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 >> Arithmetic and Number Theory Skills >> 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 MultiDigit 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. Folder Content: 11 pages. NotesFood 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 UKterms meaning of billions and trillions is indicated below.
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
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 reenforcing 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 10^{3} 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. www.whyslopes.com >> Arithmetic and Number Theory Skills >> 1 Decimal Place Value 
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. 