The next three pages are about the exploits of the Waka Matawhaorua and Ngätokimatawhaorua  for you to read. I have also published a tribal research paper on my iwi Te Rarawa, that I did in 1998 for a Massey University assignment. It is the result of a lot of work and has some whakapapa in it as well. It's a long read but hopefully an enjoyable one. Click on the link below to read it and please give me feedback about it. Kia ora rawa atu!
Check it out: Te Rarawa tribal research paper
Kupe left Hawaiki in his waka the Matawhaorua and travelled in search of the fish of his ancestor, Te-Ika-a-Mäui. He had chased Te Wheke Muturangi (a great octopus) during this search. While approaching what Kupe believed to be Te-Ika-a-Mäui, the wife of Kupe, Kuramärotini, saw the Southern Alps from a distance. She thought they were a cloud (an indication of land) and exclaimed "He ao! He ao!" (A cloud! A cloud!"). As they drew closer she exclaimed "He aotea, he aotearoa!" (A white cloud, a long white cloud!). From this, the name given to this new land was Aotearoa; referring to the land of the long white cloud seen by Kuramärotini.
Kupe had a travelling companion, Ngahue, who travelled in his waka the Tawhirirangi.
Kupe confronted Te Wheke in many places around Aotearoa finally defeating it at the entrance to Totaranui (Queen Charlotte Sound) at Kura Te Au (Troy Channel). He struck Te Wheke with his toki named Te Raka Tü Whenua. He then changed weapons to a great patu made of whale bone and finally defeated Te Wheke.
This
battle has lived on in history and is evident in the distinctly Northern
carving style, in particular Ngä Puhi Nui Tonu. This is
easily recognisable in the smooth round head shape on carvings which, it
is said, derives from the head of Te Wheke Muturangi, that so gallantly
fought with Kupe.
Kupe travelled around Aotearoa naming many places along the way. In particular he named two islands in Te-Whanga-nui-a-Tara (Wellington) after two of his daughters Matiu and Makaro.