We study open-shop and flow-shop scheduling for unit jobs under precedence constraints, where if one job precedes another job then it has to be finished before the other job can start to be processed. For the three-machine open-shop or flow-shop to minimize the makespan, we first present a simple 5/3-approximation based on a partition of the job set into agreeable layers using the natural layered representation of the precedence graph. We then show a greedy algorithm to reduce the number of singleton-job layers, resulting in an improved partition, which leads to a 4/3-approximation for open-shop scheduling. For flow-shop scheduling, we also present an improved algorithm with performance ratio 3/2. All the approximation algorithms apply to the general m-machine open-shops and flow-shops too.