Here's some websites that have free patterns. You can find pattern for all the projects on this page.
If you would like to decorate/embellish a hat, here's a cute pattern for Teeny Tiny Hearts!
Hats & Scarves
Best Hats For All!, which has both knit and crochet patterns, from Red Heart
Here's a great Snowboarder Hat Knitting Pattern, an earflap hat!
Here's a variety of hat and scarf patterns from Fave Crafts
Note: For knitted or crocheted scarves, the longer lengths would make for heavy scarves. So please use this guide:
Jr./Sr. high and adult - about 6' (72"!)
4th - 6th grade - about 5' (60"!)
1st - 3rd grade - about 4' (48"!)
Shawls / Wraps
Shawls / Wraps: they can be either long rectangular (2'-2.5' wide and 4'-5' long) or triangular (about 5’-6’ on the long edge)