put together like this, one by one, if you're going to be a ranger and you're going to get, I cannot see through. Okay. Everybody see through. But point is that if I can see through, these eight boxes are black. And also Artem says, you're going to try rotating this paper 90 degree, 90 degree. Whatever you're going to maximize the places of the black spots. Everybody's good? So this answer is, whatever you do, you're going to find out eight boxes, the maximum number. Good? Everybody? All right then, let's go next questions. Next question is also challenge problems. And wow, everybody, this is the last question we can solve together. So I am going to ask Atom's help for this. All right, Atom, I'm going to write it down. So whatever, please tell me. What should I do? Sure. Okay, so let's read it. Two girls, even Olga, and three boys, Adam, Isaac, and Urban, are playing with a ball. When a girl has the ball, she throws it to the other girl or to a boy. When a boy has the ball, he throws it to another boy, but never to the boy from whom he just received it. Eva starts by throwing the ball to Adam, who will do the fifth throw. So one of the things we can start off with is, we can obviously use physical objects in order to model this, or we can do something similar, but instead we can draw a tree. So if you could draw Eva, Eva, and then like an arrow to Adam, like E for Eva and A for Adam. All right. Okay, so representing by the alphabet, is that right? Okay, and then I just want to make sure that students can really understand what he's asked, they asked, but when you girls, they get the ball. The girl is so nice to the other girl and boy, so they can throw either boy or a girl. But when the boy gets the ball, then he throw either another boy only, no girl. So when the boy gets the ball, only boys. Everybody's good? So then let's start with Eva, and yes, first she throw the ball to Adam. According to Adam's advice, I am going to start writing Eva stands for E. Okay, and Eva throws a ball. I'm going to use that. Eva throws a ball to Adam. Okay, so then let's start from here. Okay, so, so, of course, when a boy he can only throw to another boy. So Adam has two options. So we can sort of make, you know, two different branches of a tree, two different situations that we can have. We can have Adam throws it to Isaac, or Adam throws it to Urban. Okay, so I'm going to make two arrows. This shows either way we can do. So Adam throw through to Isaac or Adam throw to his name Urban. Okay. All right. Next, so let's start with the Isaac. Let's start with Isaac. So one of the rules that it says is that that a boy cannot throw to somebody who just received it. So Isaac cannot throw back to Adam. Okay, but he must throw to a boy. So there's only one extra other boy, which is Urban. So he has to throw it to Urban. Okay, that's a logical. It makes sense. Yes. And how about if Urban is the one who is now holding the ball? What happens? So Urban can throw it to Adam as well. And since he has to throw it to another boy, he has to throw it to Isaac. Okay. All right. So do we do one more time? What is it? So this is Eva throws to Adam. So this is three throws, three arrows. So now we have two more. So Urban can't throw to Isaac. So he has to throw it to Adam. Adam. Okay. And? And Isaac can't throw it to Urban and he has to throw it to a boy. So he has to throw it to Adam. And so now it asks is who will do the fifth throw? So Adam. So the next throw will be the fifth one, right? Since we have one, two, three, four arrows. Because each arrow represents a throw. So. One, two, three, four throws. We already did it. Yes. So Adam is the one who has to do the fifth throw. Oh, then fifth throw is only Adam can do that. Wow. That's awesome. Okay. All the students. This is called tree diagram. And we are going to logically showing the process one by one. And at the end, Adam is the only one. You know why, boys? Because you don't throw back the ball to the girls. So that happens. Okay. All right, then, everybody. I think, you know, that's it. Adam, that's awesome. I think, you know, all the students really understood well. So I'm going to go wrap up. Okay. Everybody did a great job. And today's review. We talk about four-step method. We always solve mathematical problem following step one to four. Most importantly, I think, you know, sometimes people are too in a hurry. And you don't need a question. Sometimes not or impossible. That's a word you have to catch it. Okay. Next one, we talk about experimenting using that piece of that thing. The polygon or whatever. But I know at the same time, we also covered the test situation. We can draw pictures. We can actually eliminate what is completely wrong. And we talk about, remember, that dominoes. How the dominoes, you know, the second number is arranged from left up to the right down. You can see immediately, oh, that's a one. Right? So then we did it. And last one, we did actually sometimes act out or we did these things. But at the same time, there are things that explain to us that tree diagram, logically thinking, something that is more like you can use a little bit more faster way. That is really important for us. And I just want to, is there anybody who is asking any question about the exam? How to take an exam or not? Everybody then, how about this? You have a little bit of time. Instead of exit tickets, everyone, can you just jot down, write it down. What is some questions, not about the math content, but about how you take a math exam? How about the time? How about the days, you know? What you can eat or something? Any question? Can you please write it down in the chat box? Artem is going through, and then maybe we can figure out. But something, you know, we pick something important. He's going to answer to you. How long does a test? Test is 75 minutes, okay? You should know that. So many questions. Artem, what should I do? Let's see. Okay. Oh, everyone, not answer the exit tickets. If you have a question about coming math exam, which is March 17th, everybody say to yourself, March 17th. It's only less than 20 days. So how you can prepare, yeah, that is another thing. But it's more practical things. Of course, you have to practice. Go ahead. Okay. So the other thing is that if you're doing it virtually, the test will be submitted automatically if time runs out. Or if it's in person, the proctor will just collect it at that time. So do not worry about not turning the test in in time. How much time for each question you have? It depends on how challenging there are. Yeah. Okay. How long do you think I can use it? Those usually take longer. But then again, you only have 75 minutes for what? 25 questions. So sometimes three-point questions can go up to like seven, five minutes. It depends on how quickly you can do the 1.1, one-point questions. Oh, Artem, we have a 3.4.5 point. Three-point questions should take ‑‑ it depends on how ‑‑ three-point questions should take a minute maybe. Minute? Yeah, but it depends on your own pace. Yeah. You should do it as quickly as you can because those are easier questions usually. And you might not get the five-point either. And they would take much more time. Yes. Okay. As we said last week, if the question is really hard, don't stack one place and we have to keep going. And more like focusing on completing the test. Is that right? Yeah. They ask you, how about the five-point question? How many minutes we should allocate? If it's a question I read it and I can't really solve it, like I can't really think of a way to solve it like immediately, I might go back to it later. Especially if it's something in like the three-point category. And then I can go back and then I can solve all the questions that might take some more time to solve. Yes, yes. And then Alyssa is asking, how can you spread the time? Probably 75 minutes. Okay. You can finish that as quickly as possible. But five-point question, you need a good amount of time, like 25, 30 minutes. You should keep for that. Okay? Okay. Can I pick a date to answer the question? Yes. If you're online registered, yes, you can choose that. Now, Artem, when is the best time to take a test in a day? In the day, I think it depends on your schedule. For me, it's usually, it can't be too late at night because you might be feeling like tired or like sleepier or whatever. But I think usually it might be like evening. It really depends on your schedule, like when you come back from school or anything. I think for the last ones I took them at around like 6 p.m., which was evening and that worked out for me. Okay. If you're online, can you review? Actually, they are given the time frame, like they say 20, 18 to 28. So they have a weekend too. Yeah. Maybe weekend and I think, you know, like a Saturday in the morning is the most, you know, fresh that our brain is work well. What do you think? Yeah. Okay. Yeah. Also another question. Is it a good idea to finish the five point questions first? I would not really say so because usually the amount of those you can get right is, if you can get five point questions right every time, then yeah, sure, you can do them first. But usually it's much harder to get them right all the time. So I think you should start with the three pointers and then move on to the four pointers. Yeah, I agree with you. It's just a psychological effect. But, you know, I cannot finish this. It's kind of scary. So I think I'm going to go with the easier one. Okay. Let's see. Every day I practice, Jeffrey says, I do two hours every day. So you're taking the exam, huh? Okay. And is there anything that, you know, may be very urgent? Can you skip question? Yes, you can skip and go back. Yes, you can do that. And also, what if you finish early? So then these kids are probably really good at math, but Artem, what do you suggest for the kids? Did they finish early? I think they should try their best to like to go back and check. I know it can be really hard because you can be a little impatient and you already solved them and you think you got them all right. But if you sort of like force yourself to read through the question, not skim it through and like actually check it, you might catch some mistakes. I agree. Catch the mistake. Yes. You should not turn in. Until the time is run out, you have to stay on the test. In my classroom, nobody can turn in the test early. You have to check twice, three times. That is how you can get the best score. So I think, you know, I know question, you know good about this math kangaroo, but look for the best of the best. Okay. Right now, I think people's answer question is really interesting. I'm going to read it. And if I have a find out something I need to answer, I will do that. But time is 11-3, so I'm going to go one last thing. Everybody, thank you so much. Now, math kangaroo is really appreciate that, you know, you participate with us. And this year, first time we started a webinar. And I also taught the online course. There are lots of resources now. Math kangaroo is getting better and better. So everybody, come back. And first of all, wishing you the best luck on the exam. But keep loving math and keep practicing. And I love to see them, see all of you come back again next year. This year is our first year students. I know this question is kind of a little bit, you know, I got it. I don't get it, like that. But next year, you feel much better. All right. So I just wish you, everybody, good luck. And one last thing I'd like to ask you is, I want you to complete that survey. And then right now, I think Artemis is going to put the link here. So can you please finish this one? And then please, you know, Artemis is really helpful. I think you know that, please, grading together. My name is there. But that doesn't mean that me only. We are all teams. We are best team ever. So please take a survey. Oh, I don't think I was sent the survey this time around. Is it in the OneDrive? I'm sorry. Can you please find that? Actually, I put it in the speaker's keynote. Oh, okay. Sorry, I didn't have that open. Let me see chat. How many questions? There is 24 questions. All right. And 52 new messages. Wow, this is really. Oh, Derek, I know. We have to say goodbye. Please, everybody, don't do this again. Artemis, just drop it up. These are forms. Please click. And it's taking a survey. I am down here. And Artemis, is there last words? Is anything? Well, try your best, I think. I think I see a lot of you are, like, really worrying about it. But really, I think that might actually harm you more than help you. So I think you should just do it how you normally do it. Just try your best. Okay. Yeah. Well, then, can you say, we are going to come back and see you next year. Artem. Yeah. I'm going to be coming back next year. Okay. All right, then. Everybody, thank you so much for staying with us. Have a great afternoon. And good luck with your math kangaroo exam. Everybody, have a great afternoon. Bye-bye. Everybody, bye-bye. I cannot see your face, but wishing you good luck. Bye, Artem. Bye-bye, Artem. Bye, Artem. Bye-bye. Yeah, bye.

Maskanguru

webinar

math problem-solving

geometric configurations

spatial relationships

visualization

Math Kangaroo

test-taking strategies

problem-solving techniques

educational exercises