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Original Site Title: Appetizers and Lessons for Mathematics and
Reason, June 1995 to April 2012. New site title:
Logic and Mathematics Skill & Concept
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for college students, gifted teens, home-tutoring and K1-12 schooling, with chapters
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About: Site material shows how common troubles
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Teachers & Tutors: This December 2011, 5-phase framework
offers a context for mathematics & logic education. Phases 1 to
3 may focus on skills with actual or potential local value for
adult & daily life. College-oriented phases 5 & 4 focus on
calculus & preparation for it. Phases 1 to 4 may also serve
trades & professions not dependent on calculus. Reform: look
before you leap - plan all in detail first.
Site Review: Math resources ... span ... arithmetic, logic,
algebra, calculus, complex numbers, and Euclidean geometry. Lessons
and how-tos .... provide a good foundation for high school and
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Home < Arithmetic and Number Theory Skills << 10 LCM GCD and Euclid GCD Algorithm
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10 LCM GCD and Euclid GCD Algorithm
12 GCD 2700 288 via Primes
1 Least Common Multiples LCM Introduction
2 Least Common Multiple LCM intro via list method
LCM 60 45 Avoid List Method Use Primes
4 LCM of 8 and 10 via Primes
5 Common Divisors 60 45 via Primes
6 GCD from Primes
7 GCD and LCM from prime factorization
8 GCD from Euclidean Algorithm
9 GCD of 360 110 via Primes and Euclid Algorithm
10 Euclid Algorithm with 129 125 and with 45 14
11 GCD 2700 288 via Euclid Algorithm
13 GCD from given Prime Factorizations
14 GCD of 650 110 via Primes LCM via Product Rule
15 GCD of 650 225 via Euclid Alg LCM via Product Rule
16 GCD and LCM of 650 225 via Primes
17 GCD LCM of 85 and 60 via Primes
Notes
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Least Common Multiples [LCM] Introduction. This video lists
the first 14 multiples of 6, and the first 6 multiples of 14 to see
if there is a smaller common multiple that 6 × 14 = 14 × 6. The video
provides a hint of the role of primes in find the LCM of the two
numbers. ??? KILL
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Least Common Multiple LCM intro via list method. This video
answers the question what is a LCM, explains the motivation for LCM
calculation, and introduces the list method for finding the LCM of a
pair of small whole numbers, here 6 and 8. For these two numbers, the
list method begins by writing or listing the first 6 multiples of 8
and the first 8 multiples of 6 to be list
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LCM 60 45 Avoid List Method Use Primes. This video explains
why the use of prime factorization requires less work than the list
method to find the LCM for two numbers, namely 60 and 45. Includes a
clear introduction of the prime factorization based method for
finding LCMs.
-
LCM of 8 and 10 via Primes. This video shows how to find the
least common multiple of 8 and 10 using their prime factorizations. The video
explains the method. The video includes the list method as well for
confirmation.
-
Common Divisors 60 45 via Primes. This video employs the prime
factorizations of 60 and 45 - obtained in the previous lesson - may
be used to generate common divisor and to identify the greatest
common divisor.
Optional Question: How many common divisors are their. Master
section on Combinatorics to answer.
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GCDs from Primes. This video shows how prime factorization of
whole numbers may be used to find the greatest common divisors of the
whole numbers.
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GCD and LCM from prime factorization. This video gives
examples of how to compute Greatest Common Divisor and Least Common
Multiples of a pair of numbers, each equal to product of primes -
their prime factorizations.
-
GCD from Euclid's Algorithm. This video gives a
first example of Euclid Algorithm for find the greatest
common divisor of two numbers, here 875 and 300. It then
simplifies the fraction 875 over 300. Finally, it shows how
to construct a small - in fact the least - common multiple of them
for use in addition of two fractions with denominators 875 nad 300.
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GCD of 360 110 via Primes and Euclidean Algorithm. This video calculates
the GCD of 360 and 110 with Euclid Algorithm and then verifies
the same result can be obtained from prime factorization. Euclid Algorithm
may be quickest - proof of that or discovery of that is left to further
studies in mathematics.
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Euclid Algorithm for 129 125 and for 45 14. This video provides two
more examples of greatest common divisor calculation with Euclid's algorithm.
The GCD in both examples is 1. Thus implies that in each pair of numbers,
the pairs are relatively prime - their prime factorization share no common
primes.
-
GCD 2700 288 via Euclid's Algorithm. This video calculates the greatest
common divisor of 2700 and 288 via Euclidean Algorithm. Then it employs
the GCD to simplify a fraction where one is the numerator and the other
is denominator. Lastly, it employs number obtained from the algorithm
to obtain a Least Common Multiple - LCM
-
GCD 2700 288 via Primes.This video calculates the greatest
common divisor of 2700 and 288 using their prime factorizations
-
GCD from given Prime Factorizations. This video shows how to calculate
GCD for numbers given as products of primes. Three products are given. The products
are consider in pairs. Question: What the GCD of all three numbers?
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GCD of 650 110 via Primes. Then LCM via Product Rule. The product of two numbers
equals the product of their GCD and LCM. We call that relation, a product rule. If the
product GCD × LCM is known along with one of the factors, then the other
factor can be calculated. That represents a backward use of this product rule.
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GCD of 650 225 via Euclid Alg. Then LCM via Product Rule. This video
calculates the GCD of the two numbers, and then uses the product rule introduced
in the previous lesson to obtain the LCM. The next video confirms the GCD and LCM
computed here by deriving them from prime factorizations.
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GCD and LCM of 650 225 via Primes. This video confirms the GCD and LCM
computedin the previous video using prime factorizations.
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GCD LCM of 85 and 60 via Primes. This video calculates the GCD and LCM
of the two numbers 85 and 60 with the aid of their prime factorizations.
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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
- 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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