We had two math clubs this past week, because the third got snowed in. The general idea for this club activity was to make up our own elements, describe their properties, draw cartoons to represent them, and form molecules out of them.
To get inspired in the initial design part, we looked at The Periodic Table book illustrated by Basher, an offbeat British artist. We also browsed his web site Basher World. The first task was to make element names out of our names. Club members used typical element word parts to form element names such as Kellainium, Madisonin, Joshicon, or Hydrotom. Here is the slide show with club member's cartoons of the elements:
The two clubs took different paths to transition to making molecules. On Monday, Robert offered Carbon Dioxide, CO2 as a molecule example, and I asked who liked it. Nobody confessed of liking it but Lucy the environmental scientist! However, after the lovely conversation about the roles of this chemical in plants its popularity grew. We roleplayed the molecule by forming an atom of C out of two people (since it has four chemical bonds available, we needed four hands) and connecting it with two atoms of O, each a person. We talked about valence (or valency) - the number of chemical bonds an element can form, and then came up with valences for our own elements.
On Friday, we looked at the Dihydrogen Monoxide (DHMO) web site, moved from the name to the formula amidst much laughing, and arrived at valence, molecules and formulas for molecules from there. DHMO awareness is seriously lacking in the general population, and yet this odorless, colorless substance is one of the major ingredients in acid rains, leads to death or injury from prolonged exposure to its solid form, and corrodes both metal and wood structures. It almost got banned in one county in California, but... Well, read for yourself, it's hilarious.
We moved on to making molecules out of our own elements. Depending on the valency, figuring out molecular structures was easy to very challenging. Some club members needed help with the task. Examples of typical difficulties, with my comments, are here.
The advice I gave those who struggled was to start with one atom of each of the two elements, make all the possible connections (chemical bonds) and then add the atoms as needed to fill in the free connectors. For example, if you starte with an atom of Mattimilliane, valence 7, and an atom of Elisyum, valence 4, you have 3 free bonds left on Mattimilliane after making all possible connections. You add another Elisyum atom then, form all possible bonds and end up with 1 free Elisyum bond. You add another Mattimilliane atom... and start asking yourself if this will ever end! Here are some molecules club members made.
Our drawing experiments show that yes, it always ends. Moreover, Monday club members formed the hypothesis that the resulting molecule always "switches" valence. For example, the formula for Mattimilliane, valence 7, with Elisyum, valence 4, is Ma4El7 (and 4*7=28 bonds all in all - a cool multiplication model). To check this hyphothesis, I offered to everybody to investigate molecules formed from Rocksegen, valence 6 (Ro) and Alicium, valence 4 (A). Different club members made different molecules:
Ro2A3 (12 chemical bonds)
Ro4A6 (24 chemical bonds, the switched valence one)
Ro6A9 (36 chemical bonds)
All these are mathematically possible! In fact, there are infinitely many possibilities. The least possible number of chemical bonds between these elements is 12 - this is the Least Common Multiple (LCM) of numbers 6 and 4. Other common multiples, and the number of atoms of each element required to make them, are in the proportion set up above. We arrived at the topics of multiples, Least Common Multiples and proportions from our visual work with elements. Here is the slide show with diagrams of this common multiple explorations.
I am quite happy with how the activity developed. The only thing I need to figure out is how to upload everybody's work to the web faster. It takes hours to scan, do some minimal adjustments for contrast, and add comments to pictures. Any advice?