This is the 1st most frequent Japanese word.
元
"元" means "origin," "basis," "foundation," or "former."
Here, '元' (moto) is used to signify 'origin' or 'source', referring to the Edo period as the origin of the building.
この旧い建物は江戸時代が元です。
This old building originates from the Edo period.
In this usage, '元の' (moto no) means 'original', specifying that the information is from the original document.
その情報は元の文章から取りました。
That information was taken from the original document.
In this sentence, '元気' (genki) combines with '元' to mean 'vitality' or 'energy', describing the state of the children.