math competition that is held on the third Thursday in March since 1998. So Math Kangaroo is celebrating its 25th anniversary this year. And there are a lot of really cool souvenirs that are available for participants this year. You can't really see, but I'm actually wearing the Math Kangaroo 25th anniversary shirt. All right. So for first and second grade, The test is 75 minutes long and there are 24 multiple choice questions. Sometimes people think that multiple choice questions are very easy, but actually they tend to be more difficult because there are distractors in the answers that might cause you to answer incorrectly if you did not read the question carefully. And the problems are what we call unusual and interesting problems because they require you to use logical reasoning and to think very carefully. And it's not just direct math facts. That's why in Math Kangaroo, we always encourage you to use the four step method. What is the four step method? First, number one, you understand the problem. So I would suggest that you read at least the problem twice. Maybe the first time, just read it through quickly. The second time, I would suggest that you read the question and you underline or circle information that you will need to use to answer the problem. What is the question asking you? Is it looking for feet or inches? Is it looking for hairs or individuals? So take time to understand the problem. Do not rush through. Step two, you plan how to solve the problem. How can I tackle this problem? What strategy should I use? What information do I need to solve this problem? Sometimes it requires one strategy. Sometimes it requires a series of strategies. And you will find that in the Math Kangaroo test, the questions start from easy and then they get more difficult. So as the questions get more difficult, then more likely you're going to use more than one strategy to solve it. So once you have decided on what strategy, what information that you are going to use, we go to step three, where you carry out the plan. Always write down the solutions step by step. Now, it's something I tell my students every single day. It might look so easy. OK, I'll figure it out in my head. But it's always good to write it down. First, when you write it down, you don't rush because it takes a little bit of time to write things. Second, when you write it down, you can see clearly. And that will also eliminate careless mistakes and wrong answers. So you solve the problem. OK, all that. Now we go to step four, where we look back to check and reflect. Look at your answer. Does it make sense if it has known, for example, a certain amount to be shared by a certain number of people? Your answer is going to be less than what you started off with. If, for example, you are you wake up at this time and you need a certain amount of time to get somewhere, then your time will have to be later. So that's why you always check and reflect. Does my answer make sense? You do a quick check. Sometimes you do a quick rounding or estimate to make to check that. For today, our topic is work backwards. It's kind of fun, right? You work backwards. So these are problems that have usually a series of events or a sequence of steps that can be solved by working backwards. So you go to the end of the problem and then you slowly go back step by step. So when you do that, some of the things you have to remember is you reverse the operations. So if the question was subtraction, now it becomes addition. If it is multiplication, it becomes division. If you turn right now, you turn left. Right. So we are going to. We are going to try this. All right. This is just a little quick warm up exercise. So let's say you start from home and you take 30 steps left to the end of the street at the end of the street. You turn right. On Gray Street. At the end of that, you turn left on Sycamore Lane, then you turn left again on Rose Drive. Right on Schoolhouse Road and the end of Schoolhouse Road is your school. So if let's say we're going home now. What do we do? So to go home from school, we have to turn left on Schoolhouse Road. Because we'd go reverse, right? And then we turn right on Rose Drive because earlier we turn left. We turn right on Sycamore Lane. Now, where do we turn on Gray Street? Right or left? Left. If you before you take 30 steps left to the end of the street. Now you will take 30 steps right. And if you did all that, you will be back home safe and sound. So this is what we meant by working backwards. All right. So we're going to get started with some of our questions. Question one. So you have this on your handout. Who caught the fish? So you're looking for the fish. So instead of starting with Adam and then Basil and Charlie and David and Edgar, the better way would be to look for the fish. And when you look for the fish, you follow the lines from the fish to the hook and see where that leads you. So do it on your handout. I know it's really simple, but it's kind of fun. And if you have a color pencil, that helps, too. Highlighter. OK, we will release the poll for you to enter your answer. It's always very exciting to see all the answers coming on the poll and on chat. Because I know you're participating and that's the best part. All right, we'll leave it for five more seconds and then we will close the poll and share the results with you. All right, we will share the results with you. And if you follow starting from the fish, you will find that if you follow the line, it will lead to David. David is the one who will get to eat the fish. Good job. Let's go to our next question. Here we go. Which of the children will reach the rabbit? Follow the arrows to find out. So what does the question ask you? It asks you to find out who will reach the rabbit. So you will look for the rabbit and then you will go backwards. So if the arrow is going right, then you go left. If the arrow is going up, you go down. If the arrow is going down, you go up. So I'm going to let you try that. So again, this is working backwards because it's asking you to find out who will reach the rabbit. So don't forget, make sure that you do the opposite, the reverse directions for the arrows. OK, we will release the poll and let you put in the answer. Also, if the poll pop up is blocking your window, you can just click on it, hold it and then push it to the side so that it doesn't block the picture. All right. OK, so let's release the poll so you can enter the answer. Is A, B, C, D or E? I see a variety of answers, so make sure you always go the reverse direction. You can try again. Okay, so this might get a little confusing because I see a variety of answers. So remember, go the opposite direction of where the arrows are pointing. All right, five more seconds, and then we will close the poll and share the results with you. All right, we'll share the results with you. Okay, so if you look and you will find that, no, if you do the opposite, the reverse direction, it will be D who will be able to reach the rabbit. Don't worry if you enter the wrong answer. The main thing is for you to get the answer, to understand the concept, that's fine. All right, next question. You have to close two of the five gates so that your mouse cannot reach the cheese. Which gates should you close? So remember we said, read the problem carefully because it says you have to close two gates, not one. And the question asks you to prevent the mouse from reaching the cheese, not which gate will let the mouse reach the cheese. We want to close the gates. So right now, all the gates are open, right? So you're going to test and see if which gate will actually allow the mouse to get to the cheese first. Then you will close the gate because there's no point closing a gate that will not allow the mouse to reach the cheese, right? So the first thing you're going to do is see which of the gates, one, two, three, four, that will allow the mouse to reach the cheese. And remember, it says two gates, not just one, but two, okay? So trace it. It's kind of like doing a maze, right? So look for two gates that you will have to close. Not just one, but two. So that's what I mean by looking, reading the question carefully. We'll give you a little bit more time and then we will release the poll for you to enter your answer. You know, sometimes when you do questions, it's better not to look at the answer first. You know, you read the question, you solve it because sometimes, especially with multiple choice questions, the answers are a distraction. And you look at the answer and say, oh yeah, see, my answer is correct. It's in there. But then that might not be it. All right, we'll release the poll so that you can enter your answers. If you notice on the poll, the answers, some of them have only one, and that's what I meant by sometimes the multiple choice answers might be a distraction than a help because, oh yeah, I found gate five, yay, my answer is there, it's correct, but then you have to look for the ones with two answers, so it could only either be D or E. All right, we're going to end the poll and share the results with you. Okay, so you will find that both of them actually follow the same route. One is when you come down to the bottom, you just go straight down to gate 5. The other one, you go around to gate 4. So gates 4 and 5 are those you have to close. The other gates are just dead ends. Good job to all of you who got 4 and 5. Now a little different. So we have problems with numbers and we have problems where you will actually do calculation. What number do we need to write in the shaded cloud so that after performing the operations indicated in the picture, we get to the number 36? So this operation means addition, subtraction, multiplication, division. Those are the basic math operations. So this is one of the questions where you need to go backwards. You end with 36, so now you start with 36. And then remember we talked about reverse operation. So when you have a minus 6, you actually want to add 6. When you have a mark plus 3, you want to minus 3. And what's the reverse of times 3? Divide by 3. So I'm going to give you a little bit of time to solve this. It's always good to write it down. Okay, we will release the poll for you to enter your answer. So these numbers seem like they're pretty easy, but a good idea is to write it down so we don't make careless mistakes. And again, if the poll pop up is blocking your view, just click on it, hold it, move to the side. All right, five more seconds to enter your answer. And we will close the poll and share the results with you. All right, so as you can see, the first operation with it was the reverse of minus six. So you plus six. So 36 plus six gives you 42. And then the next step is to minus three. So when you take 42 minus three, you get 39. Now you do 39 divided by three. I know that for some first graders, you might not have learned division. Then you think of 39. How many groups of threes can you make? And that will give you the answer of 13, okay? Next problem is kind of similar to number four. What number do we need to put in the first square in order to get 100? Here's the result after doing all the operations shown below. So you have 100. Now you go backwards. And you want to find out what is the secret number in the first square. So again, reverse operation. So you have 100 to start with. And to get to 100, you have to multiply by two. So the opposite would be to divide by two. So if 100, you want to divide it into two equal groups, you will have 50. And then keep going. What is the reverse of plus two? What is the reverse of times four? I see all the answers coming in on chat too. And it's okay if you cannot see the poll. The poll is just for you to enter your answer, just like what you can do on chat also. It's kind of fun to do the poll, but you don't miss out on anything if you don't see the poll. Don't worry about that. All right, we'll release the poll so you can answer. Put in your answer. Wow, everybody has the same answer. Almost. You are good with your basic operations. Okay, we'll give you five more seconds to enter your answer. And we will close the poll. All right, so we first did 100 divided by 2 is 50. Then the reverse of plus 2 is minus 2, so 50 minus 2 is 48. Now, how many groups of 4 can we make to make a total of 48? So, 48 divided by 4, you get 12. All right, next question. Now, this is a longer word problem. Sam's mom left a plate of cookies on the counter. Sam ate 2 of them. His dad ate 3 of them. And they gave 12 to the neighbor. At the end of the day, only 4 cookies were left on the plate. How many cookies did she make altogether? So, we've read it once. Now, we'll read it again and we'll look for important information, such as Sam ate 2, dad ate 3. They gave 12 away. At the end, they have 4 cookies left. So, when it's eaten and given away, it's subtraction, right? You want to find out how many there were at the very beginning. So, we go backwards. So, you might want to write on your paper the whole process. Like, for example, you have a certain amount of cookies. You take away 2 that Sam ate. You take away 3 that daddy ate. And you take away 12 that you gave to the neighbor. And you end up with 4. So, it's always good to write it down because it helps you see clearer. Okay. And then you go to reverse operation like what we were doing. I find it a lot of fun. So, you can start off with 4. And what's the reverse of minus 12? It's plus 12. 12 plus 4 is 16. And then keep doing the same thing. All right, we will release the poll for you to enter your answer, or you can put it on chat. So, the other way also when you look at your answer is, remember to check and reflect, is my answer reasonable? Do you think your answer should be more or less than 4? Of course, it has to be more than 4. Can it be more or less than 12? It has to be more than 12. So, that is how you check your answer also, right? Because you end up with more and you keep giving away, giving away, giving away. So, you have to start off with a greater value than 2 or 3 or 12 or 4. All right, five more seconds to enter your answer. Good, I see all the correct answers coming in on chat. All right, we will end the poll so we can share the answer with you. So the correct answer, as we go on, you have 16, reverse of minus 3 is plus 3, so you get 19. And then reverse of minus 2 is plus 2, so you end up with 21. Right, a pat on the back for all those who got 21. Next question, it is Thursday today. Tom's birthday was four days ago. On what day of the week was Tom's birthday? So we're going to count backwards. So what do we need to know? Today is Thursday. Tom's birthday was four days ago. And we want to find out what day of the week that was. So a good idea might be to write down the days of the week. And then you are starting from Thursday. Do you count Thursday? No, so you're going to go back four days. What day was Tom's birthday? Okay, we'll release the poll for you to put in your answers. So remember, we are starting from Thursday. That is our starting point. You do not count Thursday as one of the days. All the correct answers, only one. Nobody chose any other answer. You're going to count back four days. Not one, but four. All right, we'll give you five more seconds. And then we will share the answers with you. Okay, let's release the answers so that you can see whether you got it right. All right, so if we start on Thursday and we go back four days, so we're going to go back Thursday, Wednesday, Tuesday, Monday. We don't count Thursday. That's what I noticed with a few of you is that you counted Thursday. So from Thursday to Wednesday, one day. Wednesday to Tuesday, two. Tuesday to Monday. And then back to Sunday. So the birthday was on Sunday. All right, next question. Lucy, Maria, and Anna have a meeting at 12.30. 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? Right, this is kind of a long word problem. So that's why it's always good to read it at least one more time. So let's start off. The meeting is at 12.30. Lucy's walk is 10 minutes. Maria's is a quarter of an hour. So we need to know what is quarter of an hour. That is 15 minutes. When you have the clock, you divide it into fourths, and you have 15 minutes. That's where from 12 to 1, 2, and 3. Anna will need to walk 40 minutes. Now the question asks you, at what time must the person who needs the longest time to get to the meeting leave her house? So you have to figure out, is it Lucy or Maria or Anna who takes the longest time? So after you have done that, then only you go backwards and count what is that amount of minutes from 12.30. All right. So the question does not ask you who it is, but the question asks you at what time. Because I see on chat that some of you are putting the names of the people. Once you have found out who it is that takes the longest time, then you have to count backwards on your time from 12.30. So if you look at it, you'll find that, you know, Lucy takes 10 minutes. Maria is a quarter of an hour, and that would be 15 minutes. Anna's 40 minutes. Now you have identified that Anna's is the longest. So we're going to use the 40 minutes and count backwards from 12.30. Right, we will release the poll so that you can put in your answer. So the other way, when we talk about step four, to check and reflect, so is the time going to be earlier or later than 12.30? Of course, it's going to be earlier, right? You have to leave earlier to arrive at 12.30. So, you know, it cannot be E, which is 1.10 p.m., because we don't go back in time. All right, we'll have five more seconds for you to enter your answer. Okay, and we will close the poll and share the results with you. All right, so we know it's 40 minutes. So it might be easier to break down the 40 minutes to 30 and 10, because if you want to arrive at 12.30, it's easier to just subtract the 30 minutes first, and that brings you to 12 o'clock. And then you count back another 10 minutes, leaving you 11.50 a.m. And if Anna leaves at 11.50 a.m., she will get there right at 12.30 on the dot. Next question. Ann has some apples. Maria has two apples more than Ann. Altogether, they have eight apples. How many apples does Ann have? So now we read it again. Ann has some apples. We don't know how many. Maria has two apples more than Ann. Together, they have eight apples. And our question asks us to find out how many apples Ann has. So a good way is maybe we have done this before. Draw a picture. So you can draw a picture of eight apples. You can just put circles. I just like pictures. And Maria has two more apples than Ann. So how many does Ann have? All right. Remember, it's n only, not how many apples are left. OK, so read it carefully. And after you're done, check if n has this number of apples, then Maria will have 2 plus n and all together the sum will be 8 apples. So that's how you check and reflect. OK, we will release the poll for you to enter your answer. Ah, some of you are still entering how many apples that I have shown in my picture that are not circled. So be very careful though. Only want to know how many apples n have. And n is the one with less apples because Maria has more than n. So these are information that you want to take note of when you do this type of questions. The questions sometimes look really easy. And I always tell my students when it looks so easy, read it again, because those are the ones that know a lot of students will make mistakes. I'm like, oh, it's so easy. I know it. All right. We will share the results with you. All right. So if Maria has 2 more apples more than n. So that's why we take out the 2. Now, if we take out the extra 2, we know that both of them have the same. So we split 6 into 2 and we have 3 apples. And because the question asked for n who has the lesser amount of apples, then it is 3, not 6 that many of you entered as your answer. OK, now we're going to take a break from listening to me. We're going to have Noah share with you some of the tips on how to excel in math competitions. And then he will guide you in solving a couple of the problems. OK, Noah, you can take over. I'm going to stop sharing. All right. My Zoom just crashed. I can't see anything. Do you want to log in again while I go on to the next question? All right. OK. All right. OK, duck. So let's see if I got that. OK, so I'm going to skip. Hold on. Let me stop sharing. Oh, no, it's back. Yay. All right, back. Give me a moment. I was answering a question in chat before I left. I know they told you you're frozen. You know, it depends. It's winter weather and sometimes in certain places it affects the Internet. So depending on where you are, you know, you could have some issues with Internet this time of the year. So we so this is our last session of the series of webinar. And now the math kangaroo is coming up. And if you have been practicing and applying all this, the four step method and the different strategies, I'm very sure you will do well. Now, just remember, take it slowly. Don't panic. Take a deep breath. And then you can you will be able to do well. All right. Give me a moment. So I'm not sure if you're doing the math kangaroo online or in person. So if you're doing online, a good suggestion would be to make sure that no other devices are streaming in your home when you're doing the test, because that might kind of slow down the bandwidth. I always when I do Zoom meetings, I always try to do Ethernet because that is more stable. And my eldest son, who is the tech guy, always use Ethernet, especially for gaming, but for Zoom also. So if you're doing online, it would be a good idea to do that, you know, on Ethernet. All right, I'm ready. OK. Are you able to share screen? Yep. Give me a moment. Oh, I don't want to do that. All right. So. Oops. Just in general, some tips would be about the competition is that time management is very important. So in that sense, the whatchamacallit, the questions, although they're generally in increasing difficulty, they're not strictly increasing. Sometimes there may be an easier question near the end and a harder question near the beginning. So if you were to get stuck on the harder question in the beginning, that would be a waste of time, since instead of doing this hard question, you could have just gone past it and done some more easy questions. And also in the case of the easy questions near the end, if you were to go through all the questions, if you at least read through all the questions at least once, you'd be able to find those easier questions. And then after that, if you're running low on time, but you still don't have questions answered, I would suggest that you guess since there is no guessing penalty on Math Kangaroo. And this way, you'd have at least a one fifth chance of being correct compared to a zero percent chance. And in general, for practicing for the Math Kangaroo, I would say that this math competition is pretty unique, since frequently these questions can be worded in a manner that is more confusing than some other math competitions. So the best suggestion I could give about that would be, I guess, to just do past competitions for Math Kangaroo, since these questions are sometimes pretty unique. All right. So let's move on to the next question. All right, so grandma has 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? All right, so. Just a minute, Noah. Okay. All right. I'm showing you instead of the slide. Huh. Give me a moment. Share again. Can you see this? Yes. All right, here's a question. And. So yeah. We'll give. How many minutes is it? Per question? Maybe about two or three minutes. Alright guys, don't forget that if we add 11 more cheese dumplings, then there would be the same number of blueberry dumplings and cheese dumplings, which means there are less cheese dumplings than blueberry dumplings. All right, so I'm going to release the poll now. All right, I'll give about another half a minute for the poll. All right, so I'll end the poll now. Here are the results. Correct answer is 10. All right, so let me clean this up. All right, so basically the first thing, the most important parts are that if she made, she made 31 dumplings and if there were 11, oops that's a bad line, if there's 11 more cheese dumplings, then we would have the same number of blueberry dumplings as cheese dumplings. That means if we're to just take 31 plus 11 more cheese dumplings, it was 42. As we can see down here, we will have out of these 42 dumplings, there would be the same number of blueberry dumplings as cheese dumplings, which means that if we were, we can divide them by two and then we'd find that if there were 11 more cheese dumplings, we would have 21 dumplings each. All right, but since we have that if she made 11 more cheese dumplings, well now there's two more ways you can go about it. All right, so we know that there are still, the number of blueberry dumplings didn't change, so we could just take our original amount of dumplings and subtract our 21 blueberry dumplings to reach 10 cheese dumplings. Another way we could have done this is if we took our 21 cheese dumplings after we add in these 11 more cheese dumplings, you can subtract those 11 extra ones and we also end up with 10 cheese dumplings. All right, okay, let's move on to the next question. All right, so John and Olivia exchanged sweets. First, John gave Olivia as many sweets as Olivia had. Then, Olivia gave John as many sweets as John had after the first exchange. After these two exchanges, each had four sweets. How many sweets did John have in the beginning? All right, If you are confused by the wording of this question, this basically means that let's say they had an arbitrary amount of sweets in the beginning. Let's say that this is just random, by the way, this has nothing to do with the current question. Let's say Olivia had like seven sweets and John had 17 sweets. If John were to give Olivia as many sweets as Olivia had, John would be, since Olivia has seven sweets, John would be giving Olivia seven sweets. All right, if that makes any sense. I'll be opening up the poll now. All right, I'll give another half a minute. All right, so I'll end the poll now. Here's the results. It appears that this question was a lot harder than the previous questions, so let's go over it. All right, so one way we could do this is to make a table going backwards. All right, so here's after at the very end, and then we can use these values to find what are values after the first exchange, which is before the second one exchange happened. All right, so you see here, every time someone gives the other person as many sweets as they had, the amount of sweets they have doubles, which means to go backward we can have it. All right, so since Olivia gave the second exchange, Olivia gave John as many sweets as John had after the first exchange. At the end, John has four, which means if we have it, you'll have two at the end of the first exchange. Oh, it says my internet connection is unstable. Can you hear me clearly? Yeah. All right, so and since we know that the number of sweets doesn't change, we could find out the amount of sweets Olivia has by taking the total, which is eight, and subtracting two. Or we can find out, or we know that she gave John two sweets, and if we just add those two sweets back to Olivia, she'll have six. All right, so now let's do this again to find what happens after the first exchange. So since Olivia is the one who received sweets this time, we can have the amount of sweets she has, and so this is now the amount of sweets she had at the very beginning. And then now we can take those three sweets, give them back to John, and he will have five sweets. So that is our answer. All right, thank you, Noah. All right. As you can see, those two questions are a little bit more difficult, and those are the questions that you will find at the end of the test itself. All right, so let me maximize my screen again so we can get back to it. All right, so just to recap, so when you work backwards, you always reverse the operation. Don't forget that. All right, and since I just want to review with you the four-step method, now it's very important to read the questions more than once. You always want to look for what are the important things you need to take note of, what is the question asking, how you're going to solve it, and when solving it, you always write down the solution. No matter how easy, always write it down to be sure. And when you're done, go back and check. However, if you read a problem a couple of times and you do not understand it, I would circle the question number, and then I'll skip it and come back later, because you don't want to get stuck on one problem, and then you cannot finish the test. All right, you can always skip and then come back to do it. So just to review, these are some of the strategies that we teach you at Math Kangaroo. You know, there are patterns. We have number patterns, we have shape patterns, and it helps to draw it out. It's always good to draw it out. We use logical arrangements. We work backwards like today, and then sometimes we have questions related to calendar and time that we have some of them we have done today. It's always good to make an organized list, right, so that you won't be scrambling, okay, what did I miss? Guess and check some problems. There is just nothing else you can do but to use guess and check. Making a table helps, especially like in the last question that Noah worked with us on. Making a table helps us be more organized to help solve the problem. There are also questions that are 2D and 3D visualization. You have to use your imagination, you know, to work on it. Thank you so much for spending the time with us today. There is a survey. You will also get it from Zoom, but it is on chat. So if you have the time, just spend a couple of minutes on the chat, on the survey. It's on the chat so that we know how to improve and do a better job next time. So all the best to all our Math Kangaroo contest participants. We wish you all the best. Remember to apply the four-step method, and thank you again. Enjoy the rest of the weekend. Bye-bye.

Math Kangaroo

competition

logical reasoning

multiple choice

problem-solving

time management

strategy

practice

accuracy