Volume Lesson, Crowd Sourced

I was expecting to have jury duty today so I wrote sub plans that had students working on a practice state test (ours is coming up in a few weeks).  Then, jury duty was cancelled and I wanted to plan a more interesting lesson last night, but my brain was already drained.  So I turned to twitter:

I'm planning to do this activity tomorrow, but I'm not very excited about it. Help make it more interesting please? http://www.scribd.com/doc/137815960/Volume-and-Surface-Area

Then I wandered off for a bit.  When I returned, I found ideas!

Gregory Taylor(@mathtans): Your prism is growing. Dims are twice the size, now three times. When does it cover the floor? At what point can you fit inside? 

Daniel Schneider(@MathyMcMatherso): Add prediction questions about how volume & SA will increase when doubled/tripled?  

Daniel Schneider(@MathyMcMatherso): Add questions at end: Draw prism with volume _____. Are there multiple answers? 

Gregory Taylor(@mathtans): Partly comes from Alice in Wonderland. How much more fabric do you need to cover a table that's now three times as big? #DrinkMe

 John Golden(@mathhombre): geogebra similarity enlarger http://t.co/2vu5przWhk

So, I updated the document.  One thing I remembered from past years was the tendency for students to create nets with square bases since the net I provided had a square base.  Other than that I implemented the suggestions and voila, new activity!

Volume and Surface Area New

When students arrived in class they found two questions on the board: "What is area?" and "What is volume?" that I asked them to write about individually.  (First period I had them in the reverse order but kids kept talking about area first so we did them backwards and I adjusted accordingly for the other classes).  We have talked about area plenty of times, but never volume.  I had them share anything they wrote and made a list of words, formulas, definitions and ideas for each question.  In all three classes someone provided some information that allowed me to define volume of anything with a constant cross-section as base area multiplied by height.

Post discussion I distributed the assignment sheet, graph paper and scissors; the only instructions I gave were "don't make your first box too big because you'll have to double it later."  If students wanted to know if their net was correct I said "cut it out and see!"  When students didn't know how to calculate surface area or volume I directed them back to our brainstorm.

Things that made me happy:

• nearly everyone started with different dimensions, so when they helped each other there was no cop out option of "here just copy mine"
• it was easy to see the nets that didn't work
• students were surprised how much bigger their "doubled" box was (cutting out a physical box made the realization that volume doesn't double if you double all the side lengths much more real)
• after two boxes kids were tired of counting and cutting and they wanted shortcuts (great! there's no need to do that, just draw a sketch)
• if students assumed the volume doubled without calculating, they realized I probably wouldn't have asked question three if that were true and went back to calculate the volume in question two.

The best thing of all: we spent an entire 90 minute period on rectangular prisms.  I only had a couple students try to quit mid-period and I ran this lesson with three classes today.  At our department meeting yesterday someone claimed it's good to give practice state tests because it builds perseverance.  I counter that this lesson builds perseverance in ways that a multiple choice test never can.  Did you really read that sentence above?  Let me rephrase:

Students spent 90 minutes investigating surface area and volume of their rectangular prisms.

In the process of editing this document, I dropped the question about the general case.  So I asked it as the journal question today instead:  "What happens to the volume when you double all the sides?"  I know at least one student said "it multiplies by 8" since she yelled it out.  This may be my opening question next class- compare with a partner, what do you notice?