The key competencies in the New Zealand curriculum fit perfectly with inquiry-based learning. If you are interested in developing the thinking skills of your students then check out the Thinking page.
Inquiry-based learning also provides a perfect context for the Participating and Contributing competencies. Students completing authentic inquiries such as some of these examples will be working on the skills and attitudes of the Participating and Contributing competency and many aspects of the Relating to Others, Managing Self and Using Language, Symbols and Texts competencies.
This presentation outlines some of the ways student inquiry can develop the key competencies.