*by Jennifer Knudsen, Hee-Joon Kim, Harriette Stevens, & Elise Levin-Guracar, August 1, 2019*

In the MPACT program, fifth grade students are challenged to make the seven pieces of the Soma Cube puzzle. The Soma cube puzzle follows a set of rules to create seven distinct pieces that fit together into a cube. Students use linking cubes to create the seven pieces, then use Tinkercad^{TM} to model the pieces, and finally use their Tinkercad^{TM} model to 3D print the puzzle.

- There are 7 distinct pieces made up of unit cubes
- The pieces are made up of either 3 or 4 unit cubes.
- All the pieces have a bend; none are straight; none are cuboids.
- The pieces fit together to make a cube.

If you try it, you may notice there are only seven different pieces that are possible to make following the rules for Soma cube pieces.

On our first trial round, students got into a debate about these two pieces:

Are they the same or are they different? Students who said they were the same noted they had the same volume and had two pairs of cubes crossed.

Students who said they were different held one up to the mirror, and students could see the other piece was a mirror image that was a different shape than the original. They wouldn’t occupy the same place in the puzzle. The students settled on calling the pieces “fraternal twins.” Mathematicians and scientists call them “chiral.”

If you think this is only relevant to puzzles or spatial reasoning test items, think again. Notice how the two molecules below are chiral, as are our hands. One can never be superimposed exactly onto the other.

This is the spatial reasoning and mathematical argumentation in which MPACT students engage. If you want to do this activity, you need 27 cubes per student or per pair. You can give them the requirements and have them go at it, but that is very challenging. We give students an image of four pieces already made and ask them to create those four, then the other three. Argumentation arises as students have differing opinions on whether the chiral shapes are the same or different. We also include some tasks based on classic spatial reasoning test items.

**Contact us at mpact_info@sri.com to get more information about our curriculum and program.**

[1] Uttal, D. H., & Cohen, C. A. (2012). Spatial Thinking and STEM Education. When, Why, and How? *Psychology of Learning and Motivation – Advances in Research and Theory, 57*, 147-181..

[2] https://www.sciencedaily.com/releases/2016/02/160208124237.htm.

Images from MPACT staff member Hee-Joon Kim, Uttal & Cohen article