期 period of time

That month was the period of time when we studied KEYS.

expectations ★★★★☆
期 (period of time) + 待 (wait) = 期待 (expectations)

Expectations. For example, 今回は負けたけど、次に期待しよう！　（こんかいはまけたけど、つぎにきたいしよう！） We lost this time, but I expect we'll win next time!
Or, I expect that my students will give at least 33% effort.

semester ★★☆☆☆
学 (knowledge) + 期 (period of time) = 学期 (semester)

period of time ★☆☆☆☆
期 (period of time) + 間 (a period of time) = 期間 (period of time)

period of time, usually several months. Or years. Precise, socially constructed time, not seasons or shit. 期間 is more like summer vacation. You are forbidden to enter Japan for a period of five years.

natural period of time ★☆☆☆☆
時 (time) + 期 (period of time) = 時期 (natural period of time)

period of time - refers to a natural or social phenomenon : rainy season, the time that you can see fall leaves, the humid time of year.