You don't need to hear/understand every word being spoken. We need to tell our students this!

Prominent sentence stress signals that information is new or pertinent. 

Knowledge of stress and intonational promince helps your students listen. Have students listen for the stressed words. These are the words with important meaning. Students do NOT have to hear and understand all the words in a sentence to understand. Say I listen to the following sentence, "They go to the lake at the end of the summer". But say I only hear: 

I can nonetheless understand the message being spoken.

Teach your students about stress and prominence. And encourage your students to guess what they don't catch. A knowledge of how important words and grammar words are actually spoken will help. Your students need to know.