This was always one of my favorite classic genetics activities to do in biology class. I used to always do it on paper with my students and last year I rebuilt it in 3 google docs to go paperless.
In regards to adapting this to NGSS and taking it to the next level, I am open to suggestions. I will be working on finishing the F2 generation (grandchildren) and Pedigree Docs in the near future.
Students create the monster with over a dozen different traits, many of which are real-life examples such as blood type and freckles. Then they marry off and mate their monster (not like they really need to marry but we always had fun with that I even had the school band record a monster wedding song) and create 4 children.
This is 3 google docs that you can customize if you want.
The little monster slides template
The instructions for Part 1 which is prediction and the punnet squares
The instructions for Part 2 which is the actual acquisition of gametes via good ole fashioned luck (coin flipping)