Math Class Drops the Mic

A blog about teaching, with an emphasis on math.

Thursday, October 15, 2015

Tricks for Counting Treats


There are lots of treats (including freebies) in this post! Read on...


The leaves are changing color in the Blue Ridge mountains of North Carolina. The surf is picking up at Pacific Beach in San Diego. The elk are tangling in the forests near Jackson Hole but soon the first snow will urge them to warmer plains. Great flocks of warblers are touching down and stirring the glassy waters of the salt marshes of Louisiana. A welcome reef of cloud dulls the Mediterranean sun in Alicante. Autumn.

Autumn. At high schools everywhere, the clubs and student governments and teams have gathered themselves and now they raise their voices in a full-throated Autumnal cry: Let the fundraising begin! One of my favorite fundraising efforts is the ever-enticing challenge to guess the number of candies in a jar. Of course, there is always the possibility that the candy conceals a couple tennis balls, but I always assume the jar is authentically full and attempt to calculate the number. It’s tough to do without access to the jar, but if you’ve got a ruler and can get the dimensions you’ve got something to go on.

 But then what? Then you go home and fill a much smaller jar with the same candies!


 Then calculate the volume of the small jar and the large jar. (I leave that to you!) and set up a proportion:


But there was clearly some imprecision in measuring in the interior dimensions of a not exactly cylindrical cylinder!  Also, my larger jar in this case was actually narrower, which might actually reduce the efficiency of the packing of the candies, which are pretty large.

Without trying to solve a packing problem, and assuming we couldn’t just read the volumes from the label or use a measuring cup, what other methods could we use? Perhaps we can add some tools. If we had an empty jar equal to the target jar and some water, we could find out how many small jars of liquid are required to fill the large one!


Of course, we are still relying on an imprecise measurement of the fraction of a small jar we used at the last pour. Can we do better? Let’s add a scale to the toolkit. Now, if we find the mass of water which fills each jar, we’ve got a perfect proxy for volume.


It turns out the the true number of candies was 95! And it comes as no surprise that the best solution came from a great proxy for volume. Not only is the mass a great proxy for volume, a gram of water has exactly a volume of 1 cubic centimeter.


I’ve created a freebie which you can use to guide your student through the same series of experiments. Check it out HERE, as well as all the abundant treats for you at the intriguing blogs of the innovative Teacher-Authors of Teachers Pay Teachers below! Happy Halloween!


24 comments:

  1. Fabulous post.
    Great freebie.
    And only two candies away from a perfect "guess." Impressive.
    I have already downloaded your freebie so I can see for myself how this works.

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    1. Thanks! Fabulous is effusive praise! Enjoy the freebie!

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  2. What a fun freebie! Thank you so much for offering it. Loved your beautiful introduction. :)

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    1. Thanks Leah and I'm glad you enjoyed my little tour of Fall!

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  3. This looks like a super problem solving activity. Thanks for sharing!

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  4. This looks like a really fun idea, thanks for sharing!

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  5. Fantastic! I've always wanted to know how to figure that out! I'm off to check your freebie- thank you so much!

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    1. Now go forth and calculate your way to victory, raising high your jar of well-earned candy! :)

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  6. Candy and formulas- what an awesome lesson to sweeten what for mathphobics like me is a difficult concept.

    Connie

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    1. It's always good to know your learning style--I also work best in a chocolate-centered classroom!

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  7. But what happens if you eat the candy first? Unfortunately, I'm afraid that would be my problem! 😉

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    1. Haha! When that happens to me I unfortunately learn how much I ate when I step on the scale! Ah, Halloween...

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  8. Count 1, eat 2; fill up the jar; that's all you do! I never thought about putting a tennis ball inside! I must be too honest for deceptive trade practices. :) What a fun way to get kids to go beyond randomly putting down a good-enough number and seeing the math/science behind an "educated" guess. Great freebie!

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    1. Haha! Yeah, that's why you pad with tennis balls, so you can eat more of the candy! And I agree that this challenge helps kids realize that math is a tool you can creatively apply to any problem or scenario. Thanks for the feedback!

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  9. This is such a great post! Very fun lesson/adventure. :)

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    1. Thanks, I appreciate you calling it an adventure, I like to see it that way and I think my students often do too!

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  10. Hi,

    I happened to chance upon your blog and found it very interesting!

    We have recently launched a science app that uses augmented reality to enhance classroom teaching. The app has 3D models for kindergarten to grade 12. I thought you might want to check it out and may be review it on your blog, if possible.

    It is a paid app(with a few models free) but in case you are interested in trying it out I will be happy to provide you with a free copy.

    The link to the app is:

    iPhone/iPad
    https://itunes.apple.com/us/app/augmenter-augmented-reality/id997354409?ls=1&mt=8

    android:
    https://play.google.com/store/apps/details?id=com.augmented.android

    You can also search for the app on the app store as 'Augmenter'.

    Do let me know if you would be interested. I am really Looking forward to your response.

    happy teaching!

    Antara
    antara@augmenterapp.com
    http://augmenterapp.com/

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    1. I'll check out your website and let you know, thanks!

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  11. What a yummy activity! Thank you so much for sharing! ;)

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  12. I love your introduction; it's so visual. And then you made me laugh by mentioning a topic near and dear to my heart these days: fundraising! Sheesh. I spend months every fall trying to come up with a new fundraising idea.
    I'm going to pass your wonderful freebie on to the math teacher on my team. Or maybe I'll use it with my advisory group. The kids will love it.
    Darlene
    ELABuffet

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    1. I'm glad you liked the writing, thanks for the compliment! I'm also super stoked that you found the activity interesting and I hope you or your colleagues can make use of it!

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