I've done some crazy stuff in precalc so far this year (and I'm sure it's driving some of the by-the-book kids nutso just like it would've driven me nutso when I was in high school). Today I threw a couple of questions at them to see how they would react.
1. How long would it take to pass a ball down a line of 457 people?
2. The world's tallest man was 2.72 meters. How big should his foot have been?
It was fun to see the changes in the classes (3 of 'em.)
Question #1
First period really got into it. They quickly arranged 10 people in the front of the room and passed the ball (which I conveniently had in my car... thank goodness for soccer practice last night!) down 5 times. Then they averaged their values, figured out their time/person, and multiplied to figure out 457 people. I think their final answer was something around 3 minutes, 23 seconds. And then as we moved on, 2 boys sat next to each other and passed the ball back and forth 457 times (yes, really). They were off the time by 2 seconds.
Third period took a different approach. They started with two boys about 5 feet away from each other throwing the ball back and forth 10 times. (Their interpretation of "pass".) Some of the other kids from the class intervened and decided they wanted more people in a line... they started out with 10 people in the room then asked if they could go in a hall. We ended up with 25 people in line passing the ball a variety of ways (hand to hand, rolling on the floor). Very funny to watch... and noisy, too. Sorry to my neighbors! After averaging all of the times they came up with something under 3 minutes.
Fifth period (Remember how boring they are? I'm still going with that.) was blah. A couple of kids were involved and had to drag others in to participate. Eventually we ended up with 22 people in a line in the hall passing a ball. In almost near silence. They did it a couple of times, were content with the results, and headed back to their desks. Wake me up when it's over, please. I forget their final time... I think I was sleeping.
(It was funny to me, though, that for the most part the kids were really concerned about getting the fastest time possible. The question mentions none of that.)
Question #2
Again, a winner. I showed a picture of Robert Wadlow (the man who I was referring to) and gave the kids free rein.
In first period, everyone got up to start measuring. They made a big chart of height, footsize, and ratio and went from there. My idea was for them to do a linear regression (and I gave out directions on how to do that) but their numbers were so crazy that they ended up with a negative slope and 25 cm as their final answer. (Then we got off an a discussion of his weight and BMI. A couple of kids had me checking their BMIs, too.)
Third period ended up at about the same point (with fewer people contributing their values), got a much better equation, and a final value of 51 cm.
In fifth period not too many people were jumping up to measure (surprise!) and they were all boys of about the same height and footsize. We decided we needed some variance (but they were determined to stick with people of the male persuasion) so we sent a couple of girls down to a freshman health class to grab a couple of little freshman boys. Very funny. The data ended up kinda crazy and they ended up with a 43.74 cm foot.
(In case you're wondering, I found some information saying that he wore a size 43AA shoe, which we looked up and determined that was about 49 cm.)
1. How long would it take to pass a ball down a line of 457 people?
2. The world's tallest man was 2.72 meters. How big should his foot have been?
It was fun to see the changes in the classes (3 of 'em.)
Question #1
First period really got into it. They quickly arranged 10 people in the front of the room and passed the ball (which I conveniently had in my car... thank goodness for soccer practice last night!) down 5 times. Then they averaged their values, figured out their time/person, and multiplied to figure out 457 people. I think their final answer was something around 3 minutes, 23 seconds. And then as we moved on, 2 boys sat next to each other and passed the ball back and forth 457 times (yes, really). They were off the time by 2 seconds.
Third period took a different approach. They started with two boys about 5 feet away from each other throwing the ball back and forth 10 times. (Their interpretation of "pass".) Some of the other kids from the class intervened and decided they wanted more people in a line... they started out with 10 people in the room then asked if they could go in a hall. We ended up with 25 people in line passing the ball a variety of ways (hand to hand, rolling on the floor). Very funny to watch... and noisy, too. Sorry to my neighbors! After averaging all of the times they came up with something under 3 minutes.
Fifth period (Remember how boring they are? I'm still going with that.) was blah. A couple of kids were involved and had to drag others in to participate. Eventually we ended up with 22 people in a line in the hall passing a ball. In almost near silence. They did it a couple of times, were content with the results, and headed back to their desks. Wake me up when it's over, please. I forget their final time... I think I was sleeping.
(It was funny to me, though, that for the most part the kids were really concerned about getting the fastest time possible. The question mentions none of that.)
Question #2
Again, a winner. I showed a picture of Robert Wadlow (the man who I was referring to) and gave the kids free rein. |
| Gotta love the socks! |
Third period ended up at about the same point (with fewer people contributing their values), got a much better equation, and a final value of 51 cm.
In fifth period not too many people were jumping up to measure (surprise!) and they were all boys of about the same height and footsize. We decided we needed some variance (but they were determined to stick with people of the male persuasion) so we sent a couple of girls down to a freshman health class to grab a couple of little freshman boys. Very funny. The data ended up kinda crazy and they ended up with a 43.74 cm foot.
(In case you're wondering, I found some information saying that he wore a size 43AA shoe, which we looked up and determined that was about 49 cm.)
Fun ideas! I'm going to totally steal them for introducing proportional reasoning. These two situations, although similar in the sense that we're trying to model something by collecting data and making predictions, are actually different in the sense that only ONE of them is a direct variation (ratios) problem. During my ratios unit I always teach kids to stop and think critically about whether a given situation is truly proportional or not, and these two fun situations are great examples!
ReplyDeleteThanks for sharing! :)
The funny thing is that I got the measure your foot idea from my next-door neighbor at school who uses it to collect data and write linear equations. And yet it's not a direct relationship! (I just spiced it up a bit to turn it into a question instead of "measure some feet, write the equation" type thing.)
ReplyDeleteBut I honestly didn't think about using proportions... we'll be doing that in Alg1 soon, so maybe I'll ask them to figure out the answers, too!
I have a good powerpoint for introducing what IS a proportion or what is NOT. I can send it to you or post it if you want! I got it from my prof in grad school and have always loved it as a way to spark discussions.
ReplyDeleteIf you wouldn't mind sending it, that would be awesome! My Alg1 class will be doing proportions tomorrow - I know they've seen them before so it would be fun to have something a little different. Plus, I'm going to show them Dan Meyer's Partial Product pictures http://blog.mrmeyer.com/?p=11588 and have them figure out prices. (Along with this youtube video from Father of the Bride that was mentioned in a comment on his post. http://www.youtube.com/watch?v=oYIHLUxzRr8&feature=player_embedded) My email address is klb925 at gmail.com.
ReplyDeleteThanks! :)