Dandy Candies
by Dan Meyer
skips
questions
Act One
Act Two
 ImageAll Four Packages
 1.
Rank these packages in order of which uses most cardboard to least.
 2.
Rank these packages in order of which uses most ribbon to least.
 3.
How many candies do you think we're trying to package? How many do you think you saw?
 4.
What do you think are the dimensions of each of those four packages are?
 Teacher noteAfter they've guessed, tell them that there are 24 candies. Rewind the original video and let them gather the dimensions of each package from the video.
 Teacher noteNow help them /calculate/ the volume and surface area of each package. The formula for surface area is straightforward: 2wl + 2wh + 2hl. The formula for ribbon length is trickier: 4h + 2l + 2w.
 Teacher noteOnce they determine the /actual/ ranking of the packages by cardboard and ribbon, ask them to make sure there isn't /another/ option that's even better.
Act Three
 ImageAnswer
 FileDandy Candy Packaging Options
 Teacher noteA question I have: is it always going to be a guarantee that one option will be the best for both ribbon /and/ cardboard? If we were packaging a different number of candies, might there be an option that was best for cardboard while another option was best for ribbon? I don't know the answer.
 Teacher noteHere's an unverified strategy:
1. Take the number of units you're packaging.
2. Take the cube root of that number.
3. Decrease that number until you have a factor of the number of units you're packaging.
4. Divide that number into the total.
5. Now take the square root of this new number.
6. Again decrease the number until you have a factor of the number of units.
7. Divide that number into the remainder. Now you have the third factor.
8. The smallest factor should be the height of the box.
Sequel
 5.
Is there a better option than the four we originally selected? Can you prove it is the best?
 6.
Does the way we position the box of candies matter? Up, down, left, right, top, bottom?
 7.
Pick other numbers of candies. 80 candies, for instance! What's the best way to package them? Can you figure it out faster this time?
show 83 more questions





What's the most efficient way to wrap the chocolates? The music makes it the most awesomeest question ever too.







Which is the most convenient box size? Also, which box size looks the biggest?


Which candy configuration requires the most blue ribbon to do that decorative ribbonwrapping thing? The least?







Is the volume of each of these boxes the same? What about the surface area?


Which way of packaging results in the most sales: don't thing one long skinny package is aesthetically pleasing and wouldn't sell well.






Will someone try to cram this into a "FAKE" real world polynomial problem... the length box is x + 2, the width is x + 6, x = h. Find V?


If the volume of a rectangular prism is 24 cubic units what is the greaest possible surface aea?




How many possible cuboid/cube boxes exist? Which one fits best into a standard size plastic bag?























What is the greatest and least amount of paper and ribbon needed to wrap the candies?




Awesome. Does the volume change? And the surface area? And how many ways could these candies be stacked dandily?







How to arrange the cubes so that the paper used for wrapping is minimal?














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