6: Advanced Additive - Proportions and Ratios

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The 57 students from Kapai school are going on a trip. Two thirds of the students can fit in a bus and the rest are going by car. How many are going on the bus?


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Student: I need to work out one third of fifty-seven first. Three times ten equals thirty. Three times five equals fifteen, so that's forty-five. You need twelve more, and that's three times four. Ten plus five plus four is nineteen and that's one third of fifty-seven. So two thirds of fifty-seven is nineteen plus nineteen and that's thirty-eight.

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Students at the Advanced Additive stage are learning to choose appropriately from a repertoire of part-whole strategies. They see numbers as whole units in themselves but also understand that “nested” within these units is a range of possibilities for subdivision and recombining.