Putting kids in a Box

We had a spot of difficulty recognizing dimensions of 3D space today.  L x W x H is a simple enough concept to find mathmatically, but if we are going to be Visualizers in math class, we need to be able to picture the image in our head.  First, we started with a globe.  What size of box would you need to make to fit perfectly around this globe?

We practiced our guessing skills and constructed an imaginary box around the globe.  Then, we measured that box with our imagination and wrote our guesses on the board.  Then, we measured it and saw who was closest.  Repeat with a water bottle.  The students reflected that the water bottle was thinner, so the square at the bottom would have to smaller, and the height a little lower.

This lead to new guesses and new visualizations, and new conjectures.  We are starting to think like mathematicians and show these habits of mind.  But, we still have lots of work to do.  We need to challenge our conception of what we think math is.  It is not just calculation.

[caption id="attachment_1246" align="aligncenter" width="300"] Moving in my 10m x 10m x 10m box[/caption]

[caption id="attachment_1247" align="aligncenter" width="225"] Life in the 1m x 1m x 1m box is hard[/caption]

Next, we imagine we are inside a box.  The box is 10m x 10m x 10m.  There is enough space to live in this box.  We move in our box, we dance, we jump.  Suddenly, the box gets transformed to a 2m x 2m x 2m box.  We can still stand, lay down, and jump, but it is not as comfortable.  Suddenly, 1m x 1m x 1m.  Now we are unable to move.  We are trapped inside.  1m x 50cm x 50cm.  Only enough room to lay down.  50cm x 50cm x 2m.  We can stand again, put the walls are tight against us o the sides. 1m x 1m x 2m.  A bit more room, we can finally stretch.  3m x 3m x 3m, enough room to walk a couple of steps and jump.  10m x 10m x 10m.  Finally back to the wide open space!