Beginning Activity Beginning Activity 2: Calendars and Clocks
This activity is intended to help with understanding the concept of congruence, which will be studied at the end of this section.
1.
Suppose that it is currently Tuesday.
(a)
What day will it be 3 days from now?
(b)
What day will it be 10 days from now?
(c)
What day will it be 17 days from now? What day will it be 24 days from now?
(d)
Find several other natural numbers \(x\) such that it will be Friday \(x\) days from now.
(e)
Create a list (increasing order) of the numbers 3, 10, 17, 24, and the numbers you generated in TaskĀ 1.d. Pick any two numbers from this list and subtract one from the other. Repeat this several times.
(f)
What do the numbers you obtained in TaskĀ 1.e have in common?
2.
Suppose that we are using a twelve-hour clock with no distinction between A.M. and P.M. Also, suppose that the current time is 5:00.
(a)
What time will it be 4 hours from now?
(b)
What time will it be 16 hours from now? What time will it be 28 hours from now?
(c)
Find several other natural numbers \(x\) such that it will be 9:00 \(x\) hours from now.
(d)
Create a list (in increasing order) of the numbers \(4, 16, 28\text{,}\) and the numbers you generated in TaskĀ 2.c. Pick any two numbers from this list and subtract one from the other. Repeat this several times.
(e)
What do the numbers you obtained in TaskĀ 2.d have in common?
3.
This is a continuation of ExerciseĀ 1. Suppose that it is currently Tuesday.
(a)
What day was it 4 days ago?
(b)
What day was it 11 days ago? What day was it 18 days ago?
(c)
Find several other natural numbers \(x\) such that it was Friday \(x\) days ago.
(d)
Create a list (in increasing order) consisting of the numbers \(-18, -11, -4\text{,}\) the opposites of the numbers you generated in TaskĀ 3.c and the positive numbers in the list from TaskĀ 1.e. Pick any two numbers from this list and subtract one from the other. Repeat this several times.
(e)
What do the numbers you obtained in TaskĀ 3.d have in common?