[I hope my neighbor doesn't mind that I took these pictures]. As a math student, what do you notice? What do you wonder? Hopefully you notice that's a wicked awesome gigantic spider web. And how could anyone who's feelin' the spirit of Halloween not think, "how can I make one?!" What information do you need to figure this out?
We need to know how much string to use! So how can we figure that out? Well, it looks like the web is attached to the base of the flag pole, so how high is the flag pole off the ground? Student can estimate how far off the ground the flag pole is (6 feet?) How far out do we want our spider web to reach? Maybe longer than the height? 7 or 8 feet? Now, how can we find the length of the string given all that other information...? As I'm coming up with the "possible student approaches" sheet a la 5 Practices for Orchestrating Productive Mathematical Discussion, this problem is becoming juicier. [Try the problem yourself before seeing my approaches! It's fun!] I think this is a great low-floor/high-ceiling problem where I originally intended the students to use Pythagorean Theorem to get good guesses, but there's so much more students can do with this problem. I imagine many students will estimate the lengths of the "vertical" pieces, very easily over estimating how much string to use. With estimating, these students should finish faster than those who planned a more precise approach, so I can ask, "do you see any problems with estimating the length of each rope to be X feet?" and steer them towards a more precise approach. Here's how I see student approaches: Beginner Level: Estimating (everything) On-Target Level: Pythagorean Theorem (estimating height of flag pole, how far out do we want the web to reach, and lengths of horizontal pieces) Advanced Level: Pythagorean Theorem & Circumference of Circles (with estimations from "Appropriate Level"). I have a powerpoint with these pictures, along with images from the Lowe's Home Improvement website of what lengths of spools we could buy. One spool available to purchase is 325 feet. The best part: I did 2 different student approaches so far (beginner and on-target), and one is slightly over 325 feet, and the other is under 325 feet! How many spools should we buy? Let me know if you use this task in your classrooms and tell me how it goes!
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AuthorTracy Conte is a high school math teacher in Raleigh, NC. Archives
November 2019
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