This is webinar number 8 in the Math Kangaroo series. We are doing clocks, times, and calendars today. So, let's get started with a warm-up problem. This isn't the version I wanted to use. Hang on a second. There we go. The train to Atlanta leaves in 3 1⁄2 hours from now. Paul got up 2 1⁄2 hours ago. How many hours before the train leaves did Paul get up? And I do have polls for a lot of the questions today. Bye. Okay, so most of you have answered the poll, done really well. Some students tell me I clicked the wrong thing, that's okay if you click the wrong thing, don't worry about it. The results are completely anonymous, so I don't even know who's clicked on what. The idea is just to be learning the whole time that we're here. So if there's a mistake that happens, don't worry, on your real Math Kangaroo contest, you'll be able to erase and try again. And the correct answer is six, so that's really good from everybody. One of the ways I like to do this problem is with a number line, a timeline kind of idea. So I just draw a line, and this is now. So I know that the train, I'll call this train. The train leaves in three and a half hours from now. And I got up, I'll call that up, I woke up two and a half hours ago. So to find out how many hours before the train did Paul get up, I just add the two and a half plus three and a half, and I get E6. Well, you all did really well on that. So today's problems are all going to be with clocks, times, calendars, things like that. So we do need some information in order to be able to solve these problems, and that's going to be part of how we use our plan and how we carry it out. So let's take a look. Don't forget, you're going to check your answers, look back and reflect. So the students who tell me I clicked the wrong thing, you're actually doing step number four, which is looking back and saying, I got it wrong, I need to fix it. So there's nothing wrong with that process. That's excellent that you're actually checking yourself and saying, I didn't do it right, I know I didn't do it right, I'm going to fix it. So that's amazing. Don't worry about that. So there are a few things we need to know. First of all, that there are, in one year, there are 12 months, and usually 365, and on a leap year, 366 days. Okay? One of the things that we did not write here is that there are seven days in a week. Right? Seven days in a week, which gives us 52 weeks in a year. But you'll notice 52 times seven is not 365. It's not a multiple of five, right? This is actually 364 days. So you need one extra day. And that may come in handy to know that it's one extra day, right? A day has 24 hours. An hour has 60 minutes. Half an hour is 30 minutes. Each minute is 60 seconds. So that's all probably information that you've heard before. The next thing we will have is that most months have 31 days. February has 28 or 29. There is a way to determine which months have how many days. It's not really a way, but it is a shortcut, and you can use your knuckles. And I think we did this in a webinar not too long ago, where if you hold your knuckles in front of you, the first knuckle that you see is January. The high means 31. Then the low means less than 31. So in this case, it's February, which is 28 or 29. March is the next knuckle. So that's 31. April is 30. May is 31. June is 30. July is 31. And then you get to the end of that hand, and you put the next hand right next to it. August is next month. It's also 31. So you start on the top of the knuckle. September is 30. October is 31. That's Halloween on the 31st. November is 30. And December is 31 again. So you can use your knuckles if you forget. We have the days of the week in order, and Math Kangaroo will expect you to know how to tell time on this analog. This is called an analog clock, not a digital clock, right? So when the minute hand sweeps around, the minute hand is the longer. Oops. Very crooked minute hand I have there. When the minute hand sweeps all the way around, when it goes all the way around, that is 60 minutes, one hour. And then you have your shorter hour hand, which is going to point to the hours of the time of the day. We go around the clock twice in 24 hours for one day, right? So two times around the clock. Hopefully a long time ago you learned a song or something to remember the days of the week. We will need to know those. A certain movie is 90 minutes long. It started at 5.10 p.m. During the movie, there were two commercial breaks, one lasting eight minutes and one lasting five minutes. At what time did the movie finish? At what time did the movie finish? Okay, I have the answers from most of the students in the poll, so I think that'll be enough time. And we did really, really well on that. Congratulations. The answer is 653. There are a few students who didn't get it, maybe made slight mistakes, so let's take a look at it. The movie is 90 minutes long. It starts at 510. So let's just say it's only the movie, and we'll add the commercial breaks in later. So from 510 until 6 o'clock, we have 50 minutes. Then from, we need to get to 90 minutes, right? So we need another 40 minutes. So we're going to have to go from 6 o'clock to 640. Okay, so that gives us the 90 minutes of movie time. We then have an 8-minute break and a 5-minute break. So if we do 8 plus 5, that equals 13. So we will do our 640 plus 13 more minutes, and we will get 653. Very nicely done, everybody. Problem number two. My mom's birthday is on a Sunday, and my dad's birthday is 55 days later. On what day of the week will my dad's birthday be? We'll give you just a few more seconds. Most students have answered. I know some students take just a little bit longer and that's okay. About 80 percent of you have said the answer is Saturday, and that is a correct answer. There were some other options. I will share, I think, two quick ways to solve this. The first is, you will notice that 55 is not divisible by seven, for the seven days in a week. We have seven days a week and 55 divided by seven equals seven weeks. Then you have a remainder of six, so six extra days. Seven weeks gets us to a Sunday again. Then from Sunday, if I count six days, Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, that gets us to Saturday, the remaining six days. Other students may have correctly solved it by saying 55 is not divisible by seven, but 56 is divisible by seven. We are one day less. If it was exactly eight weeks, it would be on Sunday again, but we have to go back a day and we get to Saturday. The correct answer is Saturday, and that's two methods you can use to get to it. David wants to prepare a meal with five dishes using a stove with only two burners. The times needed to cook the five dishes are 40 minutes, 15 minutes, 35 minutes, 10 minutes, and 45 minutes. What is the shortest time in which he can do it? He may only remove a dish from the stove when it is done cooking. We can't cook it partway and then take it off. There's no part cooked and it's not safe to eat uncooked food. Remember, he can use both burners at the same time, two burners. Okay, I'll offer a hint for those who have not figured out how to solve this. Put the dishes that take the longest time to cook, one on each burner. And then when one of them is finished, put on the next dish. Every time a dish is finished, you can take it off and put on another dish until all five dishes are cooked. Okay, we'll stop it here. All right, so if I have burner number one and burner number two, the longest cooking dishes are the one that takes 45 minutes and the one that takes 40 minutes. So if I put those one on each burner, I have to wait now until they're done cooking. After I do, so I can kind of check off the ones that are done. After 40 minutes, I'm going to start the next longest one, which is 35 minutes. And that's going to take me to a total of 75 minutes on this burner. After 45 minutes, I can put the 15 minute dish here. That takes me to 60 minutes. The 75 minutes is still cooking, right? The dish that takes 35 minutes is still cooking. So I'll put the 10 minute one on this side and I'll be finished on the burner number one in 70 minutes. But I'm not finished cooking on burner number two for a full 75 minutes. So that is the correct answer here. And I will show you the results of the poll. So while this question is a little more difficult for some students, I've noticed that in some other groups. More than half of you did get it correct. So it's it's a doable problem. And I think for me, the trick was starting with the dishes that take the longest and putting one on each burner. And then I'm able to go ahead and proceed with the other dishes when those are done. On Planet Kangaroo, each Kang year has 20 Kang months and each Kang month has six Kang weeks. How many Kang weeks are there in one quarter of a Kang year? Don't forget that little quarter part. Okay, so I'm going to go ahead and show you the results of the poll. So I'm going to go ahead and show you the results of the poll. I do have lots of polls today. So for those of you who are always asking, where's the poll? You're going to see a lot today. Okay, very nicely done. I'll share the results of the poll first this time. Ninety-four percent of the responses are 30 minutes, and that is correct. So, the only thing I've noticed is that some students do this in different orders. There's no correct order for doing this calculation. So, you can say in one quarter of a Kang year, since there are 20 months, I can do the 20 divided by 4. So, this is the months, and this is the one quarter of a year. So, this is five months. You can do that. That's perfect. And then you can say, okay, each Kang month has six Kang weeks. So, I can do the five months times the six weeks, and I can get the 30 weeks. That is choice B. You can change the order around. It doesn't matter. You could say, all right, 20 months times six weeks, and that is 120 weeks in a whole Kang year, and then you can say I want one-fourth of 120, which would be 30 weeks. Same answer, just a different order. There's nothing wrong with changing the order in which we multiply things. As you know, multiplication is commutative. So, you can multiply by one-fourth first. You can multiply by one-fourth last. It makes no difference to the final answer. Mary leaves her house and arrives at school at 7.32. Zoe needs 12 minutes less than Mary to get to school. Yesterday, Zoe showed up at school at 7.45. What time did she leave her house? This is a multi-step problem. If you don't know what to do, I suggest trying one sentence at a time. Okay, just a few more seconds on that poll. Most of you have done really well. Okay, that's most of you answering. So, I recommended, I gave you the hint of trying one sentence at a time. So we have Mary leaves her house at 6.55 and arrives at school at 7.32. From 6.55 until 7 o'clock is only five minutes. And then from 7 o'clock until 7.32, we have 32 minutes. So all together, we know that Mary takes 37 minutes to get to school. This is Mary. And we know that Zoe needs 12 minutes less. So if we take Zoe, it's going to be the 37 minutes, but it's 12 less, so we'll subtract. So that gives us the 25 minutes that Zoe takes to get to school. Now Zoe arrives, Zoe arrives at 7.55, at 7.45, pardon me. And you call it a typo if you're handwriting, but we know it took her 25 minutes to get there. So let's find the time that Zoe started out, five minus five is zero, 7.20 is the time that Zoe starts. And let's see how well you did. As a group, remember the polls are anonymous, so it's kind of a group average. It doesn't tell us about any individual, and 87% of you got 7.20. You are exactly correct. So very few other answers. That's really great. And I do have some students who aren't giving the answers in the chat, in the polls. So I don't know if you don't like the polls or if you needed more time, but hopefully now it's nice and clear that you've seen it solved. Again, sentence by sentence really is a great strategy that helps me a lot of the time. The ancient Romans used Roman numerals. We still use them today. I is one, V is five, X is 10, L is 50, C is 100, D is 500, and M is 1,000. John was born in February of the year MMVII. How old was John on March 16th, 2017, or 2017? Give a few moments and I'll launch the poll. And if we don't get quick answers, then I'll start giving you some more tips. So, one thing to keep in mind, if John is born in February, then in another year in March, John has had the birthday the month before. All right, we have almost all of you have answered and you've done really well. The correct answer is E, X, which is equivalent to 10 years. That was very nicely done. Let's take a look at it. So John is born in MMVII. So MM is 1,000, MMVII, 1,000 plus 1,000, plus the V is 5, plus the I and the I is a 2. So John is born in February of 2007. That's what we get when we sum it. And now we're looking at March, so it's after the birthday, in 2017. So there's 10 years have elapsed, 10 years old at this point, and 10 is X. That's what we get when we sum it up. In December, Tosha the cat slept for exactly three weeks. How many minutes did she stay awake during this month? So careful reading, December, asleep for three weeks. How long, how many minutes awake? I'm sorry, there is no poll because it didn't want to have to enter all the numbers in parentheses and everything. But you can put your answers into the chat. Many of you are chatting with me and I do like that you're doing that. Here's one little trick. If you don't remember how many days there are in December, use your knuckles or think about New Year's Eve. What is the date of New Year's Eve? That might help you remember how many days are in December. Alright, this is a little unusual for a math kangaroo problem because we usually ask you to calculate all the way to the answers, but this math kangaroo does not allow you to use calculators, so in this case they just wanted you to be able to set it up, not actually have to multiply the larger numbers. So that's really nice, it takes too long to multiply them all out. So the first thing we need to do is December. So if you remember New Year's Eve is December 31st, or if you use your knuckles, you'll find 31 days in December. We know that Tosha the cat slept for exactly 3 weeks, so if we sleep for 3 weeks, we have 3 weeks times 7 days a week, that equals 21 days of sleep. But we want to know how many days awake, so we're going to have to take the 31 days in the month and subtract the 21 days asleep. And that's going to give us the days awake, right, because you're either awake or asleep. So let's take a look. C starts with 30 days, so that's going to be incorrect. All the others start with 31, so that's a pretty good indicator that 31 days was correct. So we want to know how many minutes did the cat stay awake. So once we know the days awake, we're going to have to multiply the number of days times 24 hours in a day times 60 minutes in an hour. So we need to have times 24 times 60, and we see that here and here, but this one's out, and here and here, but here it's 60 times 60 times 60. So this would take you to the seconds, so this one is not going to be correct. So this gives us fewer choices. Now let's take a look. We want to do 31 minus 21, or 31 minus 7 times 3. This gives us 31 minus 7 times 3, but not 31 minus 21, so this is out. This gives us 31 minus 7 times 3. Using order of operations, some of you might remember, we have to do inside the parentheses and then the multiplication first, so this is 21. That's exactly what we did right here. So this looks good, 31 minus the 21 is the 10 days awake times the hours and the minutes. So this is the days, hours, and minutes. So this is correct, B. This one we're missing the times 3, right? So that one's wrong. Hopefully that helps. I don't want to wrap up yet, we still have plenty more problems to do. Bonus question number one. When Mary was leaving home between 8 and 9 o'clock in the morning, she noticed that the hour hand and the minute hand on her watch are overlapping. When she returned home between 2 and 3 o'clock in the afternoon, the hour hand and the minute hand formed a straight line, the picture. How long was Mary away from home? We're doing well on the poll. Let me help some of you who have not been able to answer. The minute hand is the long hand on the clock. And the minute hand seems to be pointing to the exact same place in both clocks. Also, it would be helpful to figure out which clock is which. Okay, a little bit more helping. If I look at the first clock, I can see that the hour hand is in between the eight and the nine, so this must be the morning clock when she leaves, right? And in this, we're between two and three o'clock, so this is the afternoon clock when she comes back, so this is come back home in the afternoon. I will share the results of the poll. So, most students have answered the poll, and of those who answered, 55%. So, a bit more than half of you say six hours. But we have a lot of other times also selected, so let's take a look together. So, there are a couple of ways to solve this. We've already discussed that the first clock has to be the morning clock, and the second clock is the afternoon clock when she returns. You'll notice that the long hand is the minute hand, and that's pointing to somewhere around, let's call it 44 minutes. So this is 844, and this is 244. Since the minute hand is in the same place, we only have to look at how much the hour hand has moved. The hour hand moves. So let's look at how much it moves. From 8 to 12, 8 to 12 is 4 hours. And then from 12 to 2 is another 2 hours. So that would give us a total of 6 hours. So one way to do this problem is to look at it that way. We've gone from 8 o'clock in the morning to 2 o'clock in the afternoon. That is 6 hours. I want to show another way to think about this that some of you may not think about, but could be helpful to others. If I kind of redraw these clocks with the hands facing in a different direction, I think that might help. So if I draw the hour hand going up directly, this would make it 12 o'clock, right? That looks like this first one. If I draw a clock that looks similar to the other one with hands going straight up and straight down, that gives me 6 o'clock. And that looks like this clock, doesn't it? Just spin them around a little bit. So to go from 12 o'clock to 6 o'clock, I've also elapsed 6 hours. So that's kind of a clever way that some students who like to visually manipulate things might solve this problem. Here's another bonus problem. There are 5 songs. Song A lasts 3 minutes. Song B, 2 minutes and 30 seconds. Song C, 2 minutes. Song D, 1 minute 30 seconds. And Song E, 4 minutes. These 5 songs are playing in the order A, B, C, D, and E in a loop without any breaks. Song C was playing when Andy left home. He returned exactly 1 hour later. Which song was playing when Andy got home? Remember, an hour is 60 minutes. You might want to see how long it takes to play the full loop of five songs. Okay, I'm going to work this one through because we're almost out of time. Like I said, this was a more challenging bonus problem. Anybody wanna stick their answer in the poll? Last chance to take a guess. Remember, on a math kangaroo contest, we do not subtract if you're incorrect, so you should always guess if you run out of time. Okay, we have a tie between A and D, but every song has been selected, so let's see what we can do here. So the first thing I noted was that he leaves for one hour, so one hour is 60 minutes. Now, if I do the list of songs, A, B, C, D, and E, I have three minutes, two minutes, 30 seconds, two minutes, right? Song two, song C is two minutes. I have one minute, 30 seconds, and the last one is four minutes. And the total of this all together is five, six, seven, eight, nine, 10, 11, 12, 13 minutes, because I have to add in those 30 second pieces. So 13 minutes for each loop. And we know that when he leaves, song C is playing. So those are all important pieces that we can get out of the problem statement. Now, how many times is this loop going to be able to play in 60 minutes? Well, 13 times four is 12, is 12, carry the one, is 52 minutes. Okay, so I can go through the loop four times, four times through the loop, but I still have eight minutes left. So I have eight minutes to keep going, to play more, to play a fifth time, right? So if I'm in song C, song D is 1.30, song E is four, so that takes me to 5.30, song A is three, so that's going to take me to 8.30. So in between five and a half minutes and eight and a half minutes, I am playing song A. The correct answer will be song A is playing when Andy gets home. All right, so we had a lot of fun today using calendars, time, clocks. So it's really important to make sure you know a couple of those basic facts about time. Make sure that you're reading the questions very carefully. So you'll notice today, reading one sentence at a time, taking out the information that you can on that song. I had to write down the times for the songs and figure out how long the loops take. For going to school, I had to figure out how long Mary takes to figure out how long Zoe takes. Always look back and check your answer. So those of you who say, I know I made it wrong, I want to do it correct, that's fine. Just make sure you are very careful. I hope that you've enjoyed these problems that we had today. We have two more sessions, two more webinars in this session B. And then in March, you will have the Math Kangaroo Contest. To practice for the Math Kangaroo Contest, keep coming to the webinars, but also look on the website. You can do past contests. And if you could look at your contest registration, you can watch some other videos of teachers solving problems from past contests. There's some video solutions available for you to watch. I hope you enjoyed the lesson today. I'll see everybody again next Sunday. Bye for now.

Math Kangaroo

webinar series

time-related problems

problem-solving skills

calculating time differences

components of time measurement

interactive problems

analytical thinking

logical deduction

time management concepts