You might find that simple things such as the cardboard rolls from paper towels can be flattened and put in the RECYCLE bin! Packages can be folded up and put in the RECYCLE bin, too!
When you go shopping buy the BIG packs instead of little packages or multi packs. Use containers. Reuse containers! Have you finished with that coloring book or school notebook? Put it in the recycle bin. Take it to a book swap. Start a class swap for unused school supplies.