An Exploration of Volume

Ok ok....So it's April and I taught volume almost a month ago.  Things can get pretty hectic this time of year, what with preparing for the OAA and making sure my kids are in tip top shape to show what they know!  Now that we're on Spring Break, I can finally sit back and reflect on what we've been learning and where we need to go after this.

I truly feel that math should be a hands-on experience for kids of all ages.  It shouldn't stop in 3rd grade.  All too often, we get caught up in making sure they know how to do it on paper and apply formulas, but kids need to be able to touch and feel what they are learning to really grasp it and understand it.  I always try to give them thorough hands-on experiences before teaching them the "math" part: formulas and equations.  So far, I think we've been pretty successful.  But, as in most cases, time is always an issue.  We just have to keep moving, moving, moving!

As will area and perimeter, we did an exploration of volume.  Many of my students had remembered the formula for finding the volume of a rectangular prism from 4th grade, but I wasn't really sure they understood or remembered WHY you multiplied LxWxH.  Thanks to Everyday Math, each student had the net of two different open rectangular prisms in the back of their math journals.  We made predictions for how many cubes we thought would fit into each.  These predictions actually gave me pretty good insight as to where each student was in their understanding of volume.  Then, of course, we began filling!

 We started by just filling the base of the prism and finding out many cubes that was.  I wanted them to see this as the area of the base: of course, some did, some didn't.  We will keep working on this idea of area! (Too often, their idea of area is just a rectangle on a page....must change that thinking!!).  Then we added another layer, and finally a third.  This allowed them to see that we were adding the area of the base however many times tall it was.  For the second prism, we only filled the base and predicted what the volume would be based on the results of the first prism.  From this, we developed the formula for finding the volume of a rectangular prism!

As an extension, and because we had a couple extra minutes at the end of class, I had each student build a rectangular prism on their desk with a volume of 24 cubic centimeters.  I didn't give them any more specifications than that.  After a minute or two of building, I began recording different lengths, widths, and heights that I saw around the room.  Once they saw all the possibilities, hands flew in the air.  They remembered what we had learned about multiplication being part of the commutative property and knew they could use the factors of 24 to build many many different prisms, all with the same volume.  Ah ha moments are the best :)

Lastly, here is the anchor chart we came up with.  They wanted me to point out that volume is "all about the threes":

Volume!