In a clean large mixing bowl, add the sugar, salt, yeast, whole wheat flour and the all-purpose flour. Mix it all thoroughly.
Drizzle in the olive oil and give it a quick mix. Then pour in the warm water and swiftly mix it through the dry ingredients.
Gently mix and bring all the ingredients together until a dough is formed.
Once the dough is formed, move it to a board or counter and begin kneading the dough by pushing and pulling it.* Continue kneading for 20 minutes. Take rest in between and ensure you cover the dough with a damp cloth while you do.
The dough will be soft and supple after kneading. Move it back to the slighlty oiled mixing bowl. Cover with its lid or a damp cloth. Let it rise for 1 hour or until the dough doubles in volume.
Preheat the oven for 20 minutes at 250 C / 480 F. Place a baking tray inside while preheating.
Once it had doubles, punch it down and transfer it to a counter. Divide the dough into 6-8 portions. Dust the counter with flour and roll out each portion in a disc with about 1/2-inch thickness.
Change sides as you roll them out and dust when it is likely to stick to you rolling pin. Do not use too much flour; use it only if it sticks too much.
Once you've rolled out all the portions arrange the discs in batches on the hot baking tray from the oven. Place the tray back inside the oven. Within 5 minutes, the dough will puff up thereby forming the pockets. Once all the discs puff up, let the pitas cook for few more minutes. In total, it would take 8-10 minutes.
Remove the tray and remove the pitas onto a thick cotton cloth. Keep it covered. Repeat the same process with the other discs. Your pita breads are ready!