A flight instructor and his student had a runway incursion citing lack of situational awareness.

Narrative

I was giving dual to an instrument/commercial student. Construction was in progress at the airport and we were given a taxi clearance to Runway 9 to takeoff from the Runway 5 intersection. After confirming our taxi instructions and runway feet available we taxied to the hold short line on Runway 5 and completed our run-up. My student can read; write and understand the English language but it is not his native language. Because of this possible translation problem I asked for progressive taxi instructions to our holding position. I had an airport facility directory taxi diagram onboard the aircraft; but after the incursion I found that a larger printed version of an airport diagram would have helped my situational awareness. We were cleared for takeoff; and we taxied to the centerline and set full power. I checked the compass reading as we were rolling into position and it appeared to show proper indication. Because we were making a rolling start; these instruments were not giving the most accurate indications. By the time I realized we were on the wrong runway the aircraft reached rotation of 55 KIAS and we were on the up-wind for Runway 13. ATC advised me that we departed off the incorrect runway and said; 'That is OK it is (Runway 13) an active runway. We could contact departure.' After the incursion happened I reviewed the items that would have helped prevent it. 1. I will ALWAYS have a blown up printed version of an airport taxi diagram. 2. The taxi route will be drawn out and reviewed before the aircraft is moved. 3. I should have let the compass stabilize before applying power and beginning the takeoff roll.