Good afternoon, everybody. This is webinar number 10 of the Level 3-4 series. So this is our final meeting for this webinar series. And today, we are going to be combining a lot of the techniques that we've learned in the past nine weeks. So all of today's problems can be solved by either combining methods, or there might be two or three different methods to get the answer. I call this one missing values, because we're going to try to figure out what is missing and what is the best way to find it. All right, so we do have polls for a lot of our questions today. We do have a good warm-up problem today, so let's get that one loaded up right away. There we go, warm-up. Susan is six years old. Her sister is one year younger, and her brother is one year older. What is the sum of the ages of the three siblings? Give you a few minutes, and then we'll be able to launch the poll. Remember, you can communicate with Shoria or with myself through the chat. So if you have questions, go ahead and ask us. We do our best to try to get to them. Sometimes we can't get to everybody, but we do appreciate your participation there. Yes, I'm going to launch the poll because I see a lot of you already answering and doing a really good job with that. Let's do that. Okay, I think we probably have just about everybody participated in the poll. This is a unanimous one. You guys are amazing. So everyone thinks the answer is 18. That is correct. You did a really good job. So just remember I said there might be more than one way to solve things. So we have that Susan is six. Susan is six. Her sister is one year younger. So her sister must be five and her brother is one year older. So her brother must be seven. And when you add those together, you of course should get 18. Why did I say there might be another way to solve it? Well, we know that if you take a sister who is six and if you take Susan who is six, a sister one year younger and a brother one year older, they're all going to average out to age six. So then you can just do three times six equals 18. And you'd be using some theory about averages to do this problem. You could also set this up with some algebra. You could use X's for the ages, but you can complete those pretty easily in this question. All right. So today, we're going to have problems that have missing values. Like we didn't know the ages of the brother or the sister. We had to figure those out in order to get to the final answer. So you're going to do this very carefully. There's going to be some information given that will help you find it to figure out what you need to do to get to the additional values. So remember, we are going to be practicing our very careful reading of the problem. We're going to practice what is our plan? What do we need to know? How will we figure that out? Okay. Then we're going to, of course, work very carefully, as carefully as we can. And if I make any mistakes, you can let me know in the chat because I am human and I make mistakes. And then we're going to check our answers. Sometimes by doing the problem in another method and getting the same answer, that's a good way to double check yourself. So you'll notice today that we have some interesting things. Like we'll be told like three of an item will cost $24. Then we'll have to mentally or even you can use your scratch paper to do that division that one item would cost one-third or $8. You might be given things like twice as much or half as much. So be careful with those. If a melon weighs twice as much as an apple. So if I have a melon that equals two apples, and then I want the sum of their weight, it would be the melon plus one apple. But that would be really three apple weights, right? So we might have to be doing some substitution like that. We would have three apple weights if we know that the melon is the weight of two apples. So hopefully that's a really good hint and gets us started on some good problems today. The sum of three numbers is 50. Karen subtracts a secret number from each of these three numbers. She gets 24, 13, and 7 as the results. Which of the following is one of the three original numbers? We're looking for is, not is not. And it says the secret number from each. She is subtracting the same number from each of the original three. And I'll give you a few moments and I do have a poll. Wonderful. I'm getting some responses. I hope Shuria is as well. So I'll launch the poll. The question does appear in the top of the poll. So hopefully you have everything you need, even with the poll showing up on your screen. Anybody else want to add to the poll? You're doing very well on the polls. I know I say it every time we meet with this webinar, but sometimes we have students who have just joined, they haven't been to previous webinars. Math kangaroo contests, we do not subtract any points for a wrong answer, so you should always guess, right? Don't leave blanks if you're running out of time. Okay, I'm going to end the poll here and I'll share the results. So almost two-thirds of you think the answer is nine, but we have some other responses. This question is a little bit trickier than the warm-up that we did, but I think once I explain it, I think you'll all know how to do it. So if we have three numbers, we can just call them A plus B plus C. Their total equals 50. We're going to subtract something from each one of those. So we're going to subtract, I don't like to use too many variables, but let's say we subtract X from everything, and now we have new numbers. We have 24, 13, and 7. So one way I like to do this problem is I know the sum of the original numbers. What is the sum of the new numbers? Well, 7 plus 13 is 20, and 20 plus 24 is 44. So I have, between here and here, I have subtracted 6. And since I subtracted the same amount from each of the original numbers, I must have actually subtracted 2 from each, right? Because 2 times 3, I don't have the X anymore. 2 times 3 comes up with that 6. So now to get the original numbers, I have to add if I'm going up, right? So my original numbers would be 26, 15, and 9. So now I can look at the answer choices, and I see the only one of these numbers that's here is 9. So 9 must be the correct answer for this problem. Some of you were a little confused about the wording, and that's why it's really good to keep practicing math kangaroo questions. We have to figure out what do all those words mean. Okay, and Shuriya wanted to lead number 2. Hey, okay. Rosanna has some balls of three different colors. Balls of the same color have the same weight. What is the weight of each white ball? So here we're given gray balls, black balls, and white balls, and we want to find the weight of the white ones. Okay, so I'll give you guys some time to think about that, and you can tell me in the chat if you think you have the answer. And there is a poll for this one. Okay guys so I'm gonna launch the poll now and the question in the picture is still on there so you can keep working. Okay, so now I'll just end the poll since I see most people have participated. Okay, so yeah, most of you got answer C, 5 kilograms, but there's some 4, some 6. Okay, all right, so let's work through this. Okay, so we want to find the weight of the white ball. Now, if we want to know what the white balls are, we're going to have to look at this scale over here. The thing is, we know that 2 white, I'm just going to call it W, plus our mass of our gray ball, and the gray ball is going to equal 14 kilograms. Now, this doesn't really tell us anything because we need the gray ball. So now we're going to work backwards a little bit, and we're going to go to the scales that have the gray balls, which are going to be this one and this one. So if you look at the one on the left, we can see that a gray ball plus a black ball is equal to 6 kilograms, whereas on the right, this one, number 2, a black ball plus 2 gray balls equals 10 kilograms. Now, if you look carefully at both of these, you'll see that this part in both of these equations is the same. So that means that we can replace, like for example, these two balls with 6 kilograms. So we can say that 6 kilograms plus our gray ball is going to equal 10 kilograms, which gives us our gray ball's weight. Our gray ball is going to be, let me use this one, our gray ball is going to be 4 kilograms. So now we have our gray, we can put it right here, 4. That means our black has to be 2, because then it makes 6. And then lastly, we just have to put in our gray into this equation. So if the gray is 4 and the overall is 14, that means the two whites are going to be 10. So that gives us one white ball as being 5 kilograms. So in this question, you could have like, you could have done it another way, like you could have maybe started out from working with the gray balls, but another way to look at it is if you are trying to find the white ball, you can work backwards from that and then go forwards after doing your calculations. So it was sort of, it's like a little algebraic problem in disguise. This fits right in with the theme of missing values, right? Because we're missing the value of the gray ball and the white ball, but we could figure them out from each other. Very good. Thank you, Sharia. Clear. And we go to the next problem. 30 children going to Adventure Park took part in at least one of two events. 15 of them took part in the Moving Bridge contest, and 20 of them went down the zip line. How many children from Adventure Park took part in both events? Okay, so important information. We started with 30 children. We know that 15 of them were in the Moving Bridge and 20 of them went down the zip line. We want to know how many took part in both events. And again, we have polls. I told you we have polls for a lot of today's questions. I know this group likes polls. Hey, everyone's participated in the poll quite quickly there. We have most of you saying five. We have a few other answers. Let's take a look at this one and see what we get. So we know that there are a total of 30 children. I'm going to draw a picture. I know that inside this picture there are 30 children. And I know that some of them are going on the moving bridge. I'll just do MB for moving bridge. And some of them are going on the zip line, ZL for zip line. And some of them go on both. I know that in this left-hand circle, there are 15. And in this right-hand circle, there are 20. But 15 plus 20 equals 35. And that is more than our 30 by 5. So what happens if I try to put 5 here in the middle? I will have 10 who only went on the moving bridge. I will have 15 who only went on the zip line. And I will have 5 who went on both. And do the green numbers add up to the correct sum? They do add to the correct sum. So the answer is 5. So how did I check myself? I did the other sums. I did it the other way. So what were the alternate methods? I could use a little bit of algebra, just some calculations here, some numerical values. Or I could draw a diagram. So there's at least two ways to do it and to check your answers. OK, this is a fun question. I think it's fun. Opinions, right? These are opinions, not facts. But here's the facts of the problem. It says, how long is the train? And it gives us these two graphics. One is a bridge with the train approaching it. And the second is the bridge with the train on it. The train is not as long as the bridge. And it shows you the difference here. If you can't read this, this is 340 meters. And this one is 110 meters. I'll write it larger for you. There is no pole because of the figure here. I thought we might need to work the working space. So put your answers in the chat. And you can ask sure. Okay. Because you're sending me information in the chat, it lets me know what you're getting correct and what other options you're choosing. Most students, I see the answers they're choosing are either B or E. And that makes sense. Both of them do make sense. I can see where it's coming from. So let's take a look at the problem together. I'm going to do something a little bit weird. I love to draw, but I don't love to draw trains and bridges. So I'm going to combine these two pictures right on top of one another. So I'm going to put the other train. Here's the other train. It has four cars and then it has an engine. I'm going to put this train on top. And then I know that this distance here is 110. Hopefully everyone can see that, right? So now I can look at this and I can say two trains plus 110 meters equals 300. Oops. What happened there? Sorry, technical difficulties here equals 340 meters. Okay, so in order to make this work, I want to know what one train is. Well, at least I can figure out what two trains is by subtracting. If I subtract 110 meters from both sides of the equation, this is an algebra situation, but I think it makes sense if we look at it. If I want to know how long is this part, then I can subtract this part from the 310, right? Cause they have the same sum. So I'm just doing the reverse operation, I'm subtracting. So I know that two trains equals 230 meters. And so that is why a lot of the students selected their answer choice as E. Okay, that's where 230 meters comes up, but that is two trains. So in order to get one train, obviously I have to divide by two, right? So that would be 115 meters. So one train is B, 115 meters. So again, my suggestion is to take a real good look at these figures and maybe I combine them. That's how it works for me. All right. Number six is a little bit similar. I think I'm having a little bit of a connection issue. Sharia, did the writing disappear on your screen? Okay. No, the annotations from the previous screen, my tablet's not updating properly. Okay. Yeah, they're gone. Okay. Each shape stands for a different number. The sum of the three numbers in each row is shown to the right of the row. Which number does the star stand for? Okay, I'm looking for the star. Like in the problem that you did with Sharia, each shape stands for a number and that's not changing. So each circle will have the same value, for example. I do have a poll for this one and I'll wait just a few minutes until we start getting some answers and I'll launch it. I'm getting nice responses. I'm going to launch the poll. I do believe the figure is still there in the top of the poll for you. Anybody else want to participate in that poll? We have most of you, but not everybody. All right. I think that's everyone. Well, we have not a unanimous answer. You can take a look, you can scroll down if you need to. But we do have 87 percent of you thinking the answer is six. That is correct. Let's take a look, make sure everyone can see how we get this answer. This is very similar to the problem that Shoria led you through. The only difference is, in Shoria's, you needed to know the values of the gray ball and the white balls. Here, I do believe you need to figure out the values of all of the shapes, all three. Where I like to start is this one, because I know that three of the circles equals 12. If I divide 12 by three, I'll be able to find out that one circle. I'm putting a dot in here so you know it's a circle and not a zero, not the number 10. One circle is 12 divided by three equals four. I can go ahead and put a four on top of all of those circles. Just keep myself organized a little bit there. That makes a lot of sense to me. I still need to figure out the star's value. Now, if I compare the top row and the bottom row, similar to what Shoria had showed you before, the star and the heart appear in both of them. I have one star and one heart in both of them. Looking at the top line, I have four plus star plus heart equals 15. Therefore, I can subtract that four and I can get four plus heart equals 11. I may not know what star and heart are individually, but I know their sum is 11. I know that this part right here has to be 11, which leads to the conclusion that 11 plus heart equals 16. Heart, the missing number here, the missing value must be five. If I write a five in here for the hearts and I write a five in here, star plus heart equals 11, but instead of heart, I can use the five. Therefore, star, what plus five equals 11? Well, six plus five equals 11. That gives me the correct answer, E is six for the star. It was the last one I could figure out, but I did have enough information to get there. Good work, everybody. Okay, number six, we're going to let Shoria read this one. Okay, Kangaroo Hamish brought some of the toys shown in the picture and gave the cashier 150 cane coins. He received 20 cane coins back, so he gave 150, he received 20 back. Then he changed his mind and exchanged one of the toys for another, so he got an additional five cane coins. What toys did Hamish leave the store with? So we're given these five toys and we know it wasn't all of them. He only took some of them and then he exchanged one of them. And now at the very end, we want to figure out which ones did he actually walk out with. Okay, so you can message me in the chat once you think you have the answer. And I don't think there's a poll for this one. Yeah, so we'll just start once I'm getting a lot of answers, we'll just walk through it. all right so i'm seeing i'm saying i'm getting a lot of good answers but some variants so let's just walk through this okay so we know that the total value of all the toys whatever they were is going to be 150 coins we'll just write 150 to be simpler okay so we know that um 150 is like the value of what hammish paid but then he got 20 back so that means the toys were actually only worth 130 now remember after that he changed his mind and exchanged one of the toys for another getting him an additional five coins so that means he got more coins which means he spent less so we're going to subtract 5 125 so overall hammish spent 125 king coins on the toys now there's a lot of different things that we're told here but one of the good um one of the clues i would say is that he exchanged one of the toys for another which got him five coins so that means that whatever toy he exchanged was five coins um five coins higher price than the other like if there was a toy that was worth for example like 50 the other was 45 so that's why he got five coins back so if we look at the picture the only one that we can see that actually does this is going to be this group of toys our 52 and 57 because if we look at all the others they are all more than five or less than five apart so 48 and 52 are like four apart 48 and 57 is too much and so so we know that hammish first must have bought the duck so he first bought the duck but then he exchanged out the duck for the horse which is why he got five coins back so think about like since the duck was cost uh more costly that's why he got five coins back for exchanging it okay so now we know that he walked out with at least the horse so we can already see that actually if we eliminate we already have our answer which is bear and horse that is the right answer but just to check our answer we can keep going and see does it work with another toy so remember the total was 157 and we know that he bought the horse which is 52 i'm not 157 sorry 125 so now we can just go do 125 minus 52 and that is going to give us three here seven here 73 which means the other thing hammish bought was the bear and that's correct because answer a is the bear and the horse so this problem was again some some of it was sort of like logical reasoning like looking at what clues do we have like if we hadn't looked at this clue at first this exchanging of the toys it would have probably taken us a bit more time to work through the question so this is a good fast way to get to it and again if if you like if you're in need of time on the actual test you could just click answer a and go on but checking is always a good thing to do if you have the time thank you sharia yes because we have a multiple choice contest you can test the different answers and you can see if you get the right amounts and that's exactly there's a really great clue here with this 5k and coin difference so we had to look for that difference in price excellent okay number seven four crows are sitting on a fence their names are dana hannah lena and benny dana or dana sits exactly in the middle between hannah and lena the distance between hannah and dana is the same as the distance between lena and benny dana sits four feet away from benny how far away is hannah sitting from benny kind of a logical question here a couple of keys in there you read read the question a few times to yourself very carefully draw it out if you need to and i do have a poll it'll take probably a few minutes to work this A lot of you are sending me some answers so I'll launch the poll. Keep working if you're not quite done. I think that's just about everybody has participated in the poll and a lot of you have sent me some messages in the chat I kind of I kind of like chatting with all of you. Okay I'm going to end the poll and share the results. So this isn't unanimous like when we started at the beginning but we do have more than half of you saying six feet so let's take a look and see if that works out when I start to draw it out and explain it. Okay so four crows are sitting on a fence. I'm not going to draw a fancy fence but I'll draw a line. How's that? Four crows are sitting on a fence. Their names are Dana, Hannah, Lena, and Benny. Dana sits exactly in the middle between Hannah and Lena. So if I put Dana here then I can put Hannah on one side and I can put Lena on the other. It's a little bit longer and it says exactly in the middle. So whatever this distance is it is the same as this distance. So these are the same. I'm just going to call it X. Okay we don't know what it is right now but I'll just label it X for now. You could call it anything you want it's the same distance apart. And then it says the distance between Hannah and Dana is the same as the distance between Lena and Benny. So Lena and Benny has to be the same. So Benny could be either over here another X away or Benny could be sitting right on top of Dana. Does that make any sense that Benny's sitting on top of Dana? Well it says that Dana sits four feet away from Benny. So Benny is not on top of Dana. Benny is four feet away. So four feet away we now know that this is four. Alright so if the distance between Dana and Benny is four then we know and we know that all of those X's are the same then this must be a two and a two because two plus two is four and that makes this a two because we're also told that that is the same. And then it's asking how far away is Hannah from Benny. Hannah from Benny is going to be two times three which equals six. Six feet away. Okay so sometimes we had a couple of options here we had to test where was Benny. Was Benny to the left or to the right? You could have set this up with it completely flipped around. Your drawing might look a little bit different than mine if you change the order around but you should still have the six feet in between Hannah and Benny because they're on the outside. We've done some questions like this before where we did like how many clothes pins does it take and we discovered that the distance in between like the number of towels and the number of clothes pins. So four people and three gaps. When we had the clothes pins if we had hung up three towels we would have needed four pins. So we did some problems with gaps and with with joints before. Okay so that is the end of the problems that we are going to work today. We're going to just do a real quick summing up of what's gone on in the past ten weeks. Okay so remember we always can use this problem-solving strategy. So we have to understand the problem and that can involve reading or highlighting, underlining. It can involve rereading, figuring out what's missing, what they tell you. Sometimes I take notes. I write down everything that the that the problem says but in my own in my own way right so that I have notes. I might use little variables or draw a picture of it and then I'm going to plan. Plan how to solve the problem. So is this going to be a drawing problem? Is this going to be a multiples problem? Is this a problem where I can find a pattern? Is this a problem where I'm going to use a little bit of my geometry? So I'm going to need to know about my areas and things like that. Carefully carefully work your problem. Always very careful with the work so that you try to eliminate errors because there's nothing nothing as frustrating for most of us is knowing what to do but making a silly mistake somewhere right and we can check those. We can catch those silly mistakes if we look back. Does our answer make sense? Also did I answer the correct question? That goes back to reading the question. Sometimes we'll say which one of these is not a possible answer or which one of these is false when we were doing the logic problems right. So make sure you very very carefully understand what answer you're looking for and that you matched up your answer choice. Remember we also have a multiple choice contest so if you are completely lost you can skip the problem and come back to it and then you can try testing the multiple choice answers. That is one option for a multiple choice contest. Okay so the things that we have gone over in all the lessons so far. We did drawing pictures and diagrams, making lists and tables to organize our data. Remember we had some missing values in those tables. We were using patterns. That was like the the hanging of the clothes. We did some guessing and checking but remember don't do random guesses. Use the information you have to start out with an intelligent smart educated guess. We did experimenting and acting out where we actually cut out papers. We were drawing and cutting and you can make your right now is a great time of year to make some paper snowflakes and see what happens when you cut in different shapes into papers that are folded in different ways. We've done working backwards, the logical reasoning where we had liars and we had one-to-one correspondence and today we did missing numbers which is a bit of algebraic thinking in a lot of ways. So I hope you've enjoyed all of these lessons. The best way to get ready for the contest now is to try some of the practice contests and to look at these solution videos that we have available. So remember we have practice contests and solution videos and if you go into your contest or your webinar applications you will find you have some codes that you can use to get discounts or even free study materials. You don't need to worry about the summer classes right now but I want you to know that we are continuing the webinar series. So some of you have asked if today's the last webinar and it is the last of this series but starting in January after New Year's I'm going to be leading another series of 10 webinars at the same time. It'll be a different Zoom so you'll need to register in order to get that new Zoom link and I hope some of you will continue if you've enjoyed these Zoom lessons. Okay one favor for me and for Shuria, when we close this Zoom there will be a survey that opens up to ask you what we what you like about the class, how we can improve the class, how we can make it the best class we've ever been in. Okay it really helps us when we get those feedbacks. Shuria do you have any parting words for our students after 10 weeks of hard work? I just say that it was really nice like for me teaching was really nice and I hope you all enjoyed this. One of the best things is just practice like that's really the only way to get better. So like Dr. Sagi said like look at the solutions, try the past contests and the more you just do those types of problems you'll just get better and better. So even if you don't have time to like do it like every week or whatever try to do it as often as you can just only try to do like one or two questions you know whenever you have the time just try to like squeeze that time in and do a few questions to keep your brain going and then eventually you'll get you'll see that you're you're gonna get like really good at them so yeah. That's a good point Shuria makes that even if you don't have time to sit down and do a whole contest you can work on a few problems because sometimes practicing a small amount at a time is going to still be a really good benefit to you. Alright so here comes the survey when I close the meeting so please stay let me go away and then you will see the survey link pop up okay. So I just have to stop my share. All right if you stay you will see it. Bye everybody.

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