Thank you for joining our webinar today. This webinar is for levels one and two, and today we will be looking at patterns. Before we start our webinar, there are a few things I would like to remind you. Make sure you have your paper printed out. You have your pencil. If you have colored pencils, that would be very good. Make sure that you have. Allowed for pop ups on your devices, because we will be doing polls and the polls are for you to enter the answers. So make sure you allow pop ups in your settings. Usually you go to your privacy and browsing settings and you should be able to allow pop ups. So please take a look at that. Also, make sure that you are able to participate in chat. OK. All right. So hi again. My name is Diana Holland and I am an educator. And my most favorite thing to do is to teach math. I I run math clubs for my students and we participate in a variety of math competitions, individual and groups, and then and they have done pretty well. So I'm glad to see you here today for a math kangaroo webinar. And let me start off by. Giving you a little background of what math kangaroo is. So what is math kangaroo? Math kangaroo is an international competition that is held every year on the third Thursday in March, and it has been going on since 1990. It has been going on since 1998, and we are celebrating our 25th year of math kangaroo. For levels one and two, there are 24 multiple choice questions and you have 75 minutes to answer them. And what type of questions do we have? We like to call it unusual and interesting problems because these are problems that require a little bit more thinking than just the regular questions where you just that are computational. All right. We would like at math kangaroo, we like to encourage our students to always use the four step method. Step one, understand the problem. So when you go to a problem, the first thing you want to figure out is what is the problem asking you? Read the question once or twice. It will be very helpful if you highlight important things, like, for example, what information you are going to use, what the question is asking, because there are a lot of words in the word problem, right? So if you just highlight or underline those, it will help you stay focused on what the problem is asking about. Then we go to step two, where it's plan. So you have to plan how to solve the problem. How can we tackle this problem? What do we need to solve it? What strategy do we use? And at math kangaroo, we teach you different strategies for solving math problems. So you'll figure out sometimes it can be one strategy and sometimes it can be more than one strategy that you will use. So it's not necessarily just one. No, we have different level of difficulty in the questions. Those that are more difficult, those are the ones that you will need to use more than one strategy. Step three, carry the plan. So once you have decided on the strategy, you are going to solve the problem. It is always good to write down the solutions step by step. Even though sometimes you think, okay, I can figure it out in my head, but it is always to write it down because you can see clearly and it also kind of slow you down so that you have time to really think about your solution. When you are done, we go to step four. Look back to check and reflect. Looking at your answer, does the answer make sense? If it's a value, a question, they ask about something that's increasing, then your answer has to be greater than what is given. Can there be a different answer? Maybe there are two options or three options, right? So you want to think about all the possibilities. So you go back, you check, read the question again, go through your solution. So this is our four-step method where you use to solve the problem. Okay, before we start our session today, I would like to do an introductory poll. So we have Noah, who is the TA for today. He's a high school student who loves math and he will be helping us today with the chat and the polls. So if you have questions, you can always put on chat. If not, the poll is there. So we are going to launch the first poll, which is the introductory poll. And you will, we're going to launch it and you can answer it. And this is also to test if you are able to see the poll pop up. Okay, so I'm going to give you about 10 seconds or so to enter the poll. Okay, looks like many of you are able to access the poll, which is great. And if you're not, check your browser settings for your device to see if you have enabled pop-ups. And even if you cannot see the poll, you're not actually missing out much because we still conduct the lesson. The only thing is you won't be able to submit your answer on the poll. And you can always put it on chat as well. But it's kind of fun to see you participating if you're able to use the poll. All right, good. Looks like about 80 of you or so are able to use the poll. All right, we are going to go on to our webinar session, the content today. So when we talk about patterns, there are two kinds of patterns we are looking at. We have the number pattern that involves numbers and we have shape patterns. I'm sure you have done a lot of patterns at school. So our questions will start a little easier. And then after that, it will require a little bit more thinking. All right, let's go to the first question. Fill in the empty space marked with the question mark on the fourth car from the left. So these are cars on the train. So we're starting on the left and we have 90, 80, 70. And what is the number in that yellow car with the question mark? I'm going to let you think about it first and then we will release the poll for you to submit it. And those of you, if you are not able to see the poll, you can always put your answers on chat as well. Also, if you have any questions, you can always put it on chat and Noah will do his very best to answer your question. Alright, so we're going to release the poll and you can put in your answers for the first question. Alright, all the answers are coming in really quickly, even on chat too. Awesome. We'll wait for a couple more people and then we will close the poll and share the results with you. Okay, so how did we get to the answer? So we find what is the pattern. So from 90 to 80, we have reduced by 10. From 80 to 70, reduced by 10. From 70 to the next one, we take 70 minus 10, we get 60. It's always good to check and see if we are right. So we go 50 to 40, we minus 10. 40 to 30, minus 10. 30 to 20, minus 10 as well. And you can even take 60, our answer, and minus 10, and we get 50. So that's what we do when you say check and reflect. Even though you are done, you check to see if you got it right. All right, good job. Let's go to number two. After one comes three, after three comes five, after five comes seven. What comes after seven? So you find out what the pattern is. Are the numbers increasing or decreasing? By how much? All right, we're going to release the poll so that you can enter your answers. Wow, the answers are coming in fast and correct. All right, we're going to end the poll and share the results with you. So in this pattern, the numbers are increasing. So when the numbers are increasing, we add. So how does 1 become 3 plus 2? 3 plus 2, 5. 5 plus 2, 7. 7 plus 2 gives you 9. And the answer is 9. And you are right, all of you. Good job. Let's go to the next question, question 3. What number comes next in this pattern? 18, 15, 12, 9. Are the numbers increasing or decreasing? So that's what you want to first think. So once you have decided that, you're going to decide how much. Is it increasing or decreasing by? Is it consistent? Is the amount always the same, or does it change? All right, and we're going to release the poll for you to enter your answers. And carefully. Okay, we're going to end the poll and share the results with you. So in this pattern, we find that the numbers are decreasing. So what is the difference between 18 and 15? We know that it is minus 3. 15 minus 3 is 12. 12 minus 3 is 9. So 9 minus 3 gives you 6. So the answer is 6. Let's go to number 4. All right. Now we have a different number pattern. Okay, this number pattern is actually in a tower. So it says, which number should replace the question mark in the pyramid? Right, this requires a little bit more thinking. So I'm going to give you a little bit more time to try to solve it before we release the poll. See if you can find any connection between the numbers on the lowest level to the numbers on the second level. You can also divide them into little groups like 1 and 3. What is the connection with 4? 4 and 2. What's the connection with 6? 6. Once you have found that, then you can find that missing number between 4 and 6. Okay, we're going to release the poll so you can answer the question. I see a few answers in there, so I would like you to go back and take a look at the question again. Make sure you have calculated correctly. All right, five more seconds to put your answer in the poll. All right, we're going to share the results with you. So if you look at this pyramid, you can find that one and three in the bottom layer adds up to four in the second layer. And we always check. So let's check on the right side. Four and two adds up to six in the second layer. So now we have found out what the connection is for the parent. Right. So we go to the second level. We want to check. Three plus four is seven. Now we know how it works. The bottom two add up to give you the one right above it. So we're going to check to see if that was correct. So we do four plus seven equals 11. Seven plus six equals 13. We are correct. Now to find the question. What's the answer to the question mark? You do 11 plus 13 and gives you 24. So well done if you got 24. Maybe a pat on the shoulder for getting it right. This is kind of a tricky question. There is also one way to check if you want. Some of you like to do it quick. Once you found the rule that you take the bottom two numbers to add up, you can add 11 and 13 without finding seven. But that would be if you are running short of time. Otherwise, we want to make sure we check all the options. Let's go to number five. We have a similar type of pyramid. So same thing. But now we are going to look for what is the value in the question mark in the second level, which is between five and two. So now you cannot kind of use the trick. OK, I'm going to take that and find it. So now you have to calculate first because the rule might be different from the previous pyramid. All right, we'll give you 10 more seconds, then I'll release the poll for you to select your answers. So if you notice with this one, the number keeps getting lesser and lesser as we go upward. With the previous one, if you notice, the numbers increase in value, right? From 1, 2, 4, 3, become 4, 7, 6, 11, and 13, and finally 24. This one, however, the numbers decrease as it goes higher. So when the number decrease, we know that it is usually subtraction or division. All right, we're going to end the poll and share the answer with you. So we use the same method as we used in the previous question. We see if there is a connection between the bottom numbers and the one right above it. So let's try 11 minus 6 gives you 5, and we always check 3 minus 1 equals 2. So now we know that, okay, the rule that we have figured out is correct. So we will check on the left side to find the question mark 11 minus 6 is 5. So 5 minus what equals 2? 5 minus 3 equals 2. On the right side, we can check also what number minus 2 equals 1? And we know that 3 minus 2 equals 1. So the answer is D, number 3, for 3. We can also keep checking. Let's see if we got it right. So we have 3 minus 2, 1, 2 minus 1, 1. So yep, we got it. Let's go to the next question. Now we have shape patterns. Luke repeats the same four stickers on his strip. Which is the 10th sticker put down by Luke? So, some of the keywords are like four stickers, so there are only four different stickers on the strip. The other one to look for is 10th sticker. You are going to figure out what is the 10th sticker. So, this information that we look for in number one, figure out what the question asks and what information we should be using. All right. We will release the poll. Oh, this is an easy one. All the answers that came in are all correct. You're good. And same thing on the chat. All right. All right. We'll wait for about 15 more people because I think we have about 80 people who are able to use the poll. All right. We're going to end the poll and share the results with you. So, we know that there are four different stickers. So, they go in the order of penguin, frog, bear, dinosaur. And then we start again. Penguin, frog, bear, dinosaur. And we keep going. So, now we also want to remember to count that we are looking for the 10th one, right? So, we go 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. And it's our friend, Mr. Frog. All right. Let's go to our next shape pattern. This time, it has beads on a string. So, it says, draw the next four beads that need to be added to the right side on the string. So, key information would be next four beads. You have to draw the next four beads. And it is to the right, not the left side of the string. Okay? I'll give you a little bit of time to draw your beads. So, look at the pattern of the white beads. Look at the pattern of the black beads. Okay, we're going to release the poll before that, oh, let me give you the answer. So these are the answer options. Good job. I know I like how those on chat are writing. W for white and B for black. All right, five more seconds to put your answers on poll. And we will end the poll and share the results with you. OK, so if you look at the pattern of the beads on the poll, you will find that it starts with one white, one black. And then you have two whites, one black. That means the black stays the same, but the white bead has increased. Then you have three whites, one black. So now we can see the pattern. Black stays the same, but each time after a black bead, the white bead increases by one. So then to continue the pattern, we will have, after the third black bead, we will have four white beads and one black bead. However, this is a little tricky because the first white bead is already given. So make sure you only answer three white beads and one black bead. All right, so this is why I'm being careful so that you don't be in a hurry and say, OK, I know one white, black, two white, black, three white, black and then four white. But one white is given. OK, all right. We'll try another pattern, beads two. And this time it's been blocked out. So Joanna made a necklace by putting beads on a string following a simple pattern as shown below. Question, what does the part of the necklace covered by the white rectangle look like? So same thing. We're going to look at white beads and red beads and see if we can find a pattern. So the hint is do the white beads separately and the red beads separately. I'll give you some time to draw in the missing beads. Okay, be very careful with the bees, all right, because I see some answers on chat that have come in and now it's not that accurate, so go back and look again, see if you can find a pattern for red bees, a pattern for white bees. So here are some, here are the answer options and we'll release the poll so that you can submit your answer. Okay, I see some mixed answers, so go back and look again. So give more people the chance to put their answers on poll before we move on. All right, we're going to end the poll and share the results with you. So, if you look at just the white beads, it's one white, two whites, three whites, four whites, five whites. Then we look at the, so the white beads are increasing by one each time. Now, let's look at the red beads. One, two, three, four, five. So, this time, both beads are increasing by one. So, we know that right after the third white bead, we'll have four white beads and then four red beads. Because it's one white, one red, two whites, two reds, three whites, three reds, four whites, four reds. And then in the box, that's where you have to be careful. The only thing missing are three whites and two reds. All right, because there's already one white given and there are three reds after it. All right, so let's go to the next question. This time we have cubes or a grid. So, the first one, we have one by itself. And then the next one, you have two rows of three. Then the next one, you have three rows of five. Question says, draw the figure that is next in the sequence. Give you a little bit of time to draw the figure. Here are the answer options. And we will release the poll so that you can enter your answers. Look at the number of squares horizontally. Horizontally means going sideways. And then look at the number of squares increasing vertically. That means upwards. Okay, let's release a poll for you to put in your answers. That's good. I can see you guys caught the pattern. All right, we will have five more seconds, then we will close the poll and share the results with you. So as you can see, the first one is one row of one. Now let's go horizontally across sideways. You have one square, then three squares, then five squares. So horizontally, the squares are increasing by two. One plus two, three, three plus two, five. And then we look at vertically. First you have one, then two, then three. So the layers or the number of squares vertically are increasing by one. So we know that the next figure in the sequence, we will have five plus two horizontally, seven squares. And then vertically, three plus one, there will be four squares vertically. Give yourself another pat on the back if you got that one right. All right, to the next question. To find her toy, Marie needs to follow the path which is marked by the following signs in this order. Triangle, heart, diamond. Which toy belongs to Marie? So you're going to follow the path and don't forget the pattern, and you will find Marie's toy. Okay, so take out your pencil or crayons and mark it along the path. Make sure you don't create your own path. Use the path that is already there. Don't draw your own lines when there isn't a path, okay? So once you have reached the third diamond, which toy is next to it? Or there's one that tricked you with a heart. At the end of the path, do you find the bear, the ball, the doll, or the bucket? We'll give you maybe another 10 seconds and then we'll release the poll for you to enter your answer. Okay, enter your answers on the poll. I see some different answers. Follow the path carefully. It must go in the sequence because this is a pattern. So don't create your own path. There cannot be two diamonds one after the other. All right, five more seconds to enter your answers on the poll. And we will share the results with you. All right, so if you go triangle, heart, diamond, there are two diamonds available after the heart. But we need a triangle to follow that diamond. So we have to go down and then triangle. And we cannot go triangle again. So we go triangle, heart, diamond. There are two options after the second heart. But we know that after the diamond is the triangle. So we go to the right triangle. We go upwards to the heart and then right to the diamond. And it's the teddy bear. So Marie's toy is the teddy bear. All right, next question. We have a pattern and this time it's little squares. But each square has a pattern. So the question is which kind of pattern, which kind of square appears most often? So count the squares by the design that is on each square. How many gray squares? How many crisscross squares? How many lines? And how many checkered squares? And the important information we are looking for is the square that appears most often. Is it the gray square, crisscross, line, checkered, or all of them? All equal means all of them have the same number of squares. All right, we're going to open the poll so that you can enter your answers. This looks like a very easy one for you because everybody got that one right. All right, five more seconds. And we will share the result with you. All right, so there are seven gray squares, six crisscross squares, six line squares and six checkered squares. So they are not all equal. So E is out and seven is greater than six. So the answer is A, gray squares. OK, we go to the next question. Sophie makes a row of 10 houses with matchsticks. In the picture, you can see the beginning of the row. How many matchsticks does Sophie need altogether? So key information would be 10 houses. And how many matchsticks? And they are all in a row. So you just continue the pattern. OK, don't draw 10 separate houses with matchsticks. You're going to continue after the fourth house. So this one, I'll give you a little bit of time to draw your picture. And I can just use lines for the matchsticks if I have to draw the matchstick, full matchstick. Once you have drawn the 10 houses, then start counting. Maybe you can circle house 1, and then house 2, 3, and so forth. And make sure you don't count the same matchstick twice. All right, we'll open the poll, you can enter your answers. This one I think I'll give a little bit more time because I can see all kinds of different answers, options that have been chosen. All right, we are going to give you five more seconds to enter your answer in the poll and then we will share with you the result. Okay, so as you can see, I have drawn 10 houses and then I make sure I check which matchstick that I'm counting. So the yellow is the first house. There are 1, 2, 3, 4, 5, 6 matchsticks being used to build the first house. Now the second house, I color with purple. However, do you notice that I did not color the one that is yellow and number five because it's already been counted for the first house. So for house two, I would only have used five matchsticks and then the same thing for the third house. I do not count the one on the left because that's already counted for the house before it. So if you keep going, you will find that you have nine houses that use five matchsticks. So five times nine or you can count by five, nine times, you get 45. 45 plus six gives you a total of 51 matchsticks. All right, so be very careful. Do not just because I saw on chat, it just appeared right away. Six times ten, 60. You have to be careful, right? We don't use 60 because they are in a row. So these are keywords. If it says Sophie is making 10 houses and each one looks like this, then it's different. But it says in a row, so one side touches the other. All right, so that's what we meant by reading it carefully for important information. We go to the next question. A certain kangaroo makes 10 jumps in one minute and rests three minutes. Then he again makes 10 jumps in one minute and rests for three minutes and so on. That means he keeps repeating the pattern. Each time he jumps, he will make 10 jumps and he does it in one minute. After that, he will rest for three minutes. What is the least amount of minutes that he needs to make 30 jumps? Okay, so there is a pattern here also between jumps and rests. So you can draw it out, put the numbers in the number pattern and draw it out. Okay, we're going to release the poll in about maybe 10 seconds. Remember, we are looking for minutes, least amount of minutes to make 30 jumps. All right, we're going to release the poll for you to submit your answer. Good, good. Okay, five more seconds to enter your answer. and we will share the results with you. All right, so the first time he makes 10 jumps, I use a triangle to represent it and then a square to represent the rest. So first jump, one minute, rest three minutes. Second jump, one minute, rest three minutes. Third jump, one minute, but you notice I didn't put the rest because the question says what is the least amount of minutes he needs to make 30 jumps. It did not say what is the least amount of minutes to make 30 jumps and three rest, four rest or 30 rest, right? So we do one plus three, plus one, plus three, plus one, that gives you a total of nine minutes. So a lot of these questions, sometimes they look really easy, but then you have to be careful to think first. And the answer options that are given, sometimes it can trick you into thinking you're right. So if you notice during our webinar, we don't give you the answers yet. We want to train you to read the question, answer it first, and then only look for the answer because sometimes those answers are so distracting, it confuses you, all right? And then we go back to the question and say, oh, it says 30 jumps, it didn't say three rest. So we don't have to add the last three minutes. All right, so we have practiced the different kinds of shape and number patterns today, and I just want to do a quick review with you on the four-step method. So remember step one, you understand the problem, you ask what the problem is for an answer, you look at the question, you circle or underline the important information. Is it how many inches or does it ask you how many feet too? Sometimes you get those kinds of questions. Number two, plan how to solve the problem. What strategy do you use? Do you only have to use one strategy or do you have to use multiple strategies? What information do you need to solve this problem? Go back to the word problem. Then you carry out the plan, okay? You solve it. It's always good to write it down no matter how tempted you are to just figure it out in your head. Write it down because then you can see more clearly if you make a mistake, and it helps when you go back and check it too. Number four, look back to check and reflect. So once you have solved it, you have your answer. Go back and think, is my answer logical? Does it make sense? Should the value increase? Should the value decrease? Should I have used this shape? Could there be a different answer? Then only you mark that as your answer and you submit that as your answer, right? So always use the four-step method because this way you are less inclined to make a mistake. Thank you very much for joining our webinar today. We have more webinars in the upcoming weeks each Saturday, and I hope to see you again soon. There are also webinars for levels three and four, five and six if you have other siblings, and you can always go to the website to sign up for the webinars. They're usually open on Mondays. So thank you for joining us today. Have a great weekend. Bye.

Math Kangaroo competition

problem-solving method

numerical sequences

shape sequences

interactive polls

geometric sequences

Diana Holland

pattern recognition

math webinar