Dan Meyer has thrown us some wonderful updates on 101qs.com. Head over to the Trashketball task where you will get all the goods when you sign in:
Act 1: video to wonder and notice about
Act 2: teacher notes, and visual data/information to help solve the task
Act 3: visual confirmation of the practical answer
Sequel: additional tasks to explore (especially for early finishers) and teacher notes
I was going to chip away at this task until I realized Pi Day was coming up. Needless to say, I started working a little quicker. Ironically, in calculating the answer to the task, Pi can actually be divided by itself or "cancelled." I grabbed (bought, not shoplifted) two trashcans from Bed Bath & Beyond. I found the exact trashcan from Suits. Woohoo!!!! That circular truncated cone trashcan is so dreamy and transparent. I also found a cylindrical trashcan for my Geometry class. As you can see from Act 1, it's not transparent, but it'll get the job done. Measuring each dimension of the can was simple. Measuring the diameter of the trashketballs is a different story. I'm open to suggestions here. You'll find this in the "Teacher Notes"
Seriously, I'm open to ideas. I quickly discovered that trashketballs are like snowflakes: no two are the same. However, I really started to perfect the form and process of making a trashketball. I'll admit, there's some buy-in with the trashketballs being perfect spheres. I'm okay with that. So maybe spend some time with your students perfecting the trashketball. Anyway, leave some ideas about measuring the diameter of the trashketballs in the comments, won't ya?How do you find the diameter of a trashketball? Have your students come up with ideas. Test those ideas. Make conjectures.I crumpled up 8.5"x11" paper and made it as compact as possible. I took a handful of trashketballs and put them down on a ruler to get a rough mental mean of the diameters. Then I traced the best-fitting circle to measure the best-fitting diameter of each trashketball. I took the mean of these five diameters.An extension to the task would be to explore the difference one-tenth the radius makes in your calculated answer.
I'm looking forward to this task. My students occasionally play trashketball in my class with their scratch paper or class handouts (not necessarily mine) contributing to their idea of going paperless. I see this happening a lot on Thursday. Happy Pi Day!
Next up! The circular truncated cone trashcan. I'll start chipping away at having enough trashketballs for the circular truncated cone. Thanks in advance to the following people for helping with the volume of the circular truncated cone trashcan:
@mjfenton, @absvalteaching, @MaryBourassa, and @RobertKaplinsky.
Swish,
1140
This is definitely a fun application of volume. In terms of measuring the diameter, and accordingly, finding the trashketball's diameter, it may be worthwhile for everyone in the class to create a trashketball and measure the diameter. If you then average all of their measurements, I would guess that you would have student buy in as to where the measurement came from and it will be reasonably close to what your mean was when you calculated it.
ReplyDeleteRegarding calculating the number of trashketballs that fill the can versus the volume of the trash can, I just recently had some experiences in a similar type of problem. I was working on the giant gumball machine problem to do with some Geometry teachers. The gumball machine says it is filled with gumballs that are diameter .92" to 1". My initial thought would be that it would be about a one-to-one ratio of gumballs to cubic inches. However, I soon realized that I was mistaken.
First, both your problem and the gumball problem involve "sphere packing" where more spheres can fit in between the gaps. Second, while the gumballs had a diameter of 1", their volume was closer to .5 cubic inches (4/3*pi*.5^3).
Going deeply into the direction of why the answer is obviously beyond the scope of the lesson, but it is definitely the basis of a good discussion.
Hi Robert,
DeleteThanks for the comment. I'll give an update on how the lesson went. I added some notes to the 101qs lesson, but more importantly I planned on having students make their own trashketball and that's exactly what we did. Some students also brought up the idea of "sphere packing." Stay tuned for an update. Thanks for the feedback man.
Robert: I now see where you got the divide by 2 concept in the gumball. It makes a lot of sense to me now why that is. But, why would dividing by 2 throw off your answer tremendously with trashketballs?
DeleteDiscussing this image after deriving the formula for a sphere from a cylinder would also be cool.
http://40.media.tumblr.com/9230046fc0b2b32b51a36d715ac22e46/tumblr_n7473u9COK1qzicj3o1_1280.jpg
Mr. Stadel,
ReplyDeleteI'm interested in trying out some 3 acts stuff. I was wondering if you could help me out. I'm curious if how you use these problems. Are you in the beginning, middle, or end of studying volume and you give a problem like this or is it out of the blue, "Today were going to do this cool problem, tomorrow we'll go back to doing ____"?
Thanks for your time,
sam
Sorry for anonymous, I don't have any of these other ids.
Thanks for your post it is very interesting for me!
ReplyDeleteThank you for this post. This is very interesting information for me.
ReplyDeleteSuch an interesting information. I always rate my paper to know level of it.
ReplyDeleteThank you for this post. This is very interesting information for me
ReplyDeleteIf you are looking for online term paper assistance, look no further! You've stumbled upon the right comment!
ReplyDeleteHello, I would like to thank you for sharing this useful material. The information you have mentioned here will be useful. I would like to share with you all one useful source which might be interesting for you as well.
ReplyDelete
ReplyDeletei love your article. you can visit my website.
https://cracksray.com/
I have read several excellent stuff here. Definitely value bookmarking for revisiting. I surprise how much attempt you set to create this type of fantastic informative web site.
ReplyDeleteBitdefender Total Security Crack
AOMEI Backupper Pro Crack
Youtube By Click Premium Crack
EaseUS Partition Master Crack
uTorrent Pro Crack
MS Office Crack
I'm going to go over a few of the most compelling recipes to use Keto Advanced Fat Burner in this column. I purchased this one at a moderate cost. Keto Advanced Fat Burner really made my day.
ReplyDeleteKeto Advanced Fat Burner
This is a just cause. I was overwhelmed. I've been doing that all week long. I've been on a roll with Keto Advanced Fat Burner the past couple weeks. Typically Keto Advanced Fat Burner includes that feature in several locales. I feel so funky.
ReplyDeleteKeto Advanced
Keto Advanced Weight Loss
Informative Blog
ReplyDeleteVisit Us
CBD Tincture For Horses