How to provide more opportunities for students to listen intensively was the subject of the tip two weeks ago. The following suggestion kills two birds with one stone: it practises intensive listening and also raises awareness of sentence stress. It can be adapted for any level. In my experience, by highlighting and practising sentence stress, other features of connected speech naturally fall into place.
1 Take a recording that you are using in class which is spoken very naturally. Isolate a sentence (or two) which you think a) students will initially find challenging to understand because of the fluidity and phonological features (not due to the complexity of words/structures/syntax), and b) which shows some naturally-occurring examples of the features of sentence stress, eg accented content words; weak forms; linking.
2 Annotate this sentence in advance of the lesson, so that you are familiar with sound changes, sound omission, weak forms, linking, etc.
3 In class, after students have listened to the whole text for content (eg after comprehension), ask students to listen to your sentence and say how many words are in the sentence.
4 Elicit the exact words to the board, replaying the recording repeatedly, as necessary.
5 Once complete, ask students to listen to the sentence again.
6 First, elicit which words are stressed in the sentence and mark this on the board, using colours.
7 Then elicit any other features worth noting, using different colours, eg linkage, elision, weak forms, etc.
8 Drill the sentence. Break it into parts to help, if necessary back-chaining (starting from the end and working backwards in phrase units). Drill chorally and individually.
9 When you think students sound fluent, challenge them to repeat the sentence at the same time and speed as you/the original speaker.
10 Repeat with one or two other example sentences, if appropriate.
11 Let students listen to the whole recording whilst reading the audioscript, attending to the way it is said.