Got the ball rolling!

Try to find and figure out the meaning of the following words and phrases as they occur in the passage below: utter,went about their business, hit it off, transpired, feeling buzzed, get the ball rolling,positive take,got into the act
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Wow! That was quite an amazing class! I really enjoyed today's English lesson with my Freshman International Relations group.
They got into five new base groups of four each. Without uttering a single word in Japanese they went about their business of getting to know each other in their groups one pair at time. After they had all had a chance to pair up with each member in the group they then started a full on group discussion. It was quite a satisfying sight to see them hitting it off with each other so well,but they were not finished yet as they started shouting across the room to other groups asking about interesting things that may have transpired in the other groups.It was a group to group encounter that left everyone feeling buzzed.
I think it was my newest student Ourai and Ayumi who really got the ball rolling today. Ourai's self-introduction about his coming to Japan from China, including his very positive take on what he likes about both countries seemed to inspire everyone from the start.Then when it was time for the groups to reach out and engage the other groups it was Ayumi's turn to get the ball rolling.She displayed a tremendous amount of confidence which she attributed to her recent travel abroad to Ohio.Anyway it wasn't long before all the students got into the act and created a very memorable day for all of us.
Many thanks from Ken