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Mathematics Concept & Skill Development Lecture Series: Webvideo consolidation of site lessons and lesson ideas in preparation. Price to be determined. Bright Students: Top universities want you. While many have high fees: many will lower them, many will provide funds, many have more scholarships than students. Postage is cheap. Apply and ask how much help is available. Caution: some programs are rewarding. Others lead nowhere. After acceptance, it may be easy or not to switch. 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. Site's Best LessonsFor Logic
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. For Arithmetic
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. For Algebra
What is
a Variable? - this entertaining oral & geometric view
may be before and besides more formal definitions - is the view mathematically
correct? |
www.whyslopes.com >> Algebra Starter Lessons >> B Real Numbers Extrinsic Development >> 23 Distributive Law - Two Derivations Next: [24 Signed Numbers - Arithmmetic Properties.] Previous: [22 Multiplication of Signed Numbers.] [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] [29] 23. Distributive Law for Real Numbers
Theorem: If a, b and c are real numbers then (a+b)c = ac+ bc
and
Remark: In the above proof, p and q are the coordinates of P and Q relative to the choice of k = cm as a unit vector for a coordinate system. Likewise pc and qc the coordinates of P and Q relative to the choice of m as a unit vector for a coordinate system. The distributive law implies the coordinates of sum P +Q can be calculated relative to k and then transformed (multiplied by c) or the addends can be transformed first and then added. So the sum of vectors can be calculated directly or in any unit -vector based coordinate system. The distributive law is equivalent to the latter invariance. www.whyslopes.com >> Algebra Starter Lessons >> B Real Numbers Extrinsic Development >> 23 Distributive Law - Two Derivations Next: [24 Signed Numbers - Arithmmetic Properties.] Previous: [22 Multiplication of Signed Numbers.] [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] [29] |
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? Site Reviews1996 - Magellan, the McKinley Internet Directory: Mathphobics, this site may ease your fears of the subject, perhaps even help you enjoy it. The tone of the little lessons and "appetizers" on math and logic is unintimidating, sometimes funny and very clear. There are a number of different angles offered, and you do not need to follow any linear lesson plan. Just pick and peck. The site also offers some reflections on teaching, so that teachers can not only use the site as part of their lesson, but also learn from it. 2000 - Waterboro Public Library, home schooling section:
CRITICAL THINKING AND LOGIC ... Articles and sections on topics such as
how (and why) to learn mathematics in school; pattern-based reason;
finding a number; solving linear equations; painless theorem proving;
algebra and beyond; and complex numbers, trigonometry, and vectors. Also
section on helping your child learn ... . Lots more!
2001 - Math Forum News Letter 14,
... new sections on Complex Numbers and the Distributive Law
for Complex Numbers offer a short way to reach and explain:
trigonometry, the Pythagorean theorem,trig formulas for dot- and
cross-products, the cosine law,a converse to the Pythagorean Theorem
2002 - NSDL Scout Report for Mathematics, Engineering, Technology -- Volume 1, Number 8
Math resources for both students and teachers are given on this site,
spanning the general topics of arithmetic, logic, algebra, calculus,
complex numbers, and Euclidean geometry. Lessons and how-tos with clear
descriptions of many important concepts provide a good foundation for
high school and college level mathematics. There are sample problems that
can help students prepare for exams, or teachers can make their own
assignments based on the problems. Everything presented on the site is
not only educational, but interesting as well. There is certainly plenty
of material; however, it is somewhat poorly organized. This does not take
away from the quality of the information, though.
2005 - The NSDL Scout Report for Mathematics Engineering and Technology -- Volume 4, Number 4
... section Solving Linear Equations ... offers lesson ideas for
teaching linear equations in high school or college. The approach uses
stick diagrams to solve linear equations because they "provide a concrete
or visual context for many of the rules or patterns for solving
equations, a context that may develop equation solving skills and
confidence." The idea is to build up student confidence in problem
solving before presenting any formal algebraic statement of the rule and
patterns for solving equations. ...
For Geometry
Maps + Plans Use - Measurement use maps, plans and diagrams drawn
to scale. For Calculus
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. |