Driving from Takayama to Shirakawa-go

Hi, we are planning to drive from Takayama to Shirakawa-go in December. Since there are 6 people, we figure that it would be cheaper to rent a car rather than to take the bus.

I have tried using Google Maps to find out the route that we should be taking:
http://maps.google.com.au/maps?f=d&saddr=%E9%AB%98%E5%B1%B1&...

Does that look correct or is there another route that would be easier/faster...?

Do I need to hire snow tires or chains to drive along this route during this period?

Many thanks

Google Map is out of date!

It does not show the new section of expressway which was opened between Takayama and Shirakawa-go in July this year.

By far the fastest way is to travel along that new section of expressway. It is explained here:
http://www.japan-guide.com/e/e5953.html

We did this a few weeks ago Will,and really enjoyed it. Even for two it was cheaper than the bus ( Nissan 3 day specials on Tocoo ). We took the small back roads as we weren't in a hurry and enjoyed the foliage colours and the empty roads. Thought S-go was ok but Gujo Hachiman was so much better. We went on to Matsumoto for a great drive (again cheaper than bus) for only $30 extra drop off fee.

Thanks for the responses, Uji and Connie Chiwa (:D).

I had a look at Wikipedia and Yahoo Maps Japan (hoping their map is newer than Google's) - so as I understand it:
- The portion from Takayama IC to Hida-kiyomi is not part of the Tokai-Hokuriku Expressway, but instead it's a National Route 41 & 158 (Chubu-Juban Expressway?)

- This is the picture of the Takayama IC...?: http://upload.wikimedia.org/wikipedia/commons/6/66/Takayama-...

- Up until Hida-kiyomi there is no toll?

Thanks!

Will