15. Project Planning
Thirty days hath September,
April, June and November;
February has twenty eight alone
All the rest have thirty-one
Except in Leap Year, that's the time
When February's Days are twenty-nine
According to the rhyme, here is a table of days in each month in a
non-leap year.
|
Month
|
Jan
|
Feb
|
Mar
|
Apr
|
May
|
June
|
July
|
Aug
|
Sept
|
Oct
|
Nov
|
Dec
|
|
Days in
|
31
|
28
|
31
|
30
|
31
|
30
|
31
|
31
|
30
|
31
|
30
|
31
|
For nonleap years, the last day of
- January is the 31st day of the year
- February is the (31+28)th = 59th day of the year.
- March is the (59+31)th = 90th day of the year.
By repeated addition, we obtain what the day of the year for the last of
each month in a nonleap year.
|
Month
|
Jan
|
Feb
|
Mar
|
Apr
|
May
|
June
|
July
|
Aug
|
Sept
|
Oct
|
Nov
|
Dec
|
|
Days in
|
31
|
28
|
31
|
30
|
31
|
30
|
31
|
31
|
30
|
31
|
30
|
31
|
Last of Month is this
day of the year.
|
31
|
59
|
90
|
120
|
151
|
181
|
212
|
243
|
273
|
304
|
334
|
365
|
While for a leap year, the days in the months and the last day of each
month are as follows:
|
Month
|
Jan
|
Feb
|
Mar
|
Apr
|
May
|
June
|
July
|
Aug
|
Sept
|
Oct
|
Nov
|
Dec
|
|
Days in
|
31
|
28+1
|
31
|
30
|
31
|
30
|
31
|
31
|
30
|
31
|
30
|
31
|
Last of Month is this
day of the year.
|
31
|
59+1
|
90+1
|
120+1
|
151+1
|
181+1
|
212+1
|
243+1
|
273+1
|
304+1
|
334+1
|
365+1
|
Days of the Year
NonLeap Year Example
April 30th is the 120th day of the year. Now May 6 happens 6 day
later. So it is (130 + 6) th = 136 th day of the year.
December 1st is one day beyond November 30, the 334 day of the year. So
December 1st is the 335th day of the year. The Northern hemisphere,
winter solstice December 22 would be the (334+ 22)th = 354th day of the
year.
The summer solstice June 22nd is 22 days later than May 31st, the
151st day of the year. So in a nonleap year, the summer solistice
is the 173rd day of the year.
Three Ways to Count Full Days Between Two Days of a Month
Suppose it is 9 am on the 10th of the month. Then 7 full more days
will take us to 9 am on the 17th of the month.
|
8
|
9
|
10
|
11
|
12
|
13
|
14
|
15
|
16
|
17
|
18
|
19
|
Here 7 = 17 - 10. In counting the days or smaller units of time
between the 10th and 17th, it is not clear when or where the count begins
on the 10th (a one day or 24 hour period) and where the count stops on
the 17th (another one day or 24 hour period).
Counting Question A: How many full days are their between
now (the start or the last second) of the 10th, and the same time on
17th.
Answer: 7 = 17 -10.
Counting Question B. How many full days are their between
the end of today the 10th, and the start of the 17th.
Answer: 6 = 7 - 1 = 17 -10 -1.
Counting Question C. How many full days are their
between the start of today the 10th, and the end of the
17th.
Answer: 7 + 1 = 17 -10 + 1.
The smallest answer is 6 corresponds to starting the count at the last
moment of the 10th - the start of the 11th, and stopping the count
at the first moment of the 17th, or the end of the 16th. The The greatest
answer is 8 corresponds to starting the count at the first moment of the
10th - the end of the 9th, and stopping the count at the last
moment of the 17th - the very start of the 18th.
Project Planning Convention
At work, we may say a project begins on the 10th and ends on the
17th.
|
8
|
9
|
10
|
11
|
12
|
13
|
14
|
15
|
16
|
17
|
18
|
19
|
When we say that, we mean the first day and the last day are
included and counted as full project work days. So the number of
project days is 8 = 17 -10 + 1.
If a 2nd project was to begin on the 18th and end on the 27th of a month,
the number of project work days would be 27 - 18 + 1 = 10.
Here 27 - 18 is the number of days in the project beyond the end of the
18th day. The +1 is due say to the inclusion of the 18th day of the
month in the project work time.
|
8
|
9
|
10
|
11
|
12
|
13
|
14
|
15
|
16
|
17
|
18
|
19
|
20
|
21
|
22
|
23
|
24
|
25
|
26
|
27
|
28
|
29
|
|
|
27 = 14 + 13.
There 13 = 27 - 14 project days here.
|
|
More generally, if 3rd project was to begin on the 45th day of the
year and continue to the 245th day of the year, the number of project
work days would be
245 - 45 + 1 = 200+1 = 201
Now suppose a 4th project begins on July 14th and ends on October
21st. According to the table
|
Month
|
Jan
|
Feb
|
Mar
|
Apr
|
May
|
June
|
July
|
Aug
|
Sept
|
Oct
|
Nov
|
Dec
|
|
Days in
|
31
|
28
|
31
|
30
|
31
|
30
|
31
|
31
|
30
|
31
|
30
|
31
|
Last of Month is this
day of the year.
|
31
|
59
|
90
|
120
|
151
|
181
|
212
|
243
|
273
|
304
|
334
|
365
|
July 14th is the (212+14)th = 226th day of the year, while
October 21st is the (304+21)th = 325th day of the year.
So from the start of July 14th (the 226th day of the year) to the end of
October 21st, the 325th project day, there are
325- 226 + 1 = 99+ 1 = 100
project days.
Skip this algebraic description of the
underlying counting rule if it after reading and re-reading
it for five minutes, you do not understand it. So far the
algebraic way of writing in mathematics has not been
introduced in a step by step manner - slowly and
carefully. An algebraic description of the
general counting rule and practice is as follows. It is given
here - but not fully justified - as reference and also as an
algebra appetizer. Do not be surprised if you do not
understand it because as said, the shorthand role of letters
and symbols in mathematic has yet to be explained or
introduced fully and carefully. That is a task for
material elsewhere.
Algebraic Description of the General Counting
Rule: Suppose M < N are whole numbers.
The number of days or objects starting at the M-th and ending
with the Mth in a sequence is N - M + 1.
|
Check:
- Project days from July 14 to July 31st is 31-14+1 = 18
- Number of days from start of the next day, August 1st to the start of
Oct 1st is 61 days.
That is from the full calendar Days table above - see the copy below.
- Project days from Oct 1st start to Oct 21st end is 21 - 1 +
1 = 21.
Now 18
61
21 +
100
1 1 <=== two
carries.
So two methods agree.
|
Full Calendar Days from start of
|
|
first of
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Dec
|
|
|
|
|
|
|
|
|
|
|
|
31
|
|
Nov
|
|
|
|
|
|
|
|
|
|
|
30
|
61
|
|
Oct
|
|
|
|
|
|
|
|
|
|
31
|
61
|
92
|
|
Sept
|
|
|
|
|
|
|
|
|
30
|
61
|
91
|
122
|
|
Aug
|
|
|
|
|
|
|
|
31
|
61
|
92
|
122
|
153
|
|
July
|
|
|
|
|
|
|
31
|
62
|
92
|
123
|
153
|
184
|
|
June
|
|
|
|
|
|
30
|
61
|
92
|
122
|
153
|
183
|
214
|
|
May
|
|
|
|
|
31
|
61
|
92
|
123
|
153
|
184
|
214
|
245
|
|
Apr
|
|
|
|
30
|
61
|
91
|
122
|
153
|
183
|
214
|
244
|
275
|
|
Mar
|
|
|
31
|
61
|
92
|
122
|
153
|
184
|
214
|
245
|
275
|
306
|
|
Feb
|
|
28
|
59
|
89
|
120
|
150
|
181
|
212
|
242
|
273
|
303
|
334
|
|
Jan
|
31
|
59
|
90
|
120
|
151
|
181
|
212
|
243
|
273
|
303
|
334
|
365
|
to start of
first of
|
Feb
|
Mar
|
Apr
|
May
|
June
|
July
|
Aug
|
Sept
|
Oct
|
Nov
|
Dec
|
Jan
|
Going Further:
In workplaces where Saturday and Sundays are holidays, there about 22 to
23 work or school days per month. Now February has 28 or 29 days
while other months have 30 to 31 days. Some months may include five
weekends while only months include only four. You need to consult
your school or work calendar to identify and count the number of school
or work days there are in each month.
That will give a table like the following
|
Month
|
Jan
|
Feb
|
Mar
|
Apr
|
May
|
June
|
July
|
Aug
|
Sept
|
Oct
|
Nov
|
Dec
|
|
Days in
|
31
|
28
|
31
|
30
|
31
|
30
|
31
|
31
|
30
|
31
|
30
|
31
|
Last of Month is this
day of the year.
|
31
|
59
|
90
|
120
|
151
|
181
|
212
|
243
|
273
|
304
|
334
|
365
|
but with the number of calendar days in the month being replaced by the
number of school or work days. If you are going to school or
college, instead of starting with January as the first month in
your table, you might begin with the first month of your school year or
term. Doing so would allow you to count and plan school days if you
are student and work days if you are teacher.
|
|
Teachers & Tutors: Site pages offer better or best practices for providing skills -
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Parent-friendly
Work Booklets for ages 3+ to 13 Use these or others to check
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Arithmetic
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Algebra
Starter Lessons
Geometry
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More
Algebra
70
Calculus Starter Lessons
Calculus Lessons Elsewhere:
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How to Ace Calculus: Street Wise Guide - Mostly
Text.
-
Flash
Video for Calculus Phobics
They cover basic topics in ways likely to complement your
notes, your textbooks and site material. When Goldilocks
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if one or more explanations is not to liking, try another. It may
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Unsolicited Advice
Learning to do and high marks if it comes to easy is often
deceptive - light rather than deep. For that reason, students
with learning difficulties determined not to let it get in their
way may go deeper and farther than those with none. High marks,
if the come easy, may be deceptive - provide a too light and not
a deep mastery. That could have been your problem in secondary
school, one that leads to comprehension shock or difficulties in
calculus and more generally in the first year of college. Bon
Appetite.
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|