Hello everyone, welcome to Masked Kangaroo webinar. Today we are going to work on the 3D shapes. You already learned the 2D shapes and today we are going to develop more on the geometry. So first, there are some ground rules. We already repeat sometimes almost every lesson. So just remember this is a large session and we try our best to answer your question in the chat but we will send you a recording after the class. So the student handout in the shared folder, please print it before the class. So Elita, would you like to go through the four-step method? Yeah, so the first step is to understand the problem. Basically what this means is you read it of course and then you look to see what information the problem gives you about the solution. And then the next step would be you need to plan how to solve the problem, right? So every class we give you guys a strategy on how to solve a certain type of problem. So this kind of builds off problem one because you have to figure out what plan to use given the information that you received in problem one. And you also need to know what other information you need in order to solve the problem. And then the third step would be to carry out the plan. So it's important to write down the solution step by step so that way you can check for any mistakes at the end. And then the last step is to check and reflect. So first of all you have to make sure the answer makes sense, right? And then second of all you have to make sure if there's you have to check to see whether there's a different answer or not. Thank you. So this is very helpful. So we strongly recommend you when you try to solve the four point or five point question, try to use this method to combine all the strategies you learned to solve the problem. So please practice this method. Otherwise it's hard for you. Just try to use it when it's necessary. So first we would like to review the lesson from the previous one. It's identical and symmetrical figures. So Elita, would you like to go through the review with this class? Yeah. So last week we saw a bunch of problems on symmetry and similar figures. So when solving a problem with identical figures, you have to compare their shape, size, and color to make sure that they're the exact same. And then symmetrical figures, we looked at that line, right? That's called the line of identical and symmetrical figures or you can call it the line of symmetry. And basically if you flip them over that line, they should be identical to each other. Like both halves of the line should be identical to each other. And then a single figure could have symmetrical parts in one or more lines of identical and symmetrical figures. So like with a square, it's going to be symmetrical across the horizontal axis, the vertical axis, and both the diagonals. Yeah. Thank you, Elita. So when you do the flipping, you remember you can flip left to right. Like you look into the mirror in front of you. So you all change everything left to right, reversed. But if you flip by the upside down, like you look down into the water to see the reflection. So that would be up, down, reversed. So remember that. So you just buy the reflection line so you can draw the cross-pounding parts. So that's symmetrical to the reflection line. So now let's work on the questions in the 3D shape lesson. First, warm-up question. Elita, please. Yeah. So this question is asking, which option shows the view from above the stack of disks? So remember the four-step method. All right, I'll give you guys a few more seconds on this one. Yeah, this is a 4-point question. It looks like you all did great. Yeah, okay. Yeah, you guys did really, really well on this one and super fast, too. Good job, everybody. So let's see, the correct answer was A, which almost all of you got. So remember, it's asking for the view from above this stack of disks, right? If it asks for from below or from the side, which we're seeing right now, the answer would be different. So let's see which disks we can see from the top, right? So the very top disk, of course, we can see that. There's nothing blocking that. And then the yellow or, I guess, light yellow disk under it, you can see the edges of it, right? Because the middle of it is going to be blocked by that small blue disk. But because it's a little bit bigger than the one on top of it, you're still going to be able to see a little bit of it on the outside. And then we're also going to be able to see the blue one underneath it because, again, it's a little bit bigger than that yellow one. So although the yellow covers the middle, you can still see the outer rim. And then the yellow one under that, that you can also see the outer edge of. Like the one before, the middle of it is blocked, but the outer edge can still be seen. And then lastly, the orange disk is the biggest of all of them. So that one, we can still see the outer edge. So the correct answer should be the one that has blue on the inside and then yellow, then blue, then yellow, then orange, which looks like A. Yeah. Thank you, Elita. For this kind of problem, you can also use elimination. So when you check each layer, you can just eliminate some wrong answers. That would be very helpful because you reduce the pool of the options. So that make you can reach to the correct answer quickly. And also we want to mention, like Elita said, when you look down, you look up, or you look from the side. That would be the different look. So you should pay attention to what question you're asking for. And this one, even that's a 3D shape, but we combine it with drawing a picture. So you draw something in the existing picture. Like you draw the arrow and show you, oh, this is the look down. Or tell you the direction where you should look at this toy. So then you could easily figure out the answer. So geometry, usually they will relate it with drawing a picture a lot. So you can use this strategy to help you solve most of questions. So here we learned a 2D shape and a 3D shape. And today we're going to learn 3D shape. So 3D, like we mentioned before, that's two dimensions. And all the shape, that's flat. So you would see like the rectangle, the circle, or square. So you usually see it's on the paper. It's flat, no rise up. But when you see the 3D shape, that's something solid that's around you. So you can have anything around you, like a pencil box, like cups, like anything else with different 3D shapes. The most often used 3D shape at your level would be cube. So you should get very familiar with cube. And then we will go through the details of the cube later. So also you want to, when you do the 3D shape, there is a different faces, different side, different views. So you need to check. So what's from the different direction. So how the object look like. So these are some kind of problem would ask you to solve. Okay, this also involved with some special thinking. Yeah. So let's see the first question. How many blocks were used to build the figure showing in the picture to the right? So they give you a picture here built by some blocks, but they ask you how many used. This is a very often question be asked in the 3D shape. Please note, we do not always have all the questions on the handout. So sometimes you might not find all the questions. So if you do not see those pictures, if you really need the picture to help you understand the question, you can draw by yourself. I think we can share the result. Yeah, it's very good. So almost everyone got the correct answer. It's nice. Let's quickly go through the solution. So for this one, you just need to count. You can see on the left side, so we have the very common method to solve this problem. You just count each cube, but pay attention to some cube. It's hidden behind or under some other cubes. Pay attention, do not miss anything. But there is another way on the right. You also can count by columns. You can see that each column, so how many cubes would be there? Then you could add them together. So both way can lead to the correct answer. Why I introduce a second way? Because later for some question, you will use this method. Let's see the question two, Elita, please. Yeah. What shape can we make using 10 blocks? For each lesson, we would like you to prepare pencils and a paper to help you to solve the problem. Also, the student handout, please prepare it before the class. I'll give you guys a few more seconds on this one. You guys are really fast today, I feel like. Yeah, but this question, not like the previous two. Yeah, I think you might need to be a little more careful on. Yeah. Pay attention to the hidden parts. Let's see. You guys can see for this question, the answers were a little more split. I think this one might be a little trickier. I would take my time on this question a little more. But I think the most popular answer was still the correct one. Yeah. Let's see. What we're going to do is we're just going to go through each figure and count how many blocks there are. If we start from A, we can see that on the bottom layer, we can count 1, 2, 3, 4, 5, and then there's 6 and 7 hidden under those two at the top. There would be 7 on the bottom layer. I see. I don't think for this one, it's hard to tell a little bit if there's any hidden under or not. Yeah, but don't overlook. For this kind of problem, they always have the blocks hidden under. Yeah. You do not overthink the question. Yeah. Like I said, there's 7 on the bottom layer because there's 2 hidden under those 2, and then there's 3 above. You can see those 3 pretty clearly. It just goes 1, 2, 3. I think the way it's written here is they count each column. There's 1 in the first column, 1 in the second, and then there's 2 there where it gets a little bit taller, and then there's 3 all the way in the back corner, and then there's 3 more columns of 1 block. If you add those up, you do 1 plus 1 plus 1 plus 1 plus 1, so that's 5 ones, and then there's 1 column of 2 and 1 column of 3, so that gives you 10 in total. There's a few different ways you can count this one. Then we can do the same thing for B. Usually, I count layer by layer, but this is written as columns, so let's do it like that. You can see in the leftmost column, there's just 1 block, but at the tallest column, there will be 3 blocks. Then in front of that, 2 blocks in front of that 1 block. Then if we move over to the third column to the right, then you see there's 1 block there in that column, 1 block in that column. Then for the rightmost, I guess layer, you could call it, there's 2 blocks there and 1 block there. We have 5 columns of 1, 2 columns of 2, and 1 column of 3. That would add up to 12. Then for C, we do the same thing. You can see there's 5 columns of 1 and 2 columns of 3, so it's 5 plus 6, that gives you 11. Then for D, it looks like there'll be 6 columns of 1. I think one of them is hidden a little bit. 6 columns of 1 and then 1 column of 5. That would give you 11 in total, because it extends out to the front with 2 and behind, there's also 2 columns of 1. Then for E, we see that this one has a lot of columns of 1. 1, 2, 3, 4, 5, 6, 7, 8 columns of 1 and then 1 column of 3. That's 11 in total. I mean, we could have stopped when we got to A, because it's just asking which shape we can make using 10 blocks. We know there's only one correct answer, but we can go through the rest of them to make sure we didn't make a mistake in A. Because if D, for example, also had 10 blocks, then we would have to go back and count A again and D again, to see which one of those actually had 10 blocks. Yeah, that's true. It's better you check through all the options, because most of the time, the math can give you the options very similar to each other. They have very minor difference. If you overlook some part, you might see the wrong answer. Please check through all the answers. Also, like Elita mentioned, you can also count by layers instead of count by columns. Whichever way you feel comfortable, you feel better, you can reach the better approach, so you can just use either way. You can count by columns, or you can count by the layers, or you can count by one by one. Or later, we will introduce you, you can even count by the different directions, like top, bottom, left, right, front, back. So those are different ways you can count the blocks. And the counting blocks would be very often to be appeared in the computation. Yeah, and if you guys have some extra time at the end, you can count in a different way than you did the first time. So that way it's checked better, I think, because you're not likely to make the same mistake using two different methods, right? Yeah. Okay, next question. The picture shows five identical bricks. How many bricks are touching exactly three bricks? Once you select your answer, please check your answer before you submit in the poll. After you submit, you cannot change your answer anymore. Remember, the fourth step, check your answer. Yeah, this three-point question, it costs a little more time to solve, yeah. I think this one is trying to trick people, the way the questions are arranged. Yeah, you have to make sure you don't get tricked by it. All right, I'll give you guys a few more seconds on this one. Okay, I'll end the poll now. Yeah, so good job. Most of you got the correct answer. And let's quickly go through the solution with you. Did you share the solution, share the result? Yeah, I think I shared it. Okay, great. So here you can see I replaced the picture and show you the bricks, the two different bricks. So you can see for this kind of problem, you either can order those bricks and name them. So that's easy for you to check each brick. So it's better you check all the bricks. So you check A, you would see A touch B, A also touch D and touch E. So A exactly touch three bricks. It's the same for the C. But if you check B, D, E, those three bricks, they all touch four bricks. Because you can see B connect with A, connect with C, connect with D and connect with E. And the same for D and E. So the answer would be two, only A and C. So they touch exactly three bricks. So you put all those bricks together. So you can see the others stick together or glue together or they just put them together. And you would see A, B, C, that's make a stack. So you can see that's a stack. And you see D and E, that's put on the side, but touch A, B, C. So they ask which brick or how many bricks could touch exactly the three other bricks? Yeah, somebody said, I do not get it. So that's not three, answer is two. Because only A, C, can you see? We named all those bricks. A and C, they both touch three bricks. But B, D, E, those three bricks, they touch four bricks. You can see B touch A, touch C. B touch A and touch C and also touch D. And also you could see B also touch E. So B touch four bricks. And D, it's the same. D touch A, B, C and touch E. And E touch A, B, C, touch D. So only A and C, they both only touch three bricks. So that's the answer. Okay, so because we talked a lot with the blocks of cubes. So here, we would like to introduce more about the cubes. Yeah, so before we continue, I would throw some questions. So now you could maybe just imagine your mind or you can draw something out on the paper, help you to solve these problems. So they ask you, how many faces does a cube have? So you can put it into the chat, yeah. And how many corners and how many edges for each cube? Yeah, so first question, yeah. How many faces for a cube? Yeah, put it into the chat, please. You can either send it to me or send it to Elita, yeah. So first question, how many faces for each cube? Good job, yeah. You send it to either of us, yeah. Okay, yeah. Do you receive answers, Elita? Um, I received one answer. Oh, okay, yeah. I think most people send them to you. Yeah, yeah, yeah. So good job. So most of your answer, there are six faces, yeah. And how many corners for a cube? Please input your answer in the chat. Yeah, we talk about the corners. The corners. How many corners for the cube? Yeah, answer the corners, the number of corners now. Yeah, so far, most of you get the correct answer. Or maybe some of you answer the wrong question. So, yeah, so that's eight corners. Good job. And how many edges, how many edges, please put into the, this is the last question. How many edges? The edge, that's the length to force each face, yeah. Okay, good job, Elita. And how many faces, how many faces for a cube, please put in the chat. The edge, that's a line to form each face. Each face is what? It's a square, is that right? So that means each face, you have four lines. That's four edges. Yeah, very good. I think some of you already get it. So that's 12 edges. So remember, remember this properties for the cube. So this are very helpful. So now let's go deeper with what a cube look like. Yeah, so when you look at the cube, if you have some cube around you, that would be great. You can just grab them and take a look. If you do not have, you can do some special thinking or you can see the picture on the screen or you can draw it out on the paper. So here, when you talk about the cube, we always see the cube, we always could see the cube has six faces. You could see the top face, bottom face, left face, right face, front face and the back face. So that's six faces. So you can see the first picture. Yeah, I put some of the sign over there. It's very easy to see on the top and the bottom, left, right, front, back. And then you would see what? You would see the top. The top is a square, is that right? You can see top has four edges. And the four edges will make the top connect with front, connect with right, connect with back, connect with left, but never connect with the bottom. Is that true? Yeah, top never connect with bottom. So that's introduced another, the knowledge about the cube. So we call that opposite faces. So top and the bottom, they never touch each other. They are parallel. So they call opposite faces. So you know, every face, you have four edges. So the four edges would have this face connected with four faces. So those four are all their neighborhood faces. And the left over face would be the opposite face. So remember that. So you would get a very clear, the top never touch bottom, the left never touch right, and the front never touch back. So those are three pair of opposite faces. So when you see the corners, where is the corners? The corner, it's a three faces connect together. So you could see on the top, you could see there are four corners, yeah? The four corners, yeah. You could see the top and the right and the front, they make one corner. Top, right, back, also make one corner. Any three faces, they connect together. So they make a corner. So you see the top has four corners and the bottom also have four corners. So that you answered eight corners, that's correct. And also they ask about how many edges. You can see the top face, you have four edges. And the bottom face also have four edges. You cannot see some edges, but they are there. So there are four edges on the bottom. And also you can see the side. You could see the side also have four edges on the side. So you add all together, that would be 12, 12 edges. Remember, six faces, eight corners, and 12 edges. And also you see this one, it looks like we open a gift box, is that right? Yeah, so what we call, why we open the cube, so we call that's net. You also will see some question, it's open the cube, it's net. And they ask you to check for something about the opposite faces. So you would see, can you see the net on the very right side? You can see the top, we open, where is the top? Top from the, you know, they open from here. So we can show you, yeah, they open from here. And then they unwrap, unwrap the box. So you could get a top connected with the front. And also the bottom is under the box. And after the bottom, that would be back. And also you open the left side, you get left. Open right side, you get right. So that would show you, this is the net. And you already know the top, bottom would be opposite faces. And the left, right, also opposite faces. And the front, back, also opposite faces. Remember that, yeah. So now I would ask you, yeah, so please, if you have a color pencil, at least three colors, so you can paint the three pair of opposite faces. So this shape is appear on the last page of the handout. So you could see the net on the last page of the handout. If you haven't printed out the handout, you can just draw this shape, copy on your paper, yeah. So this one, please use the three colors. You can color the three pairs of opposite faces. And if you do not have a color pencil, so you can just maybe just write red, blue, yellow, yeah. You can write red, blue, green, or red, blue, yellow. You can write any three colors, yeah. So write the same color in the opposite faces. You can write down the name of the color. Maybe just initial letter, not the full name. You can write red, green, blue. Yeah, whatever the three colors. Yeah, if you do not have a color pencil, yeah. So you need to identify which two squares they are opposite faces in the net. So we ask you to color the same color for the opposite faces. Yeah. If you do not have a color pencil, you can just write down the initial letter of the color. We give you three colors, red, green, blue. So you would have three pairs of the opposite faces. Each pair of opposite faces would have the same color. Yeah. If you're done, you can just send in the chat how you are done. So I will show you how they look like after the paint. If you do not get it now, no worries. I'll show you later so you would have idea. So this is a very important that you understand, help you to understand the opposite faces. And also it help you understand how the 2D shape and the 3D shape, their relationship. You can change a 3D shape, open to the net and to make the 2D shape. So this six squares, that's you open the cube and you make it flat, make it a 2D shape. So anybody made that? Okay, so I will show you how they look like. So I use a yellow, red or green. So it doesn't matter what color you use, just three pair of color. So you would see, can you see the two yellow part? That's opposite faces. And the two red part, opposite faces. And the two green part, that's opposite faces. So like the shape we share with you here, yeah? So you could see the top with the bottom, it's under the cube, that's opposite faces. So you can see this is a top, let me change the color. This is a top and this is a bottom. Yeah, so you can check this shape. Oh, if you wanna, oh, maybe we can do this way, exactly same, yeah. So this is a very helpful if you understand this part. So this one, we can compare here. We can see this one is a back, yeah. And this is a bottom. And this is a left. And this is a right. And this is a front. And this is a top. See, you can see the net we opened. So you can match each part. And you would see the back and the front, they have same color, left, right, same color, bottom and top, same color, yeah. So let's see this question, yeah. Okay, Michael glued three cubes together as shown in the picture. And then he covered all of them with paint. So think about what this question is asking because I think I get a little confused. So you cannot glue the, you cannot paint the glue, gluing part, yeah? So any faces you glue together, you cannot paint it anymore. You only paint the faces open to the air, no matter it's on the top, bottom, left, right, front, back. Right, because you can't paint between the cubes, because they're glued together. Okay, so we can share the result. Okay. So, you guys did pretty good on this one. I think this one could be a little tricky, but I think overall, for a four-point question, you guys were pretty fast. So, let's see. So, by how many squares he painted, the question is asking you how many faces of the cubes he painted, right? Because we know each face of the cube is a square. It's not asking how many cubes he painted, right? It's asking how many squares. So, on the top cube, let's see. He painted the front face, the back face, the top face, the left face, and the right face, right? So, that's five. For the cube to the very right, he painted the front face, the back face, the top face, the right face, and the bottom face, right? He didn't paint the left face because it's connected to the other cube. And then finally, for the cube that's in between those two, he painted the front face, the back face, the left face, and the bottom face, right? Because it's touching the other two cubes with its top face and its right face. So, in total, he painted five for the top one, four for the one under that, and then five for the one to the right. So, if you add those up, you get ten plus four, right? Which gives you fourteen. Yeah. So, you can check each cube. Yeah, so and then add it together. And next, we want to introduce a new way for you to count the painted faces. Because painting the faces, it would be another very often the questions we will show in the exam. So, here you could see for each individual cube, you have six faces. We already talked about. And the way you glue two cubes together, you could see each cube only have five faces left. So, the left cube has the right face glued, and the right cube has left face glued. So, each of them lose one face to glue together. So, you would remember, every time when you glue the two cubes together, you will lose total two faces. One from each cube. So, you would see this one, they ask how many faces do two cubes have. So, you can use another way. Use the total. If you do not glue together, that would be six plus six, twelve. And then, if you glue together, you make one glue, you lose two faces. And then you would minus two. You get ten faces. So, for the next one, they show you the three blocks, three cubes. So, you would see there is two glues over there. So, if you check how many glues happen, you would see the left glued with the middle one, and the middle one glued with the right one. So, you have two glues there. And each glue, you will lose two faces. So, you total lose four faces. And if you do not glue together, that would be in total eighteen faces. So, eighteen minus four, you get fourteen. So, this is another way. So, if you do not want to count each cube, or you do not want to count each direction, so you can just count how many faces you lose, you lost, and then you can do the calculation. So, this is another way you can solve the problem. It can help you to check your answer. So, let's see the question here. Each of the shapes shown is made by gluing together four cubes of the same size. The shapes will be painted. Which shape has the smallest area to be painted? So, you can use the glue parts we just did to check which one you lose more faces, you will paint less. It looks like it takes a longer time to find out the faces for each one. Yeah, I think the glue method would be faster, right, because then you don't have to count as many. Yeah. Okay, so this one take about three minutes now. So I think maybe we should go through together to have the students understand more. This is only a four-point question, right? Yeah. Okay. Okay. So good job. So for those who answer the question, we have most of you get the correct answer. So that would be B. So this is smallest area to be painted. So that means you have less spaces open to the air. Okay. So let's see the solution here. So we talked about to find the glues. So you know each glue, you will lose two phases. So you can check A, how many glues over there? So you have a three glues over there. Yeah. So that means a three pair of the blocks glue together. And then for the B, you could see there are four glues over there. So with more glues, that means you will lose more phases, and you will have less phases left. Yeah. So the C, you also can see there are three glues. And D, same as A and C, and E is the same. So I already drew after the glue. So that's very easy for you to see. So this way, you would see if you do the calculation. Yeah. So you would see the A, C, D, E, they all 18 phases, and B has 16 phases. So that's a least smallest area should be painted. Yeah. But this kind of problem, you know, if you count each of them and add them together, that might take you a longer time. But if you check how many glues you found. So with more glues, you have less phases. So you would know you have four glues. You do not really need to count how many phases. They didn't ask about that. But you know, with four glues, you will have less phases. So you can still have the correct answer and save your time. There's another way. You might can check the phases, how many phases on the different direction. But I think for the grade one, grade two students, we already reinforced this method to level three and level four students. But for the grade one, grade two students, you might need to practice more, try to understand more about the cubes. So you also can consider, you check from a different direction to find how many phases on that direction. But here, we would like to introduce you either calculate the single cube, how many phases could be painted or counted by the glues. Okay. So here we show you again, that's opposite of phases, always have the same color. We show you that same color, mark the opposite phases. Remember that. If you fold the back to the cube, you would figure out. So those phases, they never touch each other. So you can cut the picture off and then just fold it back to the cube to see if that the same, the opposite phases has the same color. So now we would use the opposite phases to solve this problem. Yeah, Elita, go ahead. Yeah. So on each of the six phases of a cube, there's one of the six symbols shown below. On each phase, there's a different symbol. In the second picture, we can see the cube shown in two different positions. Which symbol is opposite the square? Well, I think this one's also a little tricky. Yeah. But if you really understand the opposite phases, yeah, that would be much easier for you to solve this problem. Yeah. If you really understand the properties of the cube, right? Please remember what we talked about the opposite faces. So for each face, you would have only one opposite face. For the cube, total six faces, if there's only one opposite face. So that means you would have four neighborhood faces. Okay, so Elita, I think we might need some help to go through the question. Okay, so you can see that of the ones who did do this, the most popular answer was the correct one. So let's see, I think this is just mostly a logic thing more than anything. It's just, let's remember there's only one opposite face for each face of the cube, right? So let's see. So for the first cube, you can see that the circle is adjacent to, that means next to, it's touching the diamond and the clover, right? So that means that neither of those can be the opposite face. So we can cross out two of the options, right? We can cross out the clover, and we can cross out the diamond out of the options. So we know it's not B, and we know it's not E, right? And then if we look at the second picture, we can see that the circle is touching the heart and the spade. So we know it's not going to be the heart or the spade that's opposite to the circle, right? So then that leaves only one option. It must be the square that's opposite to the circle, because every face needs to have an opposite face, right? And we eliminated the other four, so that leaves us with only one that could be possible. Yeah, so this is very easy if you try to figure out the opposite faces and the neighborhood faces. Or you can use special thinking. You can rotate the second cube to match with the first cube to figure out which two faces are opposite to each other, and you would get the same result. Let's see the next question. This one looks familiar, yeah? We already talked about how to count the cubes with columns. So here, Paul and John were building using identical cube blocks. Paul made the building show in the picture one. So this first picture, that's what Paul made. And the picture two, that shows you look from above to see Paul's picture. So you look down, and you would see picture two. So now they give you the picture three that shows John's building as seen from above. So then they ask you which of the answers show John's building. So you know the picture one, that's Paul's. And the picture two, that's what you look from above of Paul's building. You can see how many blocks on each column. And then the picture three, they just give you the number of blocks of each column for John's building, and ask you to figure out A, B, C, D, which one would be John's building. So please pay attention. There's something really close to each other, the two answers. Make sure you check very carefully. Yeah, also want to mention this is the older year test. So we have four options. For all the recent years, we all have five options for each question. Okay, let's share the result. Okay. Yeah, go ahead, Elita. Did you share the result? I did, I did. Sorry, I thought I copied it. Okay. You want me to explain this one? Yeah, go ahead. Okay. So for this one, let's see. Okay, so for picture one, we can see that we're going to do the same thing where we count the number, right? So you can see that it looks like there's five columns of one. I mean, sorry, there's five different columns where there's one block in them. There's one column where there's two blocks in them. And there's one column where there's three blocks in them, right? Oh, you're muted, Elita. Yeah, so the picture one, that's a pulse building, yeah? The picture two, that's you look from above the pulse building. You could see how many blocks are in each column, yeah? Yeah. Yeah, and the picture three, they give you that Jones building. Look from above how it looks like and ask you to find which building. It should be the picture three. You could get the picture three. Yeah, so then if we go through each of the four options, right? For A, it looks like there's four on top for that one, right? There's four in the first column, one in the second, then two, two, three, right? So it can't be that one because there's no squares that say four for picture three, right? We can look at B. It looks like there's two twos, and then there's three ones, one, two, and one, three, right? So that matches with picture three. So we think right now it could be B, but we can also check the other two to make sure that it's not, right? So in picture C, we can see there's four columns of one block. So then that would be not correct because there's only three columns of one block in picture three. And then for picture D, there's no columns of three blocks, which we know there has to be from picture three. Yeah, so you can check the each columns, how many blocks and figure out which one should match. So this is also appeared sometimes in the exam. So please review this question in the recording later. So now we see the last question. Yeah, so Fred has four red cubes, three blue cubes, two green cubes, and one yellow cube. He built a tower over here. This is a little hard question. So they ask you, so in such a way, there are now two adjacent cubes have the same color. So that means you cannot put the same color next to each other. So what color are the cube with the question mark? So remember, you have four red, three blue, two green, and one yellow. So what does that mean? Two adjacent cube, you cannot have same color. So that means here, can you see this is three cube. Can you see this two, the bottom two, and with the top one? So this is three. They cannot be the same color. And also this two cannot be the same color. And also with the top. So anything you touch, even touch half. So that's something you connect with each other. So you cannot have the same color. This is a little hard question. Yeah, I think so. Because you could try a bunch of different things to see first. Yeah. Yeah, 3D shape, it looks like a little harder, so because you do not meet a lot of these questions before. So that requires special thinking, and so that would need you to practice more, get more understanding. So no worries if you feel that's very challenging, the question for you. Yeah, I'll give you guys a few more seconds, but I think this one might be a little bit too difficult for us right now. Yeah. So this one you definitely use a guess and a check. Yeah. Okay, so let's see. So let me share the results. So you guys can see that the answers were pretty spread out, right? So it doesn't seem like we really had an idea of how to do this one, right? So let's see. So obviously it has to have four red cubes, right? That's going to be the most difficult to place because we know that no two cubes can be next to each other. So through trial and error, you know, if you just try to place the four red cubes randomly and move them around like that, we see there's only one way to place them, and that's like this, right? In the bottom row, we want the two outermost cubes to be red, and then in the second row, we want the middle cube to be red, and then the very top one should also be red, right? So then it doesn't really matter how we place the other three colors, right? Because we know that it's only asking about the question mark cube, and we already made that one red. So we can answer this one pretty quickly by just saying it's red, right? We don't have to try the other three colors at all. The most difficult part is definitely just placing the red cubes first, but once you have that, you should know how to do the problem. So because the red cube, that's more cubes. So we give you all the options here. So how you place all the other colors, and you would figure out there is no way if you do not place red like this way. If they said there is a four blue, three red, so you definitely would place the blue like this way. So who has more? So you would check those one because you have to avoid the two adjacent cubes has same color. So now we'll finish this lesson. I know you'll stay a few more minutes, and thank you for your patience, and today we learned the 3D shape. Like I mentioned, this might be new to some of you, so you feel much more challenging. So please review the recording, and when you look at the question, it's about the 3D shapes. So please look at the picture very carefully, and try to imagine. So this object, you look from the different side, the different directions, like look from above, bottom, left, right, front, back. And also sometimes you might need to draw the picture. So when you turn the shape, and also the glued faces, it would be very helpful for you to check the more or less faces painted. So try to imagine the opposite faces when you look at the cubes. Sometimes the question ask for that. So we will share with you the recording soon, and please review this lesson. We feel this 3D shape might be more challenging for your level students, but with more practice, you can get better and better. Thank you, everyone, and thank you, Elita. So we will see you next week, have a wonderful rest of the day, bye-bye.

3D shapes

geometry

problem-solving

cubes

spatial representation

symmetrical faces

visualization

mental rotation

nets

spatial planning