Hello, everyone. Welcome to Masked Kangaroo webinar. This is our second lesson, and our TA, Elita, will work with you. We are so happy, so you all come back, and we will have another fun class together. So first, we will reinforce the ground rules for this class. So every student in this class, because this is webinar, so every students will keep the video off and voice muted, and we will record the whole session and share with you shortly after the class. This is a large group class, so we do not have much interaction. We let you to chat with Elita and me both, but we try our best to answer your question, because we will be busy with conduct the lesson, so we might not answer all the question. And a student who couldn't speak in the class, too. Also, there is a student handout. We already shared the link with you, so please find the handout, print it out before the class every time. That would be very helpful for you to solve the problem during the session. I know there is some new students joining in the second lesson, so we will give you a brief introduction about what is Math Kangaroo. So Math Kangaroo is an international math competition. So it happened every 30th of March, so next year, it would be March 20th. So our registration already opened. If you haven't registered for the next year, so please visit our website and to find a center to register. So if you would like your school to host the Math Kangaroo competition, please email us to let us know. So we would like to invite your school to host the competition, so you can take this competition with your friends and classmates. So this competition is an individual test. It's 75 minutes, and you will work on the 24 multiple-choice questions. So every question will have five options for answer, and you will select the one correct one. There are only one answer correct. So you will see a lot of questions. It involves logical reasoning, critical thinking, and problem solving. It's very fun. A lot of students, after they join the competition, they always say, this is a fun competition. Elita, do you agree with them? Yeah, I would say this is definitely the most fun math competition, probably when you get to higher levels. I think the questions are really interesting, and I think they try and include some fun parts in each question. Yeah, thank you, yeah. Elita also participated for Math Kangaroo competition for many years, and also she missed the last class because she went to another math competition. So she participated in many different competitions. Yeah, yeah, so I think you could share a lot of experience with our students during the lesson. So here, we want to introduce another tool to help you to solve the problem. So in addition to the strategy we would like to learn in the lessons, we also want to introduce a four-step method. So when you try to solve the problem, the first step always be understanding the question. So you read the question, read each word carefully, and check all the hidden information, and check the picture carefully, and try to understand the question, what the question ask for. And the next step, you will plan how to solve this problem. So you would figure out what strategy could help you to solve this problem. So if there's a pattern problem, we just learned the last lesson, or if there's a drawing picture, we will learn in this lesson, and we will learn more strategies in later lessons. So now the next step, step three, you would carry out your plan. So you will write down the steps, write down the solution step by step, and then try to solve this problem. So once you solve the problem, do not just move on directly. You need to check the answer to make sure you get the correct choice. So this four steps are very important. So for the three-point question, usually you might solve it mentally, or you might just draw or write down very simple information. So you might not use this four-step method if for the three-point question, the easy question. But for the four-point question or five-point question, this is a super helpful. So we will guide you when you're through all the lessons, we will remind you, use this four-step method to solve the hard problems. So here is a review for the last lesson. Some students might miss the first lesson, but remember, we have a recording for every lesson, so you always can go back to visit the recording and to do all the questions we did in the previous lessons. So what is the pattern we learned last week? Yeah, also, we talk about pattern. So it's something that changes in a specific way. So you can find that the pattern is repeating, or it's growing, or it's shrinking. You get a reducing, or you get more. So, but they always follow a rule, is that right? Yeah, Elita, do you see a lot of patterns year round? Yeah, I think in a lot of math competitions like Math Kangaroo, you can find some patterns. Usually, you might have to think a little bit harder about some of them. I think these patterns are a little bit clearer. Yeah, for the lower grade, you do not have very complex patterns. But if you grow older, you will find more and more, very interesting, but harder patterns. But remember, pattern is everywhere. So like we mentioned, today's a Sunday. Next Sunday, it's seven days later. It repeats the Sunday, yeah? So you get the repeating pattern for the weekdays, yeah. And also, you have some daily routines you repeat every day. So that's also, that's all repeating pattern. That's very often. But you also could see something. They keep growing by a specific number. Yeah, you add the same number or you add a different number by the rule. Also, you can reduce something. So that's very clear. Even you find the fruits, some vegetables, all the animals, and all some natural things, you can find a pattern too, yeah. So if you go to the zoo, you'll see the giraffe or zebra. You'll see their patterns on their body. That's all patterns, yeah. So here, we just want to reinforce pattern is very important. And today, we are going to learn another one. So this is super helpful. Even this is a math class, we use a drawing to help us to solve the problem. Because some problems, they do not have a picture, just a word. So if you read the word, it's hard to imagine sometimes. If you draw the picture, that would help you to solve the problem. And a lot of math can rule problem, also they give you the pictures. You still can work on those pictures to draw additional skill, the details, to help you to solve the problem. So when you draw the picture, you have to remember, you do not draw something very complicated, take you too much time. You do not draw a very perfect picture. So you just draw something simple, easy, and help you solve the problem. Because in the test, you have 75 minutes, you cannot stack on one question. Also, you need to draw to skill. Yeah, what means draw to skill? Yeah, Elita, would you like to give an example for draw to skill? Yeah, like a map maybe, of like the country or of some roads. Obviously, you can't fit a road size, road onto a map, so you have to shrink it by some amount. But it's still proportional. Yeah, very clear. Yeah, the map is a good example. And you would know from your home to your school, or from your home to a nearby store, that's different distance. If you want to draw on the picture, you have to show the difference. Yeah, so that's draw to skill, yeah. Okay, so let's see our first question. Yeah, so Katie is in a boat on the lake. You need to draw the picture that she sees in the lake. So there are five options. So we will give you, this is a super easy question, but you have to understand what they are looking for. We give you maybe one minute to solve. We will see if the time is not enough, we will increase the time later. Yeah, one minute to solve this problem. And then we will open the poll to let you pick the answer. Remember the answer choice. I opened the poll already. Oh, you already opened the poll? Yeah. Okay. But you have your hand up, yeah? So you need to remember A, B, C, D, E. What's our choice? We do not have the picture in the choice, so you have to remember that. You might need to reduce the window of the poll to let you see the question. Because the answer choice is A, B, C, D, E, so you see the choice, you could select them. Later for the word problem, there would be no problem for you because we put all the words in. Okay, any more choices? Okay, let's share the answer. Yeah, this is a three-point question. You can see the question eight. It's a three-point question. So let's end the poll and share the result. So you could see most of you pick the answer C. This is correct. Congratulations. And some of you pick the different answer. So let's take a look about the solution. So here, what are you looking for? So Katie, she sit in the boat and she want to see the items, you know, she could see on the shore and get a reflection to the water. Yeah, so what she could see? She see the tree and the moon in the sky, tree on the bank. And then if those things reflect to the water, you could see the tree upside down and also the moon upside down. So the answer choice would be the C. Yeah, you could see the moon is on the right side, not on the left side. If any students, you select the answer on this side. So you didn't do the reflection. So you need to consider your upside down the moon to the water, yeah? So also you could see the red line, that's reflection line. This is a mirror image. So you have to, the image and their mirror image, all with come to the reflection line, the same distance. So we call it asymmetry, yeah. So this is a reflection. So you do not put the moon on the left side or you do not get the moon like flip over, yeah, to this way. So that's not correct, yeah. So the answer would be C, yeah. So this is a reflection, yeah. Remember how to do the mirror image. Okay, next one, Elita, go ahead. Okay, together Chip and Dale have eight nuts. They divided them equally between the two of them. Chip ate one nut. How many nuts does he have left? Remember, this is a drawing picture, yeah. So this is a word problem. You can draw on the paper. So please have your pencil and paper ready each class. Okay. I think we can open the poll because this is a question without a picture in the answer. Okay. This is also three point question. Usually you might use one to two minute to solve during the competition. So some students might not know what's divided equally. So that means that, you know, you share something with your friend. So you have eight knots, you share equally between you two, that means you all get the same amount. Everybody got the same amount. Very nice. Yeah. So remember, three-point question, you already used one to two minutes to solve it. Yeah. Okay, so let's share the result. Yeah, Elita, would you like to go through this question? We can see most of the students got it right. Yeah, very good. So the correct answer was B, three nuts. So this is because when they share the eight nuts equally, that means we divide eight by two. So each squirrel will get four nuts. And then the one on the left are Dale's nuts, and the ones on the right are Chip's nuts. So if Chip eats one of his, then that would be four minus one. So he would have three nuts after he ate that one. So the answer is B. Thank you, Elita. Yeah, just pay attention. We make the picture. Yeah, it's very fancy. But for you, when you draw, you do not need to draw such a fancy picture. You just draw a circle. Yeah, draw eight circles or eight lines, whatever you like. And you divide it into two groups. Each group has the same amount, and you cross one from one group. Remember, they only asked for Chip's. They didn't ask for the other, that's for Dale's. So pay attention to what question asked for. So you don't need to draw the fancy picture. We just want to show you something. So that's why our picture is very fancy. But you make a simple drawing. Okay, let's see the next question. So 12 pairs of dancers took part in a dance competition. Johnny noticed that 18 people danced the waltz. How many of the 12 pairs of dancers did not dance the waltz? To pay attention to the words, they ask how many of the 12 pairs. So you have to pay attention to the unit. This is a four-point question. During the real computation, you might need to spend two to three minutes to solve this problem. Okay, so I think we can share the answer for this one. Yeah, so look at this time. We didn't get, you know, we get half class, choose the correct answer. So there might be confusion part for you. So we will go through this solution with you. So here you can see I underline some words. So that's a key words. When we read a question, when you do the test on the paper, I strongly recommend you to highlight the key words that would help you to solve the problem. So you can see the next one. We draw the picture. Still, I want to mention, we draw the fancy picture. You don't need to draw it. You draw the simple symbol. Yeah, so can you see the question we underline? Remember the four-step method. The first step, they ask you to read a question and understand what a question ask for. So what a question ask for here? They ask how many of the 12 pairs? Remember, here's the pairs. Even they mention 18 people in the question, but you have to figure out how many of those pairs. Yeah, so this is a different answer. So you could see it, the 18 people, you can convert to nine pairs. Is that right? And then you have a total 12 pairs. You minus nine pairs, you have three pairs. I know a lot of you select six. You mean to answer six people, but they didn't ask how many people. They ask how many of the 12 pairs. So please pay attention to what question ask for. This is very important. So this is not a hard question, but you have to pay attention. Yeah, pay attention to each word, especially for the key word. Okay, so let's move on to the next question. Elita, go ahead. A frog jumps on every rock, starting on rock number three and finishing on rock number nine. How many jumps does it make? Okay, so let's wait for a moment. Let them take a look at the picture, yeah. So this question gave you a picture. Okay, let's open the poll. This is also a three-point question. I think we can share the result. It looks like everybody did really good on this question. Yeah. So it was A and everybody picked that. So great job. Yeah. So you can draw on the picture, whatever they give to you, like draw the steps. But pay attention, it's a start with a nine, number three. Yeah, not a start with one. So from three to nine, so you need to find how many jumps. This is very important. I think you are all really pay attention to the details. So that's why you made all the students who answered made the correct answer. Very good. So let's see the next question. Oh, this question may be a little harder for you. You have to understand. They give you the picture here. You can see this is a sign. Have you ever seen the sign on the road? They give you a direction, where to go, how far to go there. So here they show the distance between the villages. You can see the four villages. You may have a Bahaisti, Mangaisti to the left and Sarapasti, Mangaisti to the right. So they ask how far is it from Bahaisti to Mangaisti? I believe you have this one on your hand out. Yeah, we can open the poll for this one. I think they have the picture on the handout. So what is a distance? Distance is how far between the two locations, two places. This is a three-point question, Elita, but I think this one is not that easy for three-point, yeah? I agree, this one seems pretty hard for question number eight. Yeah. This one is harder than the one with the dancers in pairs. Yeah, I agree with you. Okay, any more answers? We are going to share the result. Yes. So you can see most of you select the correct answer. Congratulations. We will go through this question. So first, when you see the picture here, they ask, what's the distance? The Bahá'ístí to Mahá'ístí. It's here to here. And you would consider those two places, it's on a different direction, not the same direction. It's a different direction. So when you draw your picture, so you need to draw the midpoint by the sign, and you go right five kilometers to Mahá'ístí, and four kilometers to Bahá'ístí. And then you would see how far between those two villages. You have to add the two numbers together. Is that right? If we want to ask you, how far between Sarapasti and Mahá'ístí? They go to the same direction. So you need to pay attention. When you do this way, so you would see here, where is Sarapasti? Here. Yeah, so you would see what's the difference here. You would figure out the difference here, the distance. So if you go the same direction, you have to use a subtraction. Five minus two, you get three. But here in the question, they ask you the two villages on a different direction. So you have to add all the distance to the midpoint, to the sign. So that would be the right answer. Good job. Okay, Elita. Yeah, please go ahead. The clowns at a circus are standing one behind another. So they're all in a line. Vivi said to Bibi, who was standing behind him, behind me, four co-workers are standing. Bibi answered, in front of me, only three co-workers are standing. How many clowns are standing in a line? I think for this one it's really important to draw a picture and to know that Vivi is in front of Bibi. So pay attention when you read the problem, what they are looking for, what condition they gave to you. So remember what they ask for, and then you check the conditions they give to you. So you always pay attention to the hidden information in the question. What's a hidden information here? So you have to figure it out. Otherwise, that would lead you to the wrong answer. Usually for the four-point question, it would use two to three minutes to solve. Yeah, let's share the result. Okay, Elita, I think you needed to explain this question. Yeah, it looks like a lot of people were a little bit confused. The correct answer was B, seven clowns. But let's see why. So we can see that Vivi is in front of Bibi, because it says Bibi is standing behind Vivi. And then Vivi says, behind me, four co-workers are standing. So there are four people behind Vivi, but that includes Bibi. And then Bibi says, in front of me, only three co-workers are standing. So we can see here, Vivi is in front of Bibi. The clowns in front are to the left, and the clowns behind are to the right. So we can see the four clowns behind Vivi, but Bibi is one of them. So you have to keep that in mind. I think a lot of you probably thought it was the other way around, and Bibi was in front of Vivi. And then in front of Bibi, we can see there are three clowns, but that includes Vivi. So we can just count three plus four, and we get seven, which is the correct answer. For this one, I think if you tried to do it in your head, you probably would have had a much harder time, because it's hard to visualize that. So definitely draw this one out. Yeah, thank you, Elita. Yeah, I think this question, once you see the drawing, it's very clear why you pick seven. You pick nine, you double count. You count Vivi twice, count Bibi twice. So this is the correct answer. Okay, so let's see the next question. Certain children are played hide-and-seek. Oh, this is a very popular game. One of them is a seeker. After a while, nine children have been found. How many children are still hiding? Please just draw something simple. Yeah. You draw the 13 Ks. Yeah, you just use a line or use a circle. So that's easy. Yeah. You do not need to draw the whole figure for each K. Okay, let's share the result. Good job. Most of you got it correct. Very nice. So let's quickly go through the solution. So here we still underline or highlight the keywords and you would see what's the main part of the problem. So here they said 13 Ks play hide and seek. So if you draw them out, you have to specify one K is seeker and the rest Ks, they are all hider. And then what they ask for, they didn't ask you how many children are still playing. They ask you how many children are still hiding. So that means what? If a 13 Ks minus nine Ks already been found, you have four Ks left over. So you need to take off the seeker. So there are only three Ks, they are hiders. So that's why. Yeah, most of you got it correct. Very nice. Okay, I see the question eight. This is a harder question, five point question. Yeah, Elita, yeah. Simon has two identical aquariums. There are 26 quarts of water in one and 42 quarts of water in the other. How many quarts of water does Simon need to pour from the second aquarium to the first in order to have the same amount of water in both? So you have to understand what's identical. Identical means exactly the same. Oh, we can launch the poll for this one, yeah. So this is a five point question. During the competition, sometimes you might need two to four minutes or even longer, but make sure when you do the question, do not stop on one question during the competition. Now you have some questions later, you'll need to move on to work all the questions. So this one drawing a picture could be really helpful. Yeah, you could draw two containers. Yeah, it's the same, but they have a different amount of water inside. You want to make the same amount in both containers. So you pour from the one with more water to the container with less water, but you have to make they have same amount water. If you have any question, please just send it in the chat. We try to answer you. We do not have a question answer during the session. This is a recording session. So we have to protect every kid's privacy. So we do not let you speak or make you keep your video on during the lesson. Send us chat. OK, so let's share the result. It looks like you guys did pretty good on this one. Most people chose D, which was the correct answer. So how did we get here? We can see that on the left side, there's 26 quarts of water in that container. And on the right side, there's 42 quarts of water. Obviously, the container with 42 quarts is at a higher level because it has more water in it. So what we want to do is we want to take the difference between the two quarts and move one half of that into the other quart. So first, we find the difference, that's 16 quarts, and then we divide that by 2, so 8 quarts. So if we move 8 from the right container into the left container, they will both have 34 quarts, which you can check by adding 26 and 8 and then subtracting 8 from 42. Yeah, so you cannot pour the difference of the water to another container. So you switch the place for the two containers. So in the beginning, you have 26, and the second one has 42. If you pour 16 from the second one to the first one, the first one will get 42. The second one will reduce to 26. You still don't have the same amount. So you have to divide the actual water into the equal amounts, and you pour the half of the actual amount to another one. So that makes the equal amount. And later, you'll check your answer. Make sure you check your answer. Even you do the 16, once you check your answer, you will feel, oh, this is not the correct answer. So that's why we always mention, after you finish the question, after you get the solution, please check it before you move on. I have another way to solve that question. Yeah, please feel free to share. So because we're not adding in any water, we can combine the total amount of water and then divide that into two, because we know the two containers have to have equal amounts. So what I would do is I would add 26 and 42 together to get the total amount of water. And that should give us 68. And then because both containers should have an equal amount of water, we can divide 68 by 2 to get 34. But it's not asking for how much water is in the container. It's asking for how much we have to add to get 34. So then we would have to do 34 minus 26. Thank you, Elita. Yeah, this is another way. So you see, there are so many different approaches to help you to solve the problem. So you can solve the problem in one way and check with another way. Thank you for sharing. Let's see the next question. Mara is putting up a tent for family reunion. The tent is 16 feet by 5 feet. Each four-foot section of the tent needs a post except the size that are 5 feet. How many posts will she need? So you have to draw this picture, yeah? Yeah, so how the tent look like. It's 16 by 5. You can imagine the shape. And they put the post only on the longer side, not the shorter side. That's already mentioned. Yeah, let's open the poll. This is a rectangular shape, is that right? We want to know what shape this one looks like. So for any question you do not really get it well during the class, later you can visit the recording and you can just take as much time as you want to solve the problem with recording. So let's share the result. So the correct answer would be D. So how it works. So I see you might not get a really understanding about this question. So let's take a look. So you always meet some challenging question, even you read a while two time or three times questions still do not really get it. So here they talk about the tent, you can imagine, this is a rectangle shape. This is a rectangle shape. Yeah, it's a 16 feet by five feet. They mentioned they put the post on the longer side. So that means the both 16 feet side, you will put a post, not at a five feet side. And every four feet, you have that post. But remember, I know some of you pick the answer. It's a B, eight. So remember, when you put the post. So they means every four, every four feet. If you have four feet long, you need how many posts, not one post, you need a two post. Is that right? So if you have a formal foot, feet, you need another post. So you can imagine if you have a 16 feet, even you have a four parts of four feet, but you'll need a five post. Yeah, you do not just need a four posts. Yeah, so you can see the picture very clearly. Yeah. If you draw, you do not need to draw such a fancy picture. You just draw the rectangle shape and draw the line over there. So that would help you to solve the problem. So the correct answer would be D, that's 10. You can see on each side, you have five. If you have 12 feet long, you need a four. If you have 20 feet long, even you have five parts of the four feet, you need one more post, six posts. Yeah, more than the parts. So this is a very tricky question. Yeah, not easy. Yeah. Okay, let's see the next question, Elita. A frog is at the bottom of a 10 meter well. Every day he climbs up three meters. Each night he slides down one meter. On what day will he reach the top of the well and escape? So this one, pay attention. Yeah, you climb up three, drop down one. Yeah. So you might check each day, yeah, so that would get a more accurate answer. Right, so after the first day, how many meters would he apply? After the second day, and so on. Yeah. You might think there is a faster way to solve this problem. That's correct, but that's not always applied to all the conditions. Please remember, when you draw the picture, just draw something very simple. So you just draw the lines. So you do not need to draw a very fancy picture, it will take you too much time. We will share the recording after the class, so everyone could visit that link and you will see all the slides in the recording. Okay, I think I will end the. Yeah, yes. Share the result. So you can see most people chose five, which is the correct answer. So we can see the frog on day one, he goes up to three meters, then drops down one meter, leaving him at a height of two meters. On day two, he does the same thing, up three to five, but he slides down to four. On day three, he gets to six meters. On day four, he gets to eight meters. And then finally, on day five, he can climb outside of the well, because eight plus three is greater than 10. So good job, everybody, on getting, well, most people, on getting this one right. Yeah, thank you. So I think some students might use, oh, every day, we climb up three, and we slide down one. So every day, you gain two meters. So use 10 divided by two, you get five days. So this is correct for this question. But if we change the number, we give you another question. Like if the well is five meters deep, and the frog climb two, and slide down one every day. So if you want to use the same method to solve the problem, you got the wrong answer. So we recommend you to check each day. So make sure you get the correct answer. Okay, let's see the next question. A dragon has three heads. Every time a hero cuts off one head, three new heads grow. The hero cuts one head off, and then he cuts one head off again. How many heads does the dragon have? please read the question carefully. So what, what hero did and what he, what he gets? So here they said a dragon has a three head. Yeah, so at the beginning you have three heads. So the hero would cut off the head of the dragon. He cut one of the head. But the dragon will grow three new heads. And then the hero cut one head off again. So they ask at this moment how many heads that the dragon have. I will go ahead and share the results. Yeah, thank you. So most of you got the correct answer. That's D, seven. Let's see the solution here. So here you could see the three heads of dragon. If you cut one, you get two more. You will lead to five. Is that right? Yeah, you minus one got two and add three new head, get five. And the next one, you continue the same action. And you cut off one head from the five heads. You got four left, but you need to add three more new heads. So you get seven. So this is the correct answer. So the wording might be confusing. So you need to read more times to understand. Also, underline the keywords would help you to understand the problem. Okay, let's see the next question. In a class, there are 20 students, eight of whom are boys. At how many desks do the girls sit, if two girls sit at each desk? So for this one, it's also important to make sure you know what the question is asking. So please pay attention, make sure what question you're asking for. Sometimes you might need to read two times or three times of the question to help you understand more about the problem. they look for how many desks, is that right? Pay attention to the keyword. Okay. Yeah. So you can see most people did get C, six, which is the correct answer. So our first step should be finding how many girls there are because we're asked about the desks the girls sit at. So we do 20 minus eight, which gives us 12 girls, but that's not what the question is asking for. The question is asking how many desks the girls sit at. So two per desks. So you can see each triangle represents a girl. If we group two of them together, we see we get six groups, so six desks. So the girls will sit at six desks. Yeah. They didn't ask for how many girls, they ask how many desks, and also tell you two girls sit at each desk. So this is a very important. You have to read all the details of the problem. Thank you, Elita. I think this is a good question. We already done for today. So we still continue reinforce the four-step method. You see is how important you understand the problem first, and then you can try to solve the problem. Please remember these four steps and try to practice when you do some more questions. If you practice more with the four-step method, you will get much more help later. So today we learned the drawing picture, and you would remember. So drawing picture would help you to illustrate the question. Even some question has picture already, has picture, you still can draw more details on the picture to help you to understand question to solve the problem. If the question does not have picture, so you can draw on your own, but please draw something simple, easy. Do not take you too much time. And also pay attention to draw to skill according the description. So this is today's lesson. Thank you everyone for coming. Thank you, Elita. I hope to see you all come back next week. Bye-bye.

Math Kangaroo

problem-solving

critical thinking

visualization

four-step method

multiple-choice questions

drawing tool

geometry

logical reasoning

structured methodology