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Locker Problem

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Visit this site: http://mathforum.org/alejandre/frisbie/student.locker.html

Author:Suzanne Alejandre
Description: A classroom activity (also called 1000 Lockers) aligned to the NCTM and California Standards, to be explored through the use of manipulatives and a ClarisWorks spreadsheet. Students then look for patterns and write the answer algebraically. The problem: imagine you are at a school that still has student lockers. There are 1000 lockers, all shut and unlocked, and 1000 students. Suppose the first student goes along the row and opens every other locker. The second student then goes along and shuts every other locker beginning with number 2. The third student changes the state of every third locker beginning with number 3. (If the locker is open the student shuts it, and if the locker is closed the student opens it.) The fourth student changes the state of every fourth locker beginning with number 4. Imagine that this continues until the thousand students have followed the pattern with the thousand lockers. At the end, which lockers will be open and which will be closed? Why? A teacher lesson plan is provided.

Levels: Late Elem. (3-5), Middle School (6-8), High School (9-12)
Languages: English
Resource Types: Manipulatives, Lesson Plans and Activities, Problems/Puzzles, Link Listings, General Software Miscellaneous
Math Topics: Basic Algebra, Patterns/Relationships, Logic/Foundations
Math Ed Topics: Manipulatives, Simulations, Standards

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