Activities to Encourage Collaboration #1: Surface Area and Volume of a Sand Castle!

In a time and society where students spend more time communication through text messages, Facebook, Twitter, Instagram and 14 other social media platforms that I cannot even begin to name, I find an ever increasing need to get my students talking to each other fact to face.  As a result I have been on a quest this year to implement as many collaborative activities as I can.   I have used many of them throughout this school year and have had some amazing results that include increased communication, retention of information, assessments grades and more positive attitudes (overall)!   Throughout the summer I will be sharing some of my favorites, some of my other favorite math teacher-authors and many others so that hopefully they can become your favorites too!

Today I am excited to share with you my Surface Area and Volume of a Sand Castle activity!  As we were finishing our three-dimensional figures unit in Geometry I was looking for a really good way to a) get the students talking and b) show them how the different figures can share dimensions to build the structures that we see on a daily basis.  Since I do not possess architectural skills and summer is upon us I decided to build a Sand Castle (as "Do You Want To Build A Snowman" is running through my head).  I started with a goal of including as
many of the main solids that I could and managed to include prisms, cylinders, cones, pyramids and even a hemisphere!  I worked to have the solids share bases, sides and dimensions whenever possible.  This is what I came up with!            
I also came up with a second version that has the figure divided into 11 smaller figures to help struggling students visualize a path to follow to solve it.  Additionally, this helps students to organize their work so that you and they can identify an error if they make one.  (I did not, however, hand this out to begin with as I wanted to see what they would do with it first!)


Before implementing this as partner/group collaboration piece I sat down and created a list of questions that I could ask as I walked around the room to point students in the right direction, get them thinking, communicating and solving without actually giving them the answer.  Some of the questions that I came up with:

1)  Are there any surfaces that aren't exposed?  Alternatively - are there any surfaces that shouldn't be used in surface area?

2)  Have you thought about breaking any of the larger figures into smaller ones?

3)  How are you arranging your work so that you can go back and check it later?

4)  Are there any dimensions that you don't have?  How can you find them?

5)  Do the unused surfaces from the surface area get used for volume?

FREE!!!! 

Finally the day arrived to implement this and I must say, it went AMAZINGLY!  After my students got over the expected moans and groans and sat down to start working on it, they had fun with it.  I heard great discussion, collaboration and genuinely helping each other understand instead of just giving each other the answer.  I set forth the "rule" that their final answers had to be within ten of mine (to account for rounding error) and that whoever was the closest won a prize (extra credit, candy, excusing of an assignment, ect.).  My students quickly turned it into a competition and worked hard to earn the prize.  I ended up with multiple students hitting my answer down to almost the decimal point - which is great! :)  Based on the feedback I can honestly say that they enjoyed it and felt that it really reinforced the concepts we have been learning in this unit!  

I have put the entire activity, including a multi-page answer key that highlights each piece and how to find their surface area and volume up in my teacherspayteachers store.  You can pick it for FREE here :)  I would LOVE to hear how you use it and implement it! Please comment below!