Mathematical Practice: MP7 - Look for and make use of structure.

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  • MP1 - Make sense of problems and persevere in solving them. (9)
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  • MP5 - Use appropriate tools strategically. (3)
  • MP7 - Look for and make use of structure. (7)
  • MP8 - Look for and express regularity in repeated reasoning. (6)

Liar’s Bingo

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From recognizing a pattern to generating terms, to abstracting and making inferences, tasks based on patterns embody the “low-threshold, high-ceiling” trait of good problems. Liar’s Bingo is all about patterns. This session involves recognizing patterns and searching for underlying structure, number theory, numeration, and potentially binary arithmetic. Sometimes, as in...

Lockers: An Open-and-Shut Case

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A classic Math Circle problem! At a large high school, there are 10000 lockers. The lockers are numbered, in order, 1, 2, 3, . . . , 10000, and to start, each locker is closed. There are also 10000 students, also numbered 1, 2, 3, . . . , 10000....