Good afternoon, Math Kangaroo. Welcome to the Level 3-4 webinar number four. The second, I'm gonna put a warm-up problem up on the screen so that you can do the warm-up problem while we're waiting for everybody to join. So today's subject is making a table. Here's our warm-up problem. For five days, Cassia was helping her mother pick berries. On the first day, she ate most of her berries and gave her mother only one cup of berries. She decided that each day she would be giving her mother twice as much berries as the day before. How many cups of berries did Cassia give her mother in five days? So not on day five, but in five days. Different wording, be very careful with the wording. In five days. So she starts with one cup and twice as much. If you've missed joined, we're doing a warm up problem, and I do have a poll that I can launch about a minute. Want to let enough students join and read the problem that's on the screen. I think I know the answer. Okay, we need to stay muted during the meeting. You can put the answer in the chat. You can chat to me. Sarah, or to our teaching assistant, he's also somebody you can chat. All right, I will launch the poll. You can put your answers into the poll. You can still send your answer by chat to me or to Shoria. If you have a question, you can let us know in the chat as well. We do our best. This isn't a one-on-one session, but we do our best to monitor and try to help you as much as we can, okay? If you don't hear us for every question, we're sorry. There's only so much we can do with a lot of students in the class. All right, do we have enough people participating in the poll? Anyone want to put a last second answer in there? I'm going to close it. Remember, in math kangaroo contests, you do want to put an answer to every problem. OK, because we do not subtract any points if you get it wrong and you might guess correctly. So do your very best on the problems. But if you are not 100 percent sure, at least make a try, at least guess something. OK. All right, so here are the results of our poll. More than half of you think 31 is the correct answer. Let's walk through this problem together and see how you did. So we have five days, so I'm going to make table type of format. You'll notice that tables don't have to have beautiful lines and divisions. This is good enough, right? So make sure you have scratch paper for today's lesson. So this is going to be the berries. On that day that Cassia gives to her mom, and this will be the total, the running total of all the berries. So on the first day, it says that Cassia ate most of the berries, but gave one cup of berries to her mom. So her mom's total. Mom's total is one cup. Now, if twice as much berries on the next day, one times two is twice is two. And now I'm going to add one plus two is three for the total number of berries. On the third day, we have to double that two. Two times two is four. And now I take three plus four and I get seven cups of berries total that mom is getting so far for the five days. When I double the four, I get eight. And when I do seven plus eight, I get 15. And when I double the eight, I get 16. And then when I add 16 and 15 all together, mom gets 31 berries. That is choice B. So if that was your answer, you did it very well. If you didn't get that answer, try to figure out where you might have made a little mistake and see if you can correct it. Because that's the whole point here is to learn how to do new problems. So if you're learning how to do it, if you didn't read it correctly, you get used to reading math kangaroos problems and you'll do better as we have more and more experience. Okay, I'm just going to back up one little slide to the title slide here. So we make sure that everyone who joined late can see. Today, we are going to work on making tables. Last week, our focus was on making lists. When we make a list, everything kind of gets grouped in one category. So if I want to make a list of all of the animals at the zoo, I can make a list of all the types of animals at the zoo. And I wouldn't need any categories. I wouldn't need a table. I could just make a list. But let's say I wanted to make a list of the animals at the zoo and I wanted to separate it into different categories. I wanted to put the reptiles in one category and the mammals in another category and the insects in another category. So then I would probably be making a table because I would have what we call data with more than one characteristic. Okay, so you can think about this. We have different characteristics as well, right? I might be organizing the students in the webinar by their grade. I might be organizing you by whether you've taken a math kangaroo contest before. I might be organizing you by which time zone you live in. I'm in Pacific time zone, but I know Shoria is not, right? So we're not all in the same time zone. I could make, I could categorize us. And I wouldn't be picking on anybody or be interrupting your personal integrity. I would just be trying to group us by grade or what letter our name starts with. I would be in the S group, as would Shoria, unless I was doing last names. I'd still be in the S group, but Shoria would not be in the V group. Okay, so that's data that has more than one characteristic. Okay, so we can use a table to separate that and keep it organized. So you'll notice today, the way Shoria and I will solve the problems will involve making tables. Does that mean it's the only way that any student ever in the world could solve one of these problems? No, we've talked about that. We're just showing you one type of tool when we're practicing it to get really good at that tool each week. But whichever tools you like and work best for you, that's up to your individual brain and your experience and what you like. But for today, we will practice the tables and try to get very proficient at the tables. All right, Shoria, you wanted to lead number one, if I have my notes correct. Okay, so number one says, for which of the following numbers is the product of the digits greater than the sum of the digits? So what we're trying to find out is for which of these is our digits products? Our digits products, like if we have number C, it would be like 3 times 1 times 2. How much is that greater than 3 plus 1 plus 2? How much as in like how for how many of our for which numbers is that possible? So I'll give you all a moment to think about that. Is there a poll for this one? Okay, so and once you think of something, you can private chat with me. I think I can launch the poll right away because the problem is in the top of the poll, and this is a nice short problem statement. We're going to ask the students not to annotate on the screens use your own note papers not my screens please thank you. Okay, I'm going to end the poll here and share the results. All right, Shourya, do you see how well they're doing? Yeah, that looks pretty good. Yes, that is the correct answer. So, because we're having students annotating on the screen, this is going to get a little clunkier. I'm going to have to stop my share and allow Shourya to share. Do you have the presentation open on your computer? Um, yes, I do. All right. Okay. Okay, let me... Is the, is it working right now? Yes, let me. We're going to leave that that file up and you can walk through the table. That's already pre drawn. That's fine. No, it's fine. Let me open the other 1. It's just sorry about the disruption, but this is this is due to students who were annotating on our screens, even though I asked them not to. Okay, so the question is asking us for which of the following numbers is the product greater than our sum, right? So the way I wanted to do this is making a table for each of our answer choices. So let's start with A, B, C, D, and E. Okay, and we'll just like make a table over here. So, on one side we can do, for example, the number. So let's just write down the number. So for A, it would be 112. Now, for the next one, we can do the product of the digits. So that would be 1 times 1 times 2. We know that's equal to 2, right? And now we can make one last column, and we'll do the sum of the digits. So that's 1 plus 1 plus 2, which is going to be 4. So you can see that for A, the product of the digits is less than the sum of the digits. But we want it to be greater, so this is not our right answer. We can move on to B. So 209, the product, remember anything times 0 is just going to be 0. So that's just going to be 0. And then our sum will be 2 plus 0 plus 9 gives us 11. So 0 is less than 11, so this one is wrong too. So we can just keep doing the same thing. So for 312, for letter C, we have 3 times 1 times 2 gives us 6. For the sum, we have 3 plus 1 plus 2. That is also 6. However, we want it to be greater. So if the question said greater than or equal to, then we could do C. But it says greater, so since these are equal, that's not right either. Moving on to D, we have 2, 2, and 2. So 2 times 2 times 2, that gives us 8. And then 2 plus 2 plus 2, remember, we can just simplify that into 3 times 2. That gives us 6. So here we can see that our product is greater than the sum, so we have our answer, D. And we can just check E just to make sure. So the product will be 2 times 1 times 1, that's just 2. And the sum will be 2 plus 1 plus 9, which is 4. So overall, this problem, you could have done it a different way. Like if you just wanted to multiply, add in your head. But making a table, like, it helps to stay organized. So if you have the number in a column, the product in a column, and the sum in a column, then you know which, then you can compare it by column so that your answer is really easily visible. So once you write it, you'll know that you have it. Thank you, Shuriya. I'm going to go ahead and start my screen. All right. There we go. All right. On her first turn, Diana scored 12 points total with 3 arrows. On her second turn, she scored 15 points. How many points did she score on her third turn? Some of you may be able to do this with no table, and that's perfectly fine. I will show you a table example. We do not have a poll for this one. So if the poll pops up in your way on this one, you won't have that little problem. Great, so you can see I started a table, and you might try a different type of table, but I'll use this one for now. It seems like a good start. So on my first turn, I have three turns, right? So on my first turn, I have three arrows, and it says that I got 12 points. So I have something times 3 equals 12. As you can see, all three arrows are landing in the same region of the target. So these three arrows got the same amount of points. So it must be 4 times 3 equals 12. So this is a four-point ring. So I can draw that in on my picture if I like. That's a four-point ring. It says on the second turn that we scored 15 points. And you can see that two of the arrows were four points, and then the third arrow was a mystery number of points, and I have a total of 15. So 4 plus 4 is 8, and 8 plus 7 gives me 15. So the center must be worth 7 points. Now, I don't know the total points on the third turn. That's what I'd like to find out. But I know that all three arrows scored 7 points. So I can do 7 plus 7 plus 7. That also equals 7 times 3, and it equals 21. So the correct answer here was D. All right, so there's one with no poll. And we will move on to the next question. Some students said they have a little trouble after I launch the poll, still seeing the problems or reading the polls. So I'll wait a couple of minutes before I launch the poll. That will give everyone a chance to read and take some notes if you need to, OK? On Monday morning, a snail fell down a well, which is 5 meters deep. During the days, it climbs up 2 meters. And during the nights, it slides down 1 meter. On what day of the week will the snail get out? So day of the week will, oops, sorry about that. Wrong tool. On what day of the week will the snail get out of the well? It starts on Monday. It goes down 5 meters. And during that Monday, it can climb up 2. But then at night, it slides down 1. It must get slippery, and it slides back down. So I do have a poll, but I will wait a few moments so that students who can't see when the poll is there will take their notes and can work. Hey, I already made a little start to my table. You can ignore it or you could use it as a hint, and I'm going to launch the poll. I will make a note that you might want to go through this problem step by step not try a shortcut because there's a little trick and the shortcut leads you wrong and if you know where what I mean by the end of the problem you'll know what that means. Okay, I think I'll stop the poll there. Most of you have replied in the poll. Thank you for participating. And we have a lot of different answers. Most students are saying either Thursday or Friday, with 50% saying Friday, but we have a few other options. So let's take a look at this problem. This problem has a little, I'm going to call it a pitfall, because a lot of students will read the problem and they'll say, okay, on Monday morning, the snow, it's five meters deep and it can climb up to, but it falls down one. So I can do that, right? Up to minus one means up one every day. And we know that he fell down five meters. So Monday is day one, Tuesday's day two, Wednesday's day three, Thursday's day four. He must get out on Friday, right? Is that how 50% of you got the answer Friday? I bet it is, but let's take a look at it really. Okay. So we know that on Monday, he falls down how deep? This is how deep at the beginning of the day. And if he climbs up two, then at the end of the day, the poor little snail is three meters deep in the hole. I'm using negative numbers to mean deep in the hole, underground. And I slide down one at night. So by the beginning of Tuesday morning, the poor little snail is down four meters, but climbs up two. So it was only two meters from the top by the end of Tuesday, but up during the night, it gets slippery and he slides back down. So, but when he wakes up Wednesday morning, he's three meters down. He's able to climb up two. So by the end of Wednesday, after working hard all day, this poor little snail is still one meter from the top and falls down again, two meters overnight. So Thursday morning, the poor little guy is negative two. But what happens on Thursday? Thursday our snail is very brave and strong, climbs up two more meters and gets a zero here. And when he gets a zero, this is when he is out. Once he is out of the well, that snail is going to run far away from the well and never fall down it again. So this is one of our trickier questions. The snail is out on Thursday. And if you followed it step by step, you would find that zero right there. This is also an interesting question. You're going to have to use a little bit of your logical thinking, maybe some other mathematical facts that you can figure out. I'll read it and I'll give you some time to work on it. I won't launch a poll for this one just to save a little bit of time and solve more problems today. Peter Rabbit likes cabbage and carrots. In one day, he can eat only nine carrots. Only two cabbages or one cabbage and four carrots. During one week, Peter ate 30 carrots. How many cabbages did he eat during that week? Read that problem to yourself again. See if you can make sense of it. I will come back in about a minute and go through that one more time. But I want to see what your first impression of that problem statement is. It's a lot to read. I want to read the problem statement one more time and give a little bit of cluing to some of you who might need a little more explanation. Remember, imagine you've gone to a restaurant and there are three things you can order at the restaurant. Okay, you can order only nine carrots, only two cabbages, or you can have the combo meal where you can get one cabbage and four carrots. That's basically what we're saying Peter Rabbit gets to do each day. Peter Rabbit can have only carrots today, only cabbages today, or a mix of carrots and cabbage, but less of each. Does that help? All right, so how many of you are making a good start on this problem? I hope a lot of you. Okay, so if I start this problem, I want, for me, I see that we ate 30 carrots. That's the first solid piece of information. So I know we must have a couple of some days where we eat only carrots, right? Because if there's seven days in a week, seven times four is only 28. So there must be some days of only carrots. So I'm gonna put those at the beginning of the week. It doesn't matter which day of the week you use. So if I have nine carrots on the first day, that is still, gives me 21 carrots left to eat. 21 is not divisible by four, is it? Right, so the 30 minus nine is 21, and that's not divisible by four. So I better eat another nine carrots. Now I have 21 minus nine gives me, oh my gosh, 12 carrots. That gives me 12 carrots left, and 12 is divisible by four. So I kind of like that idea. So if I ate four carrots for three days, that would give me the total of 30 that I like, right? So I know whenever I eat four carrots, I also eat a cabbage that day, if I'm Peter Rabbit, that is. But I can't eat any more carrots, right? Because if I eat more carrots, then I'm gonna be over my limit of 30 for the week. So on these days, Peter Rabbit must eat two cabbages each day. And if I take the sum of these cabbages, that's what I was looking for, it's one plus one plus one is three, plus two is five, plus two is seven cabbages. So I'm gonna divide that in one week. The days of the week and things don't matter here like the previous problem. So I can just number them one through seven and it doesn't matter what day it is. But the kind of tricky thing here was to realize that it was kind of like a menu where you could order all carrots or all cabbages or get the combo plate. And that was what he got to eat for the day. But this is kind of the tricky part where you had to figure how am I gonna make it divide out correctly so that I can either have because I can't have two carrots a day or three carrots a day, that's not possible in this question. Okay. All right, do you wanna go ahead and share your screen Shreya so that you'll be able to lead number five? Yes. I think when you go ahead and share, it'll stop mine. Yeah, it will. Okay. Okay. So, wait. Okay, so in the animal school, three kittens, four ducklings, two baby geese and several lambs are taking lessons. They haven't told us how many lambs there are. We know there's several. The teacher owl found that all the pupils have 44 legs altogether. So all of their legs combined, there's gonna be 44 legs in their class. How many lambs are there among them? So we're given the numbers of the other animals. We wanna find the number of lambs and we know the total number of legs that they had. So we just have to think about how many legs each animal has and then add them up to find our answer. So I'll give you all a moment, a minute to think about that. And remember, you can chat me if you have any answers. Right, I will launch a poll for this one. I think this is a question most students should be getting close to the answer. I will just add that the teacher owl is not counted as a pupil. Pupil means students, does not include the teacher. All right, Huria, that was one of the fastest polls. We have almost all of the students participating already. Anyone else want to put in an answer into the poll? All right, I'll share these results. Huria, please let them know how incredibly intelligent they all are picking five lambs. Yeah, that's almost 100%, wow. So yeah, the answer is five lambs. But there are many ways you could solve this, but one of the ways to keep it organized is if you make a table. So here, let's make a column with our animals. So we'll have our kittens here, let's call that K. We know we have three of them. Then we have ducklings, we have four of them. We have baby geese, let's just call them G for geese. We have two, and then we have some number of lambs. So we don't know how many we have. Oops. And these are our lambs. Okay, so now in our next column, we can find out how many legs they have, and then we can add them together from our 44. So kittens have four legs, so that gives us three times four, which is 12. Ducklings all have two legs. Remember, ducks have two legs, so that's four times two, which gives us eight. And then our baby geese, so they also have two legs, which is two times two, four. So let's add these all up. 12 plus eight plus four, that's 20 plus four, which gives us 24. So overall, all of our kittens, ducklings, and baby geese have 24 legs. Now, all of our pupils have 44 legs. So we're going to subtract these 24 from the total amount of legs to get 20 legs for our lambs. Remember, lambs have four legs, so we're going to divide 20 by four. So 20 divided by four is going to be five. So through this table, we can list out what our animals are, how many legs they have, and then multiply them out to get our amounts that we add together. And we can check our answer by having five lambs here. That gives us five times four, which is 20 legs, and 20 plus 24 is 44. All right. Thank you. All right, we're back to kangaroos. Math Kangaroo loves to do problems about kangaroos. Kangaroo noticed that each winter, he gains five kilograms of weight, and each summer, he loses four kilograms. During the spring and fall, his weight does not change. In the spring of 2008, he weighed 100 kilograms. How much did he weigh in the fall of 2004? So you notice we're going backwards in time. We're given how much he weighs in 2008, but we want to go backwards to 2004. You can solve it any way you like. I will show a table, but I'll give you some concentration time for now. I'm just getting a little some of the information from the problem I'm starting to put that into my version of a table. I will launch the poll in about one minute. All right, there is your poll. Keep in mind, we do not take any minus points for a wrong answer. So if you think you can eliminate a few choices and make a guess, you should always make guesses on your math kangaroo contest. Sharia probably can give you some advice on when you should guess and when you shouldn't, depending on if they subtract the wrong answers and there's all sorts of calculations for that, right? Yeah, they have something for that. I don't know exactly what it is with the wrong answers and leaving it blank, but I don't think the guessing will hurt you. About half of you have put an answer in the poll. If you'd like to make a guess now would be the time because I'm going to start to solve the problem. So I need to close the poll and give you your screens back so that you can see what I'm doing. All right, thank you for participating. I know this problem is a little tricky and we have just about every answer here. I think every possible answer has at least one vote. The most popular are 92, 94, and 96 kilograms. Let's see where you got those answers and which one is actually correct. All right, so it says every winter. So first of all, you have the seasons in the correct order, right? So I'm going to start with spring because we have a spring weight, but you've got to have either winter, spring, summer, fall, or spring, summer, fall, winter, something like that. Not out of order because that will get you a little confused. There's some songs that have the seasons in them. Maybe that will help you remember them. All right, it says every winter it gains five kilograms of weight. So I'm just going to write plus five for every winter. Okay, so if in the spring of 2008 our kangaroo weighs 100 kilograms and he had gained five kilograms over the winter, that means that the kangaroo weighed 95 pounds in the fall. We also know that in the summer, kangaroos must hop around a lot more. They must be a lot more active and they lose some weight during the summer. I'm just guessing. I'm not an expert on kangaroos, but somehow they lose weight in the summer, but gain it in the winter. Or there's less food because it's hot and dry in the summer. I'm not sure. So if over the course of the summer, the kangaroo lost four pounds, going backwards, we have to add it back on. That means the kangaroo weighed 99 pounds at the beginning at spring because 99 minus four is 95. So we're going to use that same working backwards. If he weighs 99 in spring, but had gained five during winter, then he only weighed 94 kilograms in the fall. Working backwards again, I'm going to have to add four instead of subtracting and I get 98. By now, you probably should see that there's a pattern, right? I can kind of fill it in using the pattern instead of having to use the calculations each time. I put an extra little box here because that's the one I want. I want to know how much did he weigh in the fall of 2004? The answer is 92 kilograms. Right? So there were some other answers that were given. Try to see where it could have been that some people might have gone to this 96. But this is the one we wanted. We weren't going all the way back to spring. We were going to fall. So 92 plus five is 97, minus four is 93, plus five is 98, minus four is 94, plus five is 99, minus four is 95, plus five is 100. So anytime you have a working backwards problem and you want to check your answer, you can work forward again. That's a great way to check yourself. Okay, here's our bonus question. The bonus question, Anna, Berta, Charlie, David, and Elsa were baking cookies on Friday and Saturday. Over the two days, Anna made 24 cookies, Berta 25, Charlie 26, David 27, Elsa 28. Over the two days, one of them made twice as many cookies as on Friday, won three times as many, won four times as many, won five times as many, and won six times as many. I read that faster because it was just in order, right? Who baked the most cookies on Friday? This is a number 24, end of the contest, when you're tired, five-point question. Just like you might be a little bit tired from an hour-long webinar now. So it's good practice to do this at the end. I'm not seeing too many answers in the chat, so I'm not going to launch the poll because it leads me to think that you aren't ready for the poll if you're not using the chat. All I've done so far is I took the information from the problem statement and I put it into a table. I put each of their names and you could always just do A, B, C, D, E, no problem, and I put in how many cookies they've made in the two days. That's all the information just from the very top here, the two-day totals. Now, they made twice as many cookies on Friday. What does this mean? Over the two days, one of them made twice as many cookies as on Friday. Let's just start with that phrase right there, and I'm going to work over here. If I make 10 cookies on Friday, this is a sample problem not in this answer. If I make 10 cookies on Friday and it said over two days, I made twice as many, then over two days, I must have made 20 cookies, which means I made another 10 cookies on Saturday. If this is Friday and this is Saturday, I must have made 10 on Friday and 10 on Saturday in order to have two times as many. This total 20 is divisible by two. That's your big hint. What am I going to put in this one? I need to make it divisible by. I know that the answers that I need to be divisible by is 2, 3, 4, 5, and 6. I have to fill those in in this column. Which is divisible by five is a really easy one. Berta's must be the one that's divisible by five. If I take 25 and divide it by five, that means that Berta baked five cookies on Friday. If I also wanted to do it, how many did she bake on Saturday? I can do another column and I could say 20. Because five times five plus 20 is 25. Now let's look at some of these others. Divisible by six. Only one of these numbers is divisible by six. The one that's divisible by six is the 24. If I take 24 divided by six, that means Anna baked four cookies on Friday and must have baked the additional 20 cookies on Saturday in order to get a total of 26. But what we're trying to do is we're trying to find the largest baked on Friday number. So five and six are done. Now, which one is divisible by four? The 26, 27, or 28? 28 is divisible by four, seven times four. So I must have had seven cookies on Friday. That would have given me 21 cookies on Saturday for the total. I've done that. Divisible by three, the rule for divisible by three is that you have to add up the digits. Two plus seven is nine, and nine is divisible by three. So 27 is divisible by three. If I divide it by three, it's three times nine. So that means that we made 18 cookies on Saturday. Then the final is divisible by two. 26 is divisible by two. It's an even number, and that means that Charlie made 13 cookies on Friday. And it's asking who made the most cookies on Friday? The most cookies on Friday is then C, Charlie. I know that's kind of a tricky problem, but hopefully that explains it when you're looking for divisible by in order to be able to organize all these numbers together. Okay. So we've gotten through all of the problems for today. So hopefully you liked this making a table strategy. Making a table is probably not the fastest strategy for math kangaroo problems. There are other strategies that are faster, but I'm going to tell you there won't be 10 problems where making a table will be the best strategy on any contest. There might be just one or two, but now you know how to do those. And this is a strategy that you can use for solving a lot of different types of riddles, logic problems, things where you're sorting out. Remember, we're talking about different categories of things, different ways of separating them. So the last one we had to separate by divisibility. We had to separate by the total cookies, by the cookies on Friday, right? We're looking at different traits about the cookie bakers. So I hope you can see that for each of these problems that we did this week, we were looking at different things about them. So how many legs does each of these animals have? We were separating by a characteristic. We were looking at carrots and cabbages, two different types of foods, right? What we could eat each day, separating into the types. So you can see that tables are really helpful for separating characteristics. Remember, the best way that you can help yourself during the week is to review the videos of the problems we solved together and to practice past contests. And when you see a problem in that past contest where you're like, oh, I remember Coach Sagi was telling me when I have multiple categories and Shuriya showed me the animals, I was able to use a table. It stayed nice and organized. So try using this technique to solve your problems. What other techniques are you using? Shuriya, what else have they learned? What other techniques can they try? Well, was it making lists? That's really good. Drawing it, drawing it out. All of that's, all of that's great for solving problems, especially if you have lots of cases, you know, splitting the problem up and then working on it. So, yeah, and then just practice. Practice is the best. All right, everyone. Yeah. Thank you for coming and we'll see you next week. We have a whole new topic. It won't be a list or a table. It'll be something new. All right. Bye, everyone. Bye.

Math Kangaroo

problem-solving

tables

math problems

organizing information

calculating totals

animals by legs

eating habits

maximum cookies

mathematical techniques