Directory of math files with respective topics
Basic Skills directory
1. (Lesson 1) Graphic flash cards for addition and subtraction of numbers 1 through 9
2. (Lesson 2) Adding numbers with several digits. Adding columns.
3. (Lesson 3) Subtraction with borrowing.
4. (Lesson 4) Introduction to decimals. Addition and subtraction of dollars and cents.
5. (Lesson 5) Multiplication as repeated addition. Multiplication tables. Commutative rule.
6. (Lesson 6) Carrying in multiplication. Several digits times 2 through 9. Three digits times two digits.
7. (Lesson 7) Concept of position in number system. Area of rectangles as multiplication problems. Rounding numbers.
8. (Lesson 8) Division as repeated subtraction. Short division. The logic of long division. One digit long division.
9. (Lesson 9) Long division with multiple digit divisors.
10. (Lesson 10) Multiplication drills. 4 digits x 3 digits. 4 digits x 4 digits.
11. (Lesson 11) X and Y coordinates. Introduction to negative numbers. Positive and negative vectors.
12. (Lesson 12) Charts. Standard operations on a number line. Subtraction as the addition of a negative. Double negative multiplication.
Fractions directory
1. (Lesson 13) Basic fraction concepts. Addition of fractions. Multiplication of fractions.
2. (Lesson 14) Whole numbers as fractions. Mixed numbers. Introduction to basic concepts of common denominators. Basic idea of reducing to lowest common denominator. Utility to calculate LCD.
3. (Lesson 15) Mixed number problems. Division by a fraction. Practice reducingfractions to lowest common denominator. Cancellation problems.
4. (Lesson 16) Introduction to decimals. Moving decimal point to find a percentage. Multiplying decimals. Concept development and drills.
5. (Lesson 17) Decimals in irrational numbers. Rounding decimals. Ratio and proportion.
6. (Lesson 18) Moving the decimal point during division. Division problems with decimals in the divisor.
Middle School Math directory
1. (Lesson 19) Angles and degrees. Meaning and spelling of common math terms. English - Metric conversion.
2. (Lesson 20) Conversion of hours to minutes and minutes to seconds. Create your own calendar (review of sets).
3. (Lesson 21) Basic terms - radius, diameter, etc. Demonstration of Pi ratio. Circle as a many-sided polygon. Why study Pi?
4. (Lesson 22) Derivation of the area formulas for rectangles, triangles, parallelograms, and trapezoids. Area problems.
5. (Lesson 23) Polygon area and perimeter problems. Derivation of equation to calculate the area of a circle. Circle area problems.
Powers directory
1. (Lesson 24) Introduction to exponents. Multiplication and division via exponents. Negative exponents.
2. (Lesson 25) Binary search. Order of calculation. Pemdas problems. Associative, Commutative, and Distributive laws. Parentheses.
3. (Lesson 26) Prime numbers. Creating a factor tree. Using prime numbers to find the lowest common denominator.
4. (Lesson 27) Scientific notation. Exponents as the basis of our number system. Other number systems.
5. (Lesson 28) Pythagorean Theorem. Distance formula. Explanation of square roots as well as other roots.
6. (Lesson 29) Problems multiplying and dividing by adding and subtracting exponents. Simplifying radicals.
7. (Lesson 30) Removing variables from a radical. Fraction problems with radicals.
8. (Lesson 31) Common logarithms.
Algebra 1 directory
1. (Lesson 32) Do the same operation to both sides of an equation. Elementary drills involving use of inverse operations.
2. (Lesson 33) Concept development on a number line pertaining to absolute value. Review of do the same operation to each of an equation's sides and addition/multiplication of negative numbers.
3. (Lesson 34) Slope and y-intercept. Explanation of how to find the x and y coordinates where two lines intersect. Supply your own slopes and y-intercepts for two intersecting lines. Graph of lines. Solution of equation. Problems concerning the intersection of two lines.
4. (Lesson 35) Introduction to factoring. Distributive equations. Factoring by grouping. Explanation of greatest common factor.
5. (Lesson 36) Algebraic fractions and the distributive rule. Problems with numbers and literals as denominators. Practice finding the greatest common factor.
6. (Lesson 37) Standard form. Solution of two equations by substitution. Solution of simultaneous linear equations.
7. (Lesson 38) Solution of three equations by substitution. Practice drills using substitution method. Introduction to matrices. What is a determinant? Drill finding the determinant of a 2 x 2 matrix.
8. (Lesson 39) Functions. Range, domain, and ordered pairs. Vertical line test.
9. (Lesson 40) Multiplying literals. FOIL. Graphic method of completing the square. Graphic explanation of (a - b) (a + b).
10. (Lesson 41) Provide the coefficients for a graphing utility to graph your own degree 2 through degree 4 polynomials. Factoring degree 2 polynomials - explanation and problems.
11. (Lesson 42) Solving quadratic equations by factoring polynomials. The zero product principle.
12. (Lesson 43) Rational expressions. Synthetic division.
13. (Lesson 44) Inequalities. Explanation, graphs, and problems.
14. (Lesson 45) Word problem strategy involving chart creation. Number word problems.
15. (Lesson 46) Word problems concerning the sizes of geometric forms
16. (Lesson 47) Age word problems.
17. (Lesson 48) Money word problems. Value mixture word problems.
18. (Lesson 49) Uniform motion word problems.
19. (Lesson 50) Percent mixture word problems. Investment word problems.
20. (Lesson 51) Work problems. Word problems that involve fractions.
21. (Lesson 52) Two variable word problems. Using methods of solving simultaneous linear equations to solve word problems.
22. (Lesson 53) Imaginary numbers. Complex numbers. The Fundamental Theorem of Algebra.
23. (Lesson 54) Completing the square. The Quadratic Formula.
Geometry and Trigonometry
1. (Lesson 55) Basic concepts of the deductive method. Beginning of a Euclidean proof of the Pythagorean Theorem.
2. (Lesson 56) Euclid's parallel postulate and related theorems. Sum of the angles of a triangle theorem. Methods of proving triangles congruent. Rest of Pythagorean Theorem proof.
3. (Lesson 57) Angles opposite equal sides of an isosceles triangle proof. Triangle's exterior angle equals the sum of the two remote interior angles. Geometric mean. Introduction to imaginary numbers.
4. (Lesson 58) Review. Corresponding sides of similar triangles are proportional.
5. (Lesson 59) Triangle geometry problems.
6. (Lesson 60) Definitions concerning the geometry of circles. Equal chords subtend equal arcs. An inscribed angle equals one-half the intercepted arc (easy proof).
7. (Lesson 61) If a line through the center of a circle is perpendicular to a chord, it also bisects the chord. If a line is tangent to a circle, it is perpendicular to the radius drawn to that point. An inscribed angle = one-half the intercepted arc. (General case)
If 2 chords intersect in a circle, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord. Review and problem set.
8. (Lesson 62) Explanation of sine, cosine, tangent. Trigonometric Pythagorean Theorem. Inverse trigonometric functions. Reciprocal functions.
9. (Lesson 63) Unit circle. Radians. Review.
10. (Lesson 64) Trigonometric problems based on the topics presented earlier.
11. (Lesson 65) Degree into radian conversion and vice versa. Graph of trigonometric functions. Law of Sines. Law of Cosines. Polar coordinates. Trigonometric problems
based on the Law of Sines, the Law of Cosines, and polar coordinates.
Advanced Algebra
1. (Lesson 66) Word problems involving quadratic equations. Factoring polynomials and using the zero product principle to solve word problems.
2. (Lesson 67) Review of the introduction to matrices in Algebra 1 (Lesson 38). An explanation of pivoting. Drill solving equations represented in matrix format.
3. (Lesson 68) Determinants. Cramer's rule with related problems.
4. (Lesson 69) How to calculate determinants of matrices that are larger than 2 x 2. Problems finding the determinant of a 3 x 3 matrix.
5. (Lesson 70) Addition of matrices. Scalar multiplication of a matrix. The transpose of a matrix. Identity matrix. An introduction to the multiplication of two matrices.
6. (Lesson 71) Non-commutative property of matrix multiplication.
7. (Lesson 72) Calculation of an inverse. Problems with the
general form Ax = B.
|
|
funmath@fundamentallymath.com