We present a steady-state analysis of threshold-ALOHA, a distributed age-aware modification of slotted ALOHA. Under threshold-ALOHA, each source remains passive until a certain age threshold G is reached. Nodes whose ages exceed the threshold attempt transmission with a fixed probability t in each slot. We study the scaling of the time average Age of Information (AoI) with the network size, n. We derive the distribution of the number of active users and establish that the policy converges into a slotted ALOHA with fewer participants, specifically, approximately one-fifth of all users under age-optimal parameter settings. We derive an expression for the average AoI and obtain that the optimal age threshold and transmission probability scale respectively as 2.2n and 4.69/n. We show that optimal AoI scales linearly as 1.4169n, at nearly half the minimum slope achievable using slotted ALOHA, while the loss from the maximum achievable throughput of e(-1) remains below 1%.