![]() Oh, and speaking of the MTBoS, expect my Week 3 post on Wednesday, the last of my three days in this classroom. Tomorrow they will work from copies of the MathLinks packets (as only "Math Lab" gets actual packets), and so I can play "Who Am I?" tomorrow. Today the students in all classes other than "Math Lab" worked on a common sub-day staple - Pizzazz worksheets. ![]() Of the three days of lesson plans provided by the teacher, tomorrow's is the most compatible with that game. Thinking back to my MTBoS Week 2 post, you may be asking, did I play the Conjectures/"Who Am I?" game that I described in that post? Actually, I didn't. So during the "Math Lab," I was forced to improvise by having them write on a blank sheet of paper, but for tomorrow I plan on making copies of the relevant pages from the packet until the teacher returns. Three new students moved into our class at the semester transition, but there weren't enough MathLinks packets for them. There were also some problems during the first two periods of the day. But some students simply refused to work at all during the period, believing that they should already be at lunch. The Unexpected Bell Paradox actually came into play - students really didn't know when the dismissal bell was going to ring. Adding to the problem was that at the semester transition, the bell schedule changes - sixth graders had first lunch during the first semester, but now they have second lunch. The toughest period of the day was fourth period. and sure enough, the grades were all A's and B's. I saw the semester grades posted on the board. Once again, there was a class that wasn't actually labeled "Honors" - fifth period - but obviously contained the strongest students. I had four sections of Common Core 6 and one "Math Lab" second period. Thinking back to my MTBoS Week 1 post, I point out that today was similar to the day mentioned in that post. Well, it's hard to say whether this packet corresponds to Chapter 6 (Expressions) or Chapter 7 (Equations), as it contains a little material from each chapter. We compare this to the Glencoe text - as this is the start of the second semester, the students out to be starting Chapter 7 (out of 12) - the first chapter of Volume 2. The class was working out of another MathLinks packet, 6-9, which is called Expressions and Equations 1. Today, as the second semester begins, I subbed in a sixth grade math classroom, for a teacher who is out for three days. Then when he tries to grab some of the oobleck, it pours through his fingers like a liquid once again. In a bowl it looks like a liquid, but when Kung punches the bowl, it feels solid on his fist. This causes oobleck to exhibit some of the properties of both solids in liquids. ![]() The Quick Conundrum for today involves something called "oobleck." Oobleck is just a mixture of corn starch and water, but the starch isn't completely dissolved in the water. My written description of this Rolling Spool Paradox won't do it justice, so let me provide a link where you can see what's going on: Basically, depending on which way you pull on the thread, it's possible to make the spool move forwards or backwards. His final paradox involves a spool of string. He adds that the idea that information takes time to transmit will show up in his later lectures. ![]() He says that it's as if information - namely, the fact that the Slinky has been cut - takes time for it to arrive at the bottom of the Slinky. The two opposing forces, gravity and the recoil, balance out exactly, so the bottom continues to float in the air until the top finishes recoiling as it falls - only then will the bottom of the Slinky fall to the ground. Well, when Kung cuts the Slinky, the bottom actually does neither. Then he asks, what would happen to the bottom of the Slinky if he were to detach the toy from the ceiling? It could be that gravity will cause the bottom to descend, but it could also be that the Slinky will recoil, thereby causing the bottom to ascend. ![]() He hangs a toy from the ceiling, which causes gravity to stretch it out a little. Next, Kung moves on to some paradoxes involving springs, but he demonstrates these by using a very large spring - also known as a Slinky. You simply take a large tank the same shape as the ship, pour in the gallon of water, and then add the ship. Kung begins the lecture by describing how to float a ship in one gallon of water. Lecture 15 of David Kung's Mind-Bending Math is called "Enigmas of Everyday Objects." I've heard of many of these mathematical paradoxes before, but actually, most of the paradoxes Dave Kung describes in this lecture pertain more to physics and are new to me. ![]()
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