'Could';'couldn't'; 'managed to'

 Certainly! Here's a chart to help explain the differences between "could," "couldn't," and "managed to":

Modal Verb	Meaning	Example Sentence
Could	Past ability or possibility	When I was younger, I could run a mile in less than 6 minutes.
Couldn't	Inability or failure to do something	I couldn't hear what she was saying over the noise.
Managed to	Achieved or succeeded in doing something	Despite the difficulty, I managed to finish the project on time.

Note: The meanings listed in the chart are not exhaustive, but provide a basic overview of their primary uses.

I hope this chart helps you understand the differences between "could," "couldn't," and "managed to"!

Here are some exercises to help practice using "could," "couldn't," and "managed to" correctly:

1. Complete the sentences with the appropriate form of "could," "couldn't," or "managed to":

• She __________ convince her boss to give her a raise. (could/couldn't/managed to)
• We __________ find a parking spot near the theater. (could/couldn't/managed to)
• He __________ swim across the lake when he was younger. (could/couldn't/managed to)
• They __________ finish the project on time, despite the obstacles. (could/couldn't/managed to)

2. Write sentences using "could," "couldn't," and "managed to":

• I __________ find my lost keys after searching for hours. (could/couldn't/managed to)
• She __________ run a marathon last year, even though she had never done it before. (could/couldn't/managed to)
• They __________ understand the instructions without any help. (could/couldn't/managed to)

Answers:

1. could, couldn't, could, managed to
2. managed to, could, could

I hope these exercises help you practice using "could," "couldn't," and "managed to" correctly!