Hello, everyone. Welcome to Maths Kangaroo webinar. Today, we are going to work on the 2D geometry lesson. I hope you are ready to explore this topic. And Elita is my TA. We would work together to help you. So I think the ground rules maybe just quickly go through, Elita, since we have some new students. Yeah, so the students should join the Zoom meeting with video off and voice muted to protect the students' privacy because each meeting is recorded. All lessons are recorded, and the link will be shared after the session. So please go back and review them if you have any questions. This is a webinar, so it's a large group class with less interaction. We'll try to accommodate most students, and we'll use the poll to collect answers and see how you guys are doing. You guys can't speak during the session, but you guys can chat me, and I will try to answer as quickly as possible. The student handouts are shared in the folder, so please print them out before each lesson. And also come with pencils and paper because those are really important for doing math. Yeah, so we strongly recommend you to write down the solutions, especially for the four-point or five-point questions. And we will let you know which question is a four-point or five-point question. Next, before we start our lesson, we always want to reinforce this combining tool. We will help you to solve the harder questions. It's called four-step method. Elita, would you like to go through this method with the students? Yeah, so the first step is to understand the problem. So this is basically just thinking about what the problem is asking for specifically, as well as looking at the clues that each problem gives you. The next step is to plan how to solve the problem. So this is where you use one of the methods that we teach you in this class. So you figure out which one to use, and you figure out what you need to use that plan. And then the third step is to carry it out. So you just follow the plan that you created. And then the last step is to check and reflect. So this is just making sure that the answer makes sense and thinking about whether there's another possible answer. Okay, so last lesson, we learned make an organized list or a table. That lesson may be a little hard, so I would recommend you to review those lesson and make more practice. Why we needed to make an organized list? Because sometimes you will see a question with a lot of possibilities, and you can group your ideas and focus on one group at a time to explore all the possibilities to avoid missing or repeating. So this is a very helpful. You can arrange the groups in a systematic order, like a sequential order for numbers or alphabetical order for the items or names. So another one we learned at the same time, it's make a table. The table is look like a chart. They have columns and rows. It's not very easy for you to make at the very first time, but when you watch more questions, how to solve this table, you would have more ideas. So the table could help you to organize the information very clearly. You can imagine there are a lot of the items over there. Like if we give you example, if we have a table information include the students from different classes, we want to record the boys or girls in the students and total students in the classes. So you might make the different columns and make the different rows. So it would be very easy for you to see in each class. So how many boys, how many girls or how many students. So when you try to make a table, you'll consider how to, what should you make for the columns and their names? And then you will add some rows. So for all the information they are giving in the question, you can just fill in. And later for the empty cells, you will try to solve the problem and fill in all the cells and try to solve it. So today we are going to work on the 2D geometry. So here's a warm-up question. Elita, please go ahead. Yeah. Johnny was making squares and rectangles using matches. He wanted to make each figure using 12 matches. He did not break any of the matches. In which figure did he make a mistake? So remember the fourth step method for this one. If you cannot see the share screen, you might need to move your mouse and try to find the sharing screen, windows, window, and then you may ask help from your parents. This question, it's a number three, it's a three-point question. Remember, number one to eight, that's a three-point question. Number nine to 16, that's four-point. 17 to 24, that's five-point. Each section, you have eight questions in total. If you confirm with your answer, you can select the poll question. Once you submit your selection, you cannot change your answer. So please check your answer before you submit your answer. Okay, it's been two minutes, so I'll end the poll now. Okay, good job everybody. It seems like you guys understood this problem really well. I thought it could be a little bit confusing, but it seems like you guys understood what they were asking for. So you can see that we're looking for the figure in which like there aren't 12 matches, right? Because that would mean he made a mistake. So in A, you can count there's five matches on the long sides and one match on the short side, so that adds up to 12 total. In B, you can see there's just three matches on all four sides, which adds up to 12. C, there's four matches on one side, three matches on the other, so that adds up to 14, which is not 12. So he made a mistake in figure C. And you can check that in D, he did not make a mistake because it's four matches on one side and two matches on the other. So that means that the only one where he could have made a mistake would be C. So pay attention. This question, they ask you which one is a mistake. Sometimes when you see the correct answer, you just say this might be the answer choice. But pay attention what the question is asking for. They ask which is the wrong statement. So you cannot just say, oh, right statement would be the answer. So you have to check what the question is asking for. So today, we are learning the 2D geometry. And here, we'll talk about what is 1D, 2D, 3D shapes. You might have already learned this at school or other places. So the 1D, we call that come from the one-dimensional. It's like the straight line, and it has only lengths. And a 2D shape, and a 2D shape, it's a two-dimension. We have a flat, we call that flat shapes. So you already, you can see them like a square, circle, triangle, or rectangle. You draw on the paper. So this shape only has a length always, but not thickness. So that's a 2D shapes. And the 3D shape, they are solid shapes. So you could see these shapes like a cube, sphere, cylinder, and a lot of other solid shapes. So these shapes, they have three dimensions, with a length, width, or height. So this is a difference between the 1D, 2D, 3D. Today, we're going to focus on the 2D shapes. So in some of the math questions, you will see pictures with the 2D shape. So please make sure you will check the picture very carefully, and pay attention to all the details. Because not only the word has some hidden information, maybe in the picture, you have to pay attention. So when you try to solve this kind of problem, you can check the picture they already gave to you, or even add something on the picture. You can make a list, like we learned in the previous lesson, or other strategy to help you to solve the problem. Let's explore more questions. Here, this question, it's from 2019 test. It's a number four, still three-point question. Karen cut one piece out of this grid. You can see this is a nine-cell grid. Which piece is the one she cut out? A, B, C, D, E. Which one's your choice? Sorry, no worries. We just started the lesson, so you can watch the recording for the previous part, if you just joined late. Please try to use the poll to answer the question, because we will wait for most of the students to answer the poll, and then we move on. Once you confirm your answer, please input in the poll. Thank you for those who send the answer to me, but I wouldn't tell you it's correct or wrong. You need to check by yourself. We're going to close the poll, so please input your answer. Okay, I'll close the poll now. Yeah, good job. Most of you got correct answer. So this E is correct. So let's see the solution here. So for this one, they mentioned Karen cut up the piece, but they didn't mention if Karen could rotate or not. So you, you can see if they didn't mention, so you can rotate the piece. So the piece wouldn't be exactly you see in the answer choices. It might be rotated. So you can see here, we have a three parts. It would be the same. Yeah, so they all like the E. But the, you can see the blue circle, a blue one, and that's same as E, but the other two parts is also the part. You just cut it off, can rotate, you still can get the same shape. So pay attention to the question what they ask for. Sometimes they said there is no rotation, or sometimes they didn't see, see that you can just rotate the piece. But remember, rotation and flipping, it's not exactly same at most time. Okay, question two, Elita, go ahead. Kanga wants to reach the koala without going through any of the colored squares. Which route can she take? So she wants to avoid those big blobs of blue, I guess. There are too many steps. Yeah, very similar. So pay attention. I'll give you guys another 10 seconds. So you read the four-point question, you might need a two to three minutes to solve. That's average time. For this one, it did require some time because you want to try all the options. Yeah. Well, it looks like almost everybody has gotten their answers in already. That's good. Yeah. So you guys are going pretty quickly. Yeah. I will close the poll now. Yeah. I think you guys did this one pretty well. Maybe also because the correct answer is the first option, but a lot of you guys got it right. So great job, everybody. So let's see. So I think the best way to do this would just be to test all of the answers, right? So you can see, you just start from the first one, which I feel like is what a lot of people did. You can see that that path lets you avoid all of the colored squares, right? So you go right twice, up twice, right twice, up twice, and then right three times. And if I had extra time when I was doing this problem, I would also check all of the other options to make sure that none of them work. And you'll end up finding that they all take you into the colored square. So that leaves A as the only option, but I think it's pretty convenient that that's the correct one because then you don't have to test the other four of them. Yeah. Thank you, Elita. I totally agree with you. You know, sometimes math can give you very similar options. So there are minor difference. So it's better if you have a time to check all the options. This question, they gave you the correct answer as A, but sometimes they might put the correct answer later. So please check all the options if possible. So question three, one of the pictures below uses a geometric shape that the others do not use. Which picture is it? Give me just 10 more seconds. Yeah. OK, good job. Most of you found the correct answer, D. So you can see very clearly from the different color we marked here. You can see A, B, C, E, they all have a square, and only the D has rectangle. So for this kind of problem, they put a lot of the shapes over there. So it's better you can make a list for each of the options. Like A, you could just quickly list out. They have a square, parallelogram, triangle. And B, they also have these three shapes. And you check C, same as A, B. And then you find D. So for the D, you couldn't find a square. And then you check E again. Make sure E has a square and all the other shapes. So please list them out. So that would be very clear for you which one would be the correct answer. Once you figure out the square and rectangle that's put on the different shape, so that would be very easy for you to find the correct answer. So answer is D. Question four. Yeah, in which of the following pictures is more of the shape shaded than in any others? Yeah, geometry is all about the shapes. So this lesson we learned the 2D shapes and later you would learn the 3D shapes. OK, I think we can share the result. Yeah? Yeah. Yeah, this one you guys also did really good on. I think you guys understand this concept pretty well. So the correct answer was B. And we can kind of count up the number of shaded squares, right? Because you'll see that some of the triangles are white. But if you put two of the white triangles together, they just end up making one white square. So you can see for A, there's four fully shaded squares plus four triangles. So 4 divided by 2 is 2. And then you add those to the five fully shaded squares. So you get seven fully shaded squares. And then for B, you'll see that we have, again, we have seven fully shaded squares. Because we have six normally shaded squares and then two of the black shaded squares. So that makes seven. But then we can also add, there's also an extra shaded triangle. So that one has one more than A. So you could stop here, because you know that it's only asking for one shape that's shaded more. But we want to check and make sure that this is the right answer. So we'll go and look at the other ones. You can see in C, it's the same thing. It has six shaded squares and then two shaded triangles. So that adds up to seven shaded squares. In 7, it has six shaded squares and then two shaded triangles. So that's seven shaded squares. And then in E, it just has seven shaded squares. So all of them have exactly seven shaded squares, except for B, which has an extra shaded triangle. So B has more of the shape shaded than the other ones. Thank you, Elita. For this question, you also can consider from an updated way. If they ask, so more of the shape shaded, that means you have less of the shape still empty. Yes, that means you could find the less white. So that would be more shaded. So you count the whites might be easier than you count the gray parts. Elita, what do you think? Yeah, I agree, because there's less of the white one in each one than there is of the gray one. Yeah, so you compare A, B, C, D, E. You would see any other answer, A, C, D, E, they all have four white triangles because you can split the square to two white triangle. So they all have four white triangles, except for B, they have three white triangles. So B has less white. They must have more shaded part. So this is another way you can solve the problem. Let's see the question five. Which figure can be made from this two pieces? This is pretty hard one. Even this four point question, but I think it's worth five point. There are so many small shapes. You have to really pay attention to the shapes or to the position. This is a little hard, yeah? Because there are too many shapes. Yeah, I think this one's pretty hard. Yeah, for this question, you can consider what other strategy it would help you to solve this problem. This is two separate pieces. You want to form a square. So how would you do? This is a little hard, yeah? We'll give you 30 more seconds, and then we will go through this question together. Let's share the result. Yeah. Okay. So some students still having to solve the problem. But we have a half students. So some of me to the correct answer. A is correct. Good job. This is a pretty challenging question because it's not that easy. To figure out the answer. There are so many small parts and also the shape being rotated. So for this one, you'll see the two separate pieces. So first, you would see what they want to form. They want to form with a square. So you can see the piece one. That would be like a T-shape, but it's a lie down. If you rotate the T-shape and then you insert to the U-shape, you would make a square. So this one, so it's better you can use the drawing a picture. You can draw the T-shape, insert to the U-shape and make the big square. Then make sure you draw all the small shapes in the right position. Then you could get the second. You can see the highlight. We can see the T-shape insert into the U-shape. But this one is not exactly show in the options. So you'll need to check the A, B, C, D, E, all the option, which one would be the correct one. So you would figure out A is the correct answer because you rotate the inserted shape to 90 degree to right and you would find A is correct one. So for the B, C, D, E, you would figure out they are not the correct one because they do not have the same shape on the same position. Even they all have the big square. So this is a pretty challenging question. For this kind of problem, we strongly recommend you to join on the current picture, help you solve the problem. Sometimes they may require you for the special thinking. Even this is 2D shape, you still need special thinking. If you have any question, please send a chat to Elita or me. This is a large session, the class. We do not let students who speak in the class. Please send your question in the chat. Yes, it's harder to imagine. That's why I think this is a pretty challenging question for you. But it did appear at your level in 2021. It's question 13. So just try to practice more. You would have more idea. Okay, let's see the next question, Elita. Yeah, so walking from K to O along the lines, pick up the letters kangaroo in the correct order. What is the length of the shortest walk in meters? So to move one block in any direction requires one meter. So just asking how many blocks is the shortest path gonna take? So the one meter here, that's one unit length, like one square, small square length. This whole session would be recorded and we will share the recording with you after the class. If you missed the previous part, you can review the recording. If you have a question, please send in the chat. This is another hard question. You cannot just solve it very quickly. You have to check all the steps, make sure you count correctly. Once you get your answer before submit, please check your answer. Make sure you count all the steps correctly. I think we can share this one, yeah. Okay, so you guys did pretty good on this one, I think, for it being such a hard problem. Mostly you guys got it right, so nice job everybody. Let's see how to solve it. So the first thing we want to do is we want to decide which A to go to first. And since it's asking for the shortest walk, I would go to the closest A. So you can see all three of these options have us going to the closest A. And then to get to that A, we'll take four steps. You can either go right first or you can go down first, but either way, it'll take the exact same number, right? Because you just need to go right three times and down once. It doesn't matter what order you do them in. So that's where the four at the top of this addition thing comes from. So it's four to get to the A, and then from the A, we need to get to the N, right? So you have to go left twice and then down once. It doesn't matter what order you go in, it's going to take three steps either way. So we put a three under the four, and we'll add them all up at the end. And then we have to go to the G, right? For to get to the G from the N, we need to go down once and to the right once. So that's another two meters. And then from the G to the A is another three meters, because you have to go up once and to the right twice. But again, it doesn't matter what order you do it in. You could go to the right once, up once, and then to the right. You can go to the right twice and then up once. It doesn't matter. It all takes the same number of steps anyway. And then to get from the A to the R, that's another three meters because you go down twice and to the left once. And then from the R to the G is two meters, because you want the shortest path. So that would just be going directly there. And then from the O, I mean from the G to the O is one. So then we have four plus three plus two plus three plus three plus two plus one, which gives us a total of 18 meters. Yeah. So you can see there are multiple routes so you can explore, not only the single routes, but they all lead to the same answer. For this question, because this is many steps, it's not a few. It's easy to count wrong. So we strongly recommend you to write down each counting step. So then you can check your answer very easily. Which step you count wrong. You count less or count more. It's very clear. So this is a recommendation for you to write down all the steps. That would help you. Question seven. Some lawns are shown below. Which lawn is the smallest? So this is a similar question as before. Remember, we have the other one. They ask the most shaded. And this question asks, which is the smallest? This question is a five-point question. It's from very recent year, 2022. Please submit your answer. We are going to review the question soon. Okay, I will reveal the answers. Okay, so most of you select A, that's correct answer. Good job. I see the answer choice. So this one, it's similar as the previous question. So you can also do the two ways to solve it. You either go forward, you count how many the green parts you have. You can see the green triangles. So which one has least amount of green triangles? You can see A has seven, B has eight, C, D, E, all has eight. Yeah, so you could figure out which one has the smallest the area. So that's A. And also you can consider the opposite way because when you count how many greens, green parts, that would be more counting. But if you count the white parts, you can all add some join to finish the whole shape to the same area. So that would be a six sided shape. So you can check how many white parts you have. So you would easily figure out that A has more white. Because you have more white, you would have less green. So this is the answer. So you can consider either way to solve the problem. Okay, Elita. The central cell of the square was removed. We cut the rest of the square into identical pieces. Which type of piece is not possible to get? This question is a little bit confusing. I think it's a five point question. This one is a little hard. You definitely need to draw on the handout. Yeah, the handout will be very useful for this one. So this question means one piece you cannot, you cannot use to fill in the rest of the shape. But the four pieces you could. Yeah, so it's hard. It means every time you use one piece, you could fill in all the rest part after you took off the middle part. Please try to draw on the shape to find which piece doesn't fit. Remember, you do not put all the pieces together. You put one piece at a time to fill in the whole shape. So you might need to rotate that piece. So if you send the question, so we would answer your question. But if you send an answer in the chat, we wouldn't give you a response. We want you to figure it out by yourself and check the question by yourself. We will release the answer after we share the poll result. Yeah, wait for 10 more seconds. Let's share the result. Okay, I will share the poll. So you guys are pretty split on a lot of these except for A. I guess nobody thought it was A, but the highest, the most popular response was E, which was the right one. So good job guys. Okay, so you can see that what we're trying to do is we just test each of the answers to see which one works. Right, so A, it seems like everybody kind of understood that that one would work, right? You can just put five of them on top of each other for one side and then five for the other side and then you put two in the middle. So that works. So it's not A because we know that one's possible to get. Now if we look at B, you can see you can arrange them in kind of this almost symmetric pattern where you put three, you put two on top of each other and then you rotate them kind of and put the next two next to it and then you do that until you fill the square. So that one is also possible and you'll notice that with C you can get kind of the same shape as if you added two of B together, right? So if you put them together like this, you also end up with a 3x2 shape that you can use to fill this this square. And then for D, D is a little harder, I think, but you can still get it. You just put two of them kind of on top of each other the same way you did with C and then you put one next to it. And then if you just flip that upside down, it works. The only one that's not possible is E. So you guys might have tried different combinations of putting E down, but you'll realize that with E there's no symmetry or anything. So that can make it really hard to decide whether it's possible or not. Thank you, Elita. For this question, do not just manipulate your mind. Do not just think it in your mind. You need to draw it out. Especially to give you a picture, you can try to draw the pieces. So, you know, the question asks for the identical pieces. So that would fill in the same piece at one time. So you have to understand what the question is asking for. So this is a pretty challenging question. This is our five-point question. So you should be prepared in the computation. There must be some very challenging questions. So today we learned the 2D shapes. So most of them you would see the flat objects appear in the question. So you can see some like a square, a circle, triangle. They show to you all their combination to make another shape. Or there would be puzzle pieces missing. Ask you to fill in the puzzle. And also there are some animal shapes that would appear in the question. So make sure you pay attention to all the details. Read the question carefully and pay attention to all the hidden information in the word. And also if they give you the picture, so you should pay more attention to the details of the picture, too. And also if needed, you can draw on the picture. Help you to solve the problem. So we still have time. Let's solve one more question. Bonus question. Yeah. I has a lot of this tile. You can see this tile. They show you the shape over there. L shape. Yeah. How many of the following shapes can I make by gluing together two of these tiles? OK, so let's share the result. So most of you picked the answer E. That's correct. So four is correct. All four shapes you can made by these two tiles. So let's look at the solution here. So you can see the shapes. We use the two different color to separate. It's very clear. You cannot just keep the same position. You have to rotate it. So they would have a different position and form all the four shapes. So this give you idea. Once they give you some pieces, so you might need to rotate them. If you do the in-person test, you might can rotate the piece of paper, the test paper. So help you to figure out what the shape look like. Or you can draw it out. So the answer would be E. So all the four shapes could be formed by the two tiles. But they do have the different position. Thank you, everyone, for joining today's session. So you would see the 2D shape, the questions. You will meet some harder questions. So please keep practicing. And also, we will share the recording after the class. And we hope to see you back next week. Thank you, everyone. Thank you, Elita. Have a wonderful day. Bye-bye. Thank you, everybody.

Math Kangaroo

2D geometry

problem-solving

geometric shapes

interactive webinar

shape transformations

systematic approaches

spatial visualization

real-time feedback

independent practice