Take the Garnet Canyon Trail - it's the same one that leads to the standard route on the Grand - and follow it to about 10,750 or so. At this point it's fairly apparent where to go, as the Middle Teton Glacier sits directly to the south, and can be seen slanting up the mountain. Leave the trail and head toward the glacier, which is where the climbing begins.
The first 3-5 piches - the number vary depending on the condition of the glacier - are straightforward and not too technically difficult. There's only one way to go... straight up the glacier. A bergschrund must be passed, and then the glacier narrows into a snow couloir. This couloir steepens - there's exposure but if conditions are good the climbing's great. The couloir leads to a small col between the Dike Pinnacle (to the southeast) and the main body of the Middle Teton (the bulk of the mountain is to the northwest).
From here, head up slabby rock to the northwest - in ideal conditions the climb should go at 5.3-5.5, but when the rock is wet the route is harder. Likewise in early season snow and ice can be found here... sometimes the entire route can be done without any rock climbing. Around 900 feet of climbing brings you to the summit of the Middle Teton. Remember to stay north when you can, as the Middle Teton has two summits - the true north one and a lower summit to the south. A rappel is needed to descend from the south summit if you reach it by accident.
The easiest (and best) way down is to descend the Southwest Couloir route.
Crampons and an ice tool are needed; two ice tools are recommended. Also bring a light climbing rack and rope.
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