1. Mix water, oil, sugar, yeast, salt, and whole wheat flour with a wooden spoon until smooth. Stir in all-purpose flour to form a shaggy mass.
2. Knead the dough until it becomes smooth and elastic (10-12 minutes), adding only very small amounts of flour if dough is too sticky to work. Form into a ball.
3. Oil a clean bowl and place the dough inside, turning once to oil. Cover bowl with a damp cloth and let rise in a warm place for 1 hour.
4. Place a baking stone on the top oven rack and preheat oven to 500 degrees F.
5. When dough has risen, punch down the dough, transfer to a lightly floured surface, and cut into 6 equal pieces, forming into balls. Cover with damp towel and rest for 10-15 minutes.
6. Roll each ball into an even circle about 1/4 inch thick. Place circles on a lightly floured surface, cover with a damp towel and proof until puffy (15-20 minutes).
7. Pick up one pita at a time and place onto the heated baking stone. Bake until pitas are puffed and lightly brown (3-4 minutes). Serve warm for the best flavor.