## Amazing Watermelons – 3 Acts

March 8, 2012 by John Scammell

I’m starting to see this stuff more places. This one could be fun. This one is easier mathematically than the Penny Pyramid that Dan Meyer describes here. In Dan’s 3 Act Format, here it is.

**Act I**

Video

Ask the kids what they wonder about. They could go lots of interesting directions with this one.

**Act II**

Video

This video will give them the information they need, assuming their perplexing questions require them to know how many watermelons are in the pyramid.

**Act III**

The Answer

The answer is in the form of a Word document with a photo and some calculations. I’d love a video. If anyone has the budget for 385 watermelons, the patience to stack them, and the video editing skills to insert a counter to the filmed stacking, I’d gladly take it.

**Sequels**

What is the mass of the pyramid?

What is the cost of the pyramid?

How many watermelons could we stack in this room?

If the truck is 20 m from the pyramid, how long would it take to build?

Any other sequels? If so, throw them into the comments.

**Download**

This zip file (29.7 MB) contains both videos.

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*Related*

on March 8, 2012 at 3:39 pm |DanIf you stacked every watermelon there, how tall would that be?

on May 10, 2012 at 12:26 pm |Bob LochelJohn, I loved this Amazing Race episode, as so many groups had issues with the structural integrity of their pyramids. All groups started by making the 10×10 watermelon base, then placing the 9×9 on top. It made me wonder if there is a better “mousetrap”. Is there an optimal strategy for stacking the melons.

Would it make more sense to start with a 2×10 base, then start the next level (a 1×9 row) on top of that. Then do the next row of 10, then the next row of 9 on top of that…in which case you’d be ready for the first row of 8. I thought perhaps this approach would increase even-ness at all levels, rather than having a few good levels, then some which we hope stay intact.

Or maybe I need to get out more….

Great blog. Please visit mine and say hello: mathcoachblog.wordpress.com

on May 17, 2012 at 1:54 pm |lilTried this today with low ability Y8 – no watermelons, but built with Maltesers!

on May 17, 2012 at 3:25 pm |John ScammellHow did it go?

I had to Google “Maltesers”. Now I want some!

on May 18, 2012 at 3:40 pm |lilYou’ve never had Maltesers!

It worked really well; they settled really quickly and were hooked by the video, later in the day they were heard telling other students “we did watermelons in maths today” and then explaining what this meant. They came up with varied ways to represent their recording/working out in diagrams and pictures as well as calculations. It is the first idea of this type that have used with a lower group. The maltesers were an afterthought as I remembered I had some for a prize, so after we built pyramids we had to eat them of course!

Thanks for suggesting this.

on June 18, 2013 at 10:14 am |Kyle PearceHi John:

Great problem! Will use in my classroom tomorrow. Just added it to my “Real World Math” directory here: http://tapintoteenminds.com/3act-math/

Check ‘er out and keep up the great work!

on July 2, 2013 at 10:27 pm |Watermelons | rebeccacouey[…] Watermelons […]

on August 4, 2013 at 10:22 am |Kelli RuleyI like the Maltesers extension. I could even say “I only have ___ Maltesers and ____ students. So how many groups do you, my students, need to make and how many students will be in each group to be able to get everyone building Maltesers pyramids?”

on December 15, 2013 at 8:45 am |Relevant Mathematics | 8th – Unit 10: Volume[…] https://thescamdog.wordpress.com/2012/03/08/amazing-watermelons-3-acts/ […]

on March 23, 2015 at 5:18 pm |dakeriahey

on July 10, 2015 at 9:12 pm |MartinTotally awesome. I found this via http://emergentmath.com/my-problem-based-curriculum-maps/ and I’m glad I did. It’s definitely something that ties your work with squares in Pythagorean theorem with a pyramid. This is the only fun pyramid problem I have seen. Is there any way we can tie it in to a 10 by 10 watermelon cube, or extension, how many would be in a cube?

Interesting. a 10 by 10 cube would be a 1000 watermelons. But 1/3 of a 1000 is 333 1/3, not 385. I’m sure I’m missing something fundamentally wrong here? Verrry interesting. Makes me think.

on January 17, 2016 at 7:33 pm |stephenTo clarify my earlier comment, if you assume that the structure is a third of a cube, then the next third needs a base layer of 10×10. Putting this by the current structure will make a structure that is 11 melons high… so not a cube but now a cuboid.

on January 16, 2016 at 5:10 am |stephenI like the count you have done Martin, but the watermelons are stacked in the gaps, which shows they don’t fit a uniform third of the space as you would find with boxes cut into thirds. interesting to demonstrate with pupils buy getting them to count the sum of a box cut in different ways.