Mathematics With Take Home Value
Ages 11 to 13 years may dedicated to providing and consolidating skills
that may serve common needs of life at home, at work and in the street.
Many French conversation textbooks for people learning that language
include stories or activities to provide a context for mastering and
extending vocabulary. Activities may include travel by bicycle, car, bus,
train, plane or taxi; buying and purchasing goods and services; visiting
a restaurant or theatre; or visiting relatives. Thus there is a context
for learning. Studying same activities in a mathematics class provides an
opportunities to meet and master examples of time and date matters, money
money including buying and selling goods and services; and including
saving too; measurement and rates matters, decision or chance in matters
where not all certain; and map and plan usage for directions or
navigation, and for indirect measurement. All the arithmetic skills with
whole numbers and fractions can be employed in the foregoing.
Practical Money Matters
In counting piles of real or play money - bills and coins - students
should expect the resulting count, its decimal form with no or two places
after the decimal point will be independent of the order of counting or
addition. Here counting may involve addition of subtotals, and the use of
subtraction or multiplication to obtain those subtotals.
For examples or activities in buying and selling goods and services,
students should be able to find the total cost or amount via exact
arithmetic. In this, student need to be show how
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to do exact arithmetic to add charges directly, to add with the aid
of subtotals to find or check the amount charged or to be billed. In
the case of repeated items, multiplication should be employed to find
the corresponding subtotal. Here subtotals themselves may be given
the sum of subsubtotals. Avoidance of double billing for the same
item should be a concern.
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how to read or measure the amount of a goods or service. Measurement
may be given in terms of mass, weight, volume, length and area.
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How to calculate cost for goods or services using cost per unit and
amount measured. Teachers may discuss brand loyalty option versus
least cost per unit option in deciding what to buy, when quality is
not a factor - or unknown. The chain rule for
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How to identify $1\%$ with the fraction $\frac1{100} = 0.01$. How
to use percentages in calculation of costs or taxes. Familarity with
common or frequently occuring percentages $100\% \quad 50\% \quad
25\% \quad 75\% 5\%$ and so on should eventually follow. Liked or
not, sales taxes, discounts in buying, mark-ups in selling, and price
or wages increases are often described using percentages.
Distance-Time-Speed
Students may be shown how to use the first two of the three formulas
\begin{eqnarray*} \mbox{average speed} & = & \frac
{\mbox{distance traveled}}{ \mbox{time taken}} \\ \mbox{distance traveled} & = &
\mbox{average speed} \times \mbox{time taken} \\ \mbox{travel time}
& = & \frac {\mbox{distance traveled}}{\mbox{average speed} }\\
\end{eqnarray*} in a mechanically manner with units carried through
calculations. The study of the last may await a greater mastery of
arithmetic or fractions with units.
Algebraically, the formulas are redundant. Seeing how these formula imply
each other may become obvious in further studies. The latter means that
the formulas are consistent. Use of any one will not contradict the use
of another.
Remark: The take-home value of the first two if
not all three justifies their rote mastery in practice. While providing
a minimal set of rules and patterns may be valued in the Euclidean
model for higher mathematical thought, the introduction to mathematical
thought and practice may provide students a redundant sets of formulas
and practices to follow, to obviate the need to derive formulas.
Redundancy in a consistent manner does not harm in the mathematics
education of people who want and need an operational command of
mathematics for immediate take-home value or for future college
programs apart from pure mathematics. Reasons for minimal sets of rules
and patterns can given in courses in pure mathematics. The
pre-requisite for mastery of a theory, algebraically put, starting from
a minimal set of assumptions or axioms is a command and appreciation of
logic and for theories, algebraically put, algebra as well.
Matters of Chance
Games of chance and gambling raise hopes while the average person in the
street who plays them will likely lose more than he or she gains. The
study of chance and probability stems for the efforts of people to beat
the available games of chance. That is impossible for well-designed
games.
Apart from game playing, decisions in daily life are often not certain.
Information may be missing. For example, the sellers or a goods or
service may decide how many goods or service to offer next month based on
averages of past months or years. A knowledge of chance and probability
may help in risk avoidance, risk hedging or risk control. Studying games
of chance involving cards, roulette wheels, throwing dice and lotteries
may show students how and why to playing them and provide awareness and
greater skills for handling and avoiding risk in life on the street.
Chance, risk, probability and odds estimates may come from observation or
theory. Theory normally employ counting practices or principles to form
fractions between 0 and 1 to estimate chance or probability of this or
that happenning. The fractions in question may be expressed in terms of
percentages. A knowledge of sets and operation with them provides the
framework, practical and useful, for the later algebraic approach to
probability calculation. An mastery of exact arithmetic with fractions is
required for probability theory and more generally for algebra in high
school and college mathematics.
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Maps and Plans (Geometry). Show students how to use
maps, diagrams and plans drawn to scale for finding distances or
missing lengths, finding angles and finding coordinates,
finding the map location of points from bearings to known points
(triangularizaton). Provide practice (empirical experience) with rule
and compass construction of congruent and similar triangular. Show
how to calculate areas of regions formed by disjoint rectangles,
circles and triangles (and fractions thereof). Apply the
foregoing to calculating floor and wall areas from building or room
plans.
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Money Matters: Show students how to find and cost per
unit length, area, volume, mass or whatever in calculations involving
fractions with units.
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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
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:
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How to Ace Calculus: Street Wise Guide - Mostly
Text.
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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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