CMP Painted Cubes Tool

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Painted Cubes Investigation

See the instructions below.

Suppose that you painted every side of a rectangular solid that has been made from unit cubes.

How can you determine the number of unit cubes that will be painted on 6 sides? 5 sides? 4 sides? 3 sides? 2 sides? 1 side? 0 sides?

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Instructions

Choose the dimensions of the solid you wish to explore using the sliders at the bottom.

Select on a color from the left and then click on a face of the solid.
To rotate the solid so that you can paint the other sides, use the or buttons from the top menu.
One way to count the number of cubes painted with a certain number of sides is to erase them as you count them using the button. You can use the rotate buttons to make sure you get them all.
An alternative way to count the number of cubes painted with a given number of sides is to use the view tool from the top menu.

A new window will open up where you can select the type of cubes to be counted. Those cubes will be highlighted and the total shown. You can also rotate the figure using the sliders at the bottom of the window.
To help you see how the faces are painted and to see the cubes that are not painted at all, you can use the explode faces tool which will move the cubes on the outside away from the inside. You can press this button more than once to move the cubes even farther.

To collapse the faces back together, use the SHIFT key together with the button as many time as as needed. You may find using this together with the view tool (see #5) to get a better sense of what is going on.