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!

I love how you opened this up. Having the students come up with the question makes it a much richer problem and more fun to solve. You must have had great student ownership of the process.

ReplyDeleteThey did...and some did choose a question that wasn't particularly challenging. we made a list of the questions students were answering and for some I redirected after they answered their question and asked them if that might be a step towards answering one of the others as well. Thanks for commenting!

DeleteWhat a great idea! I've been wondering how to introduce this to one of my classes, and here it is. The idea of just showing them, and letting them decide what to figure out is genius. Will be using this. Thanks for sharing.

ReplyDeleteThanks...I did keep a set of extra blocks around as well as some students really did need to build it to figure out what was going on!

DeleteNice idea for an open-ended problem! It'd be interesting to hear what different students come up with that they are most interested in knowing. Thanks for sharing!

ReplyDeleteI think the most interesting one was "What was the largest one in the series we could build with the supplies we had in the room". I had a lot of students just following sequences, and some that were trying to write functions for each color.

DeleteI especially like how you've modified the task over time based on your comfort with the task and your desire to open it up more for the students. I'd be curious to read your blog in a year or two to see what further ways you've refined the task. Great reflection!

ReplyDeleteThanks...that is actually one of the reasons I want to keep up a blog. I think if I made myself reflect (in writing) on my teaching it would help me when teaching similar concepts in the future. No point in history repeating itself on a not so good lesson :)

DeleteExactly why I blog! DOCUMENT, and improve it. Woohoo.

DeleteI like that you plan on just showing the picture to your students. I think their is a lot of benefit to just asking questions such as "What do you notice?" or "What do you wonder?" These can make such a difference and you have found out how to capture your student's interest. This is great!

ReplyDeleteGreat problem! I like how you are going to show a picture first and offer up the manipulatives if they need it. I also like how you said the table is a tool rather than just a worksheet. Make them WANT to do the table. Love it.

ReplyDeleteLove that image, Nicole. Thanks for sharing it. I posted about it here:

ReplyDeletehttp://blog.mrmeyer.com/2014/you-can-always-add-you-cant-subtract/

Thanks for the compliment! I always enjoy your task makeovers...good discussions all around!

DeleteThanks Nicole. This looks a little more engaging than how I was going to present the problem to my MCF3M students here in Ontarioas part of a spiralling project.

ReplyDeleteHi, Nicole. I found your post via Dan Meyer's related "makeover", and fell instantly in love with the prospect of putting the Painted Cube out there as an open-ended activity. I took it to one of my classes today and have used your photo and blogged about it here : https://lpsmathsgroups.wordpress.com/2016/05/26/cube-questions/

ReplyDeleteIt was a heap of fun, thank you for the idea!

Love the extension problems at the end of your post- I'll be adding them in to my notes for the next time we do this task!

ReplyDelete