Middle Mountain is sequenced with UN13,312 (Booby Prize) and UN13,384 (Prize Benchmark). UN13,460 (West) could also be included, but we have not done so in this sequence because we climbed that summit from the Lincoln Gulch side previously. It is a challenging ridge connection between UN13,460 and Middle Mountain. The following route avoids the ridge problems. One-way mileage and elevation gain for Middle Mtn. are measured from the summit of Prize Benchmark. Round-trip mileage and elevation gain assume completion of the sequence.
From the summit of Prize Benchmark, make your way back down the east ridge with some 3rd class scrambles to the saddle and part way up the ridge to unranked 13,090. You can either go directly over that summit or save some unnecessary elevation gain by contouring back across the SW face of 13,090. Hike to the saddle between 13,090 and Booby Prize. A game trail that crosses the saddle leads down and NE into the upper western reaches of the South Fork of Lake Creek.
Once in the basin, it's easy traveling again on grass. Contour across the basin heading around the lower east ridge of UN13,460 on a generally NE course. This will drop you into another high basin with several small tarns at 12,400 ft. This beautiful, pasture-like area is dominated by the spectacular cliffs of a ridge that connects Middle Mtn. with UN 13,460. From this heaven-for-elk pasture, head toward the low point of the southwest ridge of Middle Mtn. It is moderately steep gaining the ridge on mostly grass. Once on the ridge, things become much more rocky. The summit area of Middle Mtn. involves a little scrambling around some rock obstacles and makes an otherwise boring, low 13er, a little more entertaining.
For your descent, some may elect to take a more direct route and head downhill to the NE, hitting the old roadbed/trail not too far south of the trailhead. For our route, we headed straight down from the summit to the southeast. There were several hundred feet of scree descent before getting into more tundra. At about 12,100 feet, there is a bench that we considered following to the north, but we could not see a clear route through the dense willows farther down, so we turned more to the south and connected with a very old road shown on the map that led due south from a mining claim back down into the valley and the main road. It shows on the USGS map as a "jeep trail." This old road will diminish some of the willow-bashing problem though it is overgrown in spots and probably more so now. Once back on the main trail this will leave you with a little over a mile of walking to get back to your vehicle if able to drive to the end of the road.
Links to other information, routes & trip reports for this peak that may be helpful.