I have also not seen any reference to the 'Ancient Languages Chart' (also known as the 'Language chart of Mathematical Names') in any of the AMS albums I have read. This is a language chart of four or five ancient languages (including most importantly Latin and Greek) that is used in a lesson after the initial presentation of polygons.
This lesson is a language lesson in geometry. It generally should be introduced about the time the child has been introduced to prefixes and suffixes in the language arts. Equally it also fits in well with the language curriculum for upper elementary. This is a perfect example of the cosmic curriculum; language, geometry and history all rolled into one lesson!
Have the child lay out all the polygons on sequential order.
Present the ancient languages chart and tell the child that we are discussing the history of the names of polygons.
The name polygon comes from the Ancient Greek words "poly" meaning many and "gona" meaning angles.
Referring to the chart, we remind the child that these are ancient languages so the words may not have sounded exactly the way we say them now. The sounds, the accents and the language has evolved over time.
We ask the child (children) if we can have a one sided polygon or a two sided polygon. Then ask if we have a three sided polygon, we then focus on the triangle and go through all of the different ancient words for three on the chart.
We find the one that sounds most like what we use today:
When we move on to the next polygon, the quadrilateral, the children may call it a square. If so we say that it is a quadrilateral, and it is a very important quadrilateral as it is the king of the quadrilateral family - something we will talk about another day. Now I have seen some people use the term 'quadrangle' for this lesson as it fits with the lesson pattern. I have heard differing opinions on this, but I think it is acceptable as what the word quadrangle has come to mean would have evolved and derived from what is being discussed here. I think it comes down to personal choice, and it is about the conversation that goes with it that is important.
We continue through all of the figures, discussing the root words and what other words contain the prefixes - e.g. pentathlon, hexapod, octopus, etc. Eventually they will see that all of the prefixes are coming from the Latin and Greek columns.
At the conclusion of the lesson the children can follow up by tracing all of the polygons and writing the number of sides, the Greek or Latin prefix and the name of the polygon on a big fold out sheet:
I have my Ancient Languages Chart to share with you, it can be found HERE.
I have also made some title cards (as seen in the picture above) to print out for those who may find them useful, they are HERE.
I have just started creating booklet on important historical people in geometry and maths which I will share with you all when I am finished.
I would love to hear of your experiences with this lesson (AMS and AMI perspectives, the whole quadrilateral and quadrangle debate or any other aspect) - what works, what doesn't, what you may do differently.