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. Are you a careful reader, writer and thinker?
Five logic chapters lead to greater precision and comprehension in reading and
writing at home, in school, at work and in mathematics. Early High School Arithmetic
Deciml Place Value  funny ways to read multidigit decimals forwards and
backwards in groups of 3 or 6. Early High School Algebra
What is
a Variable?  this entertaining oral & geometric view
may be before and besides more formal definitions  is the view mathematically
correct? Early High School GeometryMaps + Plans Use  Measurement use maps, plans and diagrams drawn to scale.  Coordinates  Use them not only for locating points but also for rotating and translating in the plane.  What is Similarity  another view of using maps, plans and diagrams drawn to scale in the plane and space. Many humanmade objects are similar by design.  7 Complex Numbers Appetizer. What is or where is the square root of 1. With rectangular and polar coordinates, see how to add, multiply and reflect points or arrows in the plane. The visual or geometric approach here known in various forms since the 1840s, demystifies the square root of 1 and the associated concept of "imaginary" numbers. Here complex number multiplication illustrates rotation and dilation operations in the plane.  Geometric Notions with Ruler & Compass Constructions : 1 Initial Concepts & Terms 2 Angle, Vertex & Side Correspondence in Triangles 3 Triangle Isometry/Congruence 4 Side Side Side Method 5 Side Angle Side Method 6 Angle Bisection 7 Angle Side Angle Method 8 Isoceles Triangles 9 Line Segment Bisection 10 From point to line, Drop Perpendicular 11 How Side Side Side Fails 12 How Side Angle Side Fails 13 How Angle Side Angle Fails 
www.whyslopes.com >> Algebra Starter Lessons Algebra Skilll Development Guide. 1 Three Skills For Algebra. 2 What is a Variable. 3 Adding Words To Arithmetic. 4 A Brief Story of numbers and algebra. 5 Talking about Numbers and Quantities. 6 Three Notions of What is a Variable. § 1 Working With Sets: 1 Finite Sets. 2 Venn Diagrams. 3 Counting with Sets etc. 4 Subset Builder Notation. 5 Product Builder Notation. 6 Power Set Notation. 7 Cautious or Safe Set Construction. 8 Sets of Numbers. 9 Sets in Probability and Statistics. 10 Set View of Wordy Extensions To Arithmetic. Folder Content: 10 pages. 1 Written work formats for developing and showing skill. 2 Another Rectangle Area Formula Example. 3 Triangle Area Formula Example. 4 Circle Area Formula Example. 5 Box Volume Formula Example. 6 Pythagorean Hypotenuse Calculation Example. 7 Compound Interest Formula  Introduction. 8 Compound Interest Formula  Evaluation. 9 Volume of Cone. 10 Volume of Pyramid. 11 Volume of Sphere. 13 Naming Identifying Formulas with Words. Folder Content: 12 pages. Formula Usage  Show Work Format. Skilll Development Guide for Introducing and Solving Linear Equations. Using Letters for Physical Quantities. § Step 1 Stick diagram and fractions: 2 Three Examples. 3 Two Examples. 4 Two Examples. 5 Three Examples. 6 Three Examples. 7 Two Examples. 8 One Example. 9 Three Examples. 10 One Example. Skill Development Notes. Folder Content: 10 pages. 1 Proper Equal Sign Usage. 2 Three Examples. 3 Four Examples. 4 Four Examples Fractional Coefficients. 5 Algebraic Solutions  Introduction. 6 Algebraic Solution Example. Folder Content: 6 pages. 1 Essentially One Unknown. 2 Essentially one exercises  three with solution. 3 Solving triangular system example. 4 Solving a triangular system exercise. Folder Content: 4 pages. 1 GE Substitution  four examples. 2 GE II Comparison. 3 GE III Equation Addition and Multiplication. 3 Gaussian Elimination 3 unknowns first example. 4 GE III Animated Examples. 5 Gaussian Elimination for 3 unknowns 2nd example. Folder Content: 6 pages. Simple Exercises. More Exercises. Folder Content: 5 pages and 4 subfolders: . 1 Formulas Dependence and Function Notation. 2 Computation Rules Evaluation. 3 Geometric Formulas and Function Notation. 4 Changing Letters. 5 Independent versus Dependent Variables. Folder Content: 5 pages. 1 Whole and Natural Numbers. 2 Integers. 3 Fractions. 4 Rational Numbers. 5 Rational Numbers More. Skill Development Guide for this coverage of Real Numbers. 6 Unsigned Real Numbers. 7 Real Numbers as Line Cordinates. 8 Coordinates for Maps and Planes. 9 Coordinates for Regions in Space. 10 Real Number Lengths and Signs. 11 Real Number Addition. 12 Real Number Additive Inverses or Negatives. 13 Real Number Subtraction. 14 Real Number Multiplication. 15 Real Number Division. 16 Real Numbers Comparison. Folder Content: 17 pages. 1 Real Numbers Comparison. 2 More and Less Than for Counts and Measures. 3 More and Less Than with Unlike Signs. 4 Comparison of Negative Numbers. 5 Greater More Less Than Signs in General. Folder Content: 5 pages. 1 Equivalent Computation Rules. 2 Addition and Multiplication Axioms. 3 Product Axioms  Two Forms. 4 Subtraction and Division Axioms. 5 Equality in Algebra. 6 Equations and Systems  Equivalent or Implied. Folder Content: 6 pages. 1 Changing Calculations. 2 Linear Equation Literal Solution. 3 Linear Equation Literal Solution  More. 4 Rectangle Area and Like Formulas Backwards. 5 Triangle Area Formula Backwards. 6 Compound Interest Forward and Backwards. 7 Pythagorean Theorem Chinese Square Proof. 8 Pythagorean Relation Forwards Backwards. 9 Circle Area and Perimeter Formula BackwardsForwards. Reading Guide for this Unifying Theme for Algebra Logic and Beyond. Folder Content: 10 pages. Proportionality Forwards and Backwards Skill Development Guide. 1 What is Proportionality. 2 Algebraic View. 3 Proportionality Examples. 4 Rates Ratios and Proporitionality. 5 Proportionality in Equivalent Fractions. Folder Content: 6 pages. 1 Decimals Modular and Remainder Arithmetic. 2 Fraction Operations Physical Development. 3 Inequalities Algebraically. 4 Fraction Operations Axiomatic Development. 5 Areas of Rectangles Revisited. Folder Content: 5 pages. 1 The Counting Origins of Numbers. 2 Combing Counts  Addition Skills and Principles. 3 Multiplicative Counting Skills Principles. 4 Commutative Law  Groups Counting Form. 5 Distributive Law for Whole Numbers. 6 Column Methods for Decimal Multiplication. 7 Decimals Multiplication Methods Examples. 8 Column Multiplication Methods in General. A Decimal Addition  Columm Methods. B Decimal Comparison and Subtraction. C Three Decimal Subtraction Methods. D Long Division Methods. E Long Division Methods  more. Folder Content: 13 pages. 1 Fractions with Finite Decimal Expansions. 2 Counting Digits in Decimal Multiplication. 3 Location of Point in Decimal Multiplication. 4 Location of Point in Decimal Addition. 5 Fractions with Infinite Decimal Expansions. 6 Infinite Decimals Ending in 9 repeating. 7 Arithmetic with Infinite Decimal Expansions. 8 Division and Mulplication of Compound Fractions. 9 Division with Digits after Decimal Point. 10 Numbers given by Infinite Aperiodic Decimal Expansions. 11 Signed Number Addition and Addition Properties. 12 Real Numbers Line  Signed Coordinates. 13 Arrows and Vectors in a Plane. 14 Vector Head to Tail Sums and Resultants. 15 Head to Tails inplace Addition  Associative. 16 Collinear Horizontal ArrowsVectors. 17 Arrows Rotate to Reverse with Length Unchanged. 18 Geometrically Why Vector Addition Commutes. 19 Signed Multiples of Vectors. 20 Length and Direction of Collinear Vector Sums How to Add Definition. 21 Addition of Multiples of a Single Vector. 22 Multiplication of Signed Numbers. 23 Distributive Law  Two Derivations. 24 Signed Numbers  Arithmmetic Properties. 25 Midway Convergence to Axiomatic Approach. 26 More Less Greater Than Comparison. A Signed Number Arithmetic Review. A Modular and Remainder Arithmetic. B real numbers with signs operational development. Folder Content: 29 pages. Folder Content: 7 pages and 12 subfolders: . www.whyslopes.com >> Algebra Starter Lessons 
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? Play with this [unsigned]
Complex Number Java Applet
to visually do complex number arithmetic with polar and Cartesian coordinates and with the headtotail
addition of arrows in the plane. Click and drag complex numbers A and B to change their locations.
Pattern Based ReasonOnline Volume 1A, Pattern Based Reason, describes origins, benefits and limits of rule and patternbased reason and decisions in society, science, technology, engineering and mathematics. Not all is certain. We may strive for objectivity, but not reach it. Online postscripts offer a storytelling view of learning: [ A ] [ B ] [ C ] [ D ] to suggest how we share theory and practice in many fields of knowledge. 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; patternbased 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
crossproducts, 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 howtos 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. ...
Senior High School Geometry

Euclidean Geometry  See how chains of reason appears in and
besides geometric constructions. Calculus Starter Lessons
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. 