Hello everyone, welcome to our lesson 7 webinar. Today we are going to introduce a new strategy called Guess and Check. I believe some of you might already apply this strategy when you try to solve some problems. Elita, have you tried Guess and Check a lot to solve the problems? Yeah, to solve the problems and also to check the problem when I'm done. Especially for these multiple choice questions, Guess and Check can be really helpful to save time. Yeah, that's true. So let's see how it works. So first the ground rules we already repeated a lot of times. We try our best to answer your questions. Please send your questions in the chat, but we might not answer all. If any question is asked frequently by the students, we will announce it in the class. So here is the 4-step method. Elita, can you quickly go through this 4-step method? Yeah, so the first step is understanding the problem. So this is just reading the question carefully and knowing what it's asking. Because sometimes you immediately think to solve for one thing, but it's really asking for something else. So you have to make sure that you understand what it's asking for. And then we plan how to solve the problem. So the strategies we can use to solve them, like Guess and Check would be a strategy. Or we've done strategies like Draw a Picture. Those are all good plans for how to solve them. Then we carry out the plan. So you just go through the things we teach you and write it down step by step. So you can go back and check your work if your solution does not match anything. And then lastly, Check and Reflect. Does the answer make sense or can there be a different answer? Like if a question is asking how fast somebody is running, it wouldn't make sense for them to be running at 500 miles per hour, for example. Thank you, Elita. So before we start the new strategy, we would like to review the last lesson. We worked on the 2D geometry. So in the geometry, the 2D shapes have two dimensions. That's why we call it 2D shapes. So you usually find the length, width of length and height. So the 2D shapes always be flat, like a picture you can see. And there is no depth. So you usually would check the size, check the angles. So in the higher grades, you might be involved with the areas, also the parameters. So that's a 2D shape. So today we are going to work on the Guess and Check. So the Guess and Check is very obvious. You know you need to guess the answer first and then you check your answer. If it doesn't work, you need to make another guess and check again. I know some questions you might have a smarter way to solve other than the Guess and Check. But this lesson, we try to go through, work with you and give you a better understanding about the Guess and Check. So that's why. Please try to use Guess and Check to solve this problem. And then you can try another way to check your answer. So we can launch the poll. Because there's images in the polls. Yeah. It would be much easier. So they ask the four of the numbers 1, 3, 4, 5, 7 are used. Not all five, only use four, and you have one left over. So which one would not be used? So you need to give a few choice. For this one, you'll need to understand this equation. The left side, two number add together, make a sum. And right side, two number add together, make a sum. And they would equal each other. And the number you wouldn't use, that would be your answer. So guess and check sometimes take time, yeah. So you might not make the correct guess right away. You might give a few tries. But remember, we have five options we already gave to you. So you can pick any option to check if that work or not. OK, yeah, I know guess check might take a little longer time. So let's let's review this question because it's been 3 minutes, yeah? So look the result. We have a different choices here, but the correct answer would be C. Yeah, so we have a half class. Make it right. That's good. Let's go through the solution to say what happened. So here, when you try guess and check, first you just try. You could make 1 plus 3, make 4, yeah? And then you have 4, 5, 7 left over. And then you would want to see if any two number left over added together equal 4. That wouldn't work. Yeah, any number would be equal or bigger than 4, so that wouldn't work. And then you continue check. If you can do the 1, 4, equal 5 and you left over 3, 5, 7, so you check. Still couldn't work. You couldn't make any two number added together equal 5 in the rest numbers. So the next one you check 1 plus 5 and then you left 3, 4, 7. Still doesn't work. And then you check 1 plus 7 equals 8 and then you have 3, 4, 5 and you could easily figure out 3 plus 5 equals 8. So that's how you figure out the 4. You do not use it. And here, remember, we give you the answer choices. So the first one, maybe you can start it. Oh, I do not have 1. I only have 3, 4, 5, 7 left over. And then you can check if you could make the two pair added together equal each other. So there's one thing I want to introduce. If you guess you have 1 left over, you would have a 3, 4, 5, 7. If you want to make a two pair added together equal each other, so you never would like to add a two smaller number. Try to get equal to the two bigger number. Yeah, you also wouldn't try the first number and a third number because you see the three smaller than four, five smaller than seven. So you also wouldn't use the 3 plus 5. Try to get the same sum as a 4 plus 7. So the best way for you to use, you always use the smallest number and the biggest number make a pair and the two middle number make a pair. So that would be possible for you to find the equal sum. So that's the logic here. Yeah. So because later you might use this logic help you to solve the guess and check question. Okay, next one. Elita. Yeah. Question two. Yeah. Emil placed the numbers 1, 2, 3, 4, and 5 correctly in the boxes in the diagram. What number did he place in the box of the question mark? So you can see he started with a number. He added a different number to it. It resulted in the question mark, and then he subtracted something from that question mark, and he ended up with the last number. And he's asking what goes in the question mark so that it's true. Still, you have to use every number here. This time you use every number. And no repeats. Yeah. So they look for the question mark one. So when doing the guess and check question with a solution, that would be much easier to do because you have five choices. That would be one correct answer. If you do any question without the options, yeah, without the answer choices, that would be much harder. Yeah, almost three minutes. Yeah, I'll end the poll in five seconds when it reaches the three-minute mark. Yeah, one more thing we want to remind you, there is no guessing penalty in mass kangaroo computation. If you do not really know the answer, so you can make your guess. So you might not have time to check your guess, but make a guess. At least you might have a chance to get a correct answer. If you leave it blank, you're 100% you couldn't get any point. Yeah. Okay. Okay, so for this one, you guys can see that most of you got the right answer, which was five. Seemed like maybe some people were a little bit confused because I think everybody else chose three. But this one is also pretty straightforward to guess and check. So we start with putting one in the beginning box, and then we add two to it to get three. We have four and five left, but because we're subtracting something from that, we know that the box to the right has to be smaller than the box in the middle. So that one will not work. So then we try one plus three equals four. So what we have left is two and five. Four minus two is not two or five, and four minus five is also not two or five. So that is not a valid solution. And then we have one plus four equals five, and we have two and three left. So five minus two is three, and five minus three is two. So both of those are valid solutions. But the number in the middle is five either way. So that's why the question mark is five. Yeah. Thank you, Elita. The logic here, you need to know. You add two numbers together, and then you use that sum to subtract the rest two numbers. So actually, they already fixed this number here. This should be the biggest number. Should be the biggest number. So in the future, if you learn some negative number, that would be different story. But here, that's all positive integers. So the question mark should be the biggest number. Yeah. So that's already fixed answer. You even do not use guess and check. Yeah. Okay. Next one. Mary wants to write the numbers one, two, three, four, five, six. The sixth number inside the six squares. She wants a different number in each square. She has used up all the numbers. She wants both the sum of the number in the blue squares. So there are three blue squares. And the sum of numbers in the yellow squares to be two yellow squares. And one number must go in the square with a question mark, the white square. So, when you make a guess, you need to check your guess and then select your answer. You do not just make a guess and select the answer right away. So that's most the chance the first guess might not be correct. So you have to check your guess. So I mentioned you put your guess in the answer choice because if you have no time to check And you do not want to leave your answer choice blank. So you can just select any option you think that's correct and just put over there. So there is no guessing penalty during the real competition. So this is another test tips. But here you need to check your guess and then select your answer. You have to remember the condition. They ask the two yellow number added together equal 10, and the three blue squares added together equals 10. Yeah, Anita, we might need to close the poll soon. Yeah, I think enough people answered. Yeah, look at the result. So most of you picked the A. Yeah, that's the correct answer. Yeah, let's go through the solution to see how to use a guess and a check to solve this one. So here, they ask you to find the two numbers added together equal 10 in the yellow box. So you would say, what do you have? You have 1, 2, 3, 4, 5, 6. So any two number added together equal 10. There is no other choices. Is that right? You only have a 4 and a 6 added together. You could get a 10. So that's already been fixed. And any other two numbers you added together couldn't get a 10. So now you have 1, 2, 3, 5 left over. You need a three number added together equals 10. So that's very easy for you to figure out. 2, 3, 5 added together. Yeah, equals 10. So now you have 1 left over. Yeah, so this is the correct answer. Yeah, Anita, let's go for the question 4. Okay. The cards shown are placed into two boxes. The sums of the numbers in each box are the same. Which number must be in the box with the number 4? So we know there's two boxes. One of these boxes has the number 4. What else has to be in that box? So that when you add up all the numbers in the box, it's the same as the sum of the numbers in the other box. So, when you make a guess, you need to check your guess before you select the answer. So make sure your guess would satisfy all the conditions given in the question. They ask which number should be in the box with number 4. And the two box numbers added together inside the box. The numbers added together equal each other. We learn to draw in picture. When you try to solve the problem to help you understand the question better, you can draw a picture. So for this one, they said two boxes. You just draw the two boxes over there. Very simple, yeah? And then you put one number, number four here. And then you equal. You know they add together. The number add together, equal each other. So you already have a number four being used. You have two, three, five, six. What you could stay with number four and the rest number would make the same sum. Okay, I think I will end the poll now. So you guys can see that over half of you got the right answer. The answer was only six. I would say that this one is a little bit confusing to understand, but this is a pretty straightforward guess and check example because it gives you the only answers. So if we start by testing A, if only 3 is in the box with 4, that means 4 and 3 add up to 7. The other box must also add up to 7. But 2, 5, and 6 add up to 13, which is not the same thing as 7. So it can't be only 3 that's in the box with 4. So then if we put 5 in the box with 4, then that box has 9 in total, but the other box has 11. So that's still not the same. So it can't be 5. And then if we put 4 and 6 in the same box, that adds up to 10. 2, 3, and 5 also add up to 10. So now we know that the sums in the boxes are equal. It also cannot be D because we know 5 cannot go in there, and it's not impossible to know because we found a solution that works. So the correct answer is C. Yeah, thank you, Elita. Because they give you the option, you can just try each option, to check each option to see if any one works. For this question, if you do not use guess and check, you actually could do what? You could add all the numbers together, get the total sum. So that would be how much? You add all of them together. So you would get 20 in total because you know you need to divide it into the two groups. So that's very easy for you to know. Each group should have 10. So now you would figure out, what can stay with 4 and get 10? So only the 6 work here. So this is another way to solve this problem. So later you might meet a similar question. They give you a bunch of things. They ask you to split into the equal three groups or four groups or two groups. So you can use this way to figure out how much should be in each group. So that's another way. You do not apply for guess and check. But both will work. Number five. This is a little harder one. So like a magic squares, the number. So here they tell you they have five numbers. You'll see there are five squares. 3, 5, 7, 8, 9 were written in the squares of the cross. So that the sum of the numbers in the row is equal to the sum of the numbers in the column. Which number was written in the central square? So which number you should write in the center? So you could have five options. Is that right? So all the numbers might be able to put into the middle part. So they ask you to add all the numbers. Yeah. Let's launch the poll. Yeah. They ask you to add all the numbers on the column. Yeah. So you can see the column. Yeah. So if I gave you the A, B, C. Yeah. And this is D. And this is E. Yeah. Okay. So you could add A, B, C together. Equal D, B, E together. Yeah. And also you could figure out because they share B. So that means if for the equation, you both take B off the both sides. So you need to figure out A plus C equals D plus E. Yeah. Yeah. So that means you put a number in the middle and you need to figure out that the rest of the four numbers make two pairs. They should equal each other. So what's the correct answer? You need to try. 3, 5, 7, 8, 9. You need to try it. Once you guess, you need to check your answer. So guess and check. You need to check your answer, not only make a guess. So usually the first few guesses might not be correct. Okay, let's share the poll. Yeah, this is a harder question, five-point question, yeah? It's not easy, yeah? So maybe we just need to go through this one, and we have the similar question later. You can try on your own to solve it. Yeah, so you could see the answer. Yeah, we have a half answer, yeah, 14, 7 over 14. So half class got the correct answer, 8. Yeah, very good. Yeah, let's see the answer, the solution. So we still use guess and check. Yeah, what do you should put into the middle? Yeah, you have a 3, 5, 7, 8, 9. You can see every time when you put the different number in the middle, you can make, you can check. You can check the sum of the column and the sum of the row. Yeah, remember, because they both share the middle part, so you actually, if you do not want to add the middle part, it's fine. Yeah, so you still could get the, you know, the equal sum if that's correct answer. Yeah, so you would see the first one, if you put a 3, that wouldn't work. And then you check the next one, you put a 5 over there, yeah, still not work. Yeah, because when you put a 5, you would have a 3, 9 and 7, 8, so you try to make another pair. Yeah, like I mentioned, so when you try to make the pairs, what's the leftover numbers? So you have a 3, 7, 8, 9. How to make two pairs, the sum equal each other? Yeah, so you never try to use the two smallest numbers added together. You never want to do this way. Yeah, you, sorry, you never want to try the 3 and 7 added together could equal 8 plus 9. You cannot use two smaller numbers. You also cannot use the first number and the third number added together, try to get equal to the second number and the fourth number, because we order them in the sequential order, because that would see 3 always less than 7 and 8 always less than 9. So you never could make them equal to each other. So the best way, you make the smallest number and the biggest number and the two middle number added together, make those two pairs. So this is a logical way to do this. Yeah, so you could see the others, we all use this logic to make those two pairs, but we will figure out only 8 work. Yeah, so there is another logic here. You would see the five choices here. You have only 8, that's even number. The rest number would be odd number. So if there is a rule, yeah, so have you ever learned at a school? So the odd number would end with 1, 3, 5, 7, 1, 3, 5, 7, 9. Yeah, that's odd number. And then the even number would end with 0, 2, 4, 6, 8. Yeah, for here, you know that you only have one even number, and you know the equation. If odd number add odd number, you could get even number. Like 1 plus 3, you get 4. But even number plus even number, you still get even number. 2 plus 4, you get 6. But odd number plus even number, you would get odd number. Like 1 plus 2, you still get odd number. So this is a rule. So you would see the only choice would be 8 in the middle. Yeah, why? Because if you do not put 8 in the middle, so you would face the equation. So the one equation, you would have three odd number added together. That would be odd number. And another equation, you would have two odd number plus one even number. So that would be even number, because two odd added together even, and plus even, still even number. So you want to get odd number equal even number if you put any odd number in the middle. So only the 8 put in the middle, you both get equation. You would have two odd number plus even number for each of them. Yeah, so this is another logic. Yeah, Elita, do you think this is something they need to pay attention? But I think it might be a little harder for them. So we just give you a kind of, you know, the explanation. So maybe later you would understand more. Yeah. I think it can be harder, but it might also be more straightforward for some people. So I think it really depends on what method works best for each person. Yes. The more math you do, the more you'll realize what works best for you. Yeah, that's true. Thank you. Yeah. Okay, let's see the next one. Oh, similar one. Yeah. Okay, Elita, go ahead. Yeah. So Rou wrote the numbers 1, 2, 3, 4, and 5 in the circle such that the sum of numbers in the row is equal to the sum of numbers in the column. What number can be written in the circle with a question mark? So you guys can see that there's three circles in a horizontal row and then three circles going down vertically, and they want those to have the same sum. Yeah, we can open the poll. Yeah. Yeah. So you need to check. Look at the answer. You have only 5, you have 2, 3, 4, only 3, only 1 or 3, 1, 3, 5. So there are multiple choices. Might not be the single answer. You have to check every number. There's only 5 numbers, so it shouldn't be too hard to check. Check every number, yeah. Yeah, guess and check really takes some time to solve the problem, because there's not only one approaches, so you might need to check the different ways, so that take much more time. Yeah. But it's worth to check everything. Do not just find the one you think, oh, this is the correct one, that's my answer. But remember, there might be multiple answers. Yeah, let's close the poll. Maybe you can explain this question. Yeah. So, um, it looks like a lot of you guys were tricked a little bit by this question. You'll notice that most people said only five, but that's not the correct answer because there are numbers other than five that work. Actually, it's one, three, or five. All three of those work. So I think maybe some of you guys just stopped as soon as you tried five and you realized it worked. So let's see. So if we put one in the middle, then we see that you can put two and five in the same column and three and four in the same row. And both of those add up to eight. So one also works, but I think because only five was the first option you guys tried, and it worked, you guys stopped there and you just put that one down. But then if we go on to two, we see that you can put one and five in the vertical column and three and five in the horizontal row, but those do not add up to the same number. So two does not work. And then for three, you put two and four in the rows and then one and five in the column. And you see that those both add up to nine. And then we can put. If we put four in the middle and we put two and three in the horizontal row and then one and five in the column, we see that's not the same. And finally, most of you guys got this. Five works because you can put five in the middle and then you put one and four in the column and two and three in the row. And those both add up to 10. But I think you guys did not try all the answers. So a lot of you guys picked A, which was unfortunately not right. Yeah. So that's give you a kind of, you know, the reminder. Yeah. So when you see the options, so especially for the multiple choices and you see the answer might have a different, you know, different values. So you need to explore all the answers because you use the guess and check. So you have to make sure every option would work or not. So that would be you fully check the question. So otherwise you might miss some values. Yeah. Like this question. It's very easy. Yeah. So A, that's correct. Now I stop. No. So you would see the other answers. Once you find five is correct. So the only way you can, the only thing you can do what? You just eliminate B and eliminate C and eliminate D. Because you are confident five is correct. So B, C, D doesn't have five. And then you would see the E has one, three, five. You have to check that answer because of five over there. Yeah. So now you only have two options. You need to make the final choice. So once you check one, that's very easy for you to figure out when it's correct. Yeah. OK. So remember this. Yeah. Do not just find the first option is correct and then select your answer. So you'll need to check through all the options. Yeah. Even you do not use guess and check. Sometimes math can give you very similar options. So you think you'll select the correct answer, but there might be the minor error. So if you really check the rest of answers, you might find the real answer would be in the later options. So do not just stop at the first answer. You think that's correct. Check over all the options. OK, so next question. Six different numbers chosen from one through nine are rating on the faces of the cube. You know, the cube that's a six sided, six faces, one number on each face. So you have nine numbers, but you only use six of them, but a different. The sum of numbers on each pair of opposite faces are equal. Which number could be on the face of the face with the number five? So number five is on the top. The opposite face would be the bottom one. Yeah. So, you know, what's opposite face. You'll never touch that face. Yeah. So the parallel face, that's the opposite face. So they ask what's a number could be on the opposite face with five. Yeah. Elita, please open the poll. Yeah, in this Guess and Check class, we might not move as fast as other lessons, so we will try our best to solve as many questions as we can. But we want to give you time to try this strategy. So this question you need to figure out, you need to pick three numbers. So the three numbers all put on the opposite faces with 5, 4, 8. And those three numbers on the opposite faces added together, would they equal each other? So that means 5 plus number equals 8 plus number, equals 4 plus number. So you have to figure it out. About three minutes, so maybe in 10 or 20 seconds we close the poll. Okay, so look at the answer choice. So all five choices have been chosen. The correct answer would be C, six. So let's see the solution, how that happened. So once you work on this question, so you know the four, five, eight already been taken, and you can write down the rest of the numbers that help you to try to figure out what number would be the right answer. So you would write down one, two, three, six, seven, eight, nine, but you only need three of them. So you can make a guess what's put on opposite side of five. So first one you put a one, and you would get a sum would be six. So that wouldn't work because you see the number eight, number eight must add one of the number from the rest of numbers, two, three, six, seven, nine. So whatever, the five plus one, six, even smaller than eight, that couldn't work. So the one is not the choice. And then you would guess two, would two work? You still make a seven smaller than eight, that doesn't work. And three, when you make three, you could equal eight. But how to make eight plus something equal than eight? You have to add a zero, but there is no choice for zero. So five plus three still doesn't work. So once you already go this way, you have a six, seven, nine left over. Next one you try six, you would get 11. So you would see how to get 11 with eight. You need a three, yeah? You need a three, and then you also need a four for seven. So that definitely work. Yeah. So that's the answer. Yeah, you check, guess and check. You make your guess like this way, and you check. You don't need to write in the such much more information, but maybe just write some simple steps. So make sure you could take off the each the options. Yeah, just eliminate each options. Yeah. Okay, next question. Put the digits two, three, four, and five in the squares and calculate the sum to get the largest value. What is that value? So when you put them in the square, like if you put two and three in the first two squares, that just makes the number 23. It doesn't do two times three. It's 23 just as that number. And it's asking you for the sum, not each individual value. So make sure you read the question carefully. Yeah. Okay, I think most people answered so yeah You guys did pretty good on this one. Um, most of you got it, right? The correct answer was e 95 So good job everybody. This is also I think a harder question. It's number 20 So well done Okay, so let's see Um, if you put two and three in the first box and four and five in the second one you can or I guess Two and three is the first number and four and five is the second one you get two possible answers You could either get 68 or you could get 86 So so far 86 is our biggest number, but we don't know if that's true for everything Now if we put two and four in the same box and three and five in the other one We can either get 59 or we can get 95 So now since 95 is bigger than 86 and 59 95 is our new biggest number And then for the last one we put two and five in the same box and three and four in the other one So we can either get 25 plus 34 as 59 or we can get 52 plus 45, which is 95 Since 95 is the biggest answer out of all six of those Um, it's the correct answer because it's asking for the largest value Yeah And also this one involves the place value. So have you ever learned at a school? So the when you make the multiple digits number you have one digit you have a tens digit So here so for the ones digit and tens digit tens digit Is a higher value place So if you want to make a bigger number You always want to put the biggest digit on the highest value place so you would get more value Yeah, so that's why finally you would figure out so you would put a five And a four both on the times value and two or three both on the one's value Last place. Yeah, so that would make the biggest number. Yeah Okay, let's see the next question which number should be written in the circle with a question mark Yeah, you guys can check So maybe times four might be harder for some students So you can make a double and a double Times four make make that means you can double the number and double the number again Okay, so let's close the poll in maybe 10 to 20 seconds. Okay. Oh, I think it's good now. Yeah. Okay, so most of you pick the number 13. Yeah, that's a C. That's the correct answer. Yeah, good job. So let's quickly go through this solution here. So you would see what? The first thing they give you the answer choice 0813 2025, you can use the start with a, you can use zero or you can use any number. Yeah, you time times zero. So remember this part. If any number times zero, you would get a zero. So you would know for sure. So this is about would it be the fixed number. It doesn't matter what are you guessed. Yeah, and then here you continue, plus six to make six times four, you can type that double six makes 12 and a double 12 makes 24, and then 24 minus 15 get nine and nine plus four get 13. So this answer is a 13. Yeah. Okay. Next one. Steven wants to write each of the digits two, zero, one, and nine in one of the boxes of the sum. So you see there's a three digit number plus a question mark. He wants to get the largest possible answer, which digit can he write instead of the question mark. So the three boxes represent a three digit number. So if you put two, zero, and one in there, it would be 201, not two times zero times. So when you find one number correct, and you can check if that number appears in other options. So you have to check the other options, make sure that's not only choice. I think I'll give 10 more seconds. Yeah. Um, I think the correct answer was D. So, um, yeah, I think the answers are pretty split this time. This is definitely a harder problem and there's a lot of overlap between the answers. So you have to make sure you check every, every possible solution. So it's pretty easy to maximize the three digit number. We know we should probably put the nine in the hundreds place because 900 is a lot bigger than 100 or 200. And then two should go in the tens place because 20 is bigger than 10. So we end up getting either 920 or 921. And we see that no matter which one we put there, it works. 921 plus zero is 921 and 920 plus one is 921. So that's a maximum amount either way. So the correct answer should have been zero or one. Thank you, Elita. Yeah. So you have to guess and check. You do not just pick the answer right away once you just figure out, oh, the A has the correct answer. But you have to see if the answer you picked, if they also appear in other options, it's better you check through all the options. Do not just select the answer right away. So you can see a bunch of questions. You have the same situation. Yeah. So you have the similar answer in other choices. And finally, it lead to the answer choice, not the first one, it's later. So that's why we remind you, when you do the guess and check, you always need to make your guess and check your answer. So you have to put it back to the question to check all the conditions if that's satisfied. And also make sure sometimes if you find that this value is correct, would it appear in other answer choices? If yes, you have to check all the answer choices. So that's why sometimes you might miss some solutions. So if you do not fully check all the answer options. So guess and check really take a lot of time to solve. You can see you make a few times guess and you check again. So that's why this lesson will go over the 10 questions. We did that for the 10 questions. We know we take a longer time to solve the questions. Yeah. But we hopefully you understand how to use guess and check. And one more thing I want to mention again, in the Mexican rule computation, there is no guessing penalty. If by the last few minutes you have some question, you do not know the answer, you can just make the guess. At that moment, you might not have time to check your answer, but make your guess. Do not leave answer blank in the real computation. Thank you, everyone. Thank you, Elita. So we are happy to see you come back next week. Yeah. Bye-bye. Thank you, guys.

Guess and Check

mathematical problem-solving

multiple-choice questions

problem solving strategy

Math Kangaroo competition

number placement

digit value

iterative guessing

solution verification

problem-solving steps