I wanted to thank all of you for your suggestions and comments.
I learned a few valuable lessons yesterday afternoon. I went to Mike's Workshop, since he is closer than most. I spent about 1/2 with him and was given a lot of information and "hints". He gave me a few samples of various sizes of the Flying Dutchman and recommended that I get the #9 for my current project.
I didn't try them until this evening, a little nervous I guess... but so far, I've managed to cut out 2 hippos, 2 pigs and 2 porcupines all on the first blade. So far, so good! Previously, with my Craftsman blades, I was lucky to get one animal cut before the blade would violently "snap".
So yes, my tension was correct, my variable speed was correct, I was not pushing too hard, I was not pushing sideways...evidently the blades were "bad" or I had the wrong kind.
This is the 5th Arc I've made for my Grandchildren, I've made lots of simple puzzles, knick-knack shelves, Adirondack furniture, a 300 lb. picnic table, etc.- most of these were cut on my trusty old scroll saw for lack of other proper tools. So more of a reason for my being confused about snapping blades.
So again, Thank you all! Most of all,

Mike for your time and help and introducing me to a new blade (Flying Dutchman). You are a kind man and have a very kind wife as well!
DaVida