Math 6A, Lesson 1, Spring 2020, 1/19/2020

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Factorization by Extracting Common Factors, Factorization by grouping terms

1. The process of writing an algebraic expression as a product of its factors is called factorization or factoring:

  • 600 = 2x2x2x3x5x5
  • ax + ay = a(x+ y)
  • 15a + 20b = 5(3a) + 5(4b)=5(3a + 4b)
  • 24ax – 40ay + 8a = (8a)(3x) – (8a)(5y) + (8a)(1) = 8a(3x – 5y + 1)

2. Factorization by grouping

  • 12ax – 3ay + 8bx -2by

= (12ax -3ay) + (8bx -2by)

= 3a(4x-y) +2b(4x -y)

=(3a + 2b)(4x-y)

  • 49a + 42c -7ay -6cy

= (49a -7ay) + (42c – 6cy)

= 7a(7 – y) + 6c(7 – y)

= (7a + 6c)(7 – y)

3. Home Work:

  • Handout:
    • two pages
  • Workbook:
    • page 22: 7, 8
    • Page 24: 16, 17, 18, 20
    • Page 26: 26, 27, 28, 29
  • Hand out the report card for Fall 2019

Math 6A, Lesson 16, Fall 2019, 1/12/2020

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Distributive Law, Addition and Subtraction of Linear Algebraic Expressions

1. Use of parentheses and distributive law

  • a(x + y) = ax + ay
  • (x + y)a = a(x + y) = ax + ay = xa + xy
  • a(x – y) = a{x + (-y)] = ax + a(-y) = ax – ay
  • a(x + y + z) = ax + ay + az
  • x – (a – b) = a -a + b

2. Addition and subtraction of linear algebraic expressions: explained in class

  • (2a +3b) + (5a -4b) =
  • Find the sum of -2p + 3q – 4 and p + 5q – 3
  • (4x – 5) – (7x – 3)

3. Home Work:

  • Handout:
    • one pages
  • Workbook:
    • page 21: 3, 4, 5
    • Page 23: 11, 12, 13, 14, 15
    • Page 24: 21
    • Page 25: 22, 23

Math 6A, Lesson 15, Fall 2019, 1/5/2020

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Like Terms and Unlike Terms

1. Terms, coefficient, and constant terms

  • The expression 2x – 3y + 8 consists of three terms. They are 2x, -3y and 8. The numerical part, including the sign, of a term is called the coefficient of the variable.
  • Term 2x, the coefficient of x is 2
  • Term -3y, the coefficient of y is -3
  • Term 8, is called constant term

2. Classify the like terms and unlike terms: explained in class

3. Simplify the algebraic expression by combining (or collecting) like terms

  • 2x + 3x = 5x
  • 8y – 3y = 5y
  • 3a + 4b – 2a + 5b = (3a -2a) + (4b +5b) = a + 9b

4. Home Work:

  • Handout: two pages
  • Workbook:
    • page 21: 1, 2
    • Page 22: 6, 9, 10

Math 6A, Lesson 14, Fall 2019, 12/15/2019

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1. Exam on chapter 3 “Introduction to Algebra”

2. Home Work: 

  • Redo all the problems you got wrong in last three homework assignment.

Math 6A, Lesson 13, Fall 2019, 12/8/2019

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Writing Algebraic Expressions to Represent Real-world Situation

1. We may use algebraic expressions and formulas to express the relationship between two or more quantities in our daily life

  • Lots of examples teaching in the classroom, and lots of exercise on whiteboard
  • Visualizing, drawing
  • Variables are representing quantities with similar units.

2. Home Work:

  • Handout: three pages
  • Workbook:
    • page 17: 15, 16, 17, 18, 19
    • Page 18: 20, 21, 22, 23, 24
    • Page 19: 25

Math 6A, Lesson 12, Fall 2019, 11/24/2019

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Evaluation of algebraic expressions and formulas

1. Evaluation of algebraic expressions

  • The process of replacing each variable with its value to find the actual value of an algebraic expression is called substitution.

2. Formulas

  • The area of a rectangle is given by
    • Area = Length x Width
    • A = lw
  • This equality of connecting two or more variables is called a formula. When the values of l and w are known, we can find the value of A in the formula by substitution.

3. Home Work:

  • Handout: two pages
  • Workbook:
    • page 15: 3, 4, 5
    • Page 16: 11, 12, 13
    • Page 17: 14
    • Page 19: 26, 27
    • Page 20: 28

Math 6A, Lesson 11, Fall 2019, 11/17/2019

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The use of letters in algebra

1. The use of letters

  • In general, an algebraic expression involves numbers and letters that are connected with operation symbols such as “+”, “-”, “x” and “/”
  • In 10 + 8n, we call n a variable and 10 + 8n an algebraic expression

2. Basic notation in algebra

  • In algebra, there are rules for writing algebraic expressions. The operation symbols “+”, “-”, “x”, “/”  and “=” have the same meanings in both algebra and arithmetic.
  • Add a to b: sum = a + b = b + a
  • Subtract c from d: difference = d – c != c -d
  • Multiply g by h: product = g x h = h x g = gh
  • Divide x by y where y != 0: quotient = x/y

3. Exponential notation

  • Teach in the class on white board

4. Simplify algebraic expressions

  • Teach in the class on white board

5. Home Work:

  • Handout: two pages
  • Workbook:
    • page 15: 1, 2
    • page 16: 6, 7, 8, 9, 10

Math 6A, Lesson 10, Fall 2019, 11/10/2019

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1. Exam

2. No homework, enjoy a break.

Math 6A, Lesson 9, Fall 2019, 11/03/2019

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1. No quiz today, exam next week.

2. Real numbers and use of calculators:.

  • Rational number: can be expressed as a decimal by dividing the numerator of the rational number by its denominator
  • Terminating decimal: has a finite number of digits: ⅜, 5/16
  • Repeating decimal: 9/11, 7/11
  • Irrational number: non-terminating and non-repeating decimals
  • Use of calculators

3. Rounding numbers to decimal places

  • Mark the cut-off point after the desired place value
  • Rule of rounding up: the first digit after the cut-off point,  is >=5
  • Rule of rounding don: the first digit after the cut-off point, is  < 5
  • Nearest 10, 100, 1000, one million, …
  • Nearest tenth, hundredth, or thousandth, …
  • 1 decimal place, two decimal places, 3 decimal places, …

4. Home Work:

  • Handout: two pages
  • Workbook:
    • page 11: 24, 25, 26, 27, 28, 29
    • page 12-13: 30, 31, 32, 33, 34, 35, 36

Math 6A, Lesson 8, Fall 2019, 10/27/2019

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1. Quiz on negative number, addition and subtraction of integers

2. Multiplication, division and combined operations of integers:.

3. Rational numbers: rational numbers are numbers that can be expressed in the form of a/b, where a and b are integers, and b != 0

4. Addition, subtraction, multiplication and division of rational numbers

5. Home Work:

  • Handout: three pages
  • Workbook:
    • page 8: 6, 8, 9, 10, 11
    • page 10: 18, 19, 20, 21, 22, 23