I know you are asking how you would know which roots are Latin and which are Greek, but I also feel the need to briefly explain why I did not include this information in the curriculum. The reason I did not list the Latin or Greek derivations is because I don't think it's that important in what we are trying to teach our children about unlocking the meanings of words. These are not actual Latin or Greek lessons - they are just vocabulary building tools. In high school I took a course on Semantics/Word Origins. I don't recall learning specific derivations - at least I don't remember learning them - but I DID learn the meanings of the prefixes, suffixes, and roots, which helped me greatly in my future college education and in everyday life. There is SOOOO much to learn out there in our great, big, wonderful world - and sometimes we have to stop and examine whether or not every single piece of information is useful to us at a certain point in our lives. This curriculum was written for grades 4-8 - my goal in including the roots was to introduce your children to a WONDERFUL key - something that would help them unlock the meanings of words for the rest of their lives. It is soooo much more important for your children to remember that the word chronos means time, instead of knowing that it came from the Greek. I also think that by introducing your children to these roots now, that you are sparking their interest in studying Latin in their high school years! I know some methods of study advocate a strong Latin program for intermediate-age children, but I'm not so sure that I completely agree with that. I think that you can introduce your children to Latin and other languages in their younger years in less "formal" ways so that they are ready to tackle the more formal language programs in high school (or in the late junior high years). So . . . that's WHY I presented the roots the way I did - without derivations.
Now, I'll tell you how to find out WHICH they are - Latin or Greek: if you REALLY want to know what the derivation is, simply look in your dictionary and it will tell you! We do a study of this in the Greek unit - see Day 36 for instructions if you haven't gotten there yet. If you feel that the derivations are really important to include . . . GO FOR IT!
Hope this helps!