Language Research

The verb concern can be followed by the prepositions with and about. Based on Longman dictionary, it defines "concern with/about" in one definition, to become involved in something because you are interested in it or because it worries you. The example sentence it gives for "concern with" is, He loved his wife and concerned himself with her needs and desires. The example sentence it gives for "concern about" is, He told them not to concern themselves about him."

Based on the the english-test.net's forum, http://www.english-test.net/forum/ftopic40513.html, "concern with" means involve with or on the topic of. "Concern about" means worry about. The sample usage sentence it gives is, the Department of Health is concerned with the welfare of the population and is concerned about the increase in the number of people smoking.

The English-test.net have a clearer definition between the two. From COCA, it provides these samples sentences: "The problem - the concern with global warming is the release of carbon dioxide, okay?" and "Other teachers enter into this work more slowly, often with great ambivalence and concern about its high level of demands."

Google titles also provide some example like, "Traffic safety is concern with new Fischer Crossings movie theater ..." and "Obama expresses concern about slowing economy - Yahoo! News".
Based on my research, "concern about" means "worry about" like, I'm concern about my mother's health. "Concern with" means worry about an issue like, I'm concern with the sluggish [sluggishness] of the economy.

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The word concern has many forms and uses. This assignment was to compare be concerned with and be concerned about. You have some examples of these phrases here from a website, but the examples from COCA are different.  One example from Google is not copied correctly:

• "Traffic safety is concern with new Fischer Crossings movie theater

You need the past participle form of concern in this sentence.
I think about should be used in this sentence:

• "Concern with" means worry about an issue like, I'm concern with the sluggish[sluggishness] of the economy.