In addition to your child's overall MAP math score, do you have the report which mentions skills attained, and indicates next skills in the progression, to learn? Using those descriptions to match to a curriculum may help take some of the guess-work out of placement.

A description of what is contained in each of the "Life of Fred" math books may be found online here.

Another possible approach may be to compare the Common Core Standards for Math with a curriculum...
Here is a link to CC 4th grade math.