Making my own definitions

Due to the heavy snow, I was late for my first class this week and it seems that the main focus now was still folding paper, same as the second class last week. However, the difference was to find a pattern for the folding paper instead of simply looking at how the paper behaves. I thought it over but I could not find a pattern unless the prof gave us some hints. He asked us to keep the middle line of the crease and watch its pattern on the right side. It turned out that its right side pattern was the same as the previous pattern of the folding paper. I got it now.
Then I received a piece of exercise paper and I was totally confused what I was supposed to do according to this paper. I did not understand what was check-expect for. Should I enter all of the sentences in Dr.Racket?  What was the difference of the define thing and check expect? Were both of the steps of definition and check-expect missing something? I was stuck there and waiting for a TA to help me. Maybe I would get myself understood after I watched Dr.racket definition videos.
 Then, I went through all the definition videos. Those videos were very helpful and I learned how to make definitions and combine pictures. However, for check expect, I still didn't get it even I watched those videos.
For this week, I learned new things-making my own definition and I didn't figure out the part about check expect, but I would find someone to help me and I will know it before next week because I don't want to fall behind. Also, Thursday's class was like a history class which taught us past time's technology for computing. At least, it helped me to know computer's history but I preferred programming classes more, for example, practice Dr.Racket on your own laptop.