Hello, everyone. Welcome to Mexican Group Level 1 and 2 webinar. Today, we are going to learn make an organized list or a table. This is a hard lesson. If you have never done this kind of strategy before, you might need some time to practice and to learn more how to make the organized list and table. And we will share with you the recording. So no worries. After the class, you still can catch up with some questions if you do not understand in the class. Elita, we have some new students every week. So just quickly go through the ground rules. OK, so you guys have to join the Zoom meeting with video off and voice muted for the whole session to protect your privacy. All the lessons are recorded, and the link will be shared after the session. So feel free to go back and review if you missed anything. This is a webinar, so there's large group classes with less interaction. We'll try and slow down when we think it's necessary, and we'll also let you guys use the poll to answer so we can see how you guys are doing. You guys can't speak, but if you have any questions, please feel free to chat me, or you can just send it in the general chat, and I'll do my best to answer them. And then lastly, the student handouts are in the folder. Those are very helpful sometimes. So please print them out and have them prepared. Thank you, Elita. And also, I want to mention, we know this is a younger student. Sometimes the parents would stay with the students in the whole class. But please do not have your students answer the question. We need to know the real student's performance. If parents help, we would know, oh, this class, they are really advanced. We will go faster. So please, let the students just solve the problem on their own. OK, so the first thing, we always want to reinforce the four-step method. This one, we would apply to the harder questions. In the Mexican group competition, we have a three-point section, four-point and five-point. So we really recommend you to use this one for the four-point questions and the five-point questions. So the step one is very easy to understand. You need to read the question carefully, check the picture carefully, and then understand what question talk about. And then you will ask yourself, what is the question ask about? What you should answer for? Do not answer the wrong question. This is very important. And step two, you would identify what type of question this one would be. And then you will make your plan. You might figure out, oh, this is a pattern problem. I will try to find the rule to solve it. Oh, this problem, it's just wording. I need to draw a picture. Help me to solve the problem. So any other, like work backwards, guess and check. And today, we're going to learn the make, organize list, and the table. So those all can help you to solve the problem. So you will make your plan how to solve this problem. And step three, once you make your plan, you will write down your solutions step by step. When you write down the solution, it's also the time help you to organize yourself how to solve the problem so you wouldn't make some minor mistakes. It's easy for you to find out each step. If something happened, you need to correct them. So we want you to write down the solution step by step. And also, all the questions, you should write down the solution by the question order. That would be very helpful. And the last step, once you select the option, mask and rule question have five options. There is only one option correct. Once you select the one option, so you need to, we strongly recommend you just take a quick reflection and check the question. So you need to put the option back to the question and then check if it applied to all the conditions. So that would really help you to make sure if it's a fresh memory so you can find out if you make something wrong. So we want you to follow these four steps, help you to solve some harder questions. Please also remember there are 75 minutes for the test. You need to answer 24 questions. So you have to manage your time. Make sure you have time to get in touch with all the questions and try your best. So this is from last lesson. We learned special thinking. So why we do the special thinking sometimes? So it would help you to understand how the shapes objects fit together. Sometimes you put the sense together and you have a bunch of cubes stick together. So you would see the different, the direction. And also you sometimes, you will try to solve some puzzle questions. So that would be very helpful, special thinking. And also when you try to do the special thinking, you sometimes will identify some patterns. So how to do the special thinking? So you can use a drawing, a picture, help you to draw the object. And also you can use different color to tell you what's different part of this object. You also can act in your mind and also take notes, write down the solution. Yeah, so you also can use a real project like the paper or something else help you to understand question. So the next one, so warm up question. Yeah, Elita, can you go? Yeah, which digits are missing on the right? So out of all the numbers zero through 10 or zero through nine, which ones are missing from the pile on the right? Yes, there are five options, so you will select one option. In the poll, once you select the answer, you cannot change your answer, so you have to think carefully which is the answer you should pick. Elita, even this is a three-point question, but I think it takes some time for students to organize all the pages here, yeah. Now we do receive a lot of students that want me to answer. If you cannot select the poll, can you wait for the next question to see if it works? I'll give you guys 10 more seconds. Okay, I'm gonna end the poll. Okay, I think most of you guys got this one correct, so it's a good warm-up one. So the way we do this is we try and sort them into a list. So we'll start from the lowest digit, which is 0. You can see there's a 0 in that corner right there. So there is a 0, then we move on to 1. We see a 1, so we write it down. 2, 3, 4, 5, that's all in the pile if you just spend a little bit of time looking for them. But then you see that if you look for 6, you won't be able to find it. So it's missing, and then 7 is there, 8 is there, but again, 9 is missing. So the two digits would be 6 and 9. Yeah, thank you, Anita. So this question even three points, but I think it takes a little time because the students have to source all the digits and to find out what is missing here. So from this question, you would think about what would be the organized list? So the organized list would keep your idea organized. So like if you want to go shopping, there are a lot of things you want to buy. So you may make the shopping list, but organize it for the different categories like the vegetable you put it together, meat you put it together, or snack you put it together, and you will shop for each different category. So this is you organize the shopping list. And also, you can see the student directory in the school. So there are 100 students in the school. If you put the student's name randomly, like here, you put all the digits randomly here. So it's not easy for you to see which one you have, which one you do not have. So also for the student directory, so the student's name would be ordered by alphabetical order for their first name or last name. So you will check the students really easily if you want to find some students. But if you put the name randomly, it's very, it's very hard for you to find out. So you would see, so anything whatever for the numbers or for the items, you put them in an organized way. So that would be super helpful. And also when you try to make organized list, yeah, so you need to focus on one group at a time and think about all the possibilities. And then you can arrange the group in a very easy order like alphabetical order or sequential order. So you look over all your groups and try to make sure you do not miss anything and you do not repeat something. So we will practice more organized list questions and you will have more understanding about this type of question. Okay, so let's see the next question. Adam wrote all the numbers from 1 to 60 inclusive. How many times did he use the digit 5? So remember what we mentioned, read the question, understand and what question asked for. So you should list out all the digit 5 from 1 through 60. So we need to wait for most of the students to answer the question. Because this is a large group class, so we have to wait for the students to submit their question, and then we will go through the answer. But usually for the question 15, that's a four-point question. So in the real competition, you might need two to three minutes to answer the question. If you finish the question earlier, please check your answer. I think we can share the answer. OK. Yeah, so the correct answer would be E. So this question is a little hard. I think there are some parts really confusing. So let's take a look how to figure out all the digits. So for this one, first, you need to understand that they said 1260 inclusive. So that means you include both 1 and 60, these two numbers. And then they ask, how many times did he use the digit 5? So you only consider digit 5 appeared times. So you list them in the sequential order. If I would start, I would start with 5. You can consider 5 contains digit 5. And 15, 25, 35, 45. So then you continue. When you continue, you would know from 50, you also have digit 5 appear. It's on the 10th place. So you need to write down all the numbers with digit 5. But can you see here? We have 55 use a red color. What happened? Because 55, the digit 5 appeared twice. So you have to count both. You cannot just count 55 one time. Because they didn't ask you how many numbers contain digit 5. If that's a question, so you'll need to answer 15. But they ask, how many times did he use a digit 5? So you have to check each time the digit 5 appear. So for the 1st digit, you could see. Yeah, that's for 1st digit up here. And then you would see the 10th digit. The five is a little blended with the same color. Okay, so now you can count how many in total. It should be 16. Okay, so this is a little harder question. Okay, next one. Yeah, Elita. Yeah, in baby Rue's house, each room is connected to any neighboring room by a door. See the picture. Baby Rue wants to get from room A to room B. What is the least number of doors that he needs to go through? So I think each little gap in the wall is supposed to be a door. Yes, and these are the doors. Yeah. Before you select your answer, it's better you check your answer first. In the poll, once you select one option, you cannot correct your answer. Yeah, I think we can share the answer for this one. OK. So you guys can see it was pretty split between two of the answers. Most people thought it was either 4 or 5. The correct answer is 4, though. So you guys can see. We're going to make an organized list again. I think our list, the way we go, is we start from B and we try and end up at A. So we're assuming that the shortest path would be only rights and downs, like you wouldn't go back up, because I think that would take more doors. So we start with, we want to move right first as many times as possible. So you guys can see, if we start at B and we move right through two doors, and then down through three doors, we end up at A. So that's a possible way. Or if we want to move right once, and then we move down twice, and then right again, that's a way. We can move right once, down twice, right again, and then down. So that's the third one. You guys can see R, D, D, R, D. And then the fourth one would be right, down, down. I think that one has a mistake. Oh, yeah, I think that's all correct. So you just needed to go through each different direction to right into down. Yeah, you don't go right as far for that one as you do for the other ones. So you only go right a little bit, and then you go down three times, and then right twice. And then you guys can see, to finish off the organized list, we start by going down first instead. So we go down and then right as many times as possible. So if we go down, we can go right twice, and then down again, and then right again. Or we can go down, right, down, right, down, right. Or down, right, down, right, down, right, and then down. So that's kind of the idea of it, to just try and list out all of these. And then because we're putting down a letter every time we go through a door, we're looking for the path with the fewest letters. So that would be right, down, down, right, which is the path that's pictured there. And then that one only takes four doors. So that's why four is the correct answer. Yeah, we list all the possibilities just to let you know there wouldn't be two doors or three doors. So if you try to solve these past questions, you also, it's better, you list all the possibilities to make sure your answer is correct. So once you figure out there are four doors, actually the five or six, you just cross them out. You just need to figure out if there could be three doors or two doors, but definitely not. So only four doors is the correct answer. Okay, let's see the next question. So organize lists is not very easy, yeah. So you have to consider all the possibilities. So with more practice, we believe you can do it better. So question three, three girls and two boys were dancing. They danced in pairs so that each girl danced with each boy for exactly one minute. At any time, there was only one pair on the dance floor. For how many minutes did they dance? We also want to mention this is an advanced set. So we have a set A, so those little basic level with some more easy questions. So here, the harder questions more. If you feel this lesson would be very challenging, we recommend you to try to find our last session, set A, so you can catch up from that set. Elita, I think this question might be a little harder. Maybe we should review with the students to give them idea how to do this kind of question. Okay. Yeah. Because it's over three minutes. Yeah. For this one, they already gave. Yeah. Let's share the result and we will go through the answer with you together. Okay. Yeah. Good job. For most of you who answer the question, you select the B, that's correct answer. But some of you, you might not have idea how to solve this problem, how to make organized list. So we will show it to you. So here, you have to read the question. Make sure to highlight some keywords, help you to understand. So first, there are three girls and two boys. And then they make a pair, one boy with one girl. And then every pair will dance exactly one minute, and only one pair on the dance floor. So that will make you know how many minutes, that means how many pairs would dance. So you'll need to figure out how many pairs. So for the three girls, you would see the girl one, girl two, girl three. And also for the two boys, you will have boy one, boy two. And you can make pairs. For the girl one, you can pair with the boy one. And also you can pair with boy two. You can see the first column. And then you can see the second column. The girl two, you also can pair with both boy one and boy two. And it's the same for the girl three. So by this way, you would figure out, there are six pairs you could make. Each pair dance one minute on the floor, and only one pair at that moment dancing. So there would be six minutes passed. So this is how to make this organized list. So it's better you work on the different group. You focus on the girl one pair, and then do the girl two pair, and then do the girl three pair. So they would be very helpful. And later, you might have other matching problems, like you have the music team. So you have somebody play violin, somebody play piano. So how could you match them? You can do the same way. Okay, next question. Yeah, so the numbers one, five, eight, nine, 10, 12, and 15 are divided into groups of one or more numbers. The sum of the numbers in each group is the same. What is the largest possible number of groups? This is a pretty challenging question. I think these are all pretty hard. Yeah, because this is one set. So we have more harder questions here, more four-point and five-point questions. So, how about we give three minutes for this question and then we can review the answer solution together. Yeah, I think this one might be a little bit too challenging for these students who have no idea. Yeah, we give you time to try and then we will guide you to give you some solutions, make you have more understanding and then you could do some practice. Okay, seems like this question is likely to be a hard one. All right, so I'll end the poll then. For those of you who did do this question, you guys actually did very well. So the correct answer was three, and it looks like most of the ones who answered got that right, but I think a lot of people probably just didn't have an idea on how to start. So we'll do the organized list again, right? So the smallest number of groups would be one. That would just be us putting all the numbers in one group. So if we add them all up, we should get 60. That's the total of all the numbers. If there were two groups, then we should divide 60 by two, right, to see how much the sum in each group should be. So 60 divided by two is 30, but we still have to see if this is possible, right, given our numbers. So if we put five, 10, and 15 in one group, we see that adds up to 30. And then the other four numbers, you can tell also must add up to 30. So that is possible. Now, three groups would be 60 divided by three, which is 20 in each group, right? So let's see if this one's possible. We can put one, nine, and 10 in a group. That adds up to 20. Five and 15 add up to 20, and eight and 12 add up to 20. So three also works. And then we can look at four groups. So the sum in each should be 60 divided by four, right, which gives you 15. So we want each group to sum to 15. Let's see if this was possible. So we put 15 in one group. That's pretty simple. The second group can be five and 10. That adds up to 15. But if we look, we can see 12 can't go with anything to make 15 because there's no three in the list. So four groups is not possible. And then for five groups, 60 divided by five would be 12, but our number 15 can't be placed in any group because it's bigger than 12. And you might think, okay, what about six groups or seven groups or eight groups? But it wouldn't work because the sum would get smaller as the number of groups increases. And since 15 is already too big for five groups, we can't have it go in six groups or seven groups or so on. So the total number, I mean, the largest number of groups would be three. So also, can you see the four groups we mentioned? The 12 also could add one because they have one here. You add one, you'll need two to make 15. You cannot make. So that's we check. So that's impossible. I think this question is hard because they involve a harder calculation for the younger students. And also you have to understand how to do the division. Yeah, so you might not have that clear idea. You just consider. You make some different groups with the same amount for each group. Like if you have one group, you have 60. You have two groups, so you have to make equal amount for those two groups. And for the three groups, that's two. So if you know the times table, so you can know the reverse, the calculation for the times would be the division, yeah. Okay, so now we'll go to another one. That's make a table. We learned to make an organized list. It's not that easy, yeah. So later you can practice some more the previous test and to do some questions. So for the organized list ones, so you get more practice on that. And for the make a table, so this is a kind of a sister strategy with make organized list. So organized list, you already work on one category. For the table, you would make a few, the multiple categories, you put it together. So you will make a chart. So that's a chart. They have rows, they have columns, and you could put all the information, put all the data, and you can analyze, help you analyze the question. So the table is very helpful, but it's harder to make. So this time we will list all the table for every question and let you know how to make a table, how to tickle the question, and try to make the rows, make the columns. So once you have more idea about how to use table, so you could make your own table later. So here, look at the first question. So how many legs do these animals have altogether? So they give you the picture and then they give you the table here. So they ask the total legs for all the animals. We know this question is not hard for you to answer if you just do the simple equation add all together, but we would like use this easy question to show you how to make a table that would make you understand easily for the table questions. So look at this one. Yeah, you already have this one on your handout. You can just read the picture and fill in the data. So please try to practice the table. You can use the equation to help you to check your answer, but we want you to practice this skill. So please try to fill in all the data. If you do not have your handout printed, you can just copy the table on the screen. This question is not hard. We actually, in the real computation, we wouldn't recommend you to use table to solve this question. You can just list the equation. But here, for the practice, especially for many students, you do not know how to make a table. We would use easy question, help you to understand easily. Okay, let's share the table result. Okay. Okay. All correct. Yeah. That's good. Yeah. So the result is good. 100%. Correct. Good job. So let's see how you feel in the table. Yeah. So first, they give you the first column. You can see this one. If I try to make a table, I already consider how many columns I would do. And some students might start with how many rows you want to do. So it doesn't matter. You can start with either. So I would like to do the columns. I would consider they're different animals. I put the column for animal. And then I would count how many animals for each cat. And then I would need to know how many legs for each different animal. And then I found the total legs for each kind of animal. And at the last, you add all together, you get the total. So you would see the data. You would see there is a three hens. And each hen has two legs. So total would be six. And then you have one cat. Each cat has four legs. That would be four. And one dog. Each dog has four legs, too. So you would get six, four, four, add it together, get 14. So this is not a hard question. But have you filled in all the data correctly in the table? So that's what we want you to practice. Let's see the next question. It's a similar one. Yeah, Elita. Yeah. So Anna draws a picture of some shapes. Her picture contains three black triangles and fewer than four squares. Which could be Anna's picture? Yes, for many questions, you have different ways to solve. Some ways would be the more efficient, would be quicker. But today, we practice how to make a table. So please try to fill in the data. And then you can use other approach to check your answer. Please try to use table to solve this problem. So fill in all the data into the empty cell, and then you follow the condition they give to you to select the correct answer. Okay, that looks like you guys did really well on this one. I think most of you got it right, so good job. I think this is also a problem where maybe you don't need a table, but it's good to know how to use this concept because it can be really helpful when things get complicated. So let's see, so in picture A we can count that there's two black triangles and two squares. Notice that we only count the black triangles, not the white triangles, but the squares we count both colors. And then in B we can see there's three black triangles and four squares. In C there's one black triangle, wait, two black triangles it should be, and three squares. In D it looks like there's one black triangle and three squares. And then in E there's three black triangles and three squares. So remember, her picture has to contain three black triangles and fewer than four squares. So we can go back through our table. It looks like A there's not three black triangles, there's only two black triangles, so it can't be A. For B we need fewer than four squares, but B has exactly four squares, so fewer means that it can't equal four. It has to be less than that, so it's not B either. For C it does not have three black triangles again, it only has two, so it can't be C. D also does not have three black triangles, it only has one black triangle. And then E it looks like there's three black triangles, which is correct, and it also has fewer than four squares because three is less than four. So E is the only picture that has a possibility of being Anna's picture. Yeah, so with the table you can see very clearly in the picture A what you have, in the picture B what you have. And then you can compare each column to see who has most black triangles, who has most squares. So that's very easy for you to analyze the data with the table. So let's see the next question. It's a similar one. In which picture are there twice as many apples as carrots, and twice as many carrots as pears? First, you list all the data, and then you can check the condition. So please list all the data. List how many apples, how many carrots, how many pears. That's very easy. And then you'll need to figure out what's twice as many apples as carrots. Who should have more? You should understand this part. Yeah, let's share the result. Okay. Yeah, most of you pick the correct answer D, good job. Yeah, have you all fill in the data in the table? So this one, how we build this table? We see the five pictures and then we list the column for the picture. So, you know, A, B, C, D, E. And then we have three different kind of fruits. We list the apples, carrots, and pears. And we check each plate and we figure out how many on each. And then you fill in all the data. So next, you would need to figure out what's twice as many apples as carrots. That means apple is two times of carrots. And the next one is twice as many as carrots as pears. So carrots, that's two times of pear. So then you could figure out how the relationship ratios there. So you would have figured out that D would be the correct answer. Yeah, you can see, if you list all the number there, that's very easy for to compare. Yeah, so the chart is very easy. If you compare horizontally or you compare vertically, it's very easy for you to see the answer. Okay, next one. Oh, this is a little harder one, Elita. Yeah, that's a lot of words. So the number of dwarfs that can fit under a mushroom is equal to the number of dots on the mushroom cap. The picture below shows one side of each mushroom. The number of dots on the other side is the same. If 30 dwarfs are seeking shelter from rain, how many dwarfs will get wet? This one's definitely a little harder, but it looks like you guys still did pretty well on it. Good job, everybody. The correct answer was A, so two doors. Oops, sorry, didn't share, but there you guys can see. So let's fill out this table, because I think the table gives you a really big hint on how to do this, right? So under the first mushroom, you can see there's three dots on one side. But remember, the dots on the other side is the same, so we have to double three to get six. That's how many dots are in total on this mushroom. So since each dot fits one dwarf, that means that the first mushroom fits six dwarfs. And then the second mushroom, there's four dots on the first side, right? And then we double it to get the total number of dots, which gives you eight in total, and then that fits eight dwarfs under it. The third mushroom, you can see, has two dots. We double that. There's four dots in total on the third mushroom. So four dwarfs. And then the fourth has five dots. We double that, which gives us 10, so that fits 10 dwarfs. So if you add all four together, that's the total number of dwarfs that will fit under these mushrooms. And you can see that we'll get 28, right? Six plus eight plus four plus 10. But we have 30 dwarfs. So since we can only fit 28, but we have 30 in total, we have to do 30 minus 28, which gives us two dwarfs that will get wet. Yeah, with table. So it's very clear. Yeah, so you can see the data, very clear. So that's why we recommend you do some questions later. If you do more practice, you will find out some question you have no way to solve with a lot of data give you in the question. So you try to draw the table. So that would be very helpful. Like some kind of problem, like there are a few kids, they have a few right desserts. So they ask you to match the dessert for each different kid. So you can just use a table to figure it out. So that would be very helpful. So today we learned the organized list and also that make a table. So we just, for the younger kids, so we give you some basic ideas, but you need more practice, more understanding. And then later you could use this skill very well, help you solve the problem. So remember, when you do the list, you usually not only do list, you do organized list. So that means you group your ideas and you concentrate on one group and try to think all the possibilities in this group. So you really, if there's numbers, you want to arrange those numbers in a sequential order. And also if there is a names or some other on the items, so you might order in the alphabetical order. So it's very helpful to make organized list. So that would help you to avoid missing possibilities and also avoid the repeating something. So the next one would be the table. You would see the table. Today we didn't ask you to draw the table on your own because that's too hard for some students who has never done this before. So we give you the table, give you a more understanding how to read the question. You'll see information they give to you and draw the table. You need to make the columns, make the rows and you name the columns, name the rows. And you will have some blank cells to fill in the information giving you in the question. So you use a table and then you could use a table to fill in the missing parts. So help you to analyze whatever the information they give to you. You can even add columns or rows to help you to solve the problem. Sometimes the table is fixed. When they give you a question, you could make the table with fixed rows and fixed columns. But sometimes it's not fixed, it's a growing table. You need to make more rows or more columns until you solve the problem. So this is organized list and make a table. We would like you, when you do the more practice, some questions you can try the different approach. You can try to use make organized list and make a table to solve those problem. And also use other approach to check your answer. Thank you everyone. Today we finish this lesson and we will send you the recording after class shortly after. We hope to see you back next week and have a wonderful day. Thank you, Elita. Thank you everyone. Bye-bye. Bye.

mathematical problem-solving

organized lists

tables

Mexican group competition

four-step method

problem type identification

solution planning

answer verification

time management

mathematical reasoning