Hello, everyone. Welcome back to our webinar. Today we are going to learn make a table. So this is a very exciting technique. If you learn, if you learn it well, so it would help you to solve a lot of questions later. But maybe some of you have never made your own table before. Let's take a look. What is a make a table. So first, the ground rules we already go over many times. So just let you know if you have any question put into the chat. Elita and I could just try our best to help you with the answer. But maybe we couldn't answer all the questions. Yeah. But we will share the recording after the class. So here is a four step method. So we reinforce every class. So we want you to remember all these four steps that would help you to solve some harder questions. So you need to apply this method. You need to practice and try. Otherwise, I don't think if you meet some harder question, you could get help from this method. Please try and practice now and later you could apply to solve some of the harder questions. So this one is come from our last week guess and check. Yeah. Elita, would you like to quickly go review this guess and check with the class? Yeah. So basically, the first step is to just make a guess. Either it can be an educated guess from the problem or you can look at the solutions and those can be your guesses. And then you have to check if the guess meets the conditions. Usually in the problem, it will give you clues that give you some information on what the answer could be. So you have to make sure that your guess matches those. If that doesn't work, then you can move to the next answer or the next possible answer and try that again. This method is also called try and revise. It's exactly the same, just a different name. You try a solution and then you adjust it based on the conditions. Yeah. Thank you, Elita. Yeah. Remember, when you make a guess in Maths Can Group questions, you have five options. You actually already gave you the options for your guess. So you just try the different options. But for other questions, if you do not have answer choices, so when you try to make a guess, you have to understand the question well and try to make a reasonable guess. Do not make a random guess. And remember, your first guess might not be correct. So be patient. You need to try more. And finally, you might get the correct answer. Also, there is another thing we want to mention. It's a test tip. So when you do the computation, in Maths Can Group, you do not have a guessing penalty. So that means if you do not really know the answer, even if you guess and check, you cannot find the answer. You just pick any of the options you think might be right and fill in the answer card. So do not leave any answer blank. Yeah. So because there is no guessing penalty, so if you guess, you might get it right. If you leave it blank, you are 100% wrong. So please, yeah, when you have no idea how to solve it, you please do not leave your answer card blank. Try to make a guess and fill in the bubble. But that's your last choice. If you have a way to solve the problem, do not use a guess. Okay, so what is table? We are going to learn a new strategy, make a table. We learned organize list before. So this is a kind of a sister strategy. So make a table. Do we make this tables here? Yeah, Elita, are we going to make this tables here? No, this is a different kind of table. These tables are like desks. The other tables we make are just a way to organize information. Yeah, let's see what we are going to make here. Yeah. So we are going to make this kind of tables. Yeah. So like a charts, you might say before. Yeah. So the table has the rows, has columns, and all have names. And also there are some cells. Can you see the white part here? Yeah, you would see the cells. Yeah, you put into the data over there. Yeah. So here, the white part here is the cells. Yeah. And you fill in the data you get from the question, and then you figure out, yeah, so what you should solve the problem with the given information. Yeah, you look at the here. So the first chart, it's the class. I think this is from the school. Yeah, it's a third grade classes. We have four teachers with their class, and also how many boys and girls in each class, and how many total students there. Is that easy for you to find the information? If I ask you, oh, who has the most girls in the class? Can you find it easily? Yeah, I think this is much easier than if there was just a lot of sentences that said, there's 12 boys in this class and eight girls. It's a lot easier to visualize when it's on a table. Yeah, yes. So if they ask you whatever information, it's very easy for you to compare, especially you compare the same column, compare same row. Yeah, so that's how you use the table to help you. And also, you could look at the different samples here, examples here. Yeah, we have the table with the numbers. And we also have a table with the words. Yeah, and also with even tally marks. So we can tell you what you can put into the table, you can put any information. Yeah, even you can put some drawings in the table to help you solve the problem. So later we will work on that question. So this is a table. We will try to make a table the first time you need to figure out maybe how many columns you want to make the table for this question, and how many rows you would do. Sometimes the question gives you enough information, you will have fixed column and fixed number of rows. But sometimes you have to figure it out, like you have a growing table, you will get the table finished until you solve the problem. So that depends on the question. Yeah. Okay, so let's look at the first question. Warm up question. Yeah. Which plate has a fewer apples than pears. So can you draw the table to solve this one. We can give you a hint here. Yeah. So here, can you see the table here. Yeah, I know at the beginning, it's not easy for you to draw the table, but we can show you. Yeah, we have to step by step, learn how to build up table, and start with the easy question. We do not want to use the harder question at the beginning. Yeah, we want to use the easy question, help you to learn the strategy, and then later you practice with harder questions. If you do not have a table. Yeah, you can copy the table on the screen. Yeah, maybe the first question we will go through with you together, and then later, you can try to make your own table. Yeah, maybe first a few questions, maybe first a few questions, we work through each step with the students, that's easy for them. I think some of them might haven't never made a table before. Yeah, this is a pretty new to them. So look at this question, what are they looking for. They look for fewer apples than pears. Is that right. Yeah. So here we give you the, the, the answer choices, ABCD. Yeah, you already we have five options but here we only have four, because this is a previous year. And then you list the apples on each plate, how many, and pears, how many. So the first, the plate A, you have three apples and two pears. So if you continue, you would figure out. So how many on the second plate, three apples again. And also, two pears, three pears. And then the third plate, you would have four apples, five apples, and three pears. And then the last plate, you would have three apples and four pears. So you need to compare, you need to understand the words here, what's a fewer. Fewer means that you're less, you have less apple than pears. Yeah, so you compare amount, you should have a smaller amount of apples than pears. So what's your answer. Yeah, we have you, we have you make this table. Yeah, so you can launch the poll, Elita, so let the students select the answer. If you do not know how to make a table, just try to copy the table on the screen. So that would help you. Yeah, to learn how to make a table faster. Good. I think this is not very hard question. It's very easy. Once you put all the data there, it's very easy for you to figure out the last one. It's a smaller, that's only smaller one. The other one you also bigger or equal or bigger. Yeah, have more apples. Yeah. Okay. Good job. So I think everybody got it correct for this one. This table is easy for you to see the data. Yeah. And next one, let's see that this question, Elita, go ahead. In which picture are there two more cats than dogs. So this one's very similar to the last one. Let's see if you can solve it by drawing a table. Yeah, so we can show you the table first. Yeah. At the beginning we show you the table, and later, we will let you to create your own table. So you can see in option A, you can count three cats and three dogs. Um, so that obviously can't be right, because those are equal. But let's look at option B. In option B. Yeah. So you read, I will write down. Yeah, it looks like there's four cats and three dogs. So in option C, we can count five dogs and three cats. I think you have it flipped. Oh, okay. Oh yeah. Sorry, three cats five dogs. Okay. Did I flip the B. No, no, no, the B is. Okay. I think I just read it in the opposite order. Okay. Yeah. And then in option D there's five cats and three dogs. What's your answer. Yeah. So I can launch the poll and let them. So the table is much easier than you see the image, or you see the sentence. Yeah. So if you put all the information in the paragraph. So that's a few sentence you have to read and compare in your mind, and also see the picture, it's not clear to you have to count. But once you write down the numbers in the chart in the table, that's very easy for you to compare. Very good. Yeah. Okay, Elita, would you like to go through this question? Um, yeah. So you can see that we wrote down all of the, all of the options like we did before. So three cats, three dogs are option A, but we need two more cats than dogs. So three isn't two plus three, because three doesn't equal five. So it can't be option A. And then for B, this time, there's only one more cat than dog. So it's not B either. And then for option C, it's reversed, it has five dogs and three cats. So there's actually two more dogs than cats in option three. So that also can't be right. And then for option D, we see that there's five cats and two dogs. So because three plus two is equal to five, we know that option D is correct, because it matches the conditions. Yeah, actually a little bit like guess and check too. We're still using that skill because we check each option. Yeah. Do you like the table, everyone? Yeah, do you think it's clear when you put all the data here, compared to the picture, compared to the paragraph, the description? So the table would be very clear. Yeah, so give you very straightforward information. So let's see the next question. One hen lay one egg a day. In how many days will two hens lay six eggs? I know this is an easy question. You even can do it mentally, yeah, to solve the problem. But how you use the table to solve this problem, please try. Try to use table. I give you one minute, create your own table, and then I will show the table, the table sample for this one. So please have the pencil paper. Yeah, you need to write down, draw the table out. Okay, so do you know how to get a table? Yeah, so here, this is a table sample. Yeah, if you do not know how to make your own table, so you can do it now. So, Li Yita, can you open the poll and then can you explain this question. Yeah. Okay. So, I'll let you guys answer the poll first. Wow, you guys are very fast. So, you guys can see that almost all of you got this one right. I think this one is also pretty simple for a poll question. I mean, for a table question. So, you can see on the first day, one hen lays one egg. So, then two hens would lay two eggs, right? Because each hen lays one egg a day. And then on day two, the one hen would lay two eggs. So, two hens would lay four eggs because each hen lays two eggs. And then on day three, one hen would lay three eggs and two hens would lay six eggs, right? Because three plus three is equal to six. So, you can see that after three days, two hens lay six eggs. And using the table, it's pretty easy to organize information. And you can also kind of see the pattern. It goes one, two, three, or two, four, six with that one. Thank you, yeah, so this one, you get the table, it's very clear. Yeah, you can see all the days, yeah. So this one, I know you could solve it very easily when you try to, you know, just try to use a calculation, but we want you to experience how to create a table to solve the problem. So let's see the next one. Yeah, so next one, they tell you, when Anne was one year old, Michael was four. Now she's three years old. How old is Michael? How could you make a table? Do you want me to release the poll now or give them a minute? Yeah. So, maybe we can give the table. Yeah. So this one you never made before, so we can give you a sample. You can copy this table. Or you can make your own table. Sometimes you can switch the row and column. Yeah. Okay, so maybe we can open the poll. I think most of you got the correct answer. Did you make the table to solve it? Or you just did the direct calculations? So we recommend you to try to make a table to solve this problem. So you know here before you get n is one year old and Michael was four. So now you get n is three years old. So how old is Michael? So you can have two ways to figure out. You either can figure out how to figure out Michael is three years older than n. And then you could add three years. Michael is three years older than n. So if n is three years old today, so you add three. So Michael would be six years. So if you also can do another way, you can figure out. So from one year old to three years old, n grows two years. So Michael should also grow two years. So both ways you can figure out the answer. This is not a hard question. So this is not a hard question. Can you see my screen? Yeah, we opened the poll before. So you might not see my screen. Yeah. So can you see here? So you could figure out the Michael and n. They have three years difference. Yeah. And then if n is three years old, Michael should also add. They have three years difference. If n is three years old, you still need to add three years for Michael's age. Just want to let you know this kind of question, we think in the mathematical way. So in this question, we do not have much information about what's the exact birth date for the kids. So you don't do not need to overthink that way. Yeah. So you just need to figure out how much difference age and how many years passed and you can get the answer. Do not really consider about the exact the month or date. OK, let's see the next question. Yeah, OK. So Adam paid six dollars for 15 buns. How many dollars did Tom pay for the same kinds of buns if he bought five more? So Tom bought five more buns than Adam. This one we mentioned before, you can draw in the picture. So let's show you maybe. OK, so let you try first. Yeah, maybe you try first. We will show you the solution. So Adam, you can draw in the picture. So let's show you. OK, so let you try first. Yeah, Okay, so maybe we open the poll first and then we will show the solution. Okay, so maybe we should review the question. Yeah, we got the different answers. Yeah, so the correct answer should be eight. Yeah, but some of you got a different answer. So let's see the solution here. Yeah, to see how to use a picture. Yeah, put it into the table, help you solve this problem. Yeah, so first, you could get information from the question. Yeah, they give you the 15 pounds and also told you there are $60 paid for the 15 pounds and also they said five more. So once you see the five more, you would see for the 15 to five, so then you skip count five, you would get five, 10, 15. So that means the 15 pounds, you can divide it into three group of five. Yeah, and then they give you one more information, Tom paid the same kind of pounds, he bought five more, so he bought one more group. So for the picture here, you could see the table, you have a three group of the five pounds and also you paid $6. So you want to figure out for each five, how much you might need to pay. So you also need to split the $6 to the three groups and each group would be $2. You can make your table. So once you get five more pounds, you need two more dollars and then total $8. So this is very clear if you draw the picture out. So first, you compare the 15 pounds and five more. So you would see, you do not count the single pounds. Yeah, so because you have $6, it's hard for you to find the single price for each pound, but you can find a group price easy. Yeah, you have 15 pounds, that's a three group of five, and that's very easy for you to figure out one group of five cost how much. Is that right, Elita? Yeah, I think it's a fun way to visualize the problem. Yeah, yeah, I like this question. It's really clearly show you, yeah, if you make a drawing, you still can use the table to solve the problem. Yeah, so all the strategy we learned before, it's not just single use. Sometimes you might use multiple strategy together, help you solve the problem, especially for the harder questions, the 4.5 point questions. Okay, let's see the next one. Yeah, yeah, Elita, go ahead. Piper needs to walk from her house to a town 16 miles away. In the first hour, she walks one mile. Every hour after that, she walks two more miles than she walked during the hour before. How many hours will it take her to reach her destination? This question might be a little bit difficult to understand. So during the first hour, she walks one mile, and then during the second hour, she walks two more miles than she walked in the first hour. So in the second hour, she would walk three miles, and so on. So make sure you read the question really carefully. So maybe we open the poll. Yeah. You can still join your own table. Yeah. Please use join table to solve this problem. We always apply the technique for this lesson first. Yeah, drawing table takes some time, especially at the beginning, you are not familiar to make it. But with more practice, it would be much easier and faster for you. Yeah, we are going to close the poll soon. Okay, I think I'll close the poll now. Yeah. So, I think around half of you got the correct answer. The correct answer was four hours. But this question is a little bit harder to read, I think. Yeah, so maybe you can take a look at the table. Yeah. So, okay. So, you can see in our table, our three columns are the hours passed, the miles walked, and the total miles. So, let's see. So, you can see after one hour, we know she walks one mile, right? Yeah. So, let's see the solution here. Yeah. In one hour, she walks one mile. So, that gives you one total mile. And then after two hours, we know she walks two more miles than she walked in the first hour. But that doesn't mean we add two to the total miles. That means we add two to the miles walked during that hour. So, she walked three miles during the hour, which gives you a total of four miles, because three plus one is equal to four. And then after three hours, she walked five miles only in that one hour it took to go from two to three hours. So, that gives you nine total miles. And then by four hours, she walks seven miles during that one hour, which gives us 16 total miles. So, since her house is 16 miles away, we know that after four hours, 16 miles is enough to get her from her house to the town. So, the correct answer would be four. Thank you. Thank you, Elita. Yeah. So, this question is very clear. If you make the table, it's very clear. Yeah. So, let's see the next question. Oh, here. So, here we talk about, because we practice well, you get a little familiar with the table, how to make a table. So, now we talk about why we make a table. So, make a table is a very organized way to organize a table. It's a very organized way to organize the data and information. So, this strategy allows you to discover the relationships and patterns. Yeah. So, you will organize all the information in a very logical way, and you'll make them in a certain category to work on each category, like the each column. So, let's look like the different category you work on. And then you might group the list together. Yeah. Remember, we learned organized list before. So, that's a single list. But here, you put all the columns together, all the rows together, that's organized list, a group of them together. So, the information would be very clear for you. Yeah. So, here, we also mentioned this strategy would overlap and could work with other strategies, like patterns. Yeah. I even guess and check. Yeah. So, anything. Yeah. You can combine together to try to solve the problem. So, here. Yeah. One more question here. So, Leo is going on the boat ride. Every day, he rolls the boat two miles forward, and every night, the wind pushes his road one mile back. How many days will it take him to reach the opposite shore, seven miles away? How to make this table? Yeah. It might be not easy for you to make the table. So, let's share the table example with you. So, you can take this one. If you do not know how to make your own table, you can just copy this table, try to grab all the data from the statements and fill in. Yeah. Some easy questions may be easy to just two or three columns or rows. That's easy for you to make a table, but for some questions, a little harder. Yeah. You might need help at the very beginning. Yeah. We show you some examples. Yeah. So, here, we have a table. So, here, You can copy the table if you do not know how to make your own table. And also this one I want to mention, sometimes the table could be fixed with the amount of rows and amount of columns. But for this table, you fix with the columns but not rows. Can you see how many days you could reach? You are not sure. So you continue grow your table until you find a result. So this is a little harder one. Because you have no idea how many days you would and how many rows you need. You just need to continue grow your table. Okay, let's open the poll. This one's not an easy question. It's a little confused sometimes if you do not pay attention to the step-by-step. Yeah, it looks like everybody answered it, so. OK. So here, let's check the answer. You see, a lot of people select, students select the same. Yeah, OK. So here, OK, can you hear me? Yeah, OK, sure. So here, look at the day one. So during the day, you go forward two miles. But during the night, you go backward one. So you totally gain one mile during the day one. And the same situation happened to day two. You also gain one mile. Again, until day five, you gain totally. After night, you gain five miles. So by the next day, remember, during the daytime, you will move forward two miles. Five plus two, you get seven. That means you already reached the shore. You do not get back, push back during the night anymore. So this is very important. Yeah, so you have to go step by step, make sure what point you should stop. So during the day, you already reached the shore. You stopped. You do not have pushback. So that means you will stay at six. The day six, you will get on the shore. So this is a very special question. I know some of you just say, oh, every day, we just gain one mile. So we just use seven miles and divide it by one, and we could get seven days. But remember, during the day six, you actually already reached the shore. So if this table is very clear for you. Yeah, so this is a very classical question we want to show you. Pay attention to all the conditions they gave to you in the question. Yeah, what do you think, Elita, for this question? Yeah, I think we actually have done a similar question before where the, I think maybe it was draw a picture where there was a frog who was climbing out of a well, and he slides down a little bit every night. So I think it's good that we're repeating the same type of question and showing you that you can solve it in a lot of different ways. Yes, yes, that's correct. Thank you, Elita. Yeah, OK, let's see the next question. Yeah, Elita, go ahead. In a certain number, the first digit is greater than the second digit by two, and the second digit is greater than the third digit by three. It is one of the numbers listed below. What number is it? Do you think we show the table, or we just give one minute? I think we show the table, because otherwise the students might not know how to draw. Yeah, it's a hard one. Yeah, OK. Can you explain a little bit for this table? Yeah. So you can see on the left column has all the answers, A, B, C, D, E. And then the first digit is the next column, the second digit is the column after that, and the third digit is the rightmost column. So for each answer, you can fill out the table. So for A, the first digit would be zero, and the second digit would be five, the third digit would be three. And so on. So you guys can do that for every answer. And I'll launch the poll, too. Yeah. So you can copy the table. At the beginning, you do not know how to make a table. You try to copy the table, understand how we make the table. And later, when you practice more, you will get better understanding. Okay, so maybe we can share the results. So I think you guys did really well on this one. Most of you got it right, so well done. And you can see that we use the table to figure this out. So for A, well, the way I said it was, I said the first digit was zero, the second digit was three, and the third digit, I mean, the first digit was zero, the second digit was five, and the third digit was three. But it doesn't really matter, because either way, that option does not work, because it does not have a third digit. And then for B, you can see the first digit is five, the second digit is three, and the third digit is zero. For C, it goes two, three, three. For D, five, two, one. And for E, four, three, one. So now we can go through and really easily check to see if it satisfies the conditions. So we know the first digit has to be greater than the second digit by two, and the second digit has to be greater than the third digit by three. A does not satisfy the second condition, where the second digit is greater than the third digit by three, because it does not have a third digit. B, you can see, satisfies both conditions, so that one works. But we can also go through the rest of them to make sure that they don't work. C does not satisfy either condition, because two is actually less than three. B also does not satisfy either condition, because five minus three is two. And then E satisfies neither condition as well, because four minus one is three. So you guys can see that B is the only one that works. Yeah. Thank you, Elita. Very clear. Yeah, this table is very clear to compare all the digits, yeah? Okay. So let's see this question. Yeah, here. All the possibilities in a certain number, the first digit is greater than the second digit by two, and the second digit is greater. The same question? Oh, no. Yeah. A little bit different. Yeah. So we have a similar question, but this one's different. And the second digit is greater than the third digit by three. How many numbers are in total? Yeah. Yeah, it's the same situation happened, but you need to figure out how many numbers, how many of those numbers. Remember, the digit you could choose from zero to nine. But also, if you make the three digit number, the first digit never being zero, is that right? If the first digit being zero, like the sentence, like here, you only have a two digit number, okay? Yeah. Please draw your table. Yeah. It's a similar table you can draw, but you'll need to put in the digits, different digits, try to find more numbers, like 530. Yeah, 530 is one of the choice, but not all the numbers. They ask how many numbers in total. So I'll launch the poll. Yeah. You can use the same table. Just try to fill in the different digit to make the three digit number applies to both conditions. You can use the same table here, but you need to put your own digits there. Select from 0 to 9, make different numbers, apply to both conditions. Okay, so I think we might close the poll to share the solution. Yeah. Yeah. Look, most of you pick five. Yeah. Let's see if that five. Yeah. Okay. So we could look at all the digits. Yeah. So first, you know, you pick the digits from zero to nine. So it's better you pick from the biggest digit because the first digit bigger than second digit, second digit bigger than third digit. So it's better you pick from bigger digits first. So you will pick nine first. And then the second one would be seven and then four. Nine, seven, four would work. And then you just continue. The next one, you could start with eight. So you could get eight, eight, 63. And the next one, 752, 641 until 530. So the next, if you want to continue, you cannot do it anymore because you couldn't find the third digit. So you have to stop there. So there are five numbers in total. Look at the table. Is that easy for you to find the answer? I think this question is really good when you use a table. It's very clear. Yeah, Elita? This one's very useful for having ways to organize the numbers. So either a table or organized list would be really helpful here, I think. Yeah, yeah. It's better than you just straightforward try to solve it. Yeah. So here is very clear. And you won't miss any possibility. And you would say if you miss 800 something, it's very clear for you. Yeah. So the first digit, nine, eight, seven, six, five, four, you just follow. Yeah. Follow the descending order. Okay. Let's see the next question. Okay. Elita? Yeah. So Anna has one 5 cent coin, one 10 cent coin, one 20 cent coin, and one 50 cent coin. How many different values can she make? So let's still give you the table. Yeah, here. Yeah. So you can see this is how we're going to organize it. So first we choose how many coins she's going to use. She could either use one coin, two coin, three coins, or all four coins. And then there's obviously going to be different combinations because each coin has a different value to it. And then the total, or the subtotal. So that's how many combinations are in each row. Yeah. So you need to figure out the value. Yeah. So not only the combination, it's value. It should be different. Oh, just in case anybody didn't see the solution for the last one, because we didn't stop the sharing. So if anybody didn't take a look at this one, so I'll go back to show you. Yeah, a few seconds. The last question. Yeah. Yeah. So there are five numbers. Last question. Yeah. Okay. So you can see the table, how we feel in the digits over there. Yeah. Just in case somebody couldn't see because we didn't stop the sharing. Yeah. Okay, so now let's work on this question. Yeah. I don't think I started the poll. Do you want me to share the poll first? Let's just give them a few seconds and then let them just copy the table first. Okay, yeah, so let's launch the poll. Okay. And this is a little harder. Yeah, you need to figure out if one coins, that's very easy, how many different value you could get. Yeah. So you put a combinations in the middle column, and you put a whole many different value in the subtotal, and finally you add all the subtotal together. Let's see. Do we have the answer? Okay, here. This is a five point question, it's definitely a harder question. Yeah. Shall we share the solution? I think this one's a little bit hard for them. Yeah, so maybe we go through together. Yeah. Okay. Yeah, you guys seem to struggle a little bit on this one, which makes sense because this is a hard problem, I think. Yeah. Okay, let's take a look at the solution. Yeah, Elita, go ahead. Yeah, for this one. For one coin, it's pretty simple. You can choose any of the four coins. So you could either have 5 cents, 10 cents, 20 cents, or 50 cents. So there's four possible combinations for one coin or four different values when you're only using one coin. And then for two coins, it's a little bit harder, but I think you can make an organized list for the combinations within two coins. So let's start if, let's say we use the 5 cent coin. So if we use a 5 cent coin and the 10 cent coin together, then that's 15 cents. If we use the 5 cent coin and the 20 cent coin, we get 25 cents. If we use the 5 cent coin and the 50 cent coin, we get 55 cents. So that's all the combinations we can make using the 5 cent coin. So then we can move on to using the 20, I mean the 10 cent coin. So if we use the 10 cent coin and the 20 cent coin, we get 30 cents. If we use the 10 cent coin and the 50 cent coin, we get 60 cents. And then if we use the 20 cent coin and the 50 cent coin, we get 70 cents. So that's six different values. Notice that if you flip the value, so if you say we use a 10 cent coin and a 5 cent coin, we get 15 cents, which is already a value there. So that's not an extra value that we have to count for. And then if we use three cent, I mean, if we use three different coins, an easy way to count this is by choosing the coin that we don't use, right? So let's say we don't use the 50 cent coin. Then we have 5 cents, 10 cents, and 20 cents, which gives us 35 cents in total. If we don't use the 20 cent coin, then we get 5 plus 10 plus 50 is 65 cents. If we don't use the 10 cent coin, we get 5 plus 20 plus 50, which is 75 cents. And finally, if we don't use a 5 cent coin, then our total is 10 plus 20 plus 50, which gives us 80 cents. Since all four of these values are new, like we haven't made any four of these before, that's four new values. And then finally, if we use all four cents, that's, I mean, all four coins, that's only one combination of 85 cents, which is also a new value. So that's one new value. And then if we add up all of the subtotals together, we get 15 subtotals in total. So that's why we have 15 different values. Yeah. Thank you, Elita. Thank you. Yeah. So this is a little complicated. Yeah. So this is a little complicated, the table you try to make. We know this is hard. So that's why we go through the solution with you and we give you some idea how to solve this kind of problem. And later you can revisit with the recording and try to watch the question and make your own table and try to solve it again. Yeah. So I know this, this lesson, when we make a table, we need more time. So there is one more question. So we want to show you, yeah, we want to show you there is another way how you make a table. So we just maybe extend the two or three minutes, finish this question. Yeah. Okay. So here they said the sum of two digits, one from inside a square, you can see the inside square, you have a nine digits, one, two, three, four, five, six, seven, eight, nine. And then they, you have the five digit outside the square. So one, two, five, seven, eight. They ask you to pick one number from outside, pick one number from inside and you add it together. If the sum is greater than 10, so that's a pair you want. So then they ask you how many pairs you can find. So this one, dude, do you have an idea how to make the table for this one? Yeah. You know, we pick from outside and also pick from inside and make a pair and we need to count how many pairs we would have. Yeah. So here, yeah, this is a little harder one. Yeah. We, because this one look like a multiplication, multiplication table. Yeah. The times table. Yeah. It look like very complicated, but it's very clear. Yeah. You can find each pair if it work or not. It's very clear. Right. Yeah. So because the, we are over time for the class, so we do not open the poll for this one. We will go directly go through the solution for this one. With this table, we can show you how to find the answer for this one. So here, like we mentioned, you'll try to find the pairs. So each outside digit one, two, five, seven, eight, you will match with one inside a digit. So you can look at all the, all the sums over there. So you start with the outside, the one, and you find the pair from one, two, three, four, five, six, seven, eight, nine. So none of them work because the biggest one you could make that's 10. One plus nine makes 10. So this not greater than 10. Remember greater than 10 means you have to find the sum bigger than 10, not equal, not small. So that you look at the second outside digit two. So when you try to figure out only one work, like a two plus nine, 11, that work. Yeah. So only one choice. And then you try to figure out five. So you wouldn't know until you could make a 10. That's not working. Yeah. So five plus five, you make a 10. That's not bigger. So before that, that's not applicable. Only after that, you add more than five, you could get it more than 10 for the sum. So you would figure out five plus six until five plus nine. They all bigger than 10. You get four. And from seven, you can see there is a pattern here. Yeah. So until seven plus three, you make a 10. It shouldn't work. After that, you could get any sum. It's bigger than 10. So that's plus four, five, six, seven, eight, nine. So you'll get six choices. And that eight. So when you have a bigger upside digit, and you will have more options, more pairs working. So you would start with eight plus three, bigger than 10. And you get seven options. And then you add all them together. You would get 18 in total. Yeah. For this one, yeah, you also can use other way to simplify the table. You do not really need at least all the nine digits on the columns. Yeah. You might just list one column. Try to figure out how many digits you can pick from the nine digits and count how many pairs. Yeah. So here is a make a table. So this is a super helpful, help you to come up. Yeah. For many possibilities, organize the information and find the patterns. So we hope you can practice the sum question with a making table. Even it's hard at the beginning, but when you practice more, you would have much more idea how to make a table. Yeah. So that's for today. Thank you, everyone. I wish you a wonderful Thanksgiving. We do not have class next week, and we will see you in two weeks. Thank you, Elita. Thank you. Bye bye. Thank you guys.

make a table strategy

data organization

problem-solving

logical comparisons

mathematical problems

guess and check

data analysis

arithmetic skills

pattern identification

webinar session