**Learn for Excellence: **

** ***for those who will go far.*

**Math Program **

**Levels: 1-12 + Calculus. ** At *Learn*, we teach mathematics from the very beginning levels --

learning to count -- to a very advanced level.
Our most advanced level is calculus for advanced placement,

which is the university freshman level; however we hope
in the future to teach more advanced courses.

**Standards of Excellence.** We have stricter math standards than any school I know of. For example,

in order to pass fraction addition and subtraction, our students must work 20 worksheets, each with 20 problems,

and must make 95% correct on all 20 worksheets. Whenever a child misses more than one problem,

the worksheet will have to be redone at a later time.

** Failure not allowed.** On the other hand, we do not have failure at* Learn*. If a student does not pass a worksheet,

no "F" grade assigned.
Student simply tries again the next time until a passing grade is achieved.

In this way, we train our students
to expect the very best from themselves.

**Students work at own level.** Beginning students are tested to determine the appropriate level.

Then they are given exercises, or worksheets to do, through which
they learn. Help is given when needed.

Students are allowed to advance as fast as they are able. From time
to time (or whenever the parents ask),

the director will discuss the student's progress and level.

** Summary of Mathematics Subjects**

**Basic arithmetic.** This is the beginning. Children can and should start learning this at home, as early as age 2 or 3.

In school, this generally takes up the first 2-4 grades. The first thing is learning to count.

Although we do not take children younger than 6, I strongly encourage parents to

teach their children to count as soon as the kids start learning to talk. Teach them to count using their fingers, at first.

This greatly facilitates their ease in learning to add, subtract, etc.

Once kids can count up to 20 or more, teach them to count by 5s, 10s, and so on. Also, TEACH THEM TO COUNT

BACKWARDS, that is, from 20 backwards down to 0. Also, better to start counting at 0, rather than 1.

Zero, 0, is one of the most important numbers in math, so don't ignore it like most parents do.

Once kids can count easily, teaching to add, then subtract, multiply and divide follows.

We have many worksheets which provide the necessary practice needed for kids to become very good at arithmetic,

and this is the first step to becoming good in mathematics.

**Word Problems.** These are very important in learning why math matters, and to USE math.

Math is important because it is used in almost every field. Not only in engineering and computers,

but in many others areas: accounting and finance, investing, and so on. The reasoning and thinking

learned in math is criticial to law, medicine, practically every profession.

Learning to do a proof in geometry or algebra is the same type of reasoning used in a court of law.

We use word problems from very early -- first and second grade -- on, to teach kids how to reason with the math

they learn. This is one of the reasons I also insist on reading as well.

Math and reading go together, and complement each other greatly.

**Fractions and Decimals.** This is the next step up from basic integer arithmetic.

Once kids have become good at basic arithmetic, they begin learning fractions. In schools,

this generally begins around 4th grade, although some begin later and others earlier.

I teach kids new to fractions by getting them to visualize a "whole" -- be it a pizza or a rectanclular strip,

and learning to add and subtract at first using a strip of paper called a "fractions strip."

Once they get the idea
visually, it's much easier to teach them to find a common denominator mentally or with

pencil and paper. This is a big step up from basic integer arithmetic,

and kids who have mastered the basics of arithmetic catch on much quicker.

**Mental Math.** This is an area which schools do NOT teach, but which is very important in my opinion.

Mental math is learning to do complex calculations mentally. This goes against the current trend in society

and education today, which teaches us to be lazy mentally because, after all, we have calculators to do arithmetic,

smart phones to remember all our contacts, etc. Mental math is FUN, and despite the above is very USEFUL,

and more, serves to greatly improve math competence and general mental memory. I teach my students

to do calculations like squaring 2 and 3 digit numbers in their heads. For example, pick a 2 digit number-- say, 87 --

and my kids can tell you in a matter of seconds that 87 X 87 is 7,569.

This is very helpful in taking timed tests, and in improving their algebra skills.

**Number Bases.** This is another area which most schools don't teach, but which they should.

We use the base-10 number system, that is, we have 10 digits 0-9, and each digit represents a power of 10.

We teach our kids to use other bases, and this enhances their knowledge of numbers and math in general.

Further, we especially emphasize competence in base 2, or binary, because this is greatly used in computers, and

also bases 8, or octal, and 16, or hexadecimal, as these are also greatly used in computers and digital engineering.

Learning to understand different bases early improves students understanding of numbers and math in general,

and better prepares them to learn about how computers work.

**Algebra I and II.** Algebra is taught be a series of lessons, each lesson consisting of several worksheets.

All the topics generally covered Algebra I and II in US schools are covered, but as always, our objective

is to cover these more thoroughly. The algebra lessons begin with order of operations, and include

lessons on exponents and radicals, solving for *x*, absolute values, systems of equations,

linear equations, quadratic equations, and others.

**Geometry.** For geometry, we use a 300+ page workbook which covers all important geometry topics,

and this is augmented by an excellent video class which explains the topics in depth. Topics covered include

polygons, angles, parallel lines, and the pythagorean theorem. Named after the Greek mathematician Pythagoras,

this is perhaps the most important theorem in mathematics. In *Learn for Excellence, we show our students
how to prove this important theorem. *

**Precalculus.** This consists of advanced topics from algebra, such as the conic sections, logarithmic

and exponential functions, and perhaps more importantly, trigonometry. Trigonometry is a study of the relations

of the sides of a right triangle. The basic definitions of the trig functions -- sine, cosine, tangent, etc. -- are taught both

in terms of a right triangle, and from the unit circle.
Precalculus may be thought of as the culmination of high school math,

all that is required to go on to the university level.

**Calculus.** Calculus represents a definite step to a higher and more modern level of mathematics. Calculus was

first developed in the 17th century. Isaac Newton and Gottfried Leibniz are often considered the inventors of calculus.

Calculus consists of two major parts. The first is called *differentiation*, or taking the *derivative* of a function.

Simply put, the derivative of a function is the slope of the line tangent to the function, which is also a function itself.

The second major part is called *integration* Simply put, this is calculating the area under the graph of a function.

It turns out that these two seemingly different calculations are the inverses of each other.

Calculus provides means to solve problems which were not solvable before. It is used, for example, in calculating speed

and velocity, the trajectories of the planets, a comet, or a space ship going to the moon.

Calculus makes EXTENSIVE use of algebra, geometry, trigonometry, all the precalculus subjects.

At *Learn*, I will be offering calculus very soon, tentatively in the fall of 2015. This will require a serious commitment

on the part of the students, and a demanding schedule. More information will be provided on this soon.

**Back to Learn for Excellence Back to Bert Lundy **

** **