Maximizing Box Volume with Popcorn

IMG_2916Thanks to Fawn, my students actually cared about making the maximum sized box out of their 8.5″x10″ piece of graph paper.  If you don’t do this, you should!  It was very easy and great fun!  You will need to go and read Fawn’s popcorn post because she has all of the great lesson details.

I went minimalist and only showed them a box I had made, and the squares I had cut out to make my box.  I gave them a ruler, scissors, tape and ONE piece of graph paper.  I told them they only got ONE piece of paper.  They worked well and carefully.  Most students chose to fold  the sides in instead of cutting just in case they messed up.  Love them.

Screen Shot 2015-02-15 at 9.56.16 PMI recently bought an Orville Redenbacher air popper so I brought that in to make the popcorn.  Seriously, this is the best $22.49 I’ve spent in a long time even before I used it for a math lesson!  I even brought in butter.  One of the students took a picture of the air popper so she could buy one.  It was pretty cool with all of the popping going on right in the back of the room.  It smelled heavenly!

Once they made their box they measured it and entered the measurements and resulting volume on a Google Form.  Then I filled up their box with popcorn!  We ate while looking at the Google Form results and then I challenged them to find a general equation for an size cut.  Several students came up with it pretty quickly and then I had them graph it in Desmos to show them how their maximum volume was also on the graph.


Function Transformation Discoveries using Desmos

Calling all teachers to help me make these better!

Screen Shot 2014-10-04 at 11.40.52 AMThis summer at Twitter Math Camp, Glenn (@gwaddellnvhs) and Jonathan (@rawrdimus) showed us how they lead students through all of the functions in Algebra 2.  Basically, they put all of the equations into (h,k) form.  Fortunately, the book I am using this year, “Discovering Advanced Algebra” does basically the same thing.  Since it is a “discovery” book, they have some good ideas that I have been able to modify and made into INB (Interactive Notebook) form.  Never fear, this just means it’s a worksheet that you fold in half.

Screen Shot 2014-10-04 at 11.58.29 AMThe first discovery was also my students first introduction to graphing with Desmos on their own.  Of course they have seen me use Desmos multiple times by now since Desmos has all of those great example graphs in their side bar!

Here is how I progressed through discovery for linears, quadratics, square root, and absolute value.  The Box files with the word docs are at the end.

  • Horizontal and Vertical Shifts
    • Linear Equations (first time with Desmos)
    • Screen Shot 2014-10-04 at 12.15.08 PM
    • Quadratic Equations
    • Screen Shot 2014-10-04 at 12.14.30 PM
  • Reflections with the square root function
  • Dilations with the absolute value function – these last two are combined into one.  I would love any suggestions on this – before Monday.  I know, I’m asking for too much here! 🙂
  • Screen Shot 2014-10-04 at 12.11.32 PM

Also included is a “Transformations Parent Graph” foldable that I made to sum it up.  I kind of hate this one, and would love suggestions here for sure!  Should I add dilations?  Why is it so ugly?  What else do I need to add?  I need help here for sure.

Screen Shot 2014-10-04 at 12.10.56 PM

Algebra 2 Function Transformation Discoveries

Please note:  I did not make all of these discoveries from “scratch”.  I created some of them.  But some were inspired by the textbook I am using this year, “Discovering Advanced Algebra” and some were created by my amazing co-teacher.  I then adapted all of them for INB (Interactive Notebook) form.