I think the Manhatten Project used natural uranium metal fuel elements with graphite moderating blocks. This was certainly the case with the Magnox power reactors which I worked on in the 50s. The fuel elements were devilishly heavy, you did not want to drop one on your toe.
According to Wikipedia, it was constructed with "45,000
graphite blocks weighing 400 short tons (360 t) used as a
neutron moderator, and was fueled by 6 short tons (5.4 t) of uranium metal and 50 short tons (45 t) of uranium oxide." IIRC, the natural ratio of U235 to U237 and U238 is too small to allow a compact fission reactor.
You need to "moderate" the neutrons, cooling "fast" neutrons emitted during spontaneous decay of the uranium isotopes to much slower "thermal" neutrons that will be captured by the U235 isotope and cause fission with the release of more high-energy neutrons. There is a square-cube law at work here: the volume of the reacting nucleii increases as the cube of the radius while the surface area for escaping neutrons increases as the square of that radius. So, if you make the "pile" big enough, fewer neutrons per unit volume will escape the surface. Escaping neutrons contribute nothing to the fission reaction inside.
You still need to moderate the neutrons that do remain inside the "pile" so they will interact with the U235 nucleii and cause a chain-reaction fission, and that is where the graphite enters the picture. IIRC, the Chicago pile also used cadmium foil-covered rods to quickly dampen the fission reaction by absorbing (rather than just moderating) the neutrons. These rods were allegedly held up out of the pile by manila ropes and a large fireman's axe was stationed nearby to chop the ropes and release the dampers into the core of the pile. Hence the expression, SCRAM the reactor meaning Super-Critical Reactor, Axe Manila! Or so I have heard. Actually, this is no-doubt a back acronym invented after SCRAM become common usage for a fast shutdown of nuclear reactors. See
this NRC article for perhaps a more factual history. The more likely explanation is the control rods were motor driven and a large red button was used to electrically drop them quickly into the reactor. Someone saw this and asked, "What do we do after pressing the button?" The answer: "Scram the hell out of here!" I think that is as likely as any other explanation for the origin of the "acronym" SCRAM.