補習數學 102 - 掌握基本概念

Hi, this is Mrs. C with Innovative Tutoring. If you are looking for a plain, straightforward, to-the-point teaching of math concepts, this is your class. I do use a variety of methods to teach, but my goal is to make sure that the students master the material.  I want them to learn, to gain knowledge.  The word "teacher" means "one who is apt to teach".  A good meaning of the word "teacher" is 
"one who is able to explain and demonstrate concepts in a variety of ways for a variety of different learners and learning styles. A good teacher is a good learner—they learn how their student(s) learn—and modify their teaching accordingly." I strive to attain that goal in my classes.
In this ongoing review class, the student will review the basic principles and concepts of everyday elementary math. These are concepts that tend to be forgotten and confused as the student moves up in their grades. The topics that will be covered are fractions, percentages, decimals, measurements, and pre-algebra. This is a review class. Students can come and go at will, so that is the reason that the topics are listed. This allows the student to know what the review lesson will be and whether they need that lesson.
Scope and Sequence for Remedial Math

**Lesson schedule subject to change based on students’ needs for continued review and study.**

Lesson 1:  Order of Operations - a. Simplify within grouping symbols:  4-3 / 3 + (2) (8) **Nothing to simplify in the parentheses** b. Expand exponents **No exponents c. Multiply and divide from left to right: 4 - 1 + 16    d. Add and subtract from left to right: 3 + 16 = 19
Example:   2³ + (6 - 1) ***Parentheses:(6-1) = 5 ***Expand exponents: 2³ = 2 x 2 x 2 = 8   ***Multiply and divide from left to right:  No multiplication or division   ***Add and subtract from left to right:  8 + 5 = 13

Lesson 2:  Greatest Common Factor (GCF) and Least Common Multiple (LCM)
Greatest Common Factors of 36; 54; 63 ***1,2,3,4,6,9,12,13,36; 1,2,3,6,9,18,27,54; 1,3,7,9,21,63 Common Factors: 1,3,9 GCF: 9
Least Common Multiples of 4, 9, and 12 ***4: 2²   9:  3²   12:  2² x 3 List the prime factors of each number...use division by primes...write the prime factorization using exponents.  ***Hold a contest between the exponents for each different prime factor...circle 2²; it has the largest exponent (circle in only one factorization); circle 3²; it has the largest exponent.  ***Multiply: multiply the circled factors from each contest...expand any exponents before multiplying...LCM of 4, 9, and 12:  2 x 2 x 3 x 3 = 36

Lesson 3: Review Addition of Carrying and Checking and Speed Drill.

Lesson 4: Review Subtraction of Borrowing and Checking and Speed Drill.

Lesson 5: Review of Multiplication Facts 0-12 and Speed Drill.

Lesson 6: Review Multiply 2- & 3-digit factors.

Lesson 7: Math Jam Quiz and Game with Certificate of Lesson 6 Completion

Lesson 8: Review Division 2- & 3-digit divisors.

Lesson 9:  Review of Fractions: Proper and Improper and Mixed...5/8; 15/7; 3 1/2...equivalent fractions 1/2 = 2/4 = 3/6 = 4/8; simplify fractions 12/15 = 4/5

Lesson 10:  Review of Fractions - Addition of simple fractions 2/5 + 1/5 = 3/5; adding fractions and finding LCD 1/5 + 2/10 + 5/20= 4/20 + 4/20 + 5/20 = 13/20

Lesson 11: Review of Fractions - Subtraction of simple fractions 2/5 - 1/5 = 1/5; subtracting fractions and finding LCD 7/25 - 2/15 = 21/75 - 10/75 =11/75 

Lesson 12: Review of Fractions - Addition of Mixed Fractions 2 3/7 + 5 4/5 = 2 15/35 + 5 28/35 = 7 43/35(1 8/35) = 8 8/35

Lesson 13: Review of Fractions - Subtraction of Mixed Fractions ***Same denominator 10 3/5 - 5 1/5 = 5 2/5 ***Different denominator...find LCD  2 3/4-1 1/3=LCD4 8 12…3 6 9 12 =LCD12
2 9/12-1 4/12=1 5/12 

Lesson 14:   Review of Fractions - Advanced Addition and Subtraction of Mixed Fractions in multiple scenarios: 21 3/4 + 113 2/3 - 203 11/12 - 35 5/6 = ?

Lesson 15:   Review of Fractions - Multiplication of Fractions 4/5 x 2/3 = 8/15...multiply by cancellation 2/3 x 6/8 = 3/3 and 3/6, then 2/2 and 2/8...3/3 and 3/6 become 1/2, then 2/2 and 2/8 become 1/4...then you multiply 1/2 x 1/4 = 1/8

Lesson 16:  Division of Fractions:  4 ➗1/2 = 4/1 x 2/1 = 8/1 = 8

Lesson 17:  Finding the decimal equivalent of a fraction.

Lesson 18: Convert fractions to decimals

Lesson 19: Math Jam Quiz and Game with Certificate of 18 Lesson Completion

Lesson 20: Percent and Percentages-Writing a percent as a fraction and then reducing it to the lowest terms

Lesson 21:  Place Value and Rounding

Lesson 22:  Understanding and Comparing Absolute Value

Lesson 23: Ratios-comparing 2 numbers or quantities.

Lesson 24: English measurement system

Lesson 25: Metric measurement system

Lesson 26: Perimeter of Rectangle, Square; Area of Rectangle, Square, Triangle

Lesson 27: Algebraic equations:  Monomial equations

Lesson 28: Algebraic equations:  Polynomial equations

Lesson 29:  Algebraic equations:  Factoring Trinomials

Lesson 30:  Math Jam Quiz and Game with Certificate of 29 Lesson Completion

Lesson 31: Problem Solving

Lesson 32: Mean, Median, and Mode

Lesson 33: Statistics and Probability

Lesson 34 Finding Simple Interest

Lesson 35 Interest by the months

Lesson 36 Discounts and the Amount of Profit

Lesson 37 Adding decimals

Lesson 38 Subtracting decimals

Lesson 39 Multiplying & Dividing of decimals

Lesson 40 Math Jam Quiz and Game with Certificate of 39 lesson Completion

Lesson 41 Exponents

Lesson 42 Multiplying and Dividing by the powers of 10

Lesson 43 Radicals: square root and cube root

Lesson 44 Percent Basics

Lesson 45 Percent with fractions

Lesson 46 Percentage

Lesson 47 Finding the Base

Lesson 48 Finding the Percent of Change

Lesson 49 Finding the Discounts

Lesson 50 Math Jam Quiz and Game with Certificate of Lesson 49Completion

Lesson 51  Simple Interest formula

Lesson 52  Installment Buying

Lesson 53  Banking

Lesson 54  Planning a Budget

Lesson 55  Electricity & Gas Meters

Lesson 56  Math Jam Quiz and Game with Certificate of Completion for Course