GA flight instructor with student reported an NMAC during approach to VUO non-towered airport requiring evasive action. Reporter stated frequency congestion contributed to the event as it prevented pilots from making position calls.

Narrative

The airport was encountering heavy traffic. My student and I were remaining in a closed traffic pattern practicing landings. Multiple aircraft were reporting inbound to land on Runway 08. Having most of my experience flying at VUO; I was able to determine with the multiple calls made that there was enough distance for my student and I to continue as normal on the downwind and proceed to the base leg of the pattern without disruption. I had two inbound aircraft in sight to the north of the airport and felt a safe distance from them. However with the 5-7 close by/inbound aircraft; the CTAF frequency was congested and it was difficult for anyone to make position calls. When we turned a left base for Runway 08; Pearson Advisory called us and advised to use caution because there was another aircraft just left of us near the same altitude. The 430-GPS indicated it was to the right. I then had another aircraft in sight on base to final to the right about 500 feet horizontal and 100 feet vertical. I took the controls of the aircraft and sharply turned final for 08; began a quick descent; then made a traffic pattern call that we were on final. The other aircraft performed a go-around maneuver. From my perspective in the fast moving situation; I believe we were at the lower altitude which is why I chose to continue on final. I was unable to get the tail number of the other aircraft. I landed the plane without issue and taxied to the parking spots. No further action took place; I did not speak to the other pilot.