Can I share class files with parents?

Sure!

Go to Classes and pick your class. Then click Files in the left menu. You can now select a file and upload it to the class.

Your file is displayed in the file list. Now give the file a name and click Save. This name is displayed to parents.

 Now click the Share in Portal button. There also is an option to add this file to a Registration Email. 

Parents can now view that file in the Documents & Files section of the portal.

Related Articles: 

How do I add files for specific classes to my registration email?