## Where to Start with Life of Fred?

**Well the beginning, of course. However, maybe you need to start somewhere in the middle. Here are some suggestions from the author himself, in verbatim.**

If your child...

Hasn't learned the addition and multiplication tables cold. When you ask, "Seven times eight?" they don't respond immediately with "56."

The Elementary Series was written for those who are not yet in at least the fifth grade.

If your child...

Hasn't learned the addition and multiplication tables cold. When you ask, "Seven times eight?" they don't respond immediately with "56."

Start with

*Life of Fred: Apples*if your child does not know the addition tables cold.

Start with

*Life of Fred: Farming*if your child does not know the multplication tables cold.

Each of the books contains so much more than just doing math facts. We cover many different topics. (This true in all of the Life of Fred books.) So, you can always enjoy the first few books quickly and then find the perfect spot for your student where you see the need to slow down.

**Knows the addition and multiplication tables cold:**

If you know the addition and multiplication tables cold and are

*in at the least fifth grade*, then start with

*Life of Fred: Fractions.*Your child will learn why it is important not to run while carrying an 18" knife. There is no hurry! It would be a mistake to push kids into

*Life of Fred: Fractions*before they are developmentally ready. Students of normal academic ability and drive who begin Life of Fred: Fractions even in the 7th grade have a decent chance of starting college calculus (

*Life of Fred: Calculus*) before the end of their high school years.

**Knows all about arithmetic (fractions and decimals and percents):**

There are many home schooling math curricula out there. .......Some of them are so boring/repetitive that kids quickly forget anything they may have learned.

.......Some of them are mathematically light-weight. The kids think that they have learned all of arithmetic. That is, until they hit their SATs or a college classroom. At that point they find out that there are big gaps in their knowledge.

With that in mind, let's see how much arithmetic your child has learned.

Here are some representative questions to ask your child. They are taken from

*Life of Fred: Fractions and Life of Fred: Decimal and Percents*. Have them take out a piece of paper and play with these questions . . .

Each of these two books contains more material than their titles indicate. Here are some questions from these two books of the series. Have your child answer these questions and we'll see where in the series is the best place to start.

1. Write 99 in Roman numerals. (from

*Life of Fred: Fractions*, p. 74)

2. What is the square of two and five-eighths? (

*Life of Fred: Fractions*, p. 131)

3. What is the inverse function to "multiply by six and then add twenty-four"? (

*Life of Fred: Fractions*, p. 131

4. If a fence is 52" tall and it is made 40% higher, how tall would it be? (

*Life of Fred: Decimals and Percents*, p. 137

5. Fred had 2100 books in his office. He lent 37% of them to students. How many books are still in his office? (

*Life of Fred: Decimals and Percents*, p. 124)

**Has done the first year of high school algebra:**

Let's see how much first-year algebra your child has learned. Here are some representative questions to ask your child. They are taken from

*Life of Fred: Beginning Algebra*. Have them take out a piece of paper and play with these questions:

1. What is the coefficient of 34.7abc? (page 49)

2. Army regulations require that their pickle relish use 10 pickles per pound of relish. In one giant bowl, the cooks have relish that only used 8 pickles per pound (too weak). In another bowl, they have relish that has 16 pickles per pound (too strong). They need to make 200 pounds of relish. How many pounds of each bowl should they use?

(p. 107)

3. The point (a, b) is directly below (4, 9). What can you say about a? What can you say about b? (p. 136)

4. The cooks at the army camp have four different dinner menus. In the next four days, how many ways could they serve them so every dinner will be different? (p. 161)

5. Solve 1/(x-1) + 1/2 = 2/(x² -1) (p. 210)

6. Suppose there are two elements in the domain of some function and two elements in the range. How many possible functions could there be? (p. 282)

7. Solve 48 - 3x > 36 (p. 300)

**Has done the second year of high school algebra:**

Of the "heavyweights" in the homeschooling world, Saxon is usually considered the 800-pound gorilla, but it is sadly lacking in its content. A couple of months ago I looked at his Alg 2 and compared it with

*Life of Fred: Advanced Algebra*. I counted a dozen major topics that he leaves out that

*Life of Fred: Advanced Algebra*includes:

1. Permutations

2. Matrices

3. Linear programming

4. Series

5. Sigma notation

6. Sequences

7. Combinations

8. Pascal's triangle

9. Math induction

10. Partial fractions---needed in calculus

11. Graphing in three dimensions

12. Change-of-base rule for logarithms

All these topics should be in any full presentation of second-year high school algebra. With that in mind, let's see how much second-year algebra your child has learned.

Here are some representative questions to ask your child. They are taken from

*Life of Fred: Advanced Algebra*. Have them take out a piece of paper and play with these questions . . .

1. What is the slope of the line that is perpendicular to

y = (7/3)x - 5? (p. 131 in LOF:AA)

2. Using Cramer's Rule solve for x:

x + y = 1

3x = 2y + 18 (from p. 166)

3. What is the equation of the ellipse whose vertices are

(4, 5) and (10, 5) and which has a semi-major axis of length 1? (p. 197)

4. Let A and B be any two arbitrary sets. Suppose we have a function f:A→B that is 1-1. What can we say about the number of elements in A compared with the number of elements in B? (p. 226)

5. Resolve 8/(x²-4) into partial fractions. (p. 244)

6. What is the sum of the infinite geometric progression

1/3 + 1/9 + 1/27 + 1/81 + . . . ? (p. 282)

**Has done two years of high school algebra and geometry:**

In the government school system, that's the first three years of high school math. The fourth (and last) year will be covered with

*Life of Fred: Trigonometry*and its study guide*Fred's Home Companion: Trigonometry.*

These two hardback books will do three things:

1. Offer a complete course in trig, including:

Sines

angle of elevation

opposite and hypotenuse

definition of sine

angle of depression

area of a triangle (A = ½ ab sin θ)

Cosines and Tangents

adjacent side

slope and tan θ

tan 89.999999999999999999999º

solving triangles

Trig Functions of Any Angle

initial and terminal sides of an angle

standard position of an angle

coterminal angles

expanding the domain of a function

periodic functions

cosine is an even function

sine is an odd function

Trig Identities

definition of an identity

proving identities

four suggestions for increasing your success in proving identities

cotangent, secant and cosecant

cofunctions of complementary angles

eight major tricks to prove identities

Radian Measurement

degrees, minutes, seconds

sectors

conversions between degrees and radians

area of a sector (A = ½ r²θ)

Conditional Trig Equations and Functions of Two Angles

definition of a conditional equation

addition formulas

double-angle formulas

half-angle formulas

sum and difference formulas

product formulas

powers formulas

Oblique Triangles

law of sines

law of cosines

Inverse Trig Functions

using a calculator to find trig inverses

principal values of the arctan, arcsin and arccosine

the ambiguous case

Polar Coordinates

Cartesian coordinates

graph polar equations

converting between Cartesian and polar coordinates

the polar axis and the pole

symmetry with respect to a point and with respect to a line

Polar Form of Complex Numbers

r cis θ means r(cos θ + i sin θ)

de Moivre’s theorem

proof of de Moivre’s theorem

the five answers to fifth root of 1

2. Offer six (optional) chapters which "Look Back" to the important topics in algebra.

For example, the sixth of those Looking Back chapters covers:

functions

1-1, onto

domain, codomain

1-1 correspondence

the definition of the number 1

natural numbers

the definition of the number zero

whole numbers

rational numbers

irrational numbers

transcendental numbers

natural logarithms and common logarithms

e

real numbers

algebraic numbers

pure imaginary numbers

complex numbers

the complex number plane

i to the ith power is a real number (≈ 0.2078796)

3. Offers a Looking Forward to the two years of calculus and examines each of the 24 chapters in

*Life of Fred: Calculus*and describes what parts of high school math will be required. It provides exercises for each of the topics.

Both books together are $43.

**Has done four years of high school math (including two years of algebra, a year of geometry and trigonometry)**

College calculus is next!

*Life of Fred: Calculus*will offer a joyful romp through college freshman and sophomore calculus. $39 and we pay the shipping.

All the traditional calculus topics are covered, including first and second order differential equations.

As with all of the Life of Fred books, things happen

*first*in Fred's life, he needs a particular piece of math, and

*then*we teach the math. Every part of calculus is motivated by real life.

To mention just one example, before we introduce the hyperbolic trig funcitons (sinh, cosh, and tanh) in Chapter Nineteen, Fred and his three friends are at an all-you-can-eat buffet.

››› They are standing in a line between those ropes-on-poles.

››› One of Fred's friends (the 8'2" lion) is lassoed by some kid. The lion runs, and we look at the skid marks made by the kid.

››› The kid trips and ends up sinking in a 5000-gallon pot of cheese soup.

And suddenly, we have three uses of the hyperbolic trig functions.

In addition to the usual calculus topics, there is a "Further Ado" section at the end of the book (75+ pages) that includes many topics that are often not found in many lower division calculus books.

For example:

The proof of: If f:A –› B and g:B –› A are two 1-1 functions, then there exists a function h:A –› B that is both 1-1 and onto.

The formal defintion of limit.

Proofs of the Product Rule; the Quotient Rule; the Chain Rule; Rolle's Theorem; the Mean Value Theorem; and the Fundamental Theorem of Calculus.

The Parametric Form for Integrals.

An introduction to programming in BASIC.

Nine-dimensional vector spaces.

Lagrange Multipliers.

Green's theorem, Gauss's theorem, and Stokes's theorem.

**You may ask what about a schedule? How quickly will I progress?**

The Life of Fred series is designed for home schoolers, so there is no need to cram, squeeze, or expand the material in order to fit into some government 9-month program. When students finish one course, then they begin the next one.

The two books (

*LOF: Fractions*and

*LOF: Decimals & Percents*) together take about 65-70 lessons if you do one each day including the time for the Bridges exams.

*LOF: Elementary Physics*, 40 daily lessons.

*LOF: Pre-Algebra 1 with Biology,*46 daily lessons.

*LOF: Pre-Algebra 2 with Economics*(which does a lot of work with word problems), 34 daily lessons.

*LOF: Beginning Algebra*(with its study guide,

*Fred's Home Companion: Beginning Algebra*) are laid out in 108 lessons.

Then

*LOF: Advanced Algebra*(with its study guide,

*Fred's Home Companion: Advanced Algebra*), 101 lessons.

Then

*LOF: Geometry*2 semesters.

My laying out lesson plans, which was true up through advanced algebra, was a bit like having training wheels on a bicycle. After a while they become unnecessary—and even sometimes a hindrance.

An adult, for example, reading a novel doesn't have the number of pages to be read each day laid out by the author.

At this point in your child's education, I think it is important that some of the scheduling be done by your child. Instead of your laying out the schedule, I would suggest that you ask that your child look over the table of contents of the book and lay out a weekly outline of what will be covered in each week with the thought of finishing the book in a year's time. Expect anywhere from nine months to 14 months to complete the book—depending on how many optional chapters, such as chapter 5 1/2 for chapter 7 1/2 or chapter 8 1/2, etc. are covered—and depending on the academic ability of your child.

This is a step toward adulthood . . . taking responsibility for little part of one's own education.

Then

*LOF: Trig*(with its study guide,

*Fred's Home Companion: Trig*), 94 daily lessons.

Then they will begin

*LOF: Calculus*which covers all of the two years of college calculus. It is not broken into lessons.

*LOF: Statistics*covers a year of college statistics. For high school seniors, consider finishing the first five chapters (the first 203 pages of the book). That will give you a solid grounding in statistics.

*LOF: Linear Algebra*is a full semester upper division college course.