Mathematics Concept & Skill Development Lecture Series:
Webvideo consolidation of site
lessons and lesson ideas in preparation. Price to be determined.
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Above links to lesson links in page borders.
Deciml Place Value - funny ways to read multidigit decimals forwards and
backwards in groups of 3 or 6, US-CDN, UK-German and Metric SI style.
Decimals for Tutors - lean how to explain or justify operations.
Long division of polynomials is easier for student who master long
division with decimals.
Primes Factors - Efficient fraction skills and later studies of
polynomials depend on this.
Fractions + Ratios - See how raising terms to obtain equivalent fractions leads to methods for
addition, comparison, subtraction, multiplication and division of
fractions.
Arithmetic with units - Skills of value in daily life and in the
further study of rates, proportionality constants and computations in
science & technology.
What is
a Variable? - this entertaining oral & geometric view
may be before and besides more formal definitions - is the view mathematically
correct?
Formula Evaluation - Seeing and showing how to do and
record steps or intermediate results of multistep methods allows the
steps or results to be seen and checked as done or later; and will
improve both marks and skill. The format here
allows the domino effects of care and the domino effects of mistakes
to be seen. It also emphasizes a proper use of the equal sign.
Solve
Linear Eqns with & then without fractional operations on line segments - meet an visual introduction and learn how to
present do and record steps in a way that demonstrate skill; learn
how to check answers, set the stage for solving word problems by
by learning how to solve systems of equations in essentially one
unknown, set the stage for solving triangular and general systems of
equations algebraically.
Function notation for Computation Rules - another way of looking
at formulas. Does a computation rule, and any rule equivalent to it, define a function?
Axioms [some] as equivalent Computation Rule view - another way for understanding
and explaining axioms.
Using
Formulas Backwards - Most rules, formulas and relations may be used forwards and backwards.
Talking about it should lead everyone
to expect a backward use alone or plural, after mastery of forward use. Proportionality
relations may be use backward first to find a proportionality constant before being
used forwards and backwards to solve a problem.
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www.whyslopes.com >> Direct Current Electric Circuits >> G Series Circuit01 Next: [H Series Circuit02.] Previous: [F Unlike Resistors in Series.] [1] [2] [3] [4] [5] [6] [7][8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28]
Examples
www.whyslopes.com >> Direct Current Electric Circuits >> G Series Circuit01 Next: [H Series Circuit02.] Previous: [F Unlike Resistors in Series.] [1] [2] [3] [4] [5] [6] [7][8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28]
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Road Safety Messages
for All: When walking on a road, when is it safer to be on
the side allowing one to see oncoming traffic?
For students of reason in society, science and technology:
Pattern Based Reason describes
origins, benefits and limits of rule- and pattern-based thought and
actions. Not all is certain. We may strive for objectivity, but not
reach it. Postscripts offer
a story-telling view of learning: [
A ] [
B ] [
C ] [
D ] to suggest how we share theories and practices.
These online chapters may amuse while leading to greater precision and comprehension in reading and
writing at home, in school, at work and in mathematics.
1 versus 2-way implication rules - A different starting point - Writing or introducting
the 1-way implication rule IF B THEN A as A IF B may emphasize
the difference between it or the latter, and the 2-way implication A IF and ONLY IF B.
Deductive Chains of Reason - See which implications can and cannot be used together
to arrive at more implications or conclusions,
Mathematical Induction - a light romantic view that becomes serious.
Responsibility Arguments - his, hers or no one's
Islands and Divisions of Knowledge - a model for many arts and
disciplines including mathematics course design. Site Theme: Different entry
points may be easier or harder for knowledge mastery.
Maps + Plans Use - Measurement use maps, plans and diagrams drawn
to scale.
Euclidean Geometry - See how chains of reason appears in and
besides geometric constructions.
Coordinates - Use them not only for locating points in the plane
or space.
Complex Numbers - Learn how rectangular and polar coordinates may
be used for adding, multiplying and reflecting points in the plane,
in a manner known since the 1840s for representing and demystifying
"imaginary" numbers, and in a manner that provides a quicker,
mathematically correct, path for defining "circular" trigonometric
functions for all angles, not just acute ones, and easily obtaining
their properties. Students of vectors in the plane may appreciate the
complex number development of trig-formulas for dot- and
cross-products.
Lines-Slopes [I] - Take I & take II respectively assumes no
knowledge and some knowledge of the tangent function in
trigonometry.
What is Similarity - another view of using maps, plans and
diagrams drawn to scale in the plane and space. May buildings in
space are similar by design.
Why study slopes - this fall 1983 calculus appetizer shone in many
classes at the start of calculus. It could also be given after the intro of slopes
to introduce function maxima and minima at the ends of closed intervals.
Why factor polynomials - this 1995-96 lesson introduces calculus
skills and concepts. It may also may be given to introduce further function maxima
and minima both inside and at the ends of closed intervals.
Check Arith. Skills - too many calculus and precalculus
students do not have strong arithmetic and computation skills. The
exercises here check them while numerically hinting at
equivalent computation rules.
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