Hello, everyone. Welcome to our third webinar. Today, we are working on the work backwards, and this is Lucia and Elita. We're very glad to see you again. So first, before we start the lesson, this is the ground rules. Yeah, so most of you already joined the webinar, but we might have some new students. So we would like to reinforce during the webinar because we are doing a recording. So there is no video and a voice for the students. We can answer some questions, but we cannot answer all the questions. So there would be recording, send you after each class, so you can revisit the recording to review the lessons later. So first, we also want to reinforce the four-step method. This is a very important method help you to solve some harder questions. So every time when you try to solve the problem, you always want to understand the problem first. So this is the step one, read the question carefully, check the picture carefully, and understand what question ask for. And the step two, you need to make your plan how to solve the problem. So you want to identify what a type of problem would be. Like today's lesson, we're going to work on the working backwards. So there is something you need to figure out. Oh, this work backward question, yeah. So next step, once you figure out what type of question would it be, and you know what strategy you would use to solve the problem, maybe you pick one or maybe you pick more, and then you write down your solution step by step. So that would be easy for you to check your answer and to check your solution later. Once you finish the question, do not move forward directly. So please take a few moment to review your answer. And you can put your answer back to the question, check all the conditions, or you can use different approach. But during the competition, you have to pay attention to your time. So do not stack on one question for longer time. So this is a four-step method. It's very helpful. We want you to remember those four steps and apply the four steps when you solve the harder questions. So remember, last week, we worked on the drawing picture. So this is a very popular strategy at your level. So a lot of question, you would see they are all word, there is no picture. So it's hard for you to understand. If you draw the picture, that could help you to visualize a question and understanding the question and also find some hidden part in the words. And also some question, they give you the picture. So you might need to draw something on the picture and that help you to solve the problem. So remember, when you're doing the pictures, you do not need to draw something very complicated. You can just draw something simple, easy, and help you to solve the problem. You also need to remember, you draw the picture according to the skills. So like something, you know, in the real world, the big item, you draw big in your picture. The small one, you draw smaller in your picture. So those draw to skill. So today, we're going to work on the new strategy, working backwards, yeah. So this happened when you meet the question. They do not give you the beginning. They give you the result. So you do not know what's the start of the question, but you know what's the result. And then you need to work to solve, to find the beginning. So this is a way you always need to reverse your operations and you will work step by step. And from the end part, go back to the start part. So remember, when you work backwards, you always reverse the last step first. You do not reverse your first step. So you'll need to follow the order from the last step, go back to the first step. So this is work backwards. Elita, would you like to share something about work backwards? Yeah, sometimes working backwards is like the only option available to you when you start with the end. Usually it will be like a list of operations and then you have to reverse them as you go back. It's also very step by step. So it shouldn't be too complicated. It should be pretty clear on what the steps should be. Yeah, thank you, Elita. Yeah, we will show you the questions. So here we give you a very clear idea how we work backwards. So like, you know, here, there is a good example. You start from your home and you take 30 steps left to the end of the street. And then you turn right on Gray Street and turn left on Sacramento Lane and turn left on Rose Drive and then turn right on the schoolhouse road. And then you arrive your school. So when you work backward, you will walk from your school back to your home. So you definitely would reverse the last step first. So you would say, here, you go back home. You start with this step, you go back. Yeah, but every time the direction, you'll have to reverse the direction. So before, if you turn right, you'll have to turn left. Before, if you go east, you'll have to go west. If you go south, you'll have to go north. So that's all the reversed operations and opposite directions. So this is a work backwards. We give you the real example in your life. Yeah, very easy to understand. So now let's work on the question. So this one, we give you the picture here. You have this one on your handout and you can see who caught the fish. So A, we follow the name. The name adds alphabetical order. Adam, Basil, Charlie, David, Edgar. A, B, C, D, E. Okay, so we will open the poll and let you to answer the question. This is a three point question. Usually we recommend you to solve it in one to two minute. Whoever just joined, today we work on the new lesson, work backwards. So we are working on the first question. The picture is on your handout. So we already opened the poll and wait for you to put your answer. Okay, so let's share the result. Yeah, so you would see most of you pick the correct answer, David, yeah? Okay, so let's see here. Yeah, let's quickly go through this question. I think most of you will get the correct answer. So first, you would see what? What's the result? Result is a fish. If you do not go start with the result, you will check each cat, is that right? You check each of them and we still tangle the fish lines. So now if you start with the fish, that's very easy. That's very easy, you trace back and you found David is a cat who caught the fish. Very easy, yeah? So you only needed to work on one pass. You do not need to check all the cats, yeah? So this is the answer. Let's see the next question. Yeah, Yelita. Yeah, which of the children will reach the rabbit? Follow the arrows to find out. So you can see the five children on the left side of this box. And then each of the answer choices corresponds with one of the children. Some students ask where to find the handout. It's in the parents account and I will share the link here. So please remember those links. Okay, I think I will end the poll and share the results. Yeah, please. So you can see that most people chose D, which was the correct answer. We want the students or the children to get to the rabbit so we can follow the arrows backwards. Usually you would go from the tail of the arrow to the tip of the arrow but instead we have to go from the tip to the tail. So you can see the first arrow we make it point backwards instead and then as we follow the arrows along the path we end up at the fourth child, which is D. Yeah, and remember this time so they ask follow the arrow because when you go from the kids to the rabbit you need to follow the correct direction of the arrow but when you go back you have to reverse the arrow. Yeah, reverse the direction. Yeah, so reverse the so here that means you couldn't really follow arrow. So like you're from the rabbit they ask you start with rabbit you from rabbit you go back you have to do the opposite direction with the arrow direction so you cannot follow the arrow so any time if you would follow the arrow follow the correct direction of the arrow so that would be wrong. Yeah, so you need to reverse the direction of the arrow so that's why yeah the answer would be the D. Some of you might got confused that you really follow the arrow direction. Yeah, okay, so let's see the next question. You have to close two of the five gates so that your mouse cannot reach the teeth. Which gates should you close? This is a four-point question. You see the question number nine, that's a four-point. Usually, we recommend maybe the four-point, sometimes you spend two to three minutes. I shared the handout folder link in the chat. If you do not have the handout, you can find today's lesson 3, find the lesson 3 printed out. I recommend you to print out all the handout and put it in a folder, so that's easy for you to use in every class. Okay, so let's share the answer. Yeah, we see most of you pick the correct answer and some of you pick different answer. So let's take a look. So here, yeah, so you needed to figure out what they ask for. They ask for, you want to close the door and do not let the mouse reach the cheese, yeah? So you have the mouse, mouse can follow the maze, yeah, and try to find a way to get the cheese. So here, if you draw the route, you will figure out from the mouse and you could go down and go to the each, you know, the path, the available path, and you could find the four or five. So both through those two doors, the mouse could reach the cheese, yeah. So this is a way and you could easily to find the result. You start with mouse, even, you know, you consider, yeah, cheese will maybe be the result, but actually here, so that's a mouse come to the doors. Yeah, so you follow, you start with the mouse and here you can check the passes and then you find the cheese here, yeah? Yeah, so you finally got the cheese through the door four or door five and you want to check your answer. So you'll need to check the door three. If your door three go back, so you would get the dead end. If you go door two and also you go back from door two to door one, so you'll still go back to your cheese. So you cannot get the mouse, yeah? So here only five, four or five, so that happened. Yeah, four or five that happened. So you can find the answer. Yeah, so that's four and five. Next slide. Okay, what number do we need to write in the shaded cloud so that after performing the operations indicated in the picture, we get the number 36? So you can see that whatever numbers in the shaded cloud, we multiply by three, then add three, then divide by six and we end up with 36. So this is a four-point question, and I would like to see the question might involve the calculation is harder, yeah? Oh, you agreed, yeah, it's harder, yeah. So especially involve the two-digit, the division, so that's harder, right? You have to make sure your calculation right, even you go the right operations. Okay, so we are going to close the poll because it's almost three minutes to solve this problem. So here we see most of the students got the correct answer. Very nice. Okay, let's go through the solution, Elita, please. So the correct solution was C13, and we can get that by reversing the operation. So we know the opposite of minus six is plus six. So to get to the next cloud, we add six, giving us 42. And then the opposite of plus three is minus three. So we subtract three to get to 39. And then finally, the opposite of multiplying by three is dividing by three. So we divide 39 by three to get 13. And we see that 13 should be in the shaded cloud. Yeah. So for some of you, maybe the multiplication or division, it might be harder because you are grade one, grade two students. So please, we recommend you to remember the times table. You remember the times table up to 10. That would be super helpful because the division would be the opposite operations for the multiplication. So here, how to do the 39 divided by three. Yeah, this might be hard for some of you. So I would like to recommend you to do what we, yeah. So when you try to do this one, you split the 39 to what? To two numbers. 39 could be, get the number 30 plus nine, yeah? So this way would be easy for you. And then you try to split. You divide by three means you want to split into three groups. Each group have equal amount. So here, you would split the 30 to three groups. So that would be easy, yeah? Each one, you would have 10. And you split nine to three groups. So you get, each one has a three. So you know, you want to make them in a one, three groups. So that's each group, you would take a 10 and a three. You add it together. So that would be your answer. So if you do not really know how to direct to do the division, so you can do this way, yeah? You split into the groups, yeah? OK, next question is very similar. So it's a similar one. What number do we need to put in the first square in order to get 100 as a result after doing all the operations shown below? Elita, do you see my share screen for the solution? Yeah. Yeah, I just want to make sure because sometimes we open the poll so the student cannot see the, see the solutions. If you couldn't see the solution later when we explain the question, please let, let us know. Okay. So you solve this one step-by-step. What's the first step you solve? Yeah, we have a similar question before. You can follow those steps, work one by one back to the start. So you can see the number, that's 23, yeah? Because this one involved the calculation a little harder. Okay, so you see the result. We still have most of the students got the correct answer. Yeah. Okay, let's see the solution here. So first, you start with 100. If you go backward, so the first step, you'll need to reverse the times two. Before your times two get 100, when you go backward, you have to divide by two. You cut in half the 100, cut in half. You get 50, very clear. And then you add two to make 50. When you go backward, you need two minus two. Very clear, you get 48. I think by this step, most of you could get this step very easily. And the next step involves you need to reverse the times four. You need to do the divide by four. So this is maybe a little harder. 48 divided by four, how to get the correct answer. Like I mentioned, if you know the times table, that would be very helpful. If you do not know, you also can break the number to the tens with tens of the ones needed. So that's easy for you to split those tens and the ones needed to the four groups. So like 48 equal 40 plus eight. You want to make the four groups. Each group have same number. So then you split the four groups. So it's very easy for you to know. Each one would have 10. Very clear. And eight, each one would have a cut in half. So each one has two. So you put into the four equal groups, you would have figured out 10 plus two make the final answer. So this is how to calculate the division in an easier way. Let's see the next question. Elita, go ahead. Sam's mom left a plate of cookies on the counter. Sam ate two of them. His dad ate three of them. And they gave 12 to the neighbor. At the end of the day, only four cookies were left on the plate. How many cookies did she make all together? So, when we stop sharing, so you can see our solution page, and also in the recording. I believe we in the recording they never show the poll section. So you can see the solution and the question all the time in the recording. Also I know some students have not yet to study to learn the times table multiplication. So buddy. Yeah, maybe you can try. You can try with small numbers, learn something, because you will meet some questions involved with multiplication. Please put your answer in the poll. We're going to share the solution now. So, you can see that most people got it right, the correct answer was 21 cookies. And we can get that by starting from the end of the day where there were 4 cookies. So if we go back to before they gave their neighbor 12, that's 16, and then we do before the dad ate 3 of them, so you get 19. Then before Sam ate 2 of them, we start with 21 cookies. So his mom made 21 cookies. So this is very clear, they give you the result, and you just need to reverse all the orders here. So you can write the equation, and then you follow the step from the end, go back one step by another step. So that's very easy, and make sure you do the correct calculations. But I can tell you, during the math competition, we usually do not give you very hard calculation problems. So the question mostly involves the logical reasoning and problem solving. So you need to understand the question and know how to solve them. Let's see the next question. It's a Saturday today, Tom's birthday was 4 days ago, on what day of the week was Tom's birthday? So you need to know the order of the weekdays, know the names and order of the weekdays. So otherwise, you cannot solve this problem. Okay, I think I will end the poll now and share the results. Okay. So you can see the result. We have some different answer, but most of you pick the Sunday. That's correct answer. So let's see the solution here. So here we want to figure out what's the four days before the Thursday. So I mentioned you needed to know the order of the weekdays. So from the Thursday, if you go back four days, you would count Wednesday, Tuesday, Monday, Sunday. And then if you continue to count back, you will get a Saturday, Friday, and a Thursday again. So seven days you will repeat. But here you do not need those many days because they only count four days ahead, the previous four days, yeah. So then you would figure out, oh, Wednesday, Tuesday, Monday, Sunday, until Sunday. That's four days before, yeah. Okay, so this is the answer. Remember, remember the calendar, yeah. So the weekdays, so get familiar with those. And later we will have one lesson focused on the calendar and the time. Yeah, next question. Lucy, Maria, and Anna have a meeting at 12.30 p.m. Lucy's walk takes 10 minutes, Maria's a quarter of an hour, and Anna's 40 minutes. At what time must the person who needs the longest time to get to the meeting leave her house? So we have three people and they all take different times, but we're only looking for the longest time. Yeah, we just want to remind, um, so the, I know some parents might have the kids sometimes, but during this practice, we do not recommend that parents have the kids because we want to know your real performance. And that it's hard for us to adjust the class pace based on the student's performance. This is a four-point question, but I think that this is a harder four-point question, Yilida. Is that right? Yeah. I think so, too. I think it asks a little bit confusing of a question. So any more answers? Yeah, we're going to share the solution. So you can see that most people picked B, but also quite a few people picked A. The correct answer was B. So if the meeting is at, so first we have to figure out who needs the most amount of time to get to the meeting. Lucy needs 10 minutes. Maria needs a quarter of an hour. There's 60 minutes in an hour, so a quarter of that would be 60 divided by 4, which is 15. And Anna needs 40 minutes to get to the meeting. So we can see that out of those three numbers, 40 is the largest, so we should be looking at what time Anna needs to leave the house. Because she needs to get there at 1230, we subtract 40 minutes from 1230. If we go back 30 minutes, we get 12 o'clock, and then 10 more minutes after that is 1150. So Anna should leave her house at 1150 to be at the meeting on time. Yeah, yeah, I agree. This is a harder question, but sometimes, you know, the four-point question or five-point question, it's not exactly, you know, when you think about the hardness, yeah? Sometimes you might feel the five-point question is much easier than the four-point question, but mostly they give you the very correct, you know, the hardness of the question. So you just pay attention. Whatever you solve the problem, you understand what the question asks for. And here, you need to know the time, need to know what's a quarter of an hour. So those about the basic knowledge of the time, we will have one lesson later to introduce the time and calendar. So here, like Elita mentioned, so when you work backward, so you found the time to go back, you go back 40 minutes might not be easy. You can go back half an hour, that might be easier. Or go back by an hour, that would be easier. Also pay attention to the a.m. p.m. So once they mention the a.m. p.m., so you have to pay attention to your answer. Sometimes if they give you the answer 1150 a.m. or 1150 p.m., that's a different answer. You have to pay attention. If the question gives you a.m. p.m., a.m. is morning, p.m. is afternoon. If the question gives you a.m. p.m., you have to figure out the answer, pay attention to the answer choices. Yeah, pay attention to the answer choice with a.m. or p.m. If the question didn't give you a.m. or p.m., so you don't need to really care about that. So Elita, have you ever met those problem? You gave the a.m. p.m., you know, even the same, you know, the time, but I gave it a.m. p.m. That's totally different, you know, the result. Yeah, when the time is around 12, then they might try and trick you by giving you an a.m. answer and a p.m. answer. Yeah. So we didn't give you that tricky, tricky answer, but I want to remind you. Yeah. Let's see the next question. Anne has some apples. Maria has two apples more than Anne. Altogether, they have eight apples. How many apples does Anne have? So please read the question carefully. I think you might get confused for some part, yeah. They're just two friends. And one has more, one has less. Okay, let's share this question. I think most of you got the answer, yeah. And this one, so the correct answer should be A, but most of you picked a different answer. So you might didn't really understand the question. So let's go through this question here. So here they told you Ann has some apple and Maria also has some. They didn't tell you how many they have for each of them, but they tell you the total apples. So, you know, we learned of drawing picture. So for this one, you can draw eight apples. Is that right? Yeah, you draw eight apples and you would know what? If Maria has two apples more than Ann. So you cross after two apple and then Maria would have exact same amount apples with Ann. So you have a six apples left over and you split the six apples to the equal amounts and you would get Ann has three and Maria definitely would have five because two more than Ann. And you add those answer together, you would get eight in total. So you check your answer. So this question not really hard, but you need to pay attention. You draw the picture, help you to solve this problem would be much easier. So this is a four point question. Sometimes the question look easier, but it's still easy to make a mistake. Yeah, what do you think Edita? Yeah. Yeah, I think the first time I read it too, I almost made the same mistake. I almost thought Maria had two apples so that Ann must have six apples. But then I read it again and I saw that it says, Maria has two apples more than Ann. Yeah, pay attention. Sometimes there always be a single word. It totally changed the meaning of the question. So really pay attention, please. Next one. Grandma made some cheese dumplings and some blueberry dumplings. Altogether, she made 31 dumplings. If she had made 11 more cheese dumplings, then there would be the same number of blueberry dumplings as cheese dumplings. How many cheese dumplings did grandma make? So this question is a little bit long and it can also be a little bit difficult to understand. So make sure you read it really carefully. Yeah, you read it carefully and you need to draw a picture help you solve this problem. You do not really need to draw the 31 dumplings. Yeah, you can draw a line to stand for amount of dumplings. Oh, Edita, can you hear me? Yeah, I can hear you. Yeah, the student said it cannot hear us. So you might check your audio. Yeah, check your audio. So you can unplug or plug your audio connection. This five-point question is not easy, yeah, especially this is a kind of a long wording question for the grade one, grade two students, where you'll say a lot of words, first you might just feel, oh, this is very difficult. This is definitely a harder one. We recommend you to draw the picture and pay attention to all the conditions they give to you. The grandma actually made 31 dumplings. So that's the total, the real amount the grandma made. But they said if she had made, this is assumption. That 11 cheese dumplings, the grandma didn't make. It's just give you an assumption, example, yeah? And then you could have equal amount, cheese dumpling and blueberry dumpling. So they ask how many cheese dumplings? You have to answer the question what they ask for. So first you should understand which dumpling grandma made more. Yeah, which one made less? Yeah, by the condition. Okay, let's share the result. Yeah, I know this is a little tricky. Yeah. So most of you or half of you did get the answer right. Grandma made 10 cheese dumplings. So we see that she may actually made 31 dumplings. But if she had made 11 more dumplings, then the numbers would be equal. So let's pretend she did make 11 more. So then she would have made 42 dumplings in total. We know she made equal amounts of blueberry dumplings and cheese dumplings. So that means we can divide 42 by two to get how many dumplings of each. So that's 21 dumplings each. So that means that grandma made exactly 21 blueberry dumplings, because we didn't add any blueberry dumplings. She made 31 dumplings in total. So we can subtract 21 by 31 to get 10 cheese dumplings. Yeah. So first, from this question, you know, the blueberry dumpling is more than the cheese dumpling. Yeah. So I recommend you to draw the picture. You also can do this way. So you draw the cheese dumpling. And you also draw the blueberry dumpling. So this is a total amount grandma made. It's a 31. Is that right? Yeah. But they tell the grandma if made 11 more cheese dumpling. So this is 11 more. And then total grandma would make 42. Yeah. It's easy for you to get the sum. 31 plus 11. That's 42. So this 42 included the 11. Can you see the 11 cheese dumpling? That's we just, you know, give the assumption here. So now you could figure out, oh, half of them 21. Some of you divide 42, get a 21. You answer how many blueberry dumplings. You didn't answer how many cheese dumplings. So then you need to use a blueberry dumpling minus 11 and get a cheese dumpling. So you see, when you draw the picture, that's also very easy for you to see the answer. Yeah. Or you can list the equation. You can have a different approach to solve this problem. Oh, this question is pretty tricky. I really like this one. Yeah. It's a hard one, but a very interesting if you know how to solve it. So Joy and Olivia exchange sweets. First, Joy give Olivia as many sweets as Olivia had. So remember, what's this condition? And then Olivia give Joy as many sweets as Olivia had. And then Olivia give Joy as many sweets as Olivia had. As Joy had after the first exchange. So you see, there are two exchange. You have a first exchange and you have a second exchange. Yeah. I explain this question more because I know this is a harder one. Yeah. So give you more and help you to understand more about this question. Yeah. So you have two exchange and then finally you got four for each. Yeah. So how many sweets did John have at the beginning? This is a very good question. Yeah. We can open the poll for this one. If you know how to draw a chart, a table, so you can draw that to help you to solve this one too. So pay attention to the question here. They ask, how many suites does John have? They didn't ask your total suites, yeah? You have to pay attention what they ask for. This is definitely a harder one. Yeah, so it's a question 24. Yeah, five point. Yeah, Elita you can hear me clearly. Yeah, I can hear you very clearly. Yeah. So, if you couldn't hear us now. I think that's a problem on your end, on your side. You have to check your device. We keep the whole class muted, but the both the hosters like me and Elita, we both talking, keep talking. If you cannot hear us, you have to check your device. Okay, I think maybe we explain this question, yeah? Even we give more time, I don't think the students is on the right track. Yeah. So the answer, unfortunately, no one got the correct answer for this one. Yeah, this is a pretty tricky question. Yeah. Yeah, if you cannot solve it, it's really understandable. Yeah. Okay, so I'll give you the solution. Yeah. Somebody says they are unable to see the screen for the solution. I can see your screen. Yeah, so sometimes when we share the result, yeah, you cannot see the solution screen. But once we stop sharing, you should see the solution screen. Also, we want to tell you, when we do the recording, so there won't be any post setting appear in the recording. It's all the questions over there, all the time. So for this one, like I mentioned, there are two exchanges. And also by the end, the result, both of them have four. So you should at least notice one thing. So the total amount never change. Is that right? So because they didn't mention any of them ate something. Yeah. So that means they just switched the sweets between them two. So they have a different amount each time, but the total amount never changed. If they gave you after second exchange, you get a four and a four for each of them. The total would be eight. It's very clear. Yeah. Okay. All the time would it be eight total. Some of you pick the answer eight. That's a total amount. So now you need to work backwards. Remember before the second exchange, this is the second exchange. We always reverse the latest exchange first. So second exchange is that Olivia gave John as many sweets as John has. That means John what? John doubled. John doubled the amount at that moment. John got a double times two. Okay. When John got a double, John got a four. So when you go backward, you have to divide by two, cut in half. Is that right? So when you go backward, you have to divide by two. So you would know at that moment. Before the second exchange, John would have a two. So if you got this one, you know the total always be eight. So you would figure out. So before the second exchange, so Olivia should have a six because the two added together always equal eight. So now you'll have to reverse the first one. The reverse the first one. So the first one mentioned. Yeah. So that John gave the Olivia as many sweets as John has. So this time, so that's the first time that Olivia got the doubled. When Olivia got doubled, Olivia got a six. Is that right? Yeah. Yeah. So then you need to go backward, work backward. So when you work backward, you have to maybe use different color. When you work backward, you have to divide by two and you would get what Olivia had before the first exchange because Olivia got doubled, got doubled to six. Yeah. If you go backward, you'll have to divide by two. So Olivia would have a three before the first exchange. So you know the total eight. So what would John has at the very beginning? So that's fine. Yeah. This is a harder question. So this is when you need to know what's the conditions they change at each time. Yeah. You know the first one, Olivia got doubled. Second one, the John got doubled. So if you want to work backward, you'll need to divide by two for the amount they had. But you have to reverse the John's first. Yeah. Because you know, the second action, that's John got doubled. So you'll have to reverse this one first. So you'll have to reverse John's first divided by two. And then you'll have to reverse the first action and divide it by two for Olivia. So now it's clear. Yeah. Elita, what do you think? Is that a clear for the solution now? Yeah. I think the solution is clear, but this is a very difficult problem, I think. Yeah. We have a recording later. You can just work on this question again. Yeah. Try to get more understanding. Yeah. But this is definitely hard. Okay. Let's see the next one. Okay. Ben is trying to decide when to get up in the morning. He needs 40 minutes to get ready for school. It takes him 10 minutes to walk to school. If school starts at 8.30 AM and he wants to be on time, what time should he get up? Okay. Another time question. Yeah. So this is the last question. We want to finish it. Yeah. Sometimes we have a harder question. We'll take a longer time. Yeah. Let's finish this one. This is another time question. So we will have a lesson, time and calendar later. We will work the more questions about the time calendar, make you get more familiar. So you have to pay attention. They need 40 minutes to go to school. Yeah, to get ready for school and walk 10 minutes. Yeah, I see this class is good at the time question, yeah? Yeah. But to make a correct answer is not easy. Even if you have the basic knowledges about the time and calendar, but the way you solve the problem, sometimes, yeah, it's still easy to make a mistake. Yeah, let's review this one, yeah? Elita, can you share the answer? So, you can see half of us got the correct answer, which was 7.40. If he needs to be at school at 8.30, then we can go back 10 minutes to see when he has to walk to school. So that's at 8.20, but he also needs 40 minutes to get ready. So we have to subtract 20 minutes from 8.20 to get to 8 a.m., and then another 20 minutes to get to 7.40. Yeah. There's a mistake there. It should be 8 o'clock minus 20, not minus 30. Oh, yeah, yeah, yeah. Sorry. But, so, you can see it. This is the problem, this typo. Should it be 20 minutes here? Yeah, okay. Okay, thank you. Yeah, so this is our lesson for work backwards. Remember, we work backwards. You always see the result, and you go step by step. You always reverse the last step and go to the first step, so you'll reverse all the operations. Yeah, thank you, everyone. I also want to mention, next week I won't be here. I will go to attend the AKSF, the International Math Kangaroo Conference, and I will have the substitute teacher, Ms. Diana, work with Ilita with you. Yeah, thank you, everyone. Yeah, so I will see you in two weeks. Thank you. Bye-bye. Bye.

working backwards

problem-solving strategy

Lucia and Elita

four-step method

math competitions

logic

puzzles

word problems

time calculations

confidence in problem-solving