N. Taking Tests and Examinations:
On tests and examinations, start writing after you have read all
problems. Then while you are doing one, your mind may have ideas for
doing the others. Learning takes time and effort. No one but you can
provide both for your education.
Proper notation is must. Or, improper notation means you
do not how to express your ideas and solutions correctly, and so [ouch]
deserve to lose marks. Avoid that if you can.
For questions in mathematics, science and technology that require written
answers and you to show work, you must give [state, write] any and all
formulas used in your solution and specify the values of the numbers or
quantities that appear in them, you should give name of each formula - if
it has one - and you should give names of any rules or physical principles
used to obtain equations. Diagrams may be used by themselves or besides
words to explain your shorthand notation for geometric or physical
quantities. Try to to give enough information so that your answer makes
sense by itself to someone who has not seen the question.
Who will get a better mark?
Student A in answering the question what is the area of a rectangle
that is 8 cm wide by 5 cm high writes
50
instead of 40 alone. By itself without further explanation
of how this number was obtained, he gets 0.
Student B in answering the same question writes
50 square cm = 50 cm2
He might gets 0.5 marks out of four as the proper units are
included.
Student C in answering the same question writes
40
He gets 1 mark out of four as units do not appear. If I say I am
give you 10 units of something, you do not what what you will get until
the unit is specified. Answers to mathematics should be full and
precise - exact.
Student D draws the rectangle, marks the lengths of width and height
on it, write the formula, replaces letters by lengths, and then gets the
wrong answer 50 cm2. His mark is 3 or
3.5 out of four even though he gave the same answer as student
B. But the work done records the reasoning fully step by step, so
the marker can observe and see evidence of what the student
understands. So credit is given.
height
H = 5 cm
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width W = 8 cm
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\begin{eqnarray*}
\mbox{ Area }
A &=& W H \\
&=& (8 \mbox{ cm})(5 \mbox{ cm}) \\
&=& 50 \mbox{ cm}^2 \mbox{ Answer}
\end{eqnarray*}
If Students D had put 40 instead of 50, his answer would have been worth
4 out of 4 - or more.
The show work safety net
By drawing diagrams, stating the
formulas that you use , giving the values used in them, showing the
substitution, and then doing the arithmetic you are demonstrating
know-how and giving yourself a better chance of earning marks You may get
part to full marks if the formula is correct and the arithmetic is not,
or if the formula is wrong, while the arithmetic is correct. And in all
this, do not abuse the equal sign.
Abuse of Equal Signs:
Expressions of the form a = b = c means and
demands a = b and a = c. For instance in computing the average of numbers
1, 2, 3 and 4, it is wrong to write
\[ 1+ 2 + 3 + 4 = \frac{10}4 = 2.5\] as \[ 1 + 2 + 3 + 4 = 10 \]
Here
\[ 1+ 2 + 3 + 4 \mbox{ is not equal to }
\frac{10}4\]
The latter is the actual literal meaning of \[ 1+ 2 + 3 + 4 = \frac{10}4\]
You could and should write \[\frac{1 + 2 + 3 + 4}4 = \frac{10}4 = 2.5 \]
Proper Equal Sign Usage
When you put an equal sign between two
expressions as in
first expression
= second expression
you should mean that the value of the first expression in full has
the same value as the second expression in full.
Thus the equation 1+ 2 + 3 + 4 = 10 /4 are
incorrect as the expression 1+ 2 + 3 + 4 does not have the same value as
the full expression 10/4. That is the common standard
you need to follow. If you someone teaches you differently, send
them to this page.
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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:
-
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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