Measurement & Data - Statistics & Probability 189-200
Sal uses a number line to tell time and find the duration of an event.
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- Andrey, Andrey? Andrey starts working on his science project at 4 o'clock pm, and he finishes 50 minutes later. Which number line below has a red dot marking when Andrey finishes working on his science project? So they tell us that he starts his science project at 4 o'clock pm. This first choice over here, puts the dot at 4 o'clock, but they didn't say when did he start working on his science project, they say put a red dot marking when Andrey finishes working on his science project. So he started at 4:00, and it says he finishes 50 minutes later. So if you start at four, if you add 50 minutes to four, that's gonna put us at 4:50. So where is 4:50 on this number line? So, let's see, or on this time line, I guess I could say. So, let's see, this is 4:15, so each of these marks must be five minutes. This is 4:05, 4:10, 4:15, 4:20, 4:25, 4:30, 4:35, 4:40, 4:45, and then 4:50 would be right over here. So which of these choices has a dot at 4:50? This last choice has a dot, has the red dot, at 4:50. Notice this is 50 minutes after he started at 4 o'clock. Let's do a few more of these. Amira starts raking leaves at 2:30 pm, and she finishes 25 minutes later. Which number line below has a red dot marking when Amira finishes raking the leaves? So she starts at 2:30, and she finishes 25 minutes later. So it looks like on this one, each of these spaces is five minutes. So this is 2:30, so this five, 10, 15, 20, 25 minutes later. And this space right over her is 2:55. It looks like this first choice is actually the choice we're looking for. They put the red dot 25 minutes after 2:30. Notice this is 2:30, five minutes after 2:30, 10 minutes after 2:30, 15 minutes after 2:30, 20 minutes after 2:30, 25 minutes after 2:30. Let's keep going, this is actually a lot of fun. The number line shows when Scarlet starts and finishes art club. That's when she starts. That's when she finishes. What time did Scarlet start art club? Well, let's see, this is half way between 3 o'clock and 3:30, so that's going to be 3:15. Each of these marks go up by 15 minutes. So this is at 3:15. What time did Scarlet finish art club? So this is right in between 4:30 and 5 o'clock, or you could say it's 15 minutes more than 4:30, so that's going to be 4:45, 4:45. How long was Scarlet in art club? So let's think about it. There's a couple of ways you could do it. You could look at the line. Let's see, to go from this point to this point, that's 15 minutes, then 30, then 45, then one hour, one hour 15 minutes, one hour 30 minutes. So you could say one hour 30 minutes, or actually they want it all in minutes. One hour is 60 minutes plus 30 minutes is 90 minutes. So actually let me just do it all in minutes again. So this is, as I move my mouse, I'm gonna talk about how many minutes I'm adding, relative to this, or from the start. So 15 minutes gets us to 3:30, 30 minutes, 45 minutes, 60 minutes, 75 minutes, 90 minutes. So that's 90 minutes right over there. Another way to think about it is it would take 45 minutes to go from 3:15 to 4 o'clock, 45 minutes to go from 3:15 to 4 o'clock, that makes sense, then another 45 minutes to go from 4 o'clock to 4:45. So 45 plus 45 is going to be 90 minutes. Let's do a couple of these. So the number line shows when Anna starts and finishes reading a chapter in her book. What time did Anna start reading? It says right over there she started reading at 8:10 pm. 8:10 pm. What time did Anna finish reading? Let's see, let me make sure I'm reading this, so this is 8:20, this is 8:25, and they have one, two, three, four, five marks, so each of these go up a minute. So, you could say it's a minute before 8:25, or four minutes after 8:24, 8:21, 8:22, 8:23, 8:24. 8:24. How long did Anna read? Well, she starts reading at 8:10 and finishes reading at 8:24. To go from 10 to 24 that means she read for 14 minutes. And you could even count it over here. One, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13, 14. Let's do one more. Mohamed speaks on the phone for 15 minutes and finishes his phone call at 9:20 am. Which number line below has a green dot marking when Mohamed starts his phone call? Alright, it finishes at 9:20, so it finishes, let's see, where's 9:20 on this number line. So it looks like each of these marks go up by five minutes. So this is 9:15, and I was able to figure that out because we have three marks that go to 9:15, from 9:00 to 9:15, so this is 9:05, 9:10, 9:15. So this would be 9:20. So this is when he finishes, 9:20, and he was on the phone for 15 minutes. Remember, we don't want to mark when he finished, they tell us that it's 9:20. We want to mark when he started. So if he's on the phone call for 15 minutes, and he finishes at 9:20, he's gonna finish 15 minutes, or sorry, if he's on the phone for 15 minutes, and he finishes at 9:20, he's going to start 15 minutes before 9:20. So five, 10, 15. He's gonna start at 9:05. So that's this choice right over here. Another way you could think about it is if I'm at 9:20, and I go 15 minutes before 9:20, 20 minus 15 is five, so that's gonna get me to 9:05. And we can just make sure we feel good about it. If he starts his phone call at 9:05 and he speaks for 15 minutes, five, 10, 15, he's gonna finish his phone call right over here at 9:20, which is exactly what they described.