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This is an example of a matrix used to organize connections between concepts. In this example from the counting unit, a student who has answered the exercsise correctly, has explained why and organized that explanation into counting techniques. Eventually, this student can study just examples of separate cases by looking down that column and seeing how or why it's done in many different questions. Likewise, the student can look across and see an entire solution. The matrix can be used to connect all sorts of things, not just what is illustrated here.
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To begin creating your matrix, go to the tab below entitled "matrix".
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Counting Techniques
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Separate CasesCombinationsPermutations
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ProblemsHow many 13-card bridge hands consist of 7 of one suit, 5 of another, and 1 of yet another suit? 13C7*13C5*13C1*4P3Technique not used. Recognized by the fact that there is no situation where you need more than one quantity of one element.Required. Recognized by the fact that you need to count unique groups of seven cards in one suit, but you don't care which order, just as long as they're in your hand.Required to match a group of cards to a suit. Recognized it because there was no mention of a suit that the 7 cards could be. So it could be any of the four.
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How many passwords are there with 3 or 4 letters. Assume each letter is used only once.etc..
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Etc…
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