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Believe it or not, teachers around the world teach continents differently! Here in Canada, we teach seven continents: Asia, Africa, Antarctica, Europe, North America, South America and Oceania (Australia). Other countries may teach six continents: Africa, Antarctica, North America, South America, Eurasia and Australia (or Australasia). Some places (such as Spain) teach five continents with North America and South America combined as a single continent called the Americas.
Geographically a continent is a large, discrete land mass separated by large bodies of water -- by this scientific definition there are only four continents: Antarctica, Australia, Americas and Afro-Eurasia. However, children at a grade school level are almost never taught using a four continent model. Most educators take geography, politics and history into account when deciding how to split our world up into continents.
For older students, it's an interesting debate topic to discuss the definition of a continent. Should the Americas be taught as one since their land masses are connected? Should Europe and Asia be combined despite their very different histories and customs? Should a large island like Greenland be considered its own continent -- how "large" is large enough? Should a vitually unpopulated island like Antarctica be considered a continent -- do continents need governments, history, people and politics?