Chirality: What’s that? More on Spatial Reasoning

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 TinkercadTM to model the pieces, and finally use their TinkercadTM 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.

Chirality matters. There are two chiral molecules that make up the drug thalidomide. One of these molecules relieves morning sickness for pregnant women, while the other causes birth defects. The two molecules were mixed in pharmacological compounds, and a wave of birth defects resulted in the early 1960s.[1] Learning from this terrible mistake, chemists began a new line of work: chiral separation.[2]

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.

[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..

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

Building the Concept of Volume

by Jennifer Knudsen, March 4, 2019

Our project combines math and computational thinking with 3D modeling and printing for grades 5-7. We’re now designing a classroom unit where kids use modeling, printing, and more typical making materials to create useful, beautiful objects.

What math? Geometry is a natural for 3D modeling. And volume is a topic that cuts across geometry and measurement in grades 5-7. For example, before they design their own objects, students start by building a cube puzzle and they come to understand that volume is the amount of space an object takes up and that it can be measured in cubic units. At first, they are just counting cubes. But that leads the way to thinking about counting in an organized fashion, which leads to a multiplication view of volume (You know, length•width•height). Instead of just giving kids the formula, we have them build their understanding of volume this way. Happily, that matches up with the Common Core and many current state standards.

Image by fdecomite and used under Creative Commons 2.0.