Today's lesson is going to be an introduction to Math Kangaroo, so we'll talk a little bit about what's in the contest, about how we solve problems, and then we'll see some example sample problems. All the problems are from past contests, so they're real Math Kangaroo problems. But they'll cover like one of each different type of problem, just to give you an idea of flavor today. In our future lessons, we'll go more in-depth into each type, and we'll give you lots of experience on the different types of problems, okay? Remember the way to communicate with me and with Shurya, the TA, is to use your chat. We will have polls, all right? So during the webinar, your camera should be always off. Again, it's for your privacy, okay? I know that you probably have wonderful smiling faces, and I'd love to see them, but for your privacy, we're going to keep the cameras off. Go ahead and use that chat. I do watch the chat as I lecture, and I will know if everyone is confused, I'll know I have to start all over again and try something else, and that's okay, all right? And again, we'll have polls. If you answer questions in the polls, your name is not there. I don't know who's answered it, okay? So it's anonymous. If you get it wrong, you're just in the learning process. If you get it right, great job. It doesn't really matter. No one will know the difference. Let's just try your very best. My name is Sarah Segee. I am a biologist. I live in San Diego, California. I have been tutoring math and science for a very long time. For you, I guess I'm really old at this point. My oldest children are graduated from college. My youngest child is in eighth grade. I have been teaching for math kangaroos since they started doing these. I think I taught some of the very first webinars that math kangaroo had a few years ago. I teach small group lessons. I do private tutoring, and I do these webinars where I can talk to more students at a time. And my hobbies include teaching karate and swimming, and I like to go to Zumba classes and dance. I crochet. I make soap from scratch. It's an acid-base reaction, if anyone likes chemistry, science fair kind of stuff. And I have a new puppy, so hopefully I'll be able to walk my puppy pretty soon once he figures out how to not chew on the leash. If any of you have had a puppy, you know how they do that. All right, and I'm going to let Sharya introduce himself. Hey, I'm Sharya. There should be a Y right there. Sharya Vyas. I'm in 10th grade in Garland, Texas. So I've been participating in math kangaroos since I think third grade. As for volunteering, I also volunteer with my library, at school with different clubs, and yeah, some of my hobbies include playing chess, playing piano, hiking, biking. I do some origami, arts and crafts stuff. And when I was your age, I was mostly into Roblox, Minecraft, things like that. So that's a little bit about me. And have you taken math kangaroo contests? Yep. So for about, how much would that be, eight years? So since you were at these students' ages, so you've been doing it a long time. Why do you keep doing it, Sharya? It's just fun. It helps me practice my skills. Math kangaroo is quite different from other math competitions in the sense that there's not a lot of theory. It's more about thinking and intuition, you know, more questions with figures. So I like it. It's cool. All right. So the math kangaroo contest, for level three and four, you would have 24 questions and 75 minutes. And you can tell me in the chat, in hours and minutes, how long 75 minutes is. You'll notice when you take your contest that the contest problems can be worth three points, four points, or five points. And it is going to be eight of the three points, eight of the four points, and eight of the five points at your level. And we do think the people who write the problems think that they are getting harder. So hopefully you go through the low numbers reasonably quickly so that you'll have more time to spend on the five point problems. But it takes practice and experience to do that. So if you're finding that it's challenging to get through half of that, that's normal. Typically students who are doing very well in school will get about half of math kangaroo problems correct. And then as they practice and experience, they'll get more and more and more of them correct. So that's your goal, is to try to get more and more correct each time you do it. And that's how we do it. So let's see. We are going to talk about two different things right now. So those three point questions are going to be more of what we would probably think of as exercises. Do you know some basic math skills? Can you see some basic ideas? And then we'll get into the harder ones, which are the problems. You may not have done anything like them before, but can you use your basic skills to try some approaches and figure out how to solve it? So when you see a tough problem, you may not know exactly what to do at first, but we'll discuss it, okay? So this one is probably an exercise. I think you'll know how to do it once I read it. Pia is making shapes using the connected sticks shown in the picture. Which of the following shapes uses more sticks than Pia has? I usually get quiet after I ask a problem so that you have time to work. This is a good time to put your answer in the chat. And I will let you know which questions have polls. This one does not. There's a question about the recordings. You should receive an email from Math Kangaroo telling you how to access the recordings after the classes. It'll take a little while for them to process it and make it available, but it should be within a day or two that you'll be able to see the recordings. Okay, I have a lot of people giving the correct answer. I think this one is probably the most straightforward way to count how many sticks PA used to make this shape. So just organize counting. I draw on my papers a lot. That's fine. You can draw on the figures. For most of our figures with Math Kangaroo, you will find a handout in your class registration that you can print so that you can have them with you. If you ever forget to print it, it's okay because I'm showing you all the problems with their figures. So I see that PA has used 10 sticks, right? So now I have to figure out which of these shapes use more than 10 sticks, right? More is an important word in this problem. So in problem solving, we always want to make sure we have all the information from the problem statement. Then we want to know what the problem is asking us. So most of you have come up with the answer. It is D. And there are a couple of ways to count. We can go through and we can count all, you know, 4, 5, 6, 7, 8, 9, 10. That's exactly the same number. So it's not more. We can cross off A. On this one, we can do a little, we can do 1, 2, 3, 4, 5. And I know the other half is another 5. So it's 5 times 2 equals 10. Don't forget, you can do some shortcuts like that. For D, I can cut it up into 4 pieces. And I can see that each piece has 3. So 3 times 4 equals 12. This one is more. Again, if you counted them all individually, you'd still get to the same place. But by recognizing that there's a symmetry and a pattern, you might be able to get there a little faster. All right. We'll move on to the next problem. This one. I will clear all my drawings. And Shoria, you wanted to lead this one. There is a poll that they can do afterward. I think I'm leading 4 and 5, right? Oh, yes. My mistake. Sorry about that. I have notes and I can't interpret my own notes. All right. So this one is Luis has 7 apples and 2 bananas. He gave 2 apples to Yuri, who in turn gave some bananas to Luis. Now Luis has as many apples as bananas. How many bananas did Yuri give to Luis? In reading this problem carefully, I'm noticing a few important words. As many as. That means something mathematically, right? When I say as many as, it usually means I can write some sort of mathematical symbol. And then I want to know how many bananas did Yuri give to Luis? Not how many bananas does he have in total, but how many did Yuri give him? If you need help when you're solving these, you can send a text, a little chat message to Shoria. He might be able to help you. That's why he's here. I'm seeing a lot of correct answers. I bet this poll is gonna come out with a lot of good responses. If you don't like seeing that poll, you can always close it without answering if it ever gets in your way. Anybody else want to answer the poll? Only about half of you have put in an answer. Remember, it's anonymous. I can't tell what answer you as one person has put. I only see the whole total. Okay. I'll end the poll and I'll share the results. It looks like most of you, 73%. So that's almost three fourths, right? 75% is three fourths. I've said the answer is three bananas. So let's take a look. If that poll is still in your way, just hit that close button on the top so that you can see what I'm doing now. So if Luis had seven apples and two bananas, I just use A and B for apples and bananas. No reason to make it complicated to write my notes, right? He gave two apples to Yuri. So I'm going to subtract the two that he gives to Yuri, and that's five apples. Who in return gives some bananas. So there's some sort of number of bananas that are added. And now we know that he has as many apples as bananas. Well, as many as means it's equal. In mathematical terms, we have to use an equal sign. So I'm going to need five bananas. So what number is missing? If I have two bananas, I must get three more bananas. So the answer is that Yuri gave Luis three bananas. It's just another way to show it. All right, so you'll notice the first step is always that I'm reading the problems very carefully. Sometimes I underline things or I highlight them, I circle important information. I have to make sure I know all the information that they're giving me and what I need to find. What format is the answer going to be? Math kangaroo tends to be a little tricky about that. They might ask you to add things up or to take a difference between things. So you'll have to figure out what they want. Then you need to make a plan. Let's start and make a plan. How will I solve it? What mathematical operations do I need to do? Is it a geometry problem? Is there a formula that I need to know? Maybe I need to know about perimeter. Maybe I need to know how to multiply, or I'm going to be looking at the sides of something. Maybe I need to trace something. So when you do your plan, make sure you are careful. Okay, so once you have a plan, then you're going to go through it step by step and be very careful. Number four is when we go back and check and reflect. You're going to check your answer. Am I right? Does it make any sense? If my answer wasn't about bananas, if I said I gave him 30 bananas, I know something is wrong. You can almost always check your answer. Now, there's another way we check our answers as well, which is we sometimes proofread and help each other. So you'll notice if I make a mistake, I might have one of you tell me in the chat, or I might have Shurya say, coach Sagi, you said the wrong thing, or you wrote that down wrong. And that's okay, because making mistakes is part of being human. So we just correct them and we learn. And there's no problem in learning from mistakes. There's only a problem insisting on making mistakes over and over again. All right. So we're going to talk today about a couple of different types of problems. I think there's even more than six types. Number problems, we just did a number problem. There's going to be some geometry and measurement problems, visual and spatial thinking problems. So we will talk about visual and spatial. And I think that's what Shurya was talking about when he says there's some things in math kangaroo contests that are not so common in other contests. And I think that the visual and spatial is really a feature that math kangaroo excels in. Clocks, time, calendar. Clocks doesn't just mean like tick-tock clock, okay? It can also mean years. It can mean seconds. It can mean all sorts of stuff. Even logic problems. Like can you puzzle things out? What things are not possible to happen if something else has happened, right? So if you have three cats in a room, can you bring in a bird? Might not be logical, unless your cats are very well-behaved and the bird is very well-protected. Okay, number three. Sarah has 16 blue marbles. She can trade marbles in two ways. Three blue marbles for one red marble and two red marbles for five green marbles. What's the maximum number of green marbles she can get? I do have a poll. If this is a problem you solve very quickly, think about what other colors of marbles Sarah will have and you can put that in the chat. You'll notice sometimes I send you a little message back in the chat to let you know if you're right or if you need to retry. I can't answer every student. I'm sorry, it's just not, I don't have enough time. Here's the poll for this question. Okay, here are the results. Not everyone answered the poll, so I'm not sure if you haven't found the answer yet or if you're scared to use the poll. Don't be afraid. Like I said, it's completely anonymous. It means I can't tell what you answered. So, most of you have said 10. Let's take a look. 10 is correct, so that's good work. Again, if that poll's in your way, just hit close. I'm going to do this in a really old-fashioned way, guys, because why not? I'm going to draw 16 marbles because I can do it pretty fast. Now, remember, there's more than one way to solve a problem. If you did not draw anything, you did it without drawing, that's fine. No problem. This is just one way. All right, I have 16 blue marbles, and I can trade 3 for 1 red marble. So, I can circle 3, and I can get 1 red, 1 red, 1 red, 1 red, and I can do 1 over here. So, I now see that I can have 4 reds if I make the first choice, 3 blue marbles for 1 red marble. And you can have done that as well by saying, okay, 16 divided by 3 equals 5 with a remainder of 1. You can do that. Perfectly okay. Now, I need to know, okay, I can trade 2 green marbles for 5 red marbles. Sorry, see, I say the wrong things all the time. 2 red marbles for 5 green marbles. So, then 5 plus 5 is 10, so I do have 10 green marbles. Now, another thing to consider, since green marbles only come in groups of 5, I could have done one of my favorite tricks, which is to cross out wrong answers. Since green marbles only come in groups of 5, it couldn't have been a 9, an 11, or a 12. So, only 2 of the answers represent groups of 5. So, now I have a 50-50 chance of getting it right, but the correct answer is indeed 10 marbles. Hopefully, you did well. All right, this one was for you, Shurya. Okay, so the weight of a dog toy is a whole number. It's a whole number, and we want to find out how much one dog toy weighs. So, we can see that in the first scale, the 12-kilogram weight is heavier because it's towards the bottom, and on the second one, the two dogs are heavier. So, we just want to find out what one of them weighs. So, I guess I'll give you some time to work that out, and you can put your answers in the chat. Hey Churia, I'm receiving a lot of correct answers. I think most students get this one. Okay, so how I would work this out is, first of all, we can see we can see that our dog toy on the left is above the 12 kilograms. So that means that the heavier weight has to be lower on the scales. So that means our weight of the dog toy, let's call it d, our d has to be greater than, I mean, sorry, less than less than 12. It's easy to write the wrong thing, Churia. Trust me. Yeah, so it's going to be less than 12 kilograms in the air. Now on the other side, we have two dog toys. However, those are heavier than 20 kilograms. So we could say two dog toys are heavier than 20 kilograms. So what that means is since all the dog toys have to weigh the same, that means that we can cancel out the twos on both sides. So one dog toy has to weigh heavier than 10 if we want two of them to be heavier than 20. So now we can see that the dog toy is greater than 10, but it's less than 12. And since we want a whole number, the only number that is between 10 and 12 is going to be 11. Exactly. Very nice. Hopefully that's similar to logic to what our students were using because they did quite well. Clear off those pictures and Churia wants to do this geometry problem with you as well. Okay, so we have that this large triangle here is made up of many different squares. So all of these are squares of various sizes. The three small squares each have an area of one. And we want to find the area of this whole rectangle. So this whole big rectangle here. Okay. So I'll give you all some time to work that out and you can message me in the chat. And if you have questions, you can send them to me too. Okay, so let's start on this. If we see that these three squares have an area of one, since they're squares that means that the side lanes should multiply to one, and the only numbers that do that is one. So that means our little squares look like this, and they're one on all four sides. So because of that, we can see that this little square over here, the one above these three, that's going to have a side length of three, because of these three ones right next to each other. So using that, all side lengths of this next smallest square are going to be three. So All right, so since we know that this square is going to be 3, the square is 1, we can use the same technique on all of the other squares. So since they're all joined together, we can see that this little square has side length 1 right here. So this big square right here, it's gonna have a side length of 4, because of this 3 plus this 1. This 3 and this 1. So now, again, we can transfer this 4 over here, because again, the square has the same 4 sides. So 3 and 4 makes 7. Therefore, the length of this square is going to be 7. So we have 7 here, 3 and 4, and then the 4 comes from the 3 and 1, the 3 comes from the 3 and 1. And then lastly, we can use it on this one last square over here. That'll be 7 plus this 4. So we're gonna have a side length of 11. So let me circle these side lengths. So these are the side lengths of our 4 squares, and then we have our 3 level squares. Now, the question, remember, asked us to find the area of this large rectangle. So this whole, this whole thing right here. So that's just gonna be our length times our width. Or this could be our length, this could be our width. Same thing. So this length would be 7 plus 11. That's gonna be 18. Our width is just going to be the biggest square side length, 11. So for our area, we multiply them. So that's 11 times 18. So for multiplying this, instead of having to write it down, like 11 and then 18, we can use a trick. So we can say that 11 times 18 is the same as 10 times 18 plus 1 times 18. Right? So if I was multiplying 3 and 4, it would just be 3 4. So we could group that as 2 4s and then 1 4. So in the same way, we're grouping these 11 18s into 10 18s and 1 of them. So this makes it a whole lot easier when we're multiplying. So 10 times 18, we just add a 0, that's 180. And then we add in just 18. So 180 plus 18 gives us our answer of 198. And that is easy. Thank you, Sharia. That's right. It's 198. And remember, area of a rectangle is the length times the width. And the area of the square is the length times width, and they're the same. So it's the single side squared. Once you had those two pieces, you could solve this problem. But it did take some very careful working. So good job if you have that correct. And this is a five point question, I noted that. So you'll know that this is one one that we think is going to take you a little more time than some of the fast ones. Okay, I do have a poll for this question. George or Jorge, depending on your pronunciation glues the six stickers, a duck, an elephant, a mouse, a ladybug, a dog and a fly to the faces of a cube. The picture shows the cube in two positions, which sticker is on the face opposite the duck. So this is the same cube, they've only just turned it a little bit so you can see different sides. So you need to know what the faces of a cube are. And you need to know what the word opposite means. Hopefully, you know that the opposite of a top is a bottom. And the opposite of the right is the left. So we want opposite to the left. So we want opposite to the duck. Here's the duck. I will launch the poll pretty soon. I'm seeing good answers in the chat, that's great. Please don't comment on the screen because I don't want your names to pop up there, okay? A place to put your answer is right here in the poll. Notice I do not do a poll on every question because of the time that they take, but if you really like polls, let me know. I can make more of them for the next time. Well, we have a lot of you answering the poll and correctly. So that's amazing. All right, 30 more seconds. Again, this is a 3 point question, so it should be pretty quick. All right, here are those results. You'll see that almost all of you have said that it's the fly that's on the opposite side. Let's take a look at it. Remember, for me, I have to press close the poll in order to return to the screen. I don't know if you do or not. Okay, so if it's on the face opposite the duck, that means it will not. Be next to the duck. Right? So it's like the top and the bottom are not touching each other. So any picture that touches the duck can't be opposite the duck. So from the first view of the cube, I can see that the mouse is next to, we also call that adjacent to the duck, as is the ladybug. And then from the second picture of the cube, I see that the elephant is next to the duck, as is the dog. So the only figure that is not next to, because we can see all four sides that are next to the duck, the only one we haven't been able to see, is the fly hiding on the back. Okay. There is no poll for this one. Be careful with this one. This is spatial thinking problem. This is a 3 dimensional shape. Lowe's looks at the pyramid from above. What does Lowe's see? What do we mean by look from above? I'm going to draw these crazy, silly little eyeballs up here. When I'm looking down on it from the top, it looks like it gets flattened. Right? So these are pictures of it flattened out. And what do you see? Pay attention to the different colors. And one approach here is to cross out the ones that are impossible. Thank you for putting your answers in the in the chat. I like seeing how you're thinking and that you're actually still doing the problems with me because that's the most important part right is that you're trying your best and doing the problems as best you can. All right I'm going to start crossing off some wrong answers. I'm not going to give you the right answer just yet as some students are probably still thinking about it. So one thing I noticed is that I have two of these gray lines. So any picture that doesn't have two gray lines and you also the two gray lines are next to each other. So this only has one gray line so this is not it. This is two gray lines but they're opposite each other so that can't be correct. And then E also has only one gray line so it is also incorrect. At least C and D have the correct number and the correct colors of the lines that go to the center. What is the difference between C and D? How many of you ever turn in a screw and you know righty tighty lefty loosey or you know clockwise and anti-clockwise or counterclockwise because that's a big hint for this one. So if I look at this and I start you could start on any of them but I can start here on the uncolored one. If I go clockwise around the figure I should go uncolored black gray gray. But if I do that here you'll notice I go uncolored black gray gray. So this one matches. If I take a look at the figure the other way counterclockwise you'll notice I go uncolored gray gray black and that's what this one does which is uncolored gray gray black. So this one is backwards the correct answer here is C. It's kind of a tricky one huh having to know if it was clockwise or counterclockwise but sometimes math kangaroo problems want you to notice small details. So now we're going to work on a clock and a calendar clock or calendar problem. This one also there's maybe a reason I was talking about clockwise because here in fact are some clocks. All right I noticed four clocks on the wall. Only one of them shows the correct time. One of them is 20 minutes ahead the other 20 minutes late and yet another is broken. What time is it now? You'll notice several things are missing in the problem. One is there are no numbers on any of these clocks. So if you need to go ahead and write some numbers on the clocks there's nothing wrong with doing that as your first step. If you need it there's anyone who does not know how to tell time on a face clock that could be a good good afternoon activities to learn how to do that. On a clock it's always 12 at the top and then we go around with our right hand Okay, so one approach to this is to try to figure out what time each clock is showing. And then we'll have to figure out what it means by if it's 20 minutes ahead, 20 minutes late, then what time would be on the clock. So right now is almost exactly one o'clock where I live, because I'm in Southern California in San Diego. Where you live, it might be four o'clock or two o'clock. If it's 20 minutes, if clock is running 20 minutes late, it would look like it was 12.40 instead of being one o'clock. And if the clock was running 20 minutes ahead, it would look like 1.20, right? Some people even set the clock in their cars a little bit ahead so that they're not late for everything. They think they're in a hurry all the time and they get there on time. Ever seen that trick? So the time on the first clock, let's see if we can solve it. The hour hand is the shorthand, the hour hand is between the four and the five. So it is going to be four something. It's not yet five o'clock, but it's well after four o'clock. In the minute hand, we count five minutes for every number on the clock. So it would start over here at zero and then go five, 10, 15, 20, 25, 30, 35, 40, 45. So get five, 45. If you don't already know how to tell time on a face clock, you probably need more practice than we can do right now, but at least this should help you. Again on this top right clock, I'm now between the five and the six. So I'm at five something and I'm only one space away. So that's only five minutes, 5.05. If I look at the same on this bottom left clock, I'm between five and six with my hour hand. So I'm at five something, five, what, five, this is zero, five, 10, 15, 20, 25, 5.25. Again between five and six over here. So I'm at five something, 5.30, 35, 5.40. Now I'm going to write these times down in order, it might help me a little bit. I'm looking for times that are separated by 20 minutes. Between 45 and 4.45 and 5.05, I do have that 20 minute gap and I can look at it this way. I can look at it as five, 10, 15, 20 if I go around the clock. So this is a 20 minute difference. And again, pretty easy to subtract five from 25 and know that that's a 20 minute difference. If I do the same thing with this one between 25 and 40, I notice there's only a 15 minute difference. So that's going to tell me that this clock here is broken and 5.05 is the correct time. Okay, I do have a poll for this one. One year in March, there were five Mondays. Which day of the week below could not appear in this month also five times? You might notice that this is a five point question. This requires you to have some knowledge about how many days there could be in the month of March. The most days you ever have in any month is 31 days, right? So assume it's 31 days. When we do our lesson on the calendar, we'll go into how you'll know which months have which numbers of days. This is an important word. We're looking for the one that could not be correct. I think I can launch the poll because I think the question is on the top of it. There you go. There's a question about what is the first day of the month. The problem doesn't tell us that. It only tells us there are five Mondays. So we can't make an assumption it doesn't tell us. I know some students have joined a bit late. Just want you to know that this webinar is recorded. So any of the parts that you have missed, you'll be able to watch in a recording. When you check your class registration in a day or two, there'll be a link for you to get that video and watch it. OK? I'll allow just a few more moments on this one. We have one problem left after this, and we want to make sure we see them all today. I think this is a great question for Math Kangaroo to have made worth five points. Because if you take a look at the poll, we have students answering every possible response. That means this one is pretty tricky, right? But this is one of those problems where I think once we explain it, you won't have to make the mistake again, right? That's our whole point is to learn how to solve it. If you don't know how to solve it, but you do in two minutes from now, that is learning. So don't be hard on yourself as long as you're learning, right? Okay, so we know that there are seven days in a week, Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday. If there are, we can take the multiples of seven, seven, 14, 21, 28, but we know that there are 31 days at most in a month. So between 28 and 30, the 29th, the 30th and the 31st repeat days, right? So three days appear, I can spell, five times in a month that has 31 days. We know that Monday is one of them. We know that there can be only three. So it could be the three days and Monday is the third one. Monday could be in the middle, or it could be that Monday was the first day of the month and there are two days that come after it. So what days do we get under those situations? In the first case, we get Saturday, Sunday, and Monday. In the second case, we get Sunday, Monday, and Tuesday. And in the third case, we get Monday, Tuesday, and Wednesday. So based on this, it is possible that Saturday appears three times. It is possible that Sunday appears three times. It is possible that Tuesday appears three times, and it's even possible that Wednesday appears three times. But what never appeared three times in either of any of these options was a Thursday. So Thursday is the one that cannot appear and is the correct answer. So if you didn't solve it correctly, but now you understand how to try it the next time, congratulations. This is a logical thinking problem. This one's kind of fun. The buildings on Color Street are numbered from one to five. Each building is colored with one of the following colors, blue, red, yellow, pink, and green. We know that the red building is next to only the blue building. That's an important clue right there. Next to only the blue building is between the red building and the green building. What color is the building with the number three? This is the one we want to find. I'm already seeing some great responses in the chat. Thank you for working so hard. Okay, we're getting so many answers. I'll launch the poll. If you still need to see the problem, you can try to scooch that poll out of your way or close it if it covers up your screen. I'd rather you see the problem than answer the poll. Anybody else? There are a few who didn't put a response, but it's okay. Compare this response to the last one. This one's unanimous. Everyone who answered the poll says it's green. If you didn't answer the poll, hopefully you still think it's green. I'm gonna show the work for this one. It says the red building is next to only the blue building. So if the red is next to only one building, then red must be on one of the ends. That's an R, sorry, a little messy. And the blue building must be next to it. Now, the thing we don't know is if the red is number one or number five, but because of symmetry, it doesn't really matter. And then it says that the blue building is between the red building and the green building. So blue is next to a red and a green. So the only option for number three is green. It doesn't matter if the red was at number one or at number five because of symmetry. So green, the unanimous correct answer on the poll was absolutely right this time. Okay, so today we talked about, we are going to be moving from doing simple exercises to doing some problems where you really need to think about them. All right, we did a bunch of different kinds of kangaroo problems, and I want you to think about going through the easy ones quickly and spend more time on the difficult ones. That's gonna be to get more points. We also talked about the four-step process. The first part is always making sure you understand the problem and what's being asked, okay? That will be really important. So make sure you've done that. The next part, what can you do after today, before next week, if you want to, if you missed any of today's problems, you can review this recording. It will be available, like I said, just go to your class registration and there'll be a link. It might take a day or two until they come back to the office tomorrow and get that loaded for you. On the Math Kangaroo website are past contests. We publish all of our past contests, so you can take a look and use those. If we asked a question in the past, we won't ask the exact same problem this year, but it could be similar, right? And also, when you register for the Math Kangaroo contest, you should get a code that will let you see video solutions of teachers solving Math Kangaroo problems. Also in your registration for this webinar, you'll find a link that lets you print out, download all the figures that we're using, so that when you need to make notes on a figure, like Shurya did a lot of making notes on the squares and rectangles for the area. That one is much easier if you can actually mark on the figure. So don't forget, you can print out all the figures before you come next week. Okay? Thank you, Shurya. Thank you, all of you. We didn't get to our bonus problems this week. Sometimes we do, sometimes we don't. I appreciate all of you being here and I hope that you'll come back next time. And thank you to everyone. Thank you to Shurya and see you all next week. Bye.

Math Kangaroo

mathematical problem-solving

Sarah Segee

Shurya Vyas

geometry

logical thinking

spatial thinking

four-step process

analytical thinking

practice problems