An impending headache to the administrator in planning the locker operation in SST. He seeks your advise on how to resolve this issue:

*Here is the problem*:

In SST, there is a row of 100 closed lockers numbered 1 to 100. A student goes through the row and opens every locker. A second student goes through the row and for every second locker if it is closed, she opens it and if it is opened, she closes it. A third student does the same thing for every third, a fourth for every fourth locker and so on, all the way to the 100th locker.

source: seas.gwu.edu

**The goal of the problem is to determine which lockers will be open at the end of the process.**

__TASK 1__Working in pairs, explain your thinking to the following problems clearly. Be sure to use appropriate mathematical language and methods. Post your answers in the comment and indicate both of your names.

(a) Which lockers remain open after the 100th student has passed?

(b) If there were 500 students and lockers, which lockers remain opened after the 500th student has passed?

__TASK 2 (similar problem)__3 droplets of water fell at the following rate, droplet A at every 5 minutes interval, droplets B at every 12 minutes interval and droplets C at every half an hour interval.

(d) Identify at least 2 methods to solve this problem.

(e) Is there a particular topic in maths that analyses such problems?

source: unreasonablydangerousonionrings.blogspot.co

(c) When do you think all the droplets, that is A, B and C will fall at the same time on the ground? (d) Identify at least 2 methods to solve this problem.

(e) Is there a particular topic in maths that analyses such problems?

1a) 10 lockers remain open.

ReplyDelete1b) 22 lockers remain open.

2a) 60 minutes after they first drop together.

2bi) Lowest common multiple.

In this case, the numbers used are 5, 12, and 30. The lowest common multiple of these numbers is 60.

2bii) The table method.

This method, as its name says, uses a table.

Task 1a lockers 1, 4, 9, 16, 25, 36, 49, 64, 81, 100

ReplyDeleteTask 1b lockers 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484

Task 2a They will fall at same time at the 60th minute/1st hour

Task 2b Method 1: Find the common multiple of 5, 12 and 30.

Method 2: Make a graph and list out all the times that each droplet drops.

Task 2c Patterns

1a) 10 lockers remain open

ReplyDelete1b) 22 lockers remain open

2a) 1 hour after their first drop

2b) Lowest Common Multiple

Algebra/ Guess and Check

2c) HCF and LCM: Highest Common Factors and Lowest Common Multiples

Members: Carissa, Valery, Chelsea, Wei Qin

Task 1A locker:1,4,9,16,25,36,49,64,81,100

ReplyDeleteTask 1B locker:1,4,9,16,25,36,49,64,81,100,121,144,169,225,256,289,324,361,400,441,484

Find the square roots of the numbers which is under 100 for a and 500 for

Task 2a:They will fall at same time at the 60th minute/1st hour

Task 2b:Lowest common multiple

Method: algebra/guess and check

Task 2c:highest common factors and lowest common multiples

This comment has been removed by the author.

ReplyDeleteTask 1A locker:1,4,9,16,25,36,49,64,81,100

ReplyDeleteTask 1B locker:1,4,9,16,25,36,49,64,81,100,121,144,169,225,256,289,324,361,400,441,484

Method:Find the square roots of the numbers which is under 100 for A and 500 for B.

Task 1c: After 1 hour.

Task 1d.Lowest Common Multiple and Guess and Check

Task 1e. Patterns

Done with Darshan

1a)10 lockers:1,4,9,16,25,36,49,64,81,100

ReplyDelete1b)22 lockers: 1,4,9,16,25,36,49,64,81,100,121,144,169,225,256,289,324,361,400,441,484

2a)1 hour after their first drop

2b)Lowest Common Multiple

Method:Guess and Check

2c):Highest Common Factors and Lowest Common Multiple

Task 1a) 1,4,9,16,25,36,49,64,81.100

ReplyDeleteTask 1b) 1,4,9,16,25,36,49,64,81.100, 121, 144, 169, 196,225,256,289, 324, 361, 400,441, 484

Task 2a) 1 hour/60 min

Task 2b) Lowest Common Multiple/Listing

Task 2c) Data Anylasis

Group Members: Bowen, Ryan Lai, Sherwin

Task 2 a) 60 min

ReplyDeleteb) find common multiples and use guess and check

c) factors and multiples

i'm stuck at task 1 anyone help me

ReplyDeleteTask 1a) 10 lockers: 1,4,9,16,25,36,49,64,81,100

ReplyDeleteTask 1b) 22 lockers: 1,4,9,16,25,36,49,64,81.100,121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484

Task 2a) 60 minutes

Task 2b) Find the smallest common multiple of 5, 12 and 30

Task 2c) List out the time past as the waters drip, making a list

Task 1A is locker:1,4,9,16,25,36,49,64,81,100

ReplyDeleteTask 1B is locker:1,4,9,16,25,36,49,64,81,100,121,144,169,225,256,289,324,361,400,441,484

Method:Find the square roots of the numbers which is under 100 for A and 500 for B.

Task 1c: After 1 hour time

Task 1d.Lowest Common Multiple, Guess and Check

Task 1e. Patterns Done with Wai Kit

This comment has been removed by the author.

ReplyDeleteTask 1a) 1,4,9,16,25,36,49,64,81,100 (10 lockers)

ReplyDeleteTask 1b) 1,4,9,16,25,49,64,81,100,121,144,169,196,225,256,289,324,361,400,441,484 (22 lockers)

Task 2a) 60 minutes

Task 2b) Find the smallest common multiple of 5,12 and 30/ Guess and Check

Task 2c) Patterns

1a) lockers 1, 4, 9, 16, 25, 36, 49, 64, 81, 100

ReplyDelete1b) lockers 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484

2a) 60min

2b i) Find the smallest common multiple of 5,12 and 30(60)

2b ii) Make a table

2c)Multiples and factors

This comment has been removed by the author.

ReplyDeleteTask 1a 10 lockers: 1,4,9,16,25,36,49,64,81,100

ReplyDeleteTask 1b not sure

Task 2a 60 minutes

Task 2b LCM and Guess and check

Task 1e Factors and Multiples

I did it with Praveen

ReplyDeleteTask 1: A)10 lockers that are>1,4,9,16,25,36,49,64,81,100(square numbers)

ReplyDeleteB)all square numbers from 1 to 500>1,4,9,16,25,36,49,64,81,100,121,144...

Task 2:C)60 minutes

D) FIRST METHOD: find the lowest common multiple of all the numbers using 30mins as the reference.

SECOND METHOD: unsure

E) this years first unit: factors and multiples

^^^did with sheares

ReplyDeleteTask 1a 10 lockers: 1,4,9,16,25,36,49,64,81,100

ReplyDeleteTask 1B Lockers :1,4,9,16,25,36,49,64,81,100,121,144,169,225,256,289,324,361,400,441,484

Task 2c: 60 Minutes

Task 2d: Listing of multiples and lcm

Task 2e : Multiples

Done With Lindsay