Student 2 closed Locker 2 and every second locker after it.
Student 3 closed Locker 3 and changed the state of every third locker after it. This means that if the locker was open, Student 3 closed it; if the locker was closed , Student 3 opened it.
Student 4 changed the state of every fourth locker, starting with Locker 4. The students continued this pattern until all 30 students had had a turn. In this lab investigation, you will consider this this question: Which lockers were open after Student 30 took her turn?
1. Develop a plan for finding the answer to the question above. Write a few sentences describing your plan.
2. Carry out your plan. Which lockers were open after Student 30 took her turn? What do the numbers on the open lockers have in common?
3. Consider how a student's number is related to the lockers he touched.
a. Which lockers were touched by both Student 6 and Student 10? By both Student 2 and Student 5? By both Student 8 and Student 10?
b. Use what you have learned about factors and multiples to explain why your answers to Part a make sense.
4. How many lockers would there have to be for both students 8 and students 9 to touch the same locker? Explain.
5. Which Students touched both Locker 7 and Locker 12? Both Lockers 3 and 27? Both Lockers 20 and 24?
6. Which lockers were only touched by 2 students? Were these lockers opened or closed after Student 30's turn?
7. Which lockers were touched the greatest number of times?
Locker number 1 was open because student number 1 opened every locker.After that the second student closed the second and every second locker after that so that pattern kept going and nobody got to number one.So I think number one was the only locker open.
ReplyDeleteChetanpreet singh
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ReplyDeleteI actually did the whole thing on paper, and to what I did on the paper, lockers 1, 4, 9, 16, and 25 were left open (after student 30). I can't really find anything in common with the numbers. The students number and the lockers that they opened were alike. The locker numbers were multples of the original number. Say, Student 3 had to open Locker 3, he had to open that Locker and the other Lockers that were multiples of that number.
ReplyDeleteThe Locker touched by both student 6 and 10 was Locker 30. The Lockers touched by both student 2 and 5 were Lockers 20 and 30. No locker was touched by both student 8 and 10.
By using what i already know about factors and multiples I think my answer is correct. Because of each child having the same number as the lockers they had to open, starting from that locker number, I think that they were just multiples. Student 8 and 10 didn't touch a locker together, because the multiples of 8, going as close to 30 would be 24. Twenty-four isn't close to anything like 10, 20, or 30. The multiples of 8, going to 24 would be, 8, 16, and 24 itself. So I think it all has something to do with multiples.
A) The lockers were 1, 4,5,6,7,8, 11, 13,15,16,17,18,19,20,23,25,28,&29. Its true because student 2 closed 2 the locker that was 2 after 2. Student 3 changed or switched the position of the lockers 3 places after itself. Student 4 changed the state of every fourth locker, starting with 4. If all the students did this pattern and stopped at 30, then the only locker left was 1.
ReplyDeleteB)As I mentioned 1, 4,5,6,7,8, 11, 13,15,16,17,18,19,20,23,25,28,&29 were the only lockers that were open after student 30 went. The lockers numbers pattern have to add 3 and 1 to get the next number.
A)Student 6 and 10 both touched lockers 20. S2and 5 both touched lockers 10, 20, and 30. S8 and 10 didnt match any lockers.
B) Part A makes sense because I found the multiples of 6 and 10, between 6-30. Also 2,and 5, 8 and 10.
My plan involved finding the common multiples of the numbers 1-30 from 1-30.After Student 30 took her turn lockers 1, 3, 4, 5, 7, 9, 13, 14, 16, 17, 18, 19, 20, 21, 23, 25, 26, 27, 28, 29, and 30 were open. The only locker that was touched by Student 6 and 10 was locker 30 because this is the only common multiple of 6 and 10 out of 30. Lockers 10, 20, 30 were touched by Students 2 and 5. No lockers were touched by both Students 8 and 10 because they have no common multiples.
ReplyDeleteMy plan is to make a chart with the numbers 1-30 on it. Then I would write O for open or C for closed next to the numbers as people come across them. The lockers that were open after 30 people took their turn was #'s 1, 4, 8, 9, 16, and 25. The lockers that were closed were #'s 2, 3, 5, 6, 7, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, and 30. The numbers of the open lockers were all multiples of the student's number. Students 6 and 10 touched locker 30. Students 2 and 5 touched lockers 10, 20, and 30. Students 8 and 10 did not touch any locker similar because they dont have multiples up to 30. My answers in part a should be correct because the whole blog was basiccaly on finding the multiples of each number.
ReplyDeleteThe locker that were open were 1, 17,18, 19, 20, 22, 24, ,26, 28, 29, 30. i planed this by writing numberes up to 30 then following the steps told. i stoped at 15 because numbers after 15 had greater multiples then 30.
ReplyDeleteThe number of student was related to the locker numbers because the locker numbers were the multiples of the student number.
The students 6 and 10 both touched 30. The student 2 and 5 touched 10, 20, and 30. The students 8 and 10 didn't touch any same locker because they don't have a common multiple under 30. Since, 6 and 10 had a common multiple less then 30 they touched the same locker just like 2 and 5.
kirandeep
I drew a diagram on paper. I wrote the numbers 1-30 and used the letters c and o to represent close and open lockers. After student 30 took their turn, lockers 1,4,9,16,25,30 were left open. A students number is a factor of the lockers they touched. The open locker numbers are adding 3,5,7,9,11,etc. The locker that was touched by both Student 6 and 10 is Locker 30. Locker 10 was touched by both Student 5 and 2. No lockers was touched by Student 8 and Student 10. There would have to be 72 lockers for Student 8 and 9 to touch the same lockers. 72 is a least common multiple of 8 and 9. lockers 2,3,5,7,11,13,17,19,29,23. locker 30 was touched the greatest number of times.
ReplyDeleteNaiomi Samlall
Students 6 and 10 both touched locker 30. And Locker 10 was touched by students 2 an 5.
ReplyDelete