Hello everyone, welcome back to our webinar and today we are going to start a new lesson. So it's 2D shapes. So you might already know the 2D shapes, 3D shapes. You might have something learned at school and also those things around you in the life. You could see them every day, yeah. And today we are going to show you some interesting questions involved with a 2D shape. So first the ground rules, you all should be all very familiar. Remember we will send you the recording link shortly after the class so you can review the whole lesson later. And here the false step method, we really want to reinforce every time because this is a super helpful and some students if you do not try, you never know this could help you to solve the harder questions, especially in the computation. Next year the computation would be March 20th. So you will have 24 questions and 8 questions means 3 points, 8 questions 4 points and 8 points. This method could be super helpful for you to solve the 4 point or 5 point question. So the first step, you understand the question. This is very important. If you do not understand the question, you cannot solve it correctly, yeah. So you have to read through all the conditions and highlight or underline some key words help you to remember what mentioned in the question. And also if there is a picture, you should check the picture carefully. So the first step you figure out what question to ask for and then the next step you need to figure out what strategy you could use to help you to solve the problem. So we learned many strategies in this lesson and also you might learn at school or other classes. You can use whatever you know to help you to solve the problem. So pick the strategies, one or more. And the third step, write down your solutions step by step. So this one applies to the 4 point question or 5 point question most. Because the 3 point question, sometimes you just solve it in one step. But we still recommend you to write down very, maybe very simple how message, how you solve that one. So give you some, you know, the, record your memory easily when you go back to check the question. So the last step, once you finish question, do not move on right away. You need to check your question, put your answer back to the question to see if it apply to all the conditions. So these 4 steps are really helpful. So now let's reveal what we learned last week. We learned make an organized list. So this is very helpful when you meet many different possibilities. So we could organize numbers, we could organize the items, and we even could organize the passes. Yeah, we learned from last lesson. Yeah, first, you need to figure out how to group your ideas. You might need to work on the different groups at a time, one at a time, and then you combine all the findings together. So when you make the organized list, remember, if for the numbers, it's better you follow the sequential order. If it's items with names, you follow the alphabetical order. So that would help you to avoid you missing or repeating anything. So this is a very helpful and you will solve some question using this strategy later. So today we are going to learn the 2D shapes. So this is a warm up question. So Ellen wants to decorate the butterfly. You can see the butterfly on the right side and with the stickers. So you can see the sticker, the shape they already gave to you. And then which butterfly can she make? So look at the answer choices, five answer choices, A, B, C, D, E, which one is the correct answer? This is a three point question, yeah, you already you might solve one minute, yeah. So we will make this a stay longer just in case we open the poll, you cannot see the picture, yeah. So please have the pencil and scratch paper ready for each class. Very good. Everybody have a good eyes. Yeah, you see the difference for the answer choices. Yeah. Okay. Yeah, so far we reach almost 100% correct. Yeah. Yeah. Share the result. Yeah. Okay, so here we can see the solution. The answer is A. Yeah. And you need to check what, when you see this question, you need to check what they give to you. They give it to you the two, the two blue circle, two bigger pink circles, and two black ovals. So when you see this shapes and amount, you would definitely cross up to the sum answers. Is that right? So the C has eight shape, eight stickers. And D also have eight stickers. Is that right? This is not incorrect amount. Yeah. So you can cross out. So we always recommend you to eliminate wrong answers and help you to stay with the, you know, the correct, find the correct answer easily with less choices. So then you could check A, B, E, and you would figure out you do not have the black dot, small black dot. Yeah. So those make you to eliminate E and B, left A. Yeah. So that's why I think most of you got it very fast. Yeah. You figure out each match all the different shapes. So remember, we want to introduce for you. Sometimes if they ask you to find the difference between the shapes, so you'll need to find the, you know, eliminate something, some choices that would be super helpful. Yeah. So what's 2D shapes? Yeah. 2D shapes have two dimensions. So length, width, or length and height. 2D shapes are flat. Yeah. And 2D shapes do not have any depth. Yeah. Or height. Yeah. So sometimes you call the 2D shapes with sides, angles. Yeah. You can do it. Yeah. Very easily. Yeah. So now let's see what's 1D shape, 2D shape, and 3D shapes. So the 1D shapes, we show you the jumping rope. So this one, if you make it a street, yeah, you could only measure the length for this one. Yeah. There is, you already do not consider the width for the, for the, for the jumping rope. Yeah. So this one is 1D shape. And also you see the picture. Yeah. That's 2D shape. Yeah. So you have two dimensions, width and length. And then you see the gift box. There are three dimensions. You have width, length, and also height. Yeah. So that's, we call it 1D, 2D, 3D, because the number of dimensions. Now look at this one. So this is a kind, you know, we gave you the direct concept of what 1D, 2D, 3D, not a real object. So you can draw it out. You draw in a line, that's 1D shape. You draw a square, a circle, or triangle, or rectangle. So with two dimensions, that's 2D shape. If you draw 3D shapes, that's not easy. Yeah. The 3D shape with more dimensions, it's not easy to draw. But you can see it's clear. Yeah. So you, you, you have three dimensions. So now we have quick questions for these shapes. We ask you, what are the 2D shapes or 3D shapes? Can you send in the chat? Yeah. Number one, 2D shape or 3D shape? Number one. Can you send in the chat? Do you see the chat, Elita? Okay. I see the chat now. Yeah. Okay. Very nice. Number one. Number one, you can see the, let me just trace it. You can see this one. This is number one. Yeah. Okay. It should be straight line here. Yeah. Okay. Good. We get, we get more answers. Yeah. Very nice. Very nice. Good job. Yeah. Okay. So the number one, that's 2D shape. Yeah. Because this is a square, we have a length and we have width, but they are same size. So that's why it called square. So the next one, number two, look at number two, 2D or 3D. Number two, 2D or 3D. I know some of you might be, might be a little challenger for you to use the chat. Yeah. You know the answer. Yeah. But it may be a new tool how to use the chat. Yeah. No worries. Okay. Yeah. Okay. Whatever you can send your answer or you can know that you just know that. Yeah. So that also both good. Yeah. So 3D shape. Good job. So this is a rectangular prism. Yeah. Also we call it void. That's a new name. Yeah. Next one. If that's 3D or 2D. Next shape may be not very clear. Yeah. But you can see the number four. Yeah. So that would help you to give the correct answer. Yeah. Very nice. Yeah. Number three. That's 2D shape. Yeah. That's a circle. Yeah. Okay. Yeah. Now let's see number four. Yeah. Am I moving too fast? Because we have a lot of questions and this is actual practice. So we do not want to take too much time. So number four. Yeah. Good job. Good job. 3D. Yeah. 3D. Yeah. So this is a ball sphere. Yeah. So you will see a lot. Yeah. See a lot every day. Yeah. Okay. So next one. Number five. This one may be a little tricky. Yeah. Because you cannot see another side. Yeah. So this is 3D. Yeah. But if you want to identify what this one look. If I see the bottom. I see the bottom look like a triangle. Is that right, Elita? Yeah. So look like a triangle. So this is a triangular prism. Yeah. If the bottom is a square, that would be pyramid. Yeah. Okay. So number five is 3D. Good job. Number six. Number six. 3D. Good job. Good job, everyone. Yeah. This is a cylinder. Yeah. Cylinder. So you could see a cylinder. Like a can. Or like this one. Can you see my candy box? That's a cylinder. Yeah. Okay. Very nice. Number seven. Elita, can you go through the next few ones? Yeah. So what do you guys think number seven is? Good job, everyone. It looks like most of you agree that it's 2D. You can see that it doesn't really have any other layers, kind of. It only has height and width. So that makes it two-dimensional. What about number eight? Yeah, good job, guys. You can tell it's three-dimensional because it has height, width, and length. So, um, it has three dimensions, I guess. And then the last one. Yeah, nice job, guys. It's two-dimensional, because you can see it's pretty flat. It's not like number eight or number four, where you can kind of see how it has shadows or things like that that make it look more 3D. So good job, everybody. It looks like you guys understand pretty well 3D versus 2D. Yeah. Yeah, great job. Yeah. So the number nine, that's a pentagon. Yeah, that's five sides. Yeah, they have five equal sides pentagon. Yeah. OK, so next, let's work on our questions. Elita, can you go through this question? Yeah. How many more square tiles do we need to put on the kitchen floor to cover all of it? So you guys can see that the kitchen floor already has some square tiles, but it's missing some in the middle. And it's asking you how many more we need so that it's fully covered. We'll launch the poll. Are there answers for this one that are up here, or are they only in the poll? In the poll. OK. So sometimes we do not give you answer choice. We want you to figure out by yourself first. And then we give you answer choice. This would make the question harder, yeah? Without the answer choice, you have to figure out on your way by yourself. So that would be a little harder. OK, I'll launch the poll then. Yeah, so we will launch the poll. You can use the poll to answer the question. Please select the answer choice in the poll. We already opened. Good job, everyone. Yeah, Elita, can you share the answer? Yeah. So yes, and see, most of you got it right. The correct answer was nine. The way we can find that is, we can pretty easily just count how many you draw the grid and then you count how many squares need to be filled in. So you can see there's three in the first row, four in the second row, and two in the last row. So that adds up to a total of nine square tiles. So this is also look like an organized list. You count the different rows and you figure out how many you're missing in each row and you add it together. So you see, this way you could apply for the drawing a picture and also the organized list to help you to get the correct answer. So remember, the drawing a picture is really helpful, especially when you solve the 2D shapes. So we strongly recommend you to draw your own picture or you draw on the existing pictures, help you solve the problem. So next one, you put animals in order from the smallest to the largest. So give the number of animal in the middle. You have to understand what they ask for. You should find some pictures on your handout, student handout. So that you should print before the class and you can work on the handout, help you to solve the problem. So better prepare a folder, you can put all the class, all the lesson handouts together. Okay let's share the result. Yeah good job, I think the half class got the correct answer, the two, yeah number two that's in the middle. So here let's see the solution. So first you would see there are five animals, you want to see the size, they ask the smallest to largest, that means you have to compare the size. So how to compare the size, can you see the background, there are the squares, it looks like they give you the ruler, yeah you can use those ruler to measure the each different animals. It's very easy for you to find the smallest would be what, the number one, they have one square height, one unit height. And the next one would be the five, it's two units high. And the next one would be two, yeah it's three units high. And then that would be number four, that's one, two, three, four, five, six, six units high. And the biggest one would be the giraffe, that's seven units high. It's very easy for you to compare. And then you would figure out the number two in the middle, so that's the answer. So you need to check the question, what they ask for, and you order by the size, and then you'll figure out what's the number, what's in the middle. Okay, Elita, yeah, please go ahead. How many more small gray squares are there than small white squares? So make sure you read the question really carefully, make sure you know what they're asking about. Okay, let's share the result. Okay. Yeah, you guys can see that most of you guys got it right. The correct answer was D. So you guys were all very close. You all either said 8 or 9. So let's see how we can do this. It's asking how many more small gray squares there are in than small white squares. So we have to take the total number of gray squares, which we can count as 17 and subtract the total number of white squares. So if there's 17 gray squares and 8 white squares, then 17 minus 8 is 9. So there's 9 more gray squares. So look, when we write the number in the in the all the square because there are so many so that's easy for you to figure out. Did you miss counting any number? So that's why we recommend you sometimes you need to write or draw on the picture help you to solve the problem. So if you just just count without mark, so sometimes it's easy to cause you cause the you know, miscounting. Yeah, you might count less or count more. So pay attention. We will count more items. It's better you mark them. Next question. This is very interesting question. So in two, how many parts do the scissors cut the rope in the picture? I think enough people have answered. OK. Very good, yeah, so most of you got the correct answer. Very nice. So this way, it's very easy for you to trace each part. Is that right? So you could see here, do you still see my screen, Edita? Can you confirm you see my screen? Yeah. The solution? OK, yeah. OK, so here, you could see that each part, different part, yeah? So you can see the color, and then that's very easy for you to figure out how many should be. And there is one more, the solution I want to introduce here. So I'm not sure if you just count the part, or you count by the different way. So if I give you a, let's do a quick check. So let me give you a question here. Okay, my joy. Yeah. So now. Okay, yeah. So, there is no, no, no. Okay, let me just make sure. How many, how many parts you could have had for this one. Give you 20 seconds. Can you give me the answer in the chat. Yeah. How many? How many parts? 20 seconds. Give me an answer. It's a little hard, yeah? If you check each part, it's not that easy. You might need a longer time. Good job. I got one correct answer so far. Very nice. Okay, so one thing I want to introduce to you. How to find the parts here? This is open-ended rope. So when you try to find a part here, you also can take a look here. Yeah, so you can see the cuts. How many cuts here? How many cuts here? There are four cuts. Yeah, four cuts. You get five parts. So for the question I give to you. So you can check how many cuts there. One. Oh, let me make a clear one. Yeah. So one cuts, two cuts, three cuts, four cuts, five, six, seven, eight, nine, ten, eleven, twelve, thirteen, fourteen. So you have fourteen cuts. You should have fifteen parts. So I show you here how they look like. If you have one open-ended rope, if you make cuts, you can see here, you make one cut, you could get two parts. Make two cuts, three. Three cuts, four. So you can find the pattern. Is that right? You can find the pattern here, yeah? Yeah. So so this is open-ended rope. If this is a closed rope, that would be a different story. So I just want to show you this is an interesting question when I say this one, yeah? So if you make one cut, you only get one part because this is a closed rope. When you cut one time, you get only one piece. Cut two times, get two pieces. Three times, three pieces. So that's a totally different story, yeah? If you have open-ended rope and you have closed rope, so you could have different pattern. So the open-ended would cut plus the one, equal the parts. If a closed rope, you would get a cut equals parts. So the open-ended one, later you will meet some question. They give you a distance, a piece of road, yeah? And they tell you how many trees you can plant on the road if they have equal the distance in between the trees. So those would apply for this one, yeah? But that would be a hard question for you. Yeah, just want to introduce this is faster way help you to solve this type of question. You can find out how many cuts there and you plus one. That would be the total parts. So this is a pattern, yeah? Pattern question. Okay, let's see the next one. A square was made out of 25 small squares, but some of these small squares are now missing. How many small squares are missing? So make sure you know what information they give you in this problem. We know there's originally 25 small squares and now there's only however many are in the picture. It's asking you how many are missing, okay? This is also a three-point question. Yeah, you already be expecting you could solve it in maybe around one minute. I think most people have answered, so I'll go ahead. You guys are really good on this one. Almost all of you got it right. The correct answer was D. So there's a couple of ways you could have done this. Either you could have counted how many are in the picture, so how many squares are still there, because we know that there were originally 25 squares, so you could just do 25 minus the number that are remaining. Or you could count the ones that are missing, so you can kind of fill in the remaining ones and count how many squares that is. So if you did it the first way, you'd see there's 15 squares remaining, so 25 minus 15 equals 10, so 10 are missing. And then the second way, you can just count. There's 10 missing squares. Good job. Let's do the next one. Which of the figures below cannot be cut out of the figure on the left? So this is the left figure. So A, B, C, D. Yeah, this is the older question, 2008. So at that moment, we have four choices. But later on, we have five choices for each question. So A, B, C, D. Which one? Cannot, cannot be cut out. So you can try to draw the A, B, C, D on the left shape to see if you could. It's not only about the amount of the squares. It's also about the position of the squares. You have to consider both. OK, I'm going to share the results. OK, so this one, most of you pick the C. That's correct. Yeah. So very good. Yeah. A, B, D, you all can find in the left shape. You can see we shaded there. But if you check the C, it wouldn't work. Yeah. You can see the actual part. Yeah. The after of the shape, those two parts after of the shape. Yeah. So that's why you cannot cut C from the left shape. Yeah. Yeah. Let's see that next one. Oh, this is an interesting question. I believe a lot of you might play chess. Yeah. You know the chessboard. Yeah. Go ahead, Elita. The chessboard is damaged. How many black squares are missing on the right side of the line? So the right side. That's the side that has more squares missing. And it's asking exactly how many black squares, all squares. OK, now let's share the result. I know this is a little hard, a little challenging for this one. Yeah, so it looks like we had some trouble on this one. This one is definitely a little bit harder. Yeah, it's going to see it's problem 17. But 12 was the most selected answer, and that was right. So good job. So we look at the side, the right side, because that's what it asks for. And we can tell that there's 32 squares in total on the right side. Because they're in an alternating pattern, we know half of those should be black squares. So in total, the total number of black squares on that side should be 16. We can count that there are exactly four black squares remaining. So we can do 16 minus 4 to get 12, which is how many are missing. Or you can kind of fill in the squares that are missing and count them. So if you did that, you would also get 12. But this one is definitely harder. Yeah, so you might be very familiar with the chessboard. So chessboard, that's a square. It's 8 by 8, the whole board. And the left side, right side, share both 32 on each side. And also the white and the black, they are equal amounts. So that's how you figure it out. Yeah, this one is a five-point question. It's not that easy because there are too many parts missing on the picture. Yeah. OK, let's see the next one. Which tile should go in the middle of the pattern in the picture? So you see that on the right side. So you miss one part in the middle part. Yeah, and you have five choices. These are all hexagons, yeah? Six-sided. And this way, you have a handout. Oh, give a little more time, yeah? Edita. OK. This one, we just give a little more time because there are also choices. They are not shown in the handout. Yeah. It looks like a very fun game, yeah? Have you played this game before, Elita? This is a game, yeah? Game piece. I have not played this game before, but there are similar games that have hexagons like this. Yeah. Somebody in the chat asked for the poll, but I think we're giving them a little bit of extra time. Yeah, okay. So because we do not have answer choices in the poll, so we just give you a little more time and let you to figure out which is correct answer. And we will open poll soon, yeah? Maybe 10 more seconds? Yeah, make your choice. 10 more seconds. Yes, you can rotate the shape. Definitely. Yeah, I think you have to rotate the shape. Yeah. Let's share the result, yeah, okay. So most of you pick the A, that's correct answer. Good job, yeah. But some of you might got confused, yeah. How to rotate the piece, how to find the correct one. Yeah, this is a game, yeah, they call the tantrix, yeah. It's like the, you know, you have so many different pieces and you can connect them to make the road or something, yeah. So here we miss the middle part. So for the middle part, you actually could make a joint on that. So how you make a joint? You can extend each color on the edge. So you can see the red and after red, yeah, let me just mark it. Yeah, if you see the red over here and then you could see clockwise, you could see the blue and you could see the yellow if you go clockwise, yeah. And you'll see the red and you'll see the yellow, you'll see the blue again. You could see for this hexagon, the six sides, all the neighborhood, the sides, you do not have the same color. Can you see? You never have the neighborhood sides with the same color. Yeah, you can check all the six sides. So that would help you to eliminate all the wrong answers. So B has a red or yellow both on the neighborhood, same color. And C, D, E. So then you could very, very confident choose A as your answer, yeah. So this one, you just drew a little bit, extended the color and you would see what color next to each other, yeah. And then this one definitely you need to rotate to fit in, yeah. Okay, so this is the, you know, the very good, I think the 2D shape questions, yeah. Okay, next one, Elita, yeah. How many triangles can you see in the picture? So make sure you think about triangles of all different sizes for this one. It could be a little bit tricky to count them. Yeah, use organized list, we just learned. Do they have the picture on their handout? This one there's no picture, but I think that's very easy for you to copy this picture. Yeah. And you quickly copy this picture to your sketch paper and then we could launch the poll. Oh, you already launched? Yeah. Yeah, I launched. Okay, I think that's enough people respond. Yeah. Yeah, let's share the results. You guys did really good on this one. Better than I expected. The correct answer was eight. And it looks like a lot of you got that so great job. Sorry, I don't know if I shared it, but you guys can see it. So, we get this by making an organized list. So we start with the smallest triangles like the triangles that are on the very ends, we can count six of those. So that's, there's at least six triangles, but then there's also two bigger triangles, you can see one of them is outlined in red, and the other one is upside down and outlined in purple. So that gives us a total of eight triangles. So you have six small triangles and the two larger triangles, make the list. Yeah, you could have found the total. Some of you pick two, you only see the two larger triangles. Some of you pick the six, you only see the small triangles, you have to count all the groups. Yeah. This is the next one. Oh, this is a tricky question. This is a five point question. Which pattern can we make using all five cards given below? Yeah, so here actually given on the right side. Yeah. So you can see the five cards, how you use this five cards stack on each other and make the choices here, A, B, C, D, E. Yeah, this one we keep the question. Yeah, for some time, maybe for one, one half minute. Yeah. You have to consider how to stack all the cards together to make the shape. This question is harder, you might use your imagination how to stack the cars together and after stacking the cars, what do the cars look like? So you have to identify some shapes, not in the groups, it appears in the answer. So you have to identify those impossible shapes. Okay, this is a pretty tricky question. So we always have some challenging question in the computation. So you could see the number, when the number gets bigger, usually the question gets harder. You cannot cut the shape, yeah, okay. So we would see the correct answer is A, yeah, so we will show you why A is correct. So here you can see the five choices, with A, how could you go step by step? You put the green one, and then you stack on the one, the pink square. And then you stack one triangle on the bottom left corner, yeah. And then you stack another blue triangle, and then you stack one more, the pink square on the bottom right corner. So this could use all the shapes on the right side, yeah, that's working, yeah. But even you find this one is the correct one, but we strongly recommend you to check the rest options, because sometimes math can rule would give you some options really similar to each other, just a minor difference. Sometimes you might overlook the answer choice. So you think that A is correct, but actually B might be the correct one. But this question, A is correct, yeah. But we want to tell you, you have to look through all the answer choices. You will not just find out, oh, the A is correct, let's move on to the next question. I tell you, sometimes they give you very close answer choices. So you might overlook the question, yeah, answer choice. So make sure you check all the solutions. Yeah, pattern B, why cannot make it happen? You would see the pattern B, you need four blue triangles. That wouldn't happen. You only have two. Yeah, the pattern C, yeah, you would need the rectangle, the pink rectangle. You only have a square, not rectangle. And the pattern D, so you need one actual, the pink triangle. Okay, so this one, you need this one, yeah? You do not have this one. And the E, you also do not have the triangle one. You could have the square. You can stack the two pink square together, and then you put the one blue triangle on top of it, so that work. But you cannot get a single pink triangle. And also you couldn't get the rectangle shape, yeah, the pink rectangle shape. And also you couldn't have four blue triangles. So this is a little confused question, yeah? So you need to check all the answer choices, make sure which one is the correct one. Okay, let's see the next question. Yeah, also not easy, yeah? You should be very careful. Yeah, Elita, go ahead, please. Maria built the square shown by using four of the following five shapes. Which shape was not used? So you see, they gave you five shapes, and Maria's square was built using four of them without overlapping. And they should make the square exactly, like there shouldn't be any extra square sticking out or anything. This one is not a handout. We just maybe hold, yeah, for a while. So they ask for which ship was not used. Yeah. OK, let's launch the poll. Yeah? OK. So there's one strategy I want to recommend to you. If you really couldn't find an answer in the competition, yeah, in a competition, I mean, so you can make a guess. So once you make a guess, at least you might have a chance to make it correct. If you leave it blank, you're totally wrong. So you can make a guess. There is no guessing penalty in the competition, in mass kangaroo competition. I'm not sure other competition, but in mass kangaroo competition, there is no guessing penalty. You can guess any question you do not know, but it's the best that you can solve the question because the guess not always correct. Okay, let's share the result. I see maybe no handout with this question on the handout, so it's hard, yeah. This one was definitely a lot more challenging, maybe. So the correct answer was D. You can see this just by kind of putting each shape onto the square Maria built and seeing which one's left over. So A obviously fits into the corner if you rotate it clockwise by 90 degrees. B just slides right next to A, you don't even have to rotate it. C goes in the bottom left corner and then E can fit on the side. So it all fits pretty perfectly and the only one that's left over is D. So that's why the correct answer is D. But this one is definitely a little bit challenging because you can rotate them and you can put them anywhere. So I think this one's a little bit harder. Yeah, that's true. That's true. So especially if you do not have the picture on the handout. In the real competition, if you do the in-person, do it on the paper, so it's better you draw all the shapes. Yeah, you circle all the shapes out. Let's see the last question. Yeah, let's finish this question. I think this is a very, very good question. Yeah, let's finish this one. How many white squares need to be shaded in the picture so that the number of shaded squares is equal to exactly half of the number of the white squares? Pay attention to what they ask for. They ask how many white squares need to be shaded. And then the shaded square would be exactly half of the white squares. So this question... Do they have this picture on their handout? They do not have it. Yeah, take a look at this one. This is the last question, yeah, and this one gives you a hint, so you may not solve it directly. You can use a strategy, guess and check. Make your guess to check your answer. If it doesn't work, make another guess. So the question ask for what? After you shade some white squares, you would have the shaded square is a half number of the white square, not half number of the total squares. So you have to make sure what condition they give to you in the question. Shaded over the white, that's half, half of them, not over the total. This is a pretty challenging question, yeah? Especially for the first graders. Yeah, I agree. Yeah. So don't be afraid for the real competition. You won't meet many of those kind of challenging questions. Maybe one or two, but not many. Yeah. Okay, so let's share the result. Yeah, so this is a pretty challenging question. Yeah. The correct answer should be three. So for this one, I just give you a hint. So you might use a guess and a check. So how many white squares you need to shade? Yeah, you do not have an idea. You just make a guess. And the first, what you should start with, you need to know how many white and how many gray squares you have at the beginning. Is that right? So you should count the white square, 19, and also the gray squares, they're five. So you need to figure out that the white over gray would be 2 over 1. So then you check, if you shade one gray, so you would get how many total grays? Six. And you will minus one from the white, get 18. So 18 over 6, that's three times. So you still have more white. You should have two times. So that means you need to shade more. So you shade two. That's the second guess. And then you get 17 over seven, not two times. Still over two times. And then you make another guess. You shade one more. Yeah, so that's three. So that makes white to 16, reduced to 16. And you make the shaded part to eight in total. And then you got 16 over eight, that's two times. So this is the correct answer. You need to shade three white squares. So this way, you combine with a guess and a check. Yeah. So this is a pretty hard question. So no worries if you cannot solve it. Yeah. So we will share the recording shortly after the class. So thank you, everyone, for coming today. Thank you, Elita. I'll see you next week. Bye-bye.

2D shapes

problem-solving

four-step method

math competitions

spatial reasoning

drawing techniques

pattern recognition

mathematical thinking

strategic verification

visualization exercises