I found this activity in the resource book Five-Minute Activities by Penny Ur and Andrew Wright many years ago. I have done it hundreds of times during the course of my career.
Here’s how it works:

1. Write a list of 6-10 short sentences on the board. Good choices for the text are a dialogue or a story summary.
2. Read Sentence 1 aloud. Students repeat after you.
3. Erase a few words of the sentence and read it aloud again. Students repeat after you.
4. Continue erasing the sentence a few words at a time. After each erasure, say the entire sentence, and students repeat after you.
5. Ultimately all the words will be erased, and students will be reciting the sentence from memory.
6. Repeat Steps 2-5 with the remaining sentences, one by one.

Variation: 

1. One student reads Sentence 1 aloud and then calls out a word to be erased. You erase that word.  
2. The next student reads the sentence, including the missing word, and then calls out a second word to be erased. You erase that word.  
3. Continue around the class in this way until nobody is able to recite the sentence from memory or the whole sentence has been erased. 
4. Repeat Steps 1-3 with the remaining sentences.