Month

Can anyone help me with my granddaughters homework? What is the origin of the word 'Month.' I know it's meaning, but what is it's origin?

Main Entry: month
Pronunciation: 'm&n(t)th
Function: noun
Inflected Form(s): plural months /'m&n(t)s, 'm&n(t)ths/
Etymology: Middle English, from Old English mOnath; akin to Old High German mAnOd month, Old English mOna moon
Date: before 12th century

See previous post for a link.

MONTH - Old English. "In ancient times the passing of time was recorded by noting the revolutions of the moon. Consequently prehistoric Indo-European had a single word, 'menes-, which denoted both 'moon' and 'month.' The Romances languages retain it only for 'month'" Latin 'mensis' (source of English 'menstrual') has given French 'nois,' Italian 'mese,' and Spanish 'mes.' The Germanic languages, however, have kept both, distinguishing them by different forms. In the case of 'month,' the Germanic word was 'maenoth,' which has differentiated into German 'monat,' Dutch 'maand,' Swedish 'manad,' Danish 'maaned,' and English 'month.'" From "Dictionary of Word Origins: the Histories of More Than 8,000 English-Language Words" by John Ayto (Arcade Publishing, New York, 1990). Page 353.

Yet, the Latin for moon is "luna"!
So how did we get to "mensis" from "luna"?
Anybody?