When I find myself in possession of a bunch of scrap triangles, the first thing I do is sort them by angle and then by size. I search for a pair that are generally the same shape and size and then sew them together to make a square or rectangle. I make a lot of these little blocks and set them aside in a pile.
When the pile gets big enough or I get tired of matching and sewing, I start sewing the blocks into rows or squares. If you do rows, you have your choice of two patterns, which I call "sawtooth" and "mountain." In a sawtooth pattern, all the triangles point the same way, like a line of Rockettes. In a mountain pattern, they're arranged in pairs, back to back to make, well, mountains. Of course, you can mix and match your patterns at will.
If you do squares, you usually sew four or nine blocks together, and have your choice of various arrangements that are familiar from traditional quilts, such as pinwheel or broken dishes, in addition to sawtooth and mountain. If you go to sixteen blocks you can use any of the myriad traditional patterns such as card trick or dutchman's puzzle. Or you can just sew the squares together at random without worrying about a specific arrangement.
Now that you've sewed some of the blocks together to make rows or squares, put them back on the design wall to see what they want to do next. You may want to sew the rows or squares into larger modules, or you may want to frame them with some larger pieces of fabric.
You can do this kind of free-association piecing at any degree of precision. If you find yourself with a bunch of triangles that were all cut to size for a previous project, your blocks will all end up the same size and you might like to square them up and use a more traditional arrangement. If they are random sizes, they probably won't fit together without some creative manipulation. If you want to sew two blocks together and they aren't the same size, add a strip of fabric to the small one to make it the same size. Or sew two blocks to three. Or whatever else seems to work.
Let me know how your quilt date works out! If you want to send me a picture of what you made, I’d love to post it.