Unraveling the Locker Problem

Unit 1 – Investigation 3.4 ”Unraveling the Locker Problem” FQ: What characteristics of numbers, such as factors and multiples did you use to answer the questions? What special numbers such as prime numbers, composite numbers and square numbers, did you use? A:______C: ______E: ______

The Locker Room Challenge

 Student 5 changes the state of every fifth door.  Student 6 changes the state of every sixth door.  The pattern continues until all 1,000 students have had a turn.

Challenge Question: When all 1,000 students have finished, which locker doors are open?

Use what you learned so far in this Unit to answer these questions. A. Model the Locker Problem for the first 30 students and the first 30 lockers. Fill out the first 12 students on the table below and whether the locker door would be open or closed. Use any strategies you want to simulate the following 30 students.

1 2 3 4 5 6 7 8 9 10 11 12 Student s (below) Locker #  Stude nt 1 Stude nt 2 Stude nt 3 Stude nt 4 Stude nt 5 Stude nt 6 Stude nt 7 Stude nt 8 Stude nt 9 Stude nt 10 Stude nt 11 Stude nt 12

1) What patterns do you see as the students put their plan into action? ______

2) When the 30 students are finished, which locker doors are open? Explain why your answer makes sense. What kind of numbers are these? ______

3) When the 1,000 students are finished opening and closing the 1,000 lockers, which locker doors are open? Explain why your answer makes sense. What kind of numbers are these? ______

B. 1) Which lockers were touched by exactly 2 students? Give 3 examples. What kind of numbers are these?

2) Which lockers were touched by exactly 3 students? Give 3 examples. What kind of numbers are these?

3) Which lockers were touched by exactly 4 students?

B1) B2) B3)

4) How can you determine exactly how many students have touched a given locker? ______

C. For Questions 1-4, find the number of the first locker touched by both students.

1) Student 6 and Student 8 2) Student 12 and Student 32

3) Student 7 and Student 13 4) Student 100 and Student 120

C1) C2) C3) C4)

5) Given 2 student numbers, how can you determine which locker will be the first locker touched by both students? How can you determine which locker will be the last touched by both students?

I can determine the first locker touched by both students by ______

I can determine the last locker touched by both students by ______D 1) Which students touched both Locker 24 and Locker 36?

2) Which students touched both Locker 100 and Locker 120?

3) Which students touched both Locker 42 and Locker 273?

D1 D2 D3

4) Given 2 lockers, how can you determine which students touched both?

______