A Favorite Task: Painted Cube for "Exploring the MTBoS"

I imagine most of you have heard of the "Painted Cube" task...if you create a cube out of "x" 1 inch blocks, paint it, and take it apart, how many of the block will be painted on 3 faces, 2 faces, 1 face, or no face.  I've used this task in a variety of different places in the curriculum...patterns, surface area, writing expressions, writing functions.

In the past I've given students a copy of a prompt along with a table to collect all of their data, and lots of guiding questions of what to look at, count, extend, etc. When students struggled (or just needed the extra visual or kinesthetic support) I brought out sets of cubes and had students build models. 

Last year I wanted to really get students asking the questions so I created the following models and let students decide what we were trying to find out....

What a difference this made....rather than filling out a chart because they had to, students were genuinely engaged in trying to figure out what was going on with these cubes.  Some students wanted to know how many of each color there were, others wanted to be able to build the next model in the series.

After students came up with their question, I did provide the chart to any students who asked for something to organize their data.  By then, most were interested in completing the chart and seemed to see it as a tool for answering their question rather than just a worksheet to fill out.

This year I'm just going to share this image and off we'll go!