Nagoya to Takayama

Hi! I intend to travel with my family from Nagoya to visit Shirakawa-go and Tateyama but I am not clear on whether or not I should by JR passes.

Our itinerary is to arrive and stay at Nagoya 2D on April 7-8 to explore Nagoya City.
On April 9th Day 3, we depart for Takayama. Upon check-in at Takayama, we plan to visit Shirakawa-go in the afternoon. If we have time we can proceed to Gokayama.
On April 10th, Day 4, the following morning, we scheduled going to the Kurobe Alpine route but I heard the route is only partially open from April 10-14. So we need to do a return trip to Takayama in the late afternoon or early evening.
On April 11th, Day 5, explore Takayama
On April 12th, Day 6, return to Nagoya.
Day 7, fly home.
On this itinerary, do you recommend to buy a JR pass? How many days pass?

Hope you can help. Much thanks!

Denise