Rachel:
This sounds like a great idea. I would add that if the material is important, why is it not included in the required curriculum?
Another way to look at it is to assign those "extra chapters", and reward the students that took the time to complete them by non-point based recognition, such as naming students who turned in the EC, or reading from the submitted work and crediting the student that submitted it. The thing about EC is it is often arbitrary, and some students can feel it's unfair (gives some students an advantage because it's not required).
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