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About: Site material shows how common troubles
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Teachers & Tutors: This December 2011, 5-phase framework
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Home < Arithmetic and Number Theory Skills < 2 Arithmetic with Decimals << A Decimal Counting and Adding Methods
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A Decimal Counting and Adding Methods
1. Explaining Addition Table
2 Decimal Counting Practices
3. How to add with decimals A sans conversions
4. How to add with decimals B with conversions
5. How to add decimals C. Examples
6. Counting and adding units and mixed units
7 Adding decimal fractions using decimal point
8 What skills and work habits to require
Appendix 1 - Counting Revisited 15 minute video
Notes
Terminology: A decimal count in the following lessons means a whole
number given in decimal form. A decimal fraction in this section means
a mixed number in which the fraction part consists of tenths,
hundredths and so on. Both decimal counts and decimal fractions provide
examples of decimals.
Lessons 1 to 8:
The webvideos in each are usually two to several minutes long. Please
read the words in each page before starting the video, or while waiting
for it load, or while watching the video. Each video can be played full
screen.
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Lesson 1 - Counting Theory. Why do we take 1 + 1 = 2? How is the
addition table justified? Lesson 1 explains why 3 +5 = 8. It
is convention made in recognition of a pattern met in counting objects
or counting on fingers. This convention is founding practice for
counting and arithmetic with counts. This founding convention or
practices yields the addition table for single digit decimal numbers 1
to 9 and beyond in elementary school, and it also provides a simple to
the question why is 1 + 1 = 2?
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Lesson 2 - A Decimal Counting Principle/Practice - the basis for
decimal addition methods. Lesson 2 explains how the number
of ones, ten, hundreds and so on in decimal-based count of number of
objects should not depend on the order in which the objects are
counted. The acceptance of this assumption is another founding practice
for counting and arithmetic with counts using decimals. This counting
practice or principle is the basis for addition first with out carries
and then with carries. Exercises involving additions without carries
are introduced here.
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Lesson 3 - How to Add with Decimals when carries or
conversion are not needed. Lesson 3 continues with examples
of how counting in groups of ones, tens, hundreds and so on leads to
addition methods or practices without carries/conversions. A few
more exercises related to addition without carries appear here.
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Lessons 4 & 5 - How to Add with Carries/Conversions. Lessons
4 & 5 give more and more examples of place or column methods for
addition of decimal counts - those without Examples range from cases
with no conversions (no carries) to multiple conversions (er carries).
All exercises but one (an oversight) involve no decimal
points.
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Lesson 6. Addition of Amounts, Measures and Quantities involving
mixed units. Lesson 6 gives several examples of addition of mixed
unit of measures for money, length, time, working hours, and angles.
Column methods for addition of decimals are extended here to arithmetic
with mixed units. Exercises are included. Teachers might extend
these exercises to includes days (work days) that are 8 hours long, and
weeks (work weeks) that are 40 hours long. The numbers 8 and 40
represent economic culture in some work places, not all. Column
calculations involving regular and overtime hours could also be
included.
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Lessons 7 - How to Add Decimal Fractions with decimal points.
Lessons 7 give more and more examples of place or column methods for
addition of decimals representing whole numbers (decimal counts), or
mixed numbers (decimal fractions) involving tenths and hundredths.
Examples range from cases with no conversions (no carries) to multiple
conversions (er carries).
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Lesson 8 - What addition arithmetic teachers, parents and students
should expect and demand from themselves or others. The video in
this lesson speaks to teachers, but in retrospect it should also
address tutors, parents and students as well. It outlines the decimal
addition practices that students should master in elementary school and
not forget later.
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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
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Algebra
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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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