Verse Ex19-01 describing the Jews arrival
at Sinai, where they received the Torah, states:
In the third month after the children of Israel were gone forth out of the land of Egypt, the same day came they into the wilderness of Sinai.
Verse Nu10-11a describing the departure of the Jews
from Sinai, states:
And it came to pass in the second year, in the second month, on the twentieth day of the month, that the cloud was taken up from over the tabernacle of the testimony.
Based on these two verses Rashi infers
The Jews stayed at Sinai for a little under a year.
[The table below shows they stayed for 11 months 3 weeks)]
The spreadsheet below shows the computations that
led to Rashi's conclusion.
There is an absolutely delicious explanation of the above Rashi. The
Torah was received at Sinai. But you can't learn a whole
new law code in one day. Most probably Moses lectured at the
rate of one biblical paragraph per day thereby ensuring mastery
of biblical content. There are in fact 293 paragraphs
in the Torah.
It is reasonable that Saturdays were used for review. Hence the
whole Torah was reviewed in 293 days (one for each paragraph)
+ 49 Saturdays (293/6 = 49) = 344 days = 11 months x 29.5 days
per month + 19 days. In other words this Rashi The Jews camped
at Sinai for 344 days is not a numerical curiosity but rather a profound
method of biblical pedagogy. Here the Torah and Moses show us the proper
way to absorb new learning material thru small digestable daily learning.
This Rashi is the basis of the Page-a-day (DafYomi) Talmud learning
Praise be Him Who chose them and their learning.
Acknowledgement: This 293 calculation (with modifications)
is based on modern biblical research. The interested reader can find a
in the introduction to the Israeli Korain Tanach.