What time will the clock show?  
      ●It is now 5 o’clock; what time will it be in 2 hours?     7 o’clock
      ●What time will it be 5 hours after 9 o’clock?       2 o’clock
      ● What is 26 hours after 8 o’clock?        10 o’clock
      ● It is 3 o’clock now; what time will it be in 100 hours?
                                                     7 o’clock
              How can you model each 
                            situation?  
                                           Ideas come from Student Explorations in Mathematics, May 2012, 1-8
     Modeling Time
  Josh’s favorite song, ‘Livin’ on a prayer’ plays 
  on a radio station at 9 o’clock every day.  How 
  many hours until Josh hears his song again, if 
                        it is…
                                   Is there more than one 
                                   Is there more than one 
    ●5 o’clock?                     possible answer? 
                                    possible answer? 
 4 hours, 16 hours, 28 hours, 40 hours, 52 hours, …. 
    ●10 o’clock?
 11 hours, 23 hours, 35 hours, 47 hours, 59 hours, …. 
    ●9 o’clock?  
 12 hours, 24 hours, 36 hours, 48 hours, 60 hours, …. 
       What day will it be?  
   ●Today is Monday; what day will it be in 13 days?
            Sunday
   ●Today is Thursday; what day will it be 23 days before?
            Tuesday
   ●Today is Sunday; what day will it be in 49 days?
            Sunday
   ●Every Tuesday is ‘Taco Tuesday’ at Alyssa’s favorite 
    restaurant.  If it is Saturday, how many days until can enjoy 
    ‘Taco Tuesday’ again?  
    3 days, 10 days, 17 days, 24 days, 33 days, …
             Introduction to Modular Arithmetic
  Time is Divided to Two Twelve Hour Periods – this sets up a situation 
  for mod 12 arithmetic, instead of 1 through 12, we will use 0 through 
  11.    
  ●It is now 5 o’clock; what time will it be in 2 hours?
                           5  (mod12) + 2  (mod12) = 7 (mod12)
  ●What time will it be 5 hours after 9 o’clock?
                           5  (mod12) + 9  (mod12) = 2 (mod12)
  ● What is 26 hours after 8 o’clock?
      26 is 2 in (mod 12); 2  (mod12) + 8  (mod12) = 10 (mod12)
  ● It is 3 o’clock now; what time will it be in 100 hours?
        100 is 4 in (mod 12); 4  (mod12) + 3  (mod12) = 7 (mod12)