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Investigation 5.1
   The Locker Problem
NEW LOCKERS!!!!
NEW LOCKERS!!!!
✤   There are 1,000 new lockers installed here at
    ISB. In preparation for issuing them to
    students, the Building and Grounds crew
    has cleaned them and painted numbers on
    all of them.
NEW LOCKERS!!!!
✤   There are 1,000 new lockers installed here at
    ISB. In preparation for issuing them to
    students, the Building and Grounds crew
    has cleaned them and painted numbers on
    all of them.
✤   The lockers are numbered from 1 to 1,000.
NEW LOCKERS!!!!
✤   There are 1,000 new lockers installed here at
    ISB. In preparation for issuing them to
    students, the Building and Grounds crew
    has cleaned them and painted numbers on
    all of them.
✤   The lockers are numbered from 1 to 1,000.
✤   Before issuing the lockers, the math teachers
    thought it would be fun to make a math
    problem out of the lockers for students to
    solve.
Let’s See What Happens
Let’s See What Happens
✤   The first student, Student 1, runs
    down the row of lockers and opens
    every door.
Let’s See What Happens
✤   The first student, Student 1, runs
    down the row of lockers and opens
    every door.
Let’s See What Happens
✤   The first student, Student 1, runs
    down the row of lockers and opens
    every door.


✤   Student 2 closes the doors of
    Lockers 2, 4, 6, 8, and so on to the
    end of the line.
More students ...
More students ...
✤   Student 3 changes the state of the doors of
    Lockers 3, 6, 9, 12, and so on to the end of
    the line. (This means the student opens
    the door if it is closed and closes the door
    if it is open.)
More students ...
✤   Student 3 changes the state of the doors of
    Lockers 3, 6, 9, 12, and so on to the end of
    the line. (This means the student opens
    the door if it is closed and closes the door
    if it is open.)
More students ...
✤   Student 3 changes the state of the doors of
    Lockers 3, 6, 9, 12, and so on to the end of
    the line. (This means the student opens
    the door if it is closed and closes the door
    if it is open.)


✤   Student 4 changes the state of the doors
    of Lockers 4, 8, 12, 16, and so on.
More students ...
More students ...

✤   Student 5 changes the state of
    every 5th door, Student 6 changes
    the state of every 6th door, and so
    on, until all 1,000 students have
    had a turn.
Consider this question ...
Consider this question ...


✤   When all students have
    finished, which locker
    doors are open?
LET’S TRY IT!
LET’S TRY IT!
• After completing the group task ...
  head back to Grade 6 classrooms
  and continue to explore which
  lockers remain open ...
LET’S TRY IT!
• After completing the group task ...
  head back to Grade 6 classrooms
  and continue to explore which
  lockers remain open ...
LET’S TRY IT!
• After completing the group task ...
  head back to Grade 6 classrooms
  and continue to explore which
  lockers remain open ...


• but more importantly, WHY???

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Locker Problem

  • 1. Investigation 5.1 The Locker Problem
  • 3. NEW LOCKERS!!!! ✤ There are 1,000 new lockers installed here at ISB. In preparation for issuing them to students, the Building and Grounds crew has cleaned them and painted numbers on all of them.
  • 4. NEW LOCKERS!!!! ✤ There are 1,000 new lockers installed here at ISB. In preparation for issuing them to students, the Building and Grounds crew has cleaned them and painted numbers on all of them. ✤ The lockers are numbered from 1 to 1,000.
  • 5. NEW LOCKERS!!!! ✤ There are 1,000 new lockers installed here at ISB. In preparation for issuing them to students, the Building and Grounds crew has cleaned them and painted numbers on all of them. ✤ The lockers are numbered from 1 to 1,000. ✤ Before issuing the lockers, the math teachers thought it would be fun to make a math problem out of the lockers for students to solve.
  • 7. Let’s See What Happens ✤ The first student, Student 1, runs down the row of lockers and opens every door.
  • 8. Let’s See What Happens ✤ The first student, Student 1, runs down the row of lockers and opens every door.
  • 9. Let’s See What Happens ✤ The first student, Student 1, runs down the row of lockers and opens every door. ✤ Student 2 closes the doors of Lockers 2, 4, 6, 8, and so on to the end of the line.
  • 11. More students ... ✤ Student 3 changes the state of the doors of Lockers 3, 6, 9, 12, and so on to the end of the line. (This means the student opens the door if it is closed and closes the door if it is open.)
  • 12. More students ... ✤ Student 3 changes the state of the doors of Lockers 3, 6, 9, 12, and so on to the end of the line. (This means the student opens the door if it is closed and closes the door if it is open.)
  • 13. More students ... ✤ Student 3 changes the state of the doors of Lockers 3, 6, 9, 12, and so on to the end of the line. (This means the student opens the door if it is closed and closes the door if it is open.) ✤ Student 4 changes the state of the doors of Lockers 4, 8, 12, 16, and so on.
  • 15. More students ... ✤ Student 5 changes the state of every 5th door, Student 6 changes the state of every 6th door, and so on, until all 1,000 students have had a turn.
  • 17. Consider this question ... ✤ When all students have finished, which locker doors are open?
  • 19. LET’S TRY IT! • After completing the group task ... head back to Grade 6 classrooms and continue to explore which lockers remain open ...
  • 20. LET’S TRY IT! • After completing the group task ... head back to Grade 6 classrooms and continue to explore which lockers remain open ...
  • 21. LET’S TRY IT! • After completing the group task ... head back to Grade 6 classrooms and continue to explore which lockers remain open ... • but more importantly, WHY???

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