Yeah, we will start the class on time, and this is a recorded session. We will share with you the recording shortly after each lesson. So if you join late, so you can later check the recording. First, I want to introduce Alex and myself to you. So we will be the teacher for this webinar session. This is set to be in level three and level four, for the level three and level four. We also have a set A webinar in last fall. So this lesson would be advanced level in advanced level class. So if you feel a little challenging, so please maybe take more time to watch back our recording and to get more understanding. And also in the class, I would like to tell you, because we introduce different strategies, so we would like to start with some easy questions. So not every question hard, but we would have an easy question and a hard question mixed together. So my name is Lucia. I have been the Mastcam group, the test center manager for over 10 years, and also teach math around 10 years. So I really enjoy to learn math with a lot of passionate students. In the past 10 years, I see a lot of students join the Mastcam group competition, and they told me they really like this competition, and they really like the questions showing in the Mastcam group. And they found the question really helpful to foster their math foundation. And Mastcam group really focus on the problem solving and critical thinking. So this is a very helpful session, I hope could help you to advance in the March competition. Yeah. Alex, would you like to introduce yourself? Yeah. Hi, everybody. My name is Alex. I am a junior in high school. I'm from Illinois. I'm super excited to get to work with you guys, and I can't wait to see what you guys can do. So I'll turn it back over to Lucia, and we can get started. Yeah. Thank you, Alex. So first, I would like to tell you, in this session, this is a webinar. So we will have everybody camera off and a microphone muted. So there is no interaction for this lesson, but we will use a poll to collect your answer. And after each answer collected, we will share the result, and we will go through the solution with you. So please make sure you know how to use the poll. If you couldn't know, maybe after the session today, please learn how to use the poll. Yeah. So the recording will be shared shortly after class. Yeah. So this is a 10-lesson session. So each lesson, we will focus on one topic. For the first lesson, we will have an introduction one. There we will have the very popular types question in this level we will share with you. Like I mentioned, we start with easy question, but we would like you to experience what type of question, what kind of strategy we would use to solve those questions. And the rest of the lessons, we will focus on the specific strategies to work on. Before we start our lesson, I would like to introduce a four-step problem-solving strategy. So this is a method could help you to solve some questions, not that one step, you know, the easy question. For the harder question, in the Mexican kangaroo competition, we have three level questions, three point, four point, five point. The 24 questions you need to complete in 75 minutes. So you need to manage your time wisely, and you need to make sure you solve each question correctly so you can get a better score. So for the four-step problem-solving strategy could help you to solve the hardest questions. It's very easy to understand four steps, step one, step two, step three, step four. The first, you need to understand the question and you understand what the question ask for. So all the information in the question, you should go through, do not miss anything. There are some hidden information in the question. If you miss, you might make the wrong choice. Once you understand the question, the next step, you would plan how to solve the problem. So you pick the strategy we learned in the lessons. So maybe sometimes you plan one strategy to solve or more strategy to solve. So the second step, you pick the strategy to help you solve the problem. And the third step, you will apply all the strategies you picked to solve the problem step by step. You will write down the solution step by step, and then you can find your answer. But once you got the answer, you cannot just move on. You need the fourth step. You need to check your answer. You either put back your answer to the question to check if all the conditions apply, or you can use other approaches to do a question again to see if the two answers are the same. So you have different way to check your answer, but please check your answer. And there is one thing we need to mention. If you meet a very hard question during the test, do not stuck on the question. If you spend too much time, you need to move on. You need the time to complete the rest of questions, and then you come back to solve that question. If finally you cannot solve the problem, you might use a guess and check. So use guess to guess the answer. Don't leave the answer blank. So this is another thing we want to tell you before we start the lesson, yeah. So now we're going to work on the questions. So Alex, would you like to read through the question? Okay, so our first question is, at noon, the minute hand of a clock is in the position shown at the picture on the right. So I don't think my mouse shows up, but it's a picture on the right, past to the right of the letter E, right? What will the position of the minute hand be after 17 quarters of an hour passed? Okay. So we give you, this is a question two, yeah, yeah. So before we do this question, we might test if you could do the poll, yeah. So let's, I will launch one question, so you can answer this question. Can you see this question, answer it, and later we will work on this question. Have you participated in the Mass Canberra competition before? I see some of you couldn't, didn't, haven't completed the poll, yeah. So let's wait for a few seconds, make sure everybody could use the poll. We have four more, four more students haven't submitted their choice, four more students, or three more, I think three more, okay, maybe one more, yeah, so now we can make sure most of you could use the poll, yeah, very nice, good job, yeah. So we about, this is the result, half, half, half of you already joined the competition, I will share this, yeah, share the result, yeah, here, you can see the result, yeah. So half of you have joined the competition before, good job, yeah, half of you haven't yet, yeah, so you will experience what the question look like, yeah. Okay, so next one, yeah, maybe ask one more question. Okay, most of you. Yeah, I think a few of you might miss the deadline for the competition. I want to give you some update. So the Mexican group receive a lot of requests from students who haven't got a chance to register for 2024 competition. So they just opened some state remote virtual centers with proctors. So you can try to if you want to join this year, so you can search a website, Mexican website to find the state remote, so you will get the rank and award, like the, you know, the regular in person center. So this is a state remote remote, we just open, so you can check the registration will open until March 1, but you will do online. Thank you for sharing. Yeah, okay. So next, we will do this question now. Yeah. So now you can work on this question. This is a three point question. So usually, I hope you can complete this question in one or two minutes. Yeah, not too long. So in this session, we wouldn't have interaction. Yeah. So remember the question, once I launch the poll, you might not see the question. So Alex reminded me the time. So maybe we can launch the poll. Okay, very good. So if you haven't submitted your answer, please submit your answer now. We're going to close the poll. Okay, let me share the result now. So you can see the result. So the most of you pick A and some of you pick B, C, D, E. Yeah. Alex, would you like to go through the solution for this question? Sure. All right. So the question asks us, right, what will the clock show after 17 quarters of an hour, right? So one thing that we can notice, right, there's, I think there's two ways that you can do this. The first way you could do it is you could count around 17 quarters of the hour, right? But a better way to do this would be, you can realize that 17 quarters of an hour is four hours and then one more quarter of an hour, right? So if you realize that, you know that four hours will get you back towards the top of the clock where it started. And then one extra quarter of an hour will leave you with answer choice A, which is the correct answer choice here. Yeah. So A is the right answer. Most of you got the right answer. Good job. Yeah. Next question. Yeah. Alex, could you read through the question? So our second question is, Jack drew a point on this piece of paper. Next, he drew four different straight lines going through that point. And so the question is, into how many pieces did these lines divide the paper? Okay. So this also three-point question. So we give you one or two minute, no more than two minutes to solve this question. So this is strategy we use to draw a picture. So that means you draw on the sketch paper to solve this problem. That would help you. Okay, most of you already submitted your answer, so I would share the result. You can see the most answer would be D, 8. And we have quite a few students selected A, 4, and some selected 5 and 12. So the right answer would be D here. So for this question, I know some students, you might get confused about the line, what the line would be. So you need to remember the definition for the line and for the read that's different. So for this horizontal line, we appear here. This is a one line, this is not a two line. Some students, you pick four, you might consider this line as two lines. You know the line, you should have infinity on the both directions. So that means you do not have any point started in the middle. So this is the horizontal line would be the one line, not two lines. So the read, you only infinitely extend to one direction and you start with one point. We talk about the read here would be two reads, but for the line, it's only one line. So you need to make sure when you draw the lines, you need to draw maybe one horizontal, one vertical, and two diagonals. So that's four lines. So that would make eight work. So you need to make sure what's the line, the definition of the line. The line would be infinity lines to the two directions. Okay. So next question, yeah, make an organized list. Alex, would you like to go through this question, read through? Yep. So this question is a three digit code is needed to open a safe. How many possible codes are there if it is known that only three numbers, one, three, and five are using this code and each of them is only used once. So this is also three point question. So maybe not very hard for you, but we want to introduce, make organized list here. So you give up the options. So make sure how you order your numbers. So what is organized list? Do you want to write your number randomly or you make some orders? Yeah. Okay, I think we'll go ahead and launch the poll now so that you guys can enter your answers. Okay, it looks like most of everybody has entered their answers. And so most of you do have the correct answer, which is E, six, but some of you have put five, four, three, and two. So we'll go over this question so that we can all try to learn from it. Yeah. Go ahead, Alex. Let's see if I can annotate here, hold on. So the organized list that we can create, right, is we can order this by what number we use first, right? So the first two numbers here, one, three, five, and one, five, three, use one first. After that, we know that we can either have three second or five seconds. So now your two choices are to put three second or five second, and then the last number is whichever one you didn't use already. The same thing can be done for three and five, which in total gives us six different answers that you can choose from. Yeah. So make organized list, that's very helpful. So you do not want to put everything randomly. You can imagine if there is a list of students in the school, 400, 500 students, you put the name together, you want to make organized list, you do not want to put everything randomly. So that's why. So this is a very helpful. Later, we will have one session, we'll work on this, the specific type questions. Okay, so next, it would be making a table. So this is maybe a hard one. If you have never making table before, Alex, would you like to read us through this question? Yep. So our fourth question is, Eva lives with her parents, her brother, one dog, two cats, two parrots, and four fish. What is the total number of legs that they have all together? So we will try to make a table like a chart, if you have ever seen a chart. So you will have columns, you will have rows. How you make for this question? You can make an easy table, not a very complicated one. So Alex, we give a little more time for them to draw. So they might need to need time to make a table, yeah. Okay, I think we're going to end the poll there so that we can keep on moving. Yeah, so let's share the result. Yeah, so here most of you picked the 24, yeah, 24 legs. So have you ever made a table or you just count them? So let's share the result with you. Yeah. So here 24 is the right answer. So we see the majority make the right answer. Some of you picked 22. So you might count them wrong or you list them wrong. So here, look at the table here. This is an easy question. Yeah, so it's not very hard. Even if you do not need a table, you can just solve the question very easily. But here we want you to experience the different strategy to solve the problem. Use a table. They can list all the information very clear. They can help you to analyze the information. So that's why we want to learn this strategy and make a table. We will have the lesson ahead. So here you would see if you want to make a table. So you can list all the different parties in the question. So Eva, how many legs? Mom, dad, brother, and a dog. But remember, two cats here. So you have to make sure you count two cats and two parrots here. And for fish, so for fish, fish has no legs. So this would be zero. So then you would do the right calculation. You found 24 is the answer. So the table is not very easy to make at the beginning if you've never practiced before. So I would like you for any question, you see a lot of information there. So you might try to make your table and try to practice more. So Alex, do you remember when you started to use tables to solve the problem? Do you remember? Yeah, so I think I started using tables pretty early because I feel like they're a very good way to organize information, especially this type of question, like Lucia said, where there's a lot of things going on, right? Because you have one, two, three, four, five, six, seven, you have eight different columns in this table, but a table allows you to organize it very easily. Whereas if you just kind of write it down and try to scramble everything together, you might miss something. So I would say that I probably started using tables, you know, probably second or third grade around the time that you guys are at right now. Okay, very nice. Thank you. Thank you for sharing, Alex. Yeah. Okay, we will have a lesson for making table. Yeah. Okay, so let's go next question. Okay, Alex. Yeah. Okay. Our next question is Adam spent five days preparing for a test. The first day he solved one problem, and on each consecutive day, he solved twice as many problems as the day before. How many problems did Adam solve altogether preparing for the test? And by the way, we will be starting the polls a little bit earlier just so that we can get through all the questions. So just make sure that you have the question written down or that you know what it is so that the poll doesn't cover it up. It looks like most of you have an answer entered. The correct answer on this question is, as we've now shared the poll, the correct answer is C, which is 31, but a lot of you did put B and A, which are 15 and 16, and a couple of you put 33 and 63 as well. So let's go over this one. What we can look at, right, is we know he spent five days preparing for a test, and we know that each day he solved twice as many problems as the day before, so what we can do is we can write out how many problems that Adam solved on each day. Right, so on the first day, as it shows in the table, he will have solved one problem. That means that on the next day he'll solve two, the third day he'll solve four, the fourth day he'll solve eight, and the last day he will solve 16. Knowing all that, all we have to do now to figure out how many problems he's solved all together is just add those together, and we end up with the answer of 31. Yeah. Thank you, Alex. So patterns is very popular. So patterns everywhere. So around you, even today, we are, you know, Sunday, we have a webinar, and the next Sunday we have webinar again. So you will see the seven days a week, that's repeating pattern, and the pattern has a lot of different types, not only repeating the patterns, and we would explore more different type of patterns together, and also the rule. So you find the rule, you know what's coming next, you would find the pattern. So that way we'll have the lesson ahead. Let's go to the next question. Okay, so this question, yeah, Alex, would you like to read through this question? So for this question, we have the number 325, and about that number, five boys said, from Andy, we know that this is a three-digit number, from Charlie, the sum of the digits is 10, from Eddie, oh, I'm sorry, I should read this in a different order, from Andy, this is a three-digit number, from Barry, all the digits are different, from Charlie, the sum of the digits is 10, from Danny, the ones digit is five, and from Eddie, all the digits are odd. The question is, which one of these boys was wrong? So this is a guess and a check. So guess and check always say, oh, you do not know the answer, you just guess one answer, and then you check your answer, if it's right. If it's wrong, you make a next guess, and you check again. So this is a guess and a check. This question, not very hard, but we just want you to experience what is a guess and a check. So it looks like most of us have our answers in the poll. Yeah, so most of you picked the right answer, yeah? So here, this is not a very hard question. Yeah, we just want to show you how to do the guess and check. So when you check the first one, if you think, oh, Andy is right, is the person who said wrong. So you just think, you just check, oh, Andy said a 3-digit number. So is this a 3-digit number? Three to five, absolutely, it's a 3-digit number. So this is right. So Andy said the truth. So he's not wrong. So that's not the answer. And then you check the next one, Barry. So that's very easy. You also check all the digits different. That's also right. Yeah, he said truth too. And Charlie also said truth, and Danny also said truth. And the last one, Eddie, said all the digits odd, so that's not right. So you would figure out there's one digit that's an even number, even. Yeah, so that's wrong here. So you would find that E is wrong, if the person who said wrong. So this is a guess and a check. This is an easy question, yeah? So later in the test or in the practice, you will have a lot of questions. It's pretty hard with guess and check. Now let's see the next type of question. That's experimenting and acting out. So Alex. Yeah, so question seven is, 13 children are playing hide and seek. One of them is a seeker and the others hide. After a while, nine children have been found. So how many children are there still hiding? Okay, so we can share the answer now, yeah? So most of you picked the three, yeah? Okay. Let's stop sharing. Yeah, Alex, would you like to go through this question? Oh, you muted, Alex. Yeah, sorry. So three is the correct answer here. The only answer choices that anybody picked here were three or four. So let's just go over this real quick. The thing to remember is that one of the children is a seeker, which means that there's only 12 children hiding. So that means if nine of the children are found, there are three hiders that are left because that 12 minus nine will give you three. The thing to remember is that there is that one seeker, which means that there's only 12 children hiding and not 13. Yeah, so three is the answer. If they change the question, if they ask you how many students, how many children are still playing? So the answer would be B. So you have to pay attention to what question ask for. So the last question, I think we didn't turn off the poll. So we blank this page. So I just show you, go back to show you. So for this guess and check one. So we check each statement and then we figure out which statement is the answer. So this is a check each one, yeah. So we just talk about the question, but we have poll showed up. So we didn't show you this solution page. So that's why I go back, yeah. Okay, let's see the next one. Working backwards, yeah, Alex. Yep, so this question says that there were some birds sitting on a telegraph wire. After a while, five of them flew away and after some time, three of the birds came back. At that time, there were now 12 birds sitting on the wire. So the question is, how many of the birds, excuse me, how many birds were there at the very beginning? So this is a working backwards. So you might need to figure out how to work backwards. What do you should start with? For a few more students, would you like to submit your answer? Yeah, we have most of you answer the question now. Let's share the result, yeah? So most of you pick 14. Yeah, so this is the right answer. Good job, yeah. But some of you pick a different answer. So let's go through the solution to look what happened. So this is a work backwards. What's work backwards? Work backwards, that's some question. They do not give you the start information. They told you some birds sitting on the telegraph wire. And then there are some different actions. The first action, so the five flew away. So if you go forward, you will minus five here, yeah? So, and then there's after this, this is the first action, if you go forward. And a second action. So there's after some time, three birds come back. So this is a second action. And then we lead to the result, five birds, finally. So you'll need to figure out how to work backwards. When you work backwards, you will reverse order. You will start with the result. So that's why you see the solution. We can see the five birds, we started. And then you can see the green line. We reverse all the actions. So first, we will reverse the second action. So the three birds come back. But when we reverse, we need to take out that three birds. We need to minus three. And then we got numbers. We needed to reverse the first action. The first action, that's a five flew away. So you need to add back that five. And finally, you got 14. So this is the work backwards. So these questions are not very hard question. Because we want to introduce you all the different type, we would work on the next lessons. So we pick some easy question for you. So you just need to get an idea about what kind of those question would be, yeah. Okay, next one, logical reasoning. Yep, so for this question, we have a tour bus that can seat no more than 55 people. What is the smallest number of buses needed to seat 160 people? Yeah, this is not very hard question. But here, we talk about the logical reasoning. So what's the logical part here? Okay, some more. Some more answers. We still have some students having a sub-media answer. Yeah, very good. Yeah, let's share the result. So most of you pick the three. Yeah, this is not a hard question for sure. Yeah. Okay. So Alex, would you like to go through this one? Yep. So for this question, right, we know that a tour bus seats, 55 people, right? So one tour bus is going to see 55 people, two are going to seat 110 people. And then three is going to seat 165 people, right? We need, we know, I'm sorry. We need to know the smallest number of buses needed to see 160 people. And since three tour buses can see 165 people, that's going to be the smallest number that can see all those people. So three is our correct answer. Yeah. Thank you. So this one, the logical part here, that's how many people you need to put on one bus to make the last bus we can use. So you can imagine if you put only 10 people on one bus, you need more buses. So that's why the logical part here, that's every bus in the beginning, you have to make the capacity, you have to make the bus full, and then you will use the less buses. So this is a logical part. And later, we will have some more logical questions, it would be much harder. So let's see the last type of today's question. Yeah. Yeah, Alex. Yep. So this question is a geometry problem. And it reads out of how many blocks is the tower on the right built? Any more answers? Yeah, let's share the result for this one. We have most of you pick D. That's right answer. Good job. And some of you pick C or E. So let's check out together. So what, how we count those blocks here. For this one, the geometry part, they always involve the special thinking. Especially for the 3D shapes. So you need to consider how would you count. For this shape, you actually can separate the different wins. You can see we have four wins on the side and we have a middle pole over there. For the four wins, you would see each win would have a six, the cubes. So you would have six times four and then you would have a middle pole. The middle pole will have four over there. Some blocks are hidden. You cannot see them, but you can use your special thinking to imagine what the blocks are hidden under the other blocks. So here we would get four times six and the plus four. You would get a 28. If you got 25 or 30, so you might miss something or you over count something. So the special thinking, so that's very, we will have a lot of question during the real test. So this is a big part in the computation. So now we complete all the type of question we want to introduce you today. So first, the four-step method. Do you remember those four steps? So I would like you to practice these four steps when you try to solve some harder questions. And also remember there are some main math, the major math concepts in this level, like the number systems, like visual thinking, special thinking, time clock and geometry. So we still have some time left over. So we will do some bonus question together. So those questions would be a little harder. Like before we only do some three point question, but next one, we will do some five point question instead. Yeah, so Alex, would you like to read through this question? Yep, so for this question, Johnny builds a house made out of cards. In the pictures such as one story, two story or three story houses are shown. How many cards does Johnny need to build a four story house? Yeah, this is why you need, maybe need a little more time. This is a number 18, that's a five point question. For this question, we do not tell you what the type is it, not like the previous practice. So you need to identify what kind of problem and what strategy you might use to solve. So that's problem solving you need to involve here. So let's give maybe two minutes for this question to solve, Alex. Yeah. For the real computation, I just sometimes I manage the time for the computation for all the kind of question. So for the three point question, so maybe one to two minute, you complete. For the four point question, maybe two to three minutes, you complete. And for the five point question, maybe three to five minutes, you complete. So this is a range I give it to you. So you would manage your time during the test. So for different hard questions, so hard in these questions, you can arrange your time. All right, we'll give you plenty more time, but we'll launch the poll for anybody who wants to enter their answer. Yeah, most of you submitted your answer. We have 70% submitted so far. Yeah. Once we reach 85% submission, we can go through this question. Yeah. So, oh, good. So I would recommend you, if you do not really know the answer, you can make a guess. In the Mexican Google competition, there is no guessing penalty. So do not leave answer blank. So we are going to close the poll. Yeah. Make your guess. Maybe you are wrong, but maybe you are right. Okay. So let's end the poll. So look at the result. So there is almost a half of you pick the answer, 26. That's the right answer. Yeah. And some of you pick a different answer. Yeah. Let's check the solution. Alex, would you like to go through this solution? Sure. So, again, this might go back to what we discussed earlier in finding patterns, right? This is just a little bit more of a difficult pattern to find. So we see that for the one-story house, we need two cards, right? That means that for the two-story house, we need two cards for the first floor, and then five for the second floor. In the three-story house, we see that we need two cards for the first floor, five cards for the second floor, and eight cards for the third floor. So what we can see is that with each additional floor that we add on, we need three more cards to add on that floor. So when we go to the four-story house, we'll need two cards for the first floor, five cards for the second floor, eight for the third floor, and then 11 for the fourth floor. Adding that together, we'll get 26 cards in total. So that's our correct answer. Yeah. So finding pattern is very helpful. So something you cannot... Here, they only ask you for the four-story. If they ask you for the 100-story house, can you draw every card out? You cannot. Is that right, Alex? So if they ask you 100 stories, so you need the pattern to help you to make a quick solution. You can calculate quickly, yeah, once you figure out the rule here. The rule here is add three for each level, and that's very easy for you to figure out the answer. Yeah. We still have time, so maybe we can work on one more bonus question. Yeah. Let's do this one, also five-point question. Yeah, Alex. So our final question is, a conductor wanted to make a trio consisting of a violinist, a pianist, and a drummer. He had to choose from one of two violinists, one of two pianists, and one of two drummers. He decided to try each of the possible trios. So how many attempts did he have to make in total? So first, identify what kind of problem this one. So what strategy you would like to apply for? So this is one strategy we already go through in the previous I'm going to launch the poll for anybody who wants to enter their answer, but feel free to take your time. We'll give you plenty of time to keep working on this question. So it's better you write down the solution, yeah, that would help you to find your answer. Okay, let's go through the result for this one, yeah. Some more, I saw some more, some more students are still submitting the answer, yeah. Okay, so. Okay, at this moment, most of you pick six. And some, the second answer, second, you know, most of the students pick the answer. Would it be the B, eight? So we also have four, five, 10 be picked here. So which is the right answer? So let's go through this question. So this one, they gave you what? They gave you the six players in total. You would have three kind of players, yeah. So this would be the make organized list. So if you could make organized list, that would be very helpful for you to solve this problem. So here you have a violin one, you have a violin two. You also have a piano one and a piano two. You have a drummer one and a drummer two. So there are six players and you want to make the trials. So that's a three different instrument come together. So the first one, if you want to make, you can just start it with violin one. So violin one, you could work with a piano one, a drum one, piano two, a drum two. So you would see what's the combination here. So first you can go with violin one with piano one, and then you would leave two choices. So violin one, piano one only can come with a drum one and drum two. So you make this two combination. And this is the one you want to choose. That's a different, different combo. Yeah, different combination here. And the next one, you would change, still keep violin one and you change it to piano two. So once you have violin one, piano two combination, you also can match with drum one and drum two. You make two more combinations. So now you come, you finish, complete the violin one because violin one already matched with all the other players. So now you have to introduce violin two. So violin two will go through the same combination as violin one. So then you list all them out. So you will figure out eight is the right answer. So here, you know, the make organized list, like a five point question would be a much harder than the practice we did before. So, but all the strategies, you know, we will learn in the next lessons. So the next lesson we will learn patterns. So I hope you all print the handout in the shared folder and that today's recording will be shared with you shortly after. Thank you, Alex. And thank you everyone for joining today's webinar and see you next week. Have a good day. Bye bye. Bye everyone. Thank you, Alex.

advanced math

problem-solving strategies

level three and four students

Mastcam group competition

four-step strategy

organized lists

pattern recognition

real-time practice

critical thinking

webinar