Verbs show the action or state of a noun. "I have a broken leg" is the state of the person in the present tense. Other stative verb sentences could be "I have a bad cold" or "I am really sick." "Broken" is an adjective in this sentence.
"I broke my leg" is referring to an action that happened in the past tense. It is focusing on what happened sometime before now. Other action verb sentences could be "I coughed all night" or "I sneezed three times before I got out of bed." "Broke" in this sentence is the main verb.
Ask the students: When is the speaker referring to? Before now or now? Then ask: What is the main idea the speaker wants to communicate? What happened (action) or how he/she is (state).
Try using different examples, such as "I have a crashed car" and "I crashed my car." Have the students act out the sentences to get the idea.
Look up verbs that change into adjectives for other examples. You could give them a list and make sentences together as a class or in small groups.
Cheers!