You will need a large bread bowl, a rolling pin, and unglazed quarry tiles or several baking sheets, or alternatively a castiron or other heavy skillet or griddle at least 9 inches in diameter.
Sprinkle the yeast over the warm water in a large bread bowl. Stir to dissolve. Add whole wheat flour, one cup at a time, then 1 cup white flour. Stir 100 times (one minute) in the same direction to activate the gluten in the flour. Let this sponge rest for at least 10 minutes or as long as 2 hours.
Sprinkle salt over the sponge and stir in the olive oil. Mix well. Add white flour, one cup at a time. When the dough is too stiff to stir, turn it out onto a lightly floured bread board and knead for 8 to 10 minutes, until dough is smooth and elastic. Return the dough to a lightly oiled bread bowl and cover with plastic wrap. Let rise until at least double in size, approximately 1 1/2 hours. Gently punch down. Dough can be made ahead to this point and then stored, covered, in the refrigerator for 5 days or less.
If at this time you want to save the dough in the refrigerator for baking later, simply wrap it in a plastic bag that is at least three times the size of the dough, pull the bag together, and secure it just at the opening of the bag. This will give the dough a chance to expand when it is in the refrigerator (which it will do). From day to day, simply cut off the amount of dough you need and keep the rest in the refrigerator, for up to one week. The dough will smell slightly fermented after a few days, but this simply improves the taste of the bread. Dough should be brought to room temperature before baking.
This amount of dough will make approximately 16 pitas if rolled out into circles approximately 8 to 9 inches in diameter and less than 1/4-inch thick. You can also of course make smaller breads. Size and shape all depend on you, but for breads of this dimension the following baking tips apply:
Place unglazed quarry tiles, or a large baking stone or two baking sheets, on a rack in the bottom third of your oven, leaving a one inch gap all around to allow air to circulate. Preheat oven to 450 degrees. Divide dough in half, then set half aside, covered, while you work with the rest. Divide dough into eight equal pieces and flatten each piece with lightly floured hands. Roll out each piece to a circle 8 to 9 inches in diameter. You may wish to roll out all eight before starting to bake. Cover rolled out breads, but do not stack.
Bake 2 at a time (or more if your oven is larger) directly on quarry tiles or baking sheets. Bake each bread for 3 or 4 minutes, until the bread has gone into a full "balloon" or until it is starting to turn lightly golden, whichever happens first. If there are seams or dry bits of dough - or for a variety of other reasons - your bread may not go into a full "balloon". Don't worry, it will still taste great. The more you bake pitas the more you will become familiar with all the little tricks and pitfalls, and your breads will more consistently "balloon." But even then, if you're like us, it won't always "balloon" fully and you won't mind because the taste will still be wonderful. When baked, remove, place on a rack for about five minutes to let cool slightly, then wrap breads in a large kitchen towel (this will keep the breads soft). When first half of the dough has been rolled out and baked, repeat for rest of dough, or store in refrigerator for later use, as described above. You can also divide the dough into more, smaller pieces if you wish, to give you smaller breads.