Durante el tercer trimestre en nuestra serie de lectura "Open Court"
翻訳についてのコメント
Según la Wikipedia en lengua inglesa (http://en.wikipedia.org/wiki/Open_Court_Reading), "Open Court Reading" es un programa de libros didácticos publicados por "Open Court Publishing Company" (http://www.opencourtbooks.com/), adoptado por muchas escuelas elementarias en los EE.UU.
Also from Wikipedia:
"The Open Court Publishing Company is a publisher with offices in Chicago and La Salle, Illinois. It is part of the Carus Publishing Company of Peru, Illinois."
As you see the proper name which is not supposed to be translated is "Open Court".
"reading series" can perfectly be translated as Goncin did.