Hello everyone, welcome to Mexican rule webinar for level one and two. And today is a lesson five and we will work on the organized list. I'm so happy to see many of you come back. Yeah, so we will have a great time together to work on some of the questions you can use organized list to solve. So before we start our lesson. So here that's a ground rules, we already go through many times, and we do not just go it by the details. But remember, we try our best to answer your question in the chat. But this is a bigger class. Yeah, so you won't get a chance to unmute yourself. So that's you just put your question in the chat, we will try to answer. So this method, I really want to reinforce every time. So because this one, it would help you to solve a lot of harder questions. So usually if you go to take the Mexican rule computation, the three point session, and that's usually that's a one step, one step solution. So sometimes you just use mental math or you just write down very simply, so you could solve the problem. But for the four point or five point question, it's better you apply this four step method. So that would help you to solve the very complicated questions. So the first step, you always should remember, you understand the question. Yeah, you have to read the question carefully, check all the pictures, make sure you understand all the hidden information and all the conditions. Then you try to plan how to solve the problem in the second step. And you can pick the strategies, you can check, oh, what type of question this one would be. It's a joint picture patterns work backwards. So for whatever the strategy could help you. So you can use one or more to make the plan. And the third step, you need to write down your solution. Do you have your paper and pencil ready? Yeah. So I hope everyone have your paper and pencil ready and also your handout. So that would help you to solve the problem. We do not encourage you to do the mental math for all the questions. Yeah. Yeah. Elita, you can share. Yeah. So sometimes the mental math is really helpful, but not for all the time. Yeah. You need to write down. Yeah. Yeah. It makes it more efficient, but it's also much easier to make mistakes or over count and under count, especially when you're trying to make a list. Thank you. Also, the last step, when you already get the solution, you need to check your answer. You put your answer back to the question to check all the conditions or use other approaches to check if you get the same solution. So that's the fourth step. Remember that. So before we start our new lesson, we just quickly review what we learned the last week. We learned the calendar and the time. Yeah. So I think Miss Diana gave you a very excellent lesson for the calendar and time. And you should remember all the facts of the time, like one year, 12 months, 52 weeks, 365 or 366 days. So and also here you could see the chart here, the table here. So that's January through December. There are how many days for each month. Yeah. So remember those because sometimes they do not tell you how many days of that month, but they ask you to find how many days from maybe from March to April or from April to May. So you need to know how many days in the previous month you could find the right days. Otherwise, you cannot get the correct answer. So remember those numbers. Remember, February is a very special. Yeah, February, you have 28 days or 29 days because the leap day, leap year, every four years. Yeah. Like this year, we have 29 days in February, every four years. And then January, March, you could see the big amounts. We have a pattern here. Yeah. So big amounts, small amounts, and then March, big amounts, April, small amounts, May, big amounts, June, small amounts. But July, August, look here. That's a special here. You have two big amounts together. You just think you want a summertime longer. So that's why you have two big amounts together. And then you go back to the pattern. You have small amounts, big amounts, small amounts, big amounts. And now you could see you have seven big months. You have seven months with 31 days and you have four months with 30 days and one month, February, with a special amount. And remember, one day, how many hours? 24. One hour, 60 minutes. So I saw some students solve the problem. They know one hour equals 60 minutes. But when they try to solve the time, they borrow one hour to get the elapsed time. So they usually borrow 100 minutes. So remember, do not make that mistake, okay? When you borrow one hour, that would be 60 minutes, not 100 minutes. That happened. Yeah. So this is all the fact you need to remember. And also, when you try to find the elapsed time, whatever for the time or for the dates, you need to draw clocks or you need to draw the calendar, simple calendar, to help you to figure out how much time passed. And sometimes you might can draw the timeline to help you to solve the problem if you do not want to draw the clock. So like if you draw, if you tell you, oh, today we have a class at 3.15, yeah, 3.15. Yeah, you say 3.15 p.m. And they ask, oh, how long for the class? Yeah, so you start with 3.15. You know the class would be one hour, yeah? So you add hour to 3.15. So we will finish class at 4.15 p.m. It's EST, okay? If you're from different time zone, you might have your local time different. So you would know the timeline really helpful. When you draw the timeline, you can add half an hour and you can add a whole hour. That would be easy for you to find the time. Okay, now let's start our new lesson. So before we start, we will brainstorm. Yeah, so in one minute, I give you one minute. How many scenes can you think of? Yeah, you might see in the sky. You can write down. Yeah, just remind yourself. Do not forget. Yeah, just give you a minute. You write down as many as you can. And you can send in the chat how many you could find. Send you the chat, yeah. In one minute. I know there might be a lot of scenes, yeah, so you cannot really count in one minute. But whatever, how many you count in one minute, you send your result. Elita, just check the time. Yeah. I think that's one minute. Yeah, OK, I see. Yeah, that means it's not long, yeah? So some shared, oh, you thought about seven things. And some of you, oh, you list something here. Yeah, you could see different things, like clouds, birds, sun, airplane, and also Many, yeah. Some of you say, so many things, I cannot count them out. Yeah, so, oh, some of you got five things. Very good, very good, yeah. So I want to show you here. Oh, can you see? I count this many things. I count star, sun, cloud, bird, kite, plane. Oh, star again, and cloud again. You see? Yeah, if you count something randomly, sometimes you will repeat your counting, or you miss something. Yeah, so we want to introduce you. Yeah, some of you got 8 cents, 6 cents. Thank you for sharing, yeah. So we want to introduce to you. Make an organized list. Yeah, you know, in one minute, you couldn't count many, but you can count as many as you can. If you define the different small groups, like the first one, you would see sun, moon, stars, planets together, yeah? And then you could see the clouds, the northern lights, the snow, the rain, yeah? And also birds, whatever. You make the small groups. I know, so many things you cannot think, cannot imagine. But if you make the groups, the small groups, make each group, like the similar things, you put it together. So that's easy for you to, you know, think of the things. Is that right? You can add longer, add longer easily. Yeah, so that's why we introduce organized list to you. And you can imagine in your school, there are a few hundred students. If we want to find some students by the name, if we put the student's name randomly, could you find that easily? No, you have to check a few hundred student's name to locate that student you want to find. That's horrible, yeah? So you want to use organized list. So usually school will organize the student's list by the alphabetical order. Yeah, whatever your first name or last name, or by the grades, or sometimes even by the teacher's name. So that's easy for you to find, yeah. Elita, would you like to share how the organized list to help you? Yeah, I think not just students, but also in some computer science things, it can be really hard to just guess and check. So they try to make it as organized as possible, or you can maybe make a table, or you can say like case one, this, so that you can really make sure that you don't under count or over count. Yeah, thank you, Elita. Very good, Sharon, yeah. So now let's do the number hunt. Yeah, we didn't give you the answer choices. This is on purpose, because we want to give you time to think about how to organize your list, to get all the possibilities. So we give you maybe one minute to solve this one, or 30 seconds, question give you 30 seconds. That's very short. Just try your best. Yeah, Elita, you can launch the poll, maybe give another 30 seconds of your lunch now. Okay. That was 30 seconds. Yeah, I know. That's a shot. Yeah. Yeah, this is a beacon number isn't So, you will have a monkey and kangaroo to find out the answer. Write down your numbers, okay? Write down your numbers. Try to make it organized as you think. And then we will show you the solution. So maybe give you a hint. So here, that answer got from monkey. Monkey found nine. But you can see monkey found the random numbers. Yeah, I believe monkey must miss something. So they ask you, you have three in the number. That means you see the number with the digit three. Yeah. You have the number and 100. You have a one-digit number. You also have a two-digit number until 99, yeah? And you need to find all the numbers with digit three. But remember, they didn't ask you how many times digit three appeared. They ask you how many numbers. That means if one number, both tens digit and ones digit have three, you only count one time. Okay, so let's share the result. I know this is not easy. It takes a longer time to count, yeah? So can you share the poll? Yeah. Yeah. And we would see, oh, the correct answer would be D, yeah? So almost half got the correct answer. It's not easy in such a short time. Okay. Let's see the solution here. I want to make organized list. You can see my list. First, the list, I have a single number, three. That's one-digit number. And the next one, I put a two-digit number, but I put a three on the ones digit. You can see very clearly, yeah? Is that right? Yeah. So you actually could combine the first list and the second list together. It all have three on the ones digit, yeah? And then you could see the next, the small group, I have the three on the tens digit. But remember, 33, you also have three on the tens digit, but you cannot count the 33 one more time because they ask for how many numbers they didn't ask for, how many times the digit three appeared. So that's different. That make different. So the answer would be 19, not 20, yeah? Okay. So this question would give you a very clear idea. Make organized list. You make the number follow sequential order. So that would be easy for you to find the correct answer. You do not escape any number, do not over counting some number. Okay. Let's see the next one. Yeah. We still not have a choice here, yeah? Just try your best. It look like the number even bigger. Yeah. Elita, can you go ahead with this question? Yeah. In 30 seconds, how many numbers can you find under 200 that are even and have a five? So this time we have two conditions, or three, I guess, under 200, even, and with a five. So I'll set a timer for 30 seconds. Yeah. So you'll need to understand what's even number, yeah? So the even number should end with what? End with 0, 2, 4, 6, 8, on one digit, yeah? If you have learned the place value, but I think that might be hard for the first grader or second grader, yeah? But you know the two-digit number. There are two-digit number, just give you a hint. Yeah, I think some of you might not really understand what's the even number, yeah? So you have a two-digit number, or you have a three-digit number, or you have a one-digit number. So whatever you have a lowest digit, so that's one's place. So this is one's place. And then you have a ten's place. How many tens? How many ones? When you count, I think teachers, school teacher might teach you, yeah, use the dots to count how many tens, how many hundreds, yeah? Yeah. Make your organized list, try to find out all the possibilities. Okay, I think that's 30 seconds. Yeah, I'll launch the poll. So make your list in an organized way. For the numbers, you already follow the sequential order. Like 1, 2, 3, 4, you increase the number. Even this question, not a long question, but this one take you some time to get all the possibility. Okay, I think that's almost everyone. So I'll end the poll now. Okay. You guys did a lot better on this one. I think maybe you might've had a little more time, but most people got it right. The correct answer was D. Yeah. So if we do what we did last time, we can sort by the place. So because it's even, we know there won't be any fives in the unit digit because only zero, two, four, six, and eight are even ones in the unit digit. So we go to the tens place. So we see there's 50, 52, 54, 56, and 58. And then because we're under 200, there's also 150, 152, 154, 156, and 158. If it was under 600, then we would also have 500s, but because it's just under 200, we only have to worry about the tens place. Yeah. Thank you. Yeah. Thank you, Elita. Very clear. You see, with organized list, you also make small groups with a two-digit group and a three-digit group. And then it's easy for you to find all the possibilities. Yeah. Good job. I think you all get the idea. Yeah. Elita, what do you think? They get idea. Yeah. So they find all the possibilities. Yeah. Very nice. Let's see the next one. Okay. This is a little harder. These 30 seconds are good. I think 30 seconds are too short. You just try your best, okay? Find all two-digit numbers. Whose digits sum to eight? You know, two-digit number. So what's the range for the two-digit number? You have to get that in your mind first. And then you select number from those two-digit number. You get their sum. That means you add both digits together. You add one's digit and ten's digit together. You get sum of eight. So how many of those numbers you could find? That's a lot to pull, yeah? Okay. So the two-digit number issued from 10 to 99, is that right? If you want to figure out sum to eight, that means what two single digit added together equal eight. So those combination, you need to figure it out. And then you could figure out the numbers. Is that right? Do not look through all the numbers from 10 to 99. That's hard. So you need to find a way. So what's the, you know, the easy way to solve? You find what digit add together make eight. And then you could make the number, yeah? Okay, let's share the solution, yeah? Yeah, most of you, you made the correct answer. Yeah, very good. The answer is D, eight. Okay, we sum to eight and we find eight numbers. So you could see here, like we have so many two digit numbers. You do not want to go through each of them. So you'll need to figure out how you make the two single digit add together equal eight. So one plus seven, that's very easy for you, yeah? So you could make two numbers, 17 and 71. And then two plus six, you get 26 and 62. And next one, 35 and 53. Yeah, because three plus five equals eight. And next one, four plus four. Yeah, that's only one choice. Whatever you switch the ones digit and the tens digit, it's the same number. And also there is a very special one. So you have to pay attention to this one, 80. So you'll have eight plus zero equals eight, two. But you cannot get a zero eight because they want two digit number. If you make a zero eight, that's eight. That's a single digit. That's not a two digit. So that's why you only have one choice here, yeah? So now you could get eight numbers, yeah? Make organized way, that would be much easier for you to find the answer. Okay, so let's look, take a look. So because we already do some practice, you have idea about the organized list. So when you try the practice, you would see this strategy is very helpful. So when you come with a different, many different possibilities, use organized list will help you to group your ideas and you'll concentrate on one group at a time. And then you'll find all the possibilities. You won't miss or over count something, yeah? So that would be super helpful, yeah? And you could arrange the numbers because we do the numbers. You would arrange the numbers in sequential order. If it's items by the names, you could arrange by the alphabetical order. So that would be easy for you to find. Find anything if you missed or if you over counted. So here, yeah, make organized list. So this is a super helpful. You generate a list of solutions and you pick maybe the correct choice from the list of the possibilities to help you to solve the problem, yeah? So we really encourage you to consider about the organized list when you meet a bigger data set, when you have a question related with a lot maybe different possibilities, yeah? So use organized list. So here, oh, now we're back to our normal question. We have the answer choice here, yeah? So look at this question, yeah? Elita, please go ahead. What number is missing in the picture? So you can see there's a clown juggling three numbers. It could be him. And then give you three, 209, 902, and 290. Okay, so let's just stay on this question for a while because we do not have a picture in the poll. So yeah, just give the time to the students to figure out to the question, yeah. But when you try to solve a mathematical question, sometimes they only have one correct answer. So to help you to solve the question faster, so you can eliminate some wrong answers. If you think some answer is not correct, just cross it out. Just work on the answers you think that might be the choice. So that would reduce your options, make it easier for you. Um, I will release the poll now. Yeah, so we have the poll open now. Because we do not have a picture in the poll so we, we just keep the question longer time for you to solve the question. You need to check what number they give to you in the boxes. And that you consider was a missing number. You need to follow the same, the rule. Yeah. Find the different group. Yeah, I think this question not that hard. Most of you got the correct answer. Let's share the solution now. Yeah. Yeah, all of you guys were split between two answers, either 92 or 920. The correct answer was 920 but I understand why some people would pick 92 because that seems like it could also work. But really 920 is the better answer, because the answer choice of 92 doesn't have a zero in it. And we're trying to make three digit numbers that have all three of the digits. Yeah, so you need to find the best answer. Yeah, so compared to what condition they give to you. So 920, you have all the three balls and 92, you only have two balls. So you compare those two answers. So E would be the best answer. Yeah, the others, they do not have all the three digits. So you just cross it out. Yeah, very good. Yeah, I think you're all good at organized list. Yeah. So now let's see the next question. Bibi the turtle writes different numbers on flowers. She uses only the digit one and two. The picture shows what she wrote on the first flower. You can see the picture over there. How many of the flowers shown in the picture? Yeah, the flower gives you six here. Yeah. Including the first flower, can she write? You only use the digit one and two. Check the condition. Yeah, this question saying that each number on the flower has to be different. So on the remaining flowers, you can't use one or two again. They didn't tell you. So you can do anything you want. Yeah. Read the question. If they didn't see, you cannot repeat the digits. Oh, they didn't see how many digits of the number. So you can do whatever you want. Okay, I think we can launch the poll for this time. Yeah. I think this question is a little tricky, yeah, little tricky, so you might get confused. So what are they looking for? Yeah. So let's share the result. The correct answer is E. You could write on all the flowers. So you actually could even write more than six, but they didn't give you that many flowers. You just answer what the question asked for. So you can see they didn't ask you to not repeat the digit. They didn't ask you to not only limit to two digit. You could get a three digit, four digit, five digit. So you have infinity solutions for this one. Is that right? But remember, they only gave you six flowers. So that's a logic reasoning here. You only could write on the six flowers. So that's your choice, six. Yeah. You could get more than six. Yeah. Don't be afraid. Check. Get all your possibilities. Yeah. So you just follow what condition gave it to you and try to figure out as many possibility as you can. But for this question, once you get a six number, you do not need to take more time work on this question because you need to save your time for the later question. You only have a six flower. You found the six numbers. That's good enough. You would have select the answer and then move on to the next question. Yeah. So you really do not need to write down the 100 numbers for this one. You can do that for the practice, but not for the computation. In the test, you have to manage your time. Okay. Let's see the next question. Elita. Yeah. How many different numbers greater than 10 and smaller than 25 with all different digits can we make by using the digits 2, 0, 1, and 8? And I think they actually give you some hints on the bottom of what kangaroo and monkey tried to do. So you can see they listed out all of the numbers and they eliminated some, but their answer might not be correct. So you should double check their work, but it gives you a good idea of where to start. So you can read. Yeah. Elita, you can read all the steps. Yeah. Okay. So kangaroo and a monkey made a list of all the numbers you can make with 2, 0, 1, and 8. They got 10, 11, 12, 18, 20, 21, 22, and 28. Then they eliminated 11 and 12. Think about why they did that. They eliminated 28 because it was too big. See the condition that says they have to be smaller than 25. And then they were left with five numbers, but this could be wrong. So help monkey and kangaroo check their work. Okay. So you have to follow all the conditions and figure out which one is the correct answer. So copy, copy this list on your paper. And then you could work on this list to figure out the final answer. Give you 30 more seconds. Copy the list and read through all the conditions, and try to figure out it's fiber cracked or not. I think this question may be the wording a little longer, so that's hard for the first grade or second grade to read, yeah. So you have to understand all the conditions they mentioned there. They all follow the points they gave to you in the question. So they tell you the number should be bigger than 10, smaller than 25. And you should have a different digit to make those numbers. And the digit you should put from 2, 0, 1, 8. You should get from there and also make a different number. So that would reduce the possibility to get the numbers. So the condition they gave it to you here, that's correct. But the final answer might not be the final step. So you just needed to compare all the conditions they gave it to you. Okay, let's share the result. Yeah, Yilita. Okay, the most common answer was four, which is right. But the answers were pretty split this time. So you can definitely tell this one was a little bit harder. Okay, so let's follow kangaroo and monkey steps first. So first they eliminated 11 and 22. They did this because they have to be all different digits and 11 has two of the same digit and so does 22. Then they eliminated 28 because it was too big. This is also correct, but they should also eliminate 10 because it's too small. Remember, the question says it has to be greater than 10. So that was their mistake. So instead of being left with five numbers, they would only be left with four and you can see them above. There's 12, 18, 20, and 21. So the correct answer is just four numbers. Okay, so I know here there are so many steps might confuse you, yeah. So you just try to understand the question, yeah. So the steps are correct, but they didn't finish the steps. They eliminate 11, 22, and also eliminate 28, follow all the conditions, but they didn't eliminate the 10. The number 10 also is not in the range. They tell you greater than 10. That means not include the 10. Smaller than 25, not include 25. So you have to understand. And also the digits should be from these four digits. Yeah, you cannot get other digits to make the number. Yeah, so that's the answer. Okay, let's see the next one. Yeah, this one's even harder. You can see this is 2019, question 20. Yeah, so that's a five point question, yeah. So here, three squirrels, Annie, Asia, and Ellie, collected seven nuts in total. Okay, remember what they mentioned in the question, okay? Each collected a different number of nuts, but each collected at least one nut. Annie collected the most, the least, Asia the most, and how many nuts did Ellie collect? So you know the number? Yeah, from Annie, Ellie, to Asia. That's from least to most. I think we can launch this question, yeah, there are no picture here. So this way you can use a drawing picture, or you can use a combination. You remember, all the collections add together up to seven. And each of them collect a different amount. And at least one for each of them. This is a five point question. During the computation, you only use three to four minutes. Yeah, if you could save time in the session earlier, yeah. But your average time, yeah, so should it be less than that? So they look for Annie. If you figure out the answer, you need to put how many Annie got, how many Aisha got, and then you add it together. Could you make seven? Also, everybody has different amount. Okay, I think I'll share the poll now. Okay, very good. Yeah, most of you got correct answer, two. Yeah, two is correct. Let's see the solution here. You actually can do the two way. Yeah, whatever you can make organized list or you can draw the picture. Yeah. So here, first, make organized list. So how many numbers you could add up to seven? So you can make the different group, yeah? So you can start at everybody at least have one. So you could get one, one, five. Yeah, so that could add up to seven. Or you could get one, two, four. Or you could get one, three, three. Or you could get two, two, three. Yeah, so those different combination. Yeah, so you could add up to seven. But you have to remember, they ask, you have to have a different number. Everybody collect different numbers. So one, one, five doesn't work. One, three, three doesn't work. Two, two, four. Two, two, three doesn't work. And then you have one, two, four left over. So you compare all the conditions here. So everybody get at least one. And from, this is Annie, yeah? From Annie to Ellie and Aisha. So that's from least to most. So that's correct. Yeah, so two would be the answer. Yeah, because Ellie, correct amount in between the least and the most amount. So you also can use a join picture. Yeah, we learned this one before. So you make the list. You know from least to most. That's Annie, Ellie, Aisha. And also you know what? First thing you know, everybody should get one. So you put one for each of them. But you also would know they all have a different amount from small to big. So at least you could put this way, yeah? One, two, three. Yeah, for these three people, three kids. So now you have one nuts left over to reach seven in total. So what you put here? If you put this nuts to Annie, oh, that wouldn't work because you'll make Annie and Ellie same amount. Not working. If you put that one to Ellie, also not work. You will make Annie and Aisha same amount. So you try, yeah? You can draw the picture. Also could help you to solve this problem. Yeah, so both way, yeah? But make organized list, it's actually you understand, yeah? That's then all the combinations easier, yeah? Okay, so finally you've got Aisha has most, is four, yeah. Okay, let's see the next question. Elita, go ahead. How many different three digit numbers can we make that have three different digits using the digits one, two, and three? So every single digit of these numbers has to be either one, two, or three. I'll launch the poll since there's no pictures. Yeah. So remember, they ask for the three-digit number. They ask you to use the digits 1, 2, 3. But also, you need to make every time make the digits not the same. So that means 1, 1, 1, 1, 1, 2, it wouldn't work. Yeah, I think that's enough. Yeah. That's a pretty good on this question. I think this one's pretty hard, and most of you got it right. So, good job. Um, the correct answer was seat six. So like the ones before we just write out a list, but it's a little bit hard to do randomly and you definitely don't want to go check every single number, every single three digit number. So I think what they did was they started with the number that started with one, so 123 and 132. You can see pretty easily that there's only two of those and then you do the same for two, 213 and 231, and then for three, 312 and 321. So as long as you have a system for organizing your numbers, this problem shouldn't be very hard to do. Very good. Yeah. So this, I think this is a combination question. It would be appear in the higher grades. Yeah, but you all did a great job because you know how to organize your list. So let's see the next question. Oh here, this one, similar as the question seven. Yeah. So three kids, Anna, Barik, and Claire, each have a fishbowl with at least one fish. They all have a different number of fish and there are nine fish all together. And Claire has the most fish, Anna has the least. Claire has two more fish than Anna, a little different than before. Yeah. And how many fish does Barik have? So we did a similar question before. Yeah. so once you get your answer you need to check all the three kids how many they got the fish and then you add it together if up to nine you have to follow all the conditions it looks like Barack got the in the middle yeah so not the most not the least Okay, let's share this question, yeah, because this is similar question, yeah, similar question as before. Yeah, we have a most of you got the correct answer. Very good. Yeah. So this one, the correct answer is A3. So here, it's a similar, you need to find all the combinations. And with the different number of fish. Yeah. And also you should have Anna. Claire has two more than Anna. So there would be what? So you would have Claire has most, Anna has least. Anna has least. And you have Barack in the middle. And you have Claire at most. So you follow this way. And you check all the different combinations, make up to nine. And you also need to remember, they said Claire has two more fish than Anna. So you would check out which one would work. Yeah. One, two, six wouldn't work. Yeah. So Claire is five more. Yeah. One, three, five, four more. Yeah. One, four, four, you have the same amount. And also not two more than Anna. And then you have two, three, four. So this one work for all the conditions. So the answer would be three. You also can draw the picture to solve this problem. Yeah, good job. Okay, so we organize the list with the numbers. But next, we would work on organized list for the passes. Yeah, I know the organized list also take a little longer time for you to solve the problem. Yeah. So let's just try the first one. Yeah, Elita. A cat and a bowl of milk are in opposite corners of the board. The cat can only move as shown by the arrows. And how many ways can the cat reach the milk? So you can see in the top corner, there's a cat and in the bottom corner, there's a milk and the cat can only move to the right or down. So our class will end in three minutes, but because the past question is very special, so we might extend it to three minutes to finish the past questions. You have this one on your handout, yeah? The handout, it's in your parents' account. I recommend you to print all the handout and put into a folder. So that's easy for you to find every time. This one's not really easy, not really easy. So let's work together. We have another past question we can give you time to solve. But this one, I would like to work with you together to find out how to find all the passes to make sure you do not miss anything. Yeah. Yeah, end of the poll. Yeah. Okay, so the correct answer would be E, the six. So let's see how, why there are six here. Yeah. So let's see the answer choice. Yeah. Okay, Elita. Yeah. So this is a little bit like before. We're just making a list of all the possible options. We know because we can only go right or down that we'll take four steps for every single path. So you can see on the right, we start with, okay, what if we go right first? And then our next case would be the second step, which we're also going to go right on. And then because we can only go right twice, that means our next two steps have to be down. So then for the next case, we go right first again, and then we choose to go down this time. And then we go right again, which leaves us with one going down. And then our final case where we go right first is we go down twice, and then we go right for our last move. And then there's also three cases where we go down first. So you can kind of see that these cases mirror each other. So if we choose to go down twice, then we have to go right twice. If we go down once and then right twice, we have to go down for our last move. And then if we go down for our first move again, then we can alternate going right, down, and right. And they kind of match up with each other. Yeah, very good. So this is very clear. They give you every different paths. And you would say that's not the same. You could see the direction and see the color. They are not exactly the same paths. There are six for them. So it's better you work with the first move. You check all the first move to right first, and then you check all the first move to going down later. So you find the different possibilities. So we have one more question, also the past question, a little different. So this one, they said in one jump, Jake the kangaroo jumps from one circle to the neighboring circle along a line. That means you do not jump diagonally. You only jump, follow the line. But he cannot jump into any circle more than one time. So he cannot jump back. Yeah, he starts at circle S and finish four jumps. Remember, he need four jumps to get to the finish part, the end, in how many different ways can Jake do this? So you can also consider what's the first move, yeah? And that first move could lead how many different paths. Yeah, so first move could have how many different choices. But remember, you need four jumps. Yeah, we will finish this question. Yeah, because the past question, it's a very special. Yeah, you do not see a lot. Let's launch this one. I think because we're a little short on time. Yeah, OK. So this question, not that easy, because there is a confused part. If you go to right first, you couldn't make four steps. So that's why some of you pick four. Actually, the answer would be six. So let's see the result, yeah. So here, the jig can make three different directions. You can see the red, it's go right. You see the green go up, and you see the blue go down. So you would see, if the first move, you go up. So you would have a, you can see the rest of the steps. You go right, right, down. And you go up, you could go right, and go down, and go right. So that's two passes, yeah. And then you see the next, the first move, you go right. But if you continue go right, you only make two steps. So not right. You need go right, go up, and then go right, go down. So that's you make four steps. And also, you make a same way. You go right, but you go down, and go right, go up. You can see all the different arrows, and you would see the different direction. And this is a second. I know this part confuse you here, yeah. So this is the confusing part. So you go right first. You do not, I think you do not count this one, if you make the answer as four. Yeah, because you miss this. You miss the, you go right, go up. You could go up, make two more steps. Or you could go down, make two more steps. And then the last one, very easy for you. Yeah, so you could go down, and go right, right, up. So that's very easy. We give you all the directions. So this is organized list. You could organize numbers. You could organize passes. And you could organize all the items. This is a very helpful strategy. So we would like you to remember this, and practice this when you solve some questions. Thank you, everyone. Thank you, Elita. So see you next week. Bye-bye. Thank you, guys.

organized lists

mathematical problem-solving

systematic approaches

problem-solving accuracy

combinations and paths

grid paths

logical grouping

sequential arrangement

even numbers

unique numbers