3. Units and Lengths of Time
Clocks were initially mechanical. Today, they may be electronic. With the
aid of reliable clocks, days are currently divided into 24
hours - each equal in length according to a clock.. . With the aid
of clocks, each hour is divided into 60 minutes, and each minute
into 60 seconds.
Now seven days form a week, and four weeks or 28 days form a lunar
month.
A calendar year consists of 365¼ days, approximately. That represents the
time for the earth to travel once around the sun.
In Western European methods for tracking time, the calendar year is
divided into twelve calendar months
30 days hath September, April, June and November,
All the rest have 31, Excepting February alone
(And that has 28 days clear, With 29 in each leap year).
According to this rhyme
January has 31 days
February has 28 days and one more in each leap year
March has 31
April has 30
May has 31
June has 30
July has 31
August has 31
September has 30
October has 31
November has 30
December has 31.
The first line is the most important. Every one needs to remember it. By
the clock or time measurement devices, seconds, minutes, hours, days,
weeks and lunar months are represent units of time with fixed lengths.
But months vary in length and so do years. Non leap years have 365 days.
Leap years (about one in four years) have 366 days. So the average is
about 365¼ days.
Identification of Leap Years
In the present-day occidental calendar, year is a leap year when the
year is a multiple of 4, but the year is not a multiple of 100, except in
the case it is a multiple of 400.
Examples:
- The year 2036 is a leap year as it divisible by 4 and not a multiple
of 100
- The year 2033 is not a leap year as is not divisible by 4 nor 100
- The year 2400 is a leap year as it is multiple of 400.
- The year 2200 is not a leap year as it multiple of 100 that is not a
multiple of 400.
These example require a knowledge of decimal representation and the
ability to recognize multiples of 4, 100 and 400.
Pedantic: When we speak of a 2, 3, 4 or more digit whole
number, we mean a whole number with a 2, 3, 4 or more digit decimal
representation.
The following rules are help here.
- A two or more digit whole number is a multiple of 4 when and only
when its last two digits give a multiple of 4: 96, 92, 88, 74, 72, 68,
64, 60, 56, 52, 48, 44, 40, 36, 32, 28, 24, 20, 16, 12, 08 = 8, 04 = 4
and 00 = 0.
- A three digit whole number is a multiple of 100 when the last two
digits are both 0.
- If the division of a whole number given by multiple of 100 by 100
gives a multiple of 4, the whole number is a multiple of 400.
One year later, what is the the day of the week
- Each non-leap year consists of 365 days, that is one day more than
the 364 days present in 52 weeks. So if January 1st falls on a Monday of
a non-leap year, the next January 1st falls on a Tuesday.
- Each leap year consists of 366 days, that is two days more than the
364 days present in 52 weeks. So if January 1st falls on a Monday of a
leap year, the next January 1st falls on two days later in the week. Here
that would be a Wednesday.
If the year from a given day of a given month (not February 29) to the
same day of the next year does not include a February 29, then latter is
one day later in the week
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Day
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One Day
Later
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Two Days
Later
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Monday
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Tuesday
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Wednesday
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Tuesday
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Wednesday
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Thursday
|
|
Wednesday
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Thursday
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Friday
|
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Thursday
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Friday
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Saturday
|
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Friday
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Saturday
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Sunday
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Saturday
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Sunday
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Monday
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Sunday
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Monday
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Tuesday
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But if a February 29 is included, due to the presence of a leap year,
then the latter is two days later in the week. Use the table.
Alternate Approach: The foregoing calculations reflect the
following.
- If there is no February 29 between a given date of this year and the
same date of next year, the latter is 365 days or 52 weeks and 1 day
later.
- If there is a February 29 between a given date of this year and the
same date of next year, the latter is 366 days or 52 weeks and 2 days
later.
The above table will be useful here.
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Secondary
Mathematics for Ages 11+, A Practical Approach for home-tutoring or -schooling, or for schools & colleges
with local curriculum control. Study how to include site content - its skill development how-TOs and innovations
into present or future lesson plans - some reading required.
Road
Safety Messages and Questions: When and why should you face
traffic when walking along a road or cycle path? Is it a good
idea to hang limbs outside of cars etc? What gives more
protection in a crash: a car, motorbike or bicycle?
See too, the BBC-Belgium story Texting and
Driving - texting & the impossible test - the article links to a gruesome utube video on the subject
The Logic of Injustice:
How Texas sent
an innocent man to his death - The wrong Carlos. Some judgments are irreversible. Procescution: Where and when prosectors play to win rather than for
justice, guilt beyond a reasonable doubt goes unrespected due to prosecutors who putting winning
first, those innocence before the law may be convicted. Some procescutors offices in continuing to accuse after a pardon
due to reasonable doubt or innocent being shown, may sucessfully oppose compensaton for false convictions
by asserting a pardon individual is still under suspicion. Then the pardoned individual or the latter's estate
is not compensation for years or decade
of improper or false imprisonment, or for execution. Site chapters on Logic
and some in Pattern
Based Reason may slowly lead to greater precision in reading, applying and
writing laws.
May 2012, Composition Starting:
Pre-School and Primary Mathematics - Quantitative Skills, An
Intellectual View, Feedback Welcome:
The 8 Most Popular Site Inlinks
Parent Center: Help your child or teen
learn:
Parent-friendly
Work Booklets for ages 3+ to 13 Use these or others to check
or build skills. Other booklets are available but these booklets
allow parents unsure of themselves in mathematics to help their
children. The selection acquired in Canada is published in the
USA. So it has a US orientation. In retrospect, the selection
shows parents what to check with the booklets or by other ways,
the choice is theirs. But in retrospect, the selection does not
cover integral and fractions liquid weights and measures - ask
the publishers to correct that! For ages 9 to 12 say, parents may
compensate by showing boys and girls how to use weights or mass,
and further measures in food preparation. Beyond that children
may be shown how to measure and calculate angles, lengths and
areas [proportional amounts too] directly or by using maps and
plans drawns to scale. Learning how to gather and measure all the
ingredients, pots and pans for a dish or a meal, along with
cleaning up sets the stage for like activities or experiments in
science courses, and in developing organizational skills,
gives boys and girls a head start. Good luck. At the other
extreme, more comprehensive than light, if your motto is
McCainian: drill, drill, drill then Toronto
mathematician and actor John Mighton's jump math organization has jump math
workbooks for at least grades 3 to 8 for at-home and in-school
use - training sessions for teachers available. Jump math has
been expanding to cover older students. Jump Math Samples: plus
Fractions for
Grades 3-4 & Grades 5-6 [Read] Free Resources grades 1 to 8
[unread - likely to be good]. and
Mathematics
Skills For Ages 3 to 14 - technical!
Skills with take
home value - A few ideas
Basic skills include
time-date-calendar Matters; money matters; map, plan and
scale diagram matters;counting, measuring and figuring;
decision making with logic and likelyhood; being careful and
being aware of the domino effect of mistakes; reading and
writing with precision.
Is your child able to add, subtract and multiply amounts
of money, work with fractions, work with clocks and calendars,
work with maps and plans, and measure length, weight-mass and
volume? Schools may promote your son or daughter without
providing basic skills in reading, writing and
arithmetic.
Arithmetic
and Number Theory Skills
Algebra
Starter Lessons
Geometry
- maps plans trigonometry vectors
More
Algebra
70
Calculus Starter Lessons
Calculus Lessons Elsewhere:
-
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
trespassed in the house of the three bears, she found three bowls
of porridge, two not to her liking, and one just right. Different
bears have different tastes. As invited guest here and elsewhere,
if one or more explanations is not to liking, try another. It may
be better or just right.
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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