The medal's obverse bears Washington portrait, facing quarter-left, under eye in the sky with radiant beams of light; underneath, streamer with inscription (acorn) SUO (acorn) SE (acorn) ROE - ORE (acorn) FIRMAT (acorn); right angle and compass at center bottom. Around bottom half, HE WAS A BROTHER - OF THE MYSTIC TIE
The reverse seal of Fredericksburg lodge with masonic symbols and Washington's progress throught the masonic hierarchy. From left throught bottom, to right, NOV. 4 / 5752 / ENTERED / APPRENTICE; MAR. 3 - 5753 / FELLOW - CRAFT; AUG. 4 / 5753 / MASTER / MASON; signed at bottom, I. F. WOOD, DES. G. H. LOVETT, FEC.
The dates on the medal are numbered in the masonic calendar, which can be a bit confusing to non-masons, but we can simply subtract 4,000 from the numbers to get the "common" calendar years. Washington advanced quickly through the apprenticeship stage to emerge a master mason at the young age of 21.
The medal was designed by Isaac F. Wood and the dies were cut by George H. Lovett. It measures 51mm in diameter and was struck in bronze. It appears to be a pretty rare medal though I am not aware of its exact mintage.