Phrases used to Position
or Signed Amounts and Quantities
In all the different comparisons below, at least one of the
phrase more than and less than can be used. All other
phrases cannot be universally employed.
On a number line, signed numbers may serve as coordinates. The
coordinates give the position of a point or number or quantity on the
line.
Temperature Examples
Thermometers may show positive and negative temperatures. So 20 degrees
Celcius is higher than and more than -10 degree Celcius by 30 degrees.
Here we can imagine 0 degrees 20 degrees lower than +20 degrees and 10
degrees higher than -10 degrees. The sum is
20 degrees Celcius + 10 degrees Co = 20 degrees Co
- (-10 degrees Co)
Likewise, 70 degrees Fahrheniet is higher than, warmer than, greater
than and more than -30 degrees Fahrheniet by a difference of 100 degrees
Fahrenheit. The difference is given by
70 degrees Fo - (-30 degrees Fo) = 70 degrees
Fo + 30 degrees Fo)
We may also say -10 degrees Co is less than 20 degree
Co by 30 degrees Co
In general, positive temperatures are more than negative temperatures.
Money Examples
Imagine one person has no money and a second has 100 pennies. The second
person has 100 more than pennies than the first. If both buy an object
for 30 cents. The first person now has a debt of 30 cents. We may write
that as -30 cents, with the minus sign showing amount owed. The second person
after spending 30 of the 100 pennies, now has 70 pennies left. The second person
is still a 100 hundred pennies ahead of the first person on the debt number line.
The 100 pennies is given by the difference
70 pennies - (-30 pennies) = 70 pennies + 30 pennies.
We will extend the common use of the phrase more than, by saying the second person position
in 100 pennies more than the position of the first person. Likewise, we
will extend the common use of the phrase less than by saying the
position of the first person is 100 pennies less than that of the second person.
In general, a person with pennies has more pennies than a person who owes pennies.
Average Water Level
At docks for boats and ships, water level may be above or below a reference point.
Here +150 cm may indicate a height above, while -200 cm may indicate a hieght below
the reference point. The first height is 150 cm above the reference point. The reference
in turn is 200 cm above the second hieght. Thus the 150 cm hieght is more than
the -200 cm height by 150 cm + 200 cm = 350 cm. The later is also given by the
difference
150 cm - (-200 cm) = 150 cm + 200 cm.
With the phrase lower than, we may say -200 cm is lower than
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Teachers & Tutors: Site pages offer better or best practices for providing skills -
simpler than expected & comprehensive but for exercises. For your charges, your duty is to study them alone or in
groups and develop skill building exercises & activities to share. Start now. The effort here is the best I can do.
Others are welcome to refine or exceed it. Please do.
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
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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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