1 Decimal Place Value
1 Place Value in Three Digit Whole Numbers
2 Groups of Three Place Value for Multidigit Decimals
3 More on Groups of 3 Multi-Digit Place Value
4 Groups of 3 Place Value in Decimal Fractions
5 More on Groups of 3 Place Value in Decimal Fractions
6 Groups of 3 Place Value in Mixed Decimal Fractions
7 More on Groups of 3 Place Value in Mixed Decimal Fractions
8 Review Lesson 1 2 4 and 6 - All in One
9 Place Value Review - Decimal form of Avogrados number included
10 Names for Big Numbers and Powers of Ten Expansion
11 Place Value SI Standard International way
Notes
Food for thought. The SI lesson below would be
sufficient for upper secondary schools in many countries , and
independent of the use of local naming systems for big and small
numbers and measures.
The exercise of reading decimal aloud with several places before and
after the decimal point is not a practical skill. It is a skill which can
provide comic relief in a mathematics class while developing and
reinforcing place value comprehension. A possible modification of the
following lessons to favour UK-terms meaning of billions and trillions is
indicated below.
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Place Value in Three Digit Whole Numbers describes the ones,
tens and hundreds place value of the digits and, more importantly,
says how 3 digit number aloud, digit by digit.
-
Groups of Three Place Value for Multidigit Decimals gives a
single example to introduce or review the ones, thousand,
millions, billions, trillions and quadrillions place value of
groups of three in multidigit decimals. Here place value is
determined by reading a number backwards (from right to left) while
the normal way of reading identifies the groups of three and their
place value from left to right.
-
More on Groups of 3 Multi-Digit Place Value gives more
examples to example to introduce or review the ones, thousand,
millions, billions, trillions, quadrillions and quintillions
place value of groups of three in multidigit decimals. Here again
place value is determined by reading a number backwards (from right
to left) while the normal way of reading identifies the groups of
three and their place value from left to right. Recognizing place in
groups of three backwards has to be done before the number is read
aloud.
-
Groups of 3 Place Value in Decimal Fractions gives a single
example to introduce or review the thousandths, millionths,
billionths, trillionths and quadrillionthss place value of groups
of three in multidigit decimal fractions. Here place value is
determined by reading a number forwards(from left to right and can be
done while the decimal fraction is read aloud.
-
More on Groups of 3 Place Value in Decimal Fractions gives a
more examples to introduce or review the thousandths, millionths,
billionths, trillionths, quadrillionths and quintrilionth place
value of groups of three in multidigit decimal fractions. As just
said, place value is determined by reading a number forwards(from
left to right and can be done while the decimal fraction is read
aloud.
-
Groups of 3 Place Value in Mixed Decimal Fractions gives a
single example in which place value of groups of three in a mixed
decimal number or fraction is based on place value of groups of three
determined backwards, that is, contrary to the normal direction of
reading in English from a decimal point while place value of groups
of three after the decimal point is determined in accordance with the
normal reading direction.
-
More on Groups of 3 Place Value in Mixed Decimal Fractions
gives more examples of the appearance of place value from
quintillions to quintillionths in a multidigit decimals that included
a decimal point.
-
Review Lesson 1 2 4 and 6 - All in One present four examples,
one from each lesson.
-
Place Value Review - Decimal form of Avogrados number
included. Students in science courses may appreciate the order of
magnitude of Avogrado's number after this stand-alone extension of
the previous lessons introduces them to 602 septrillions.
-
Names for Big Numbers and Powers of 1000 Expansion goes from
the power of ten expansion of multidigt decimals to powers of 1000 =
103 groups of three expansion of multidigit decimals with
digits before and after a decimal point. A reference is given.
-
Place Value SI Standard International way. The SI (System
International) systems of units and measures provides "standard
names" for big and small numbers from yota to yocto for powers of
103 and it reciprocal 10-3 that can occur in
discussing group of three place value in multidigit decimals. The
alternative names are given along side dare-we-say common US-style
names for numbers, big and small. A reference is given. for
Modification for UK big and small number naming.
In the UK, a billion is not a thousand million, is it is a million
million. Further, a trillion is not a thousand million, it is a million
billions. That suggests a variation of the foregoing in which multidigit
decimals may be read aloud in full or partial groups of six, where each
group of six consists of two groups of three. Thus
56 789 345 230 456 678 . 560 678 999 12
might be read aloud as
56 thousand and 789 billions
345 thousand and 230 millions
456 thousand and 678 ones or units,
560 thousand and 678 millionths, and
999 thousand and 120 billionths
That being said, some variation of this ideas may work better. Again, the
skill of reading multidigit decimals aloud in groups of three or six is
not a practical. It is a skill aimed at developing and re-enforcing place
value.
Is this better? For reading in full or partial groups of three
digits, UK instructors might emphasize the use of SI terms yota to yocto
for powers of 103 and it reciprocal 10-3 because
groups of three are easier to digest than groups of six, and groups of
three may lead to better comprehension of the SI naming system for large
and small numbers and measure.
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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
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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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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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