1 Maps Plans Measurement
1 Length Measurement
2 Measuring Area Directly
3 Lengths and Areas on Maps and Plans
4 Angles on Maps Plans drawn to scale
5 Drawing to Scale Avoids Angle Distortions
6 Figuring with Maps Not to Scale
8 More Use of Maps Not Drawn to Scale
A Measurement with Ruler - Proper Use
Folder Contents
This folder Maps Plans and Measurements describes length measuring
devices, direct area calculation, length and area calculation from maps
and plans, the preservation of angles on maps and plans drawn to scale,
the distortion of angles and proportions on maps and plans not drawn to
scale, and the use of maps and diagrams not drawn to scale. Here are
skills to check via questions and exercises.
Late primary and early secondary quantitative skill development should
emphasize measuring skills with rulers, tape measures and protractors for
measuring lengths and angles in the environment and on maps and plans
drawn to scale. Tutors and teachers may observe that the map measurements
are often easier to make - require less movement. This level may show
students how to recognize different kinds of triangles and quadrilaterals
and connect the latter to parallel lines or line segments. All the
foregoing may be done on paper with maps, plans or drawings. Coordinates
signed and unsigned should be introduced along line segments and for maps
and plans. The game of Battleship may be adapted to test mastery of
coordinates. Students may be further given a sequence of coordinates for
points in the plane to join to test and reward coordinate mastery. The
joined points or dots may form a picture of objects or animals in the
local environment.
Familarity with maps and diagrams drawn to scale should make the
assumptions or axioms of coordinate free Euclidean more self-evident. An
operational mastery of maps and plans drawn to scale sets the stage for
site simplified treatment of Euclidean Geometry, one reserved for the
keener students in senior highschool, one sufficient to introduce
students to the use of deductive reason in mathematics.
The previous two paragraphs and the next are duplicated in the site discussion of
what is similarity.
Proportionality of Map and Actual Measurements Explained
A map unit length corresponds to a given length, a unit length, in the
real world. Here the number N of map unit lengths needed to cover a path
on the map is the same as the number N of given lengths needed to cover
the corresponding path in the real world. The ratio of the number N of
given lengths to the number N of map unit lengths equals the the ratio of
the given length to the map unit length, that is the map scale factor.
Likewise, the number M of map square units needed to cover a region in
the the map equals the number M of of squares with sides provided by the
given lengths needed to cover the corresponding region in the real world.
The ratio of the number M of given lengths squared to the number M of map
unit squares that equals the the ratio of the given length squared to the
map unit square, that is the map scale factor, squared.
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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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