The Israelites were commanded to select on the tenth of Abib (Nisan) a he-lamb of the first year, without blemish, to kill it on the eve of the fourteenth and to sprinkle with its blood the lintel and sidepost of the doors of their dwellings so that the Lord should "pass over" them when he went forth to slay the first-born of the Egyptians.
In memory of this the Israelites were for all time to eat unleavened bread (matzoth) for seven days, as well as keep the sacrifice of the Passover on the eve between the fourteenth and the fifteenth of Nisan.
As before remarked, there seems no direct connexion between the paschal sacrifice and what appears to be essentially an agricultural festival; the Hebrew tradition, to some extent, dissociates them by making the sacrifice on the 14th of Nisan and beginning the Feast of Unleavened Bread on the 15th.
These were presented in the month Rajab, corresponding to Nisan (Smith, Religion of Semites, p. 210).
This would seem to point to a time when the fixing of the sabbath was determined by the age of the moon, so that the first day of the Passover, which is on the 15th of Nisan, would always occur on a sabbath.