Section 1: 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

Section 2: 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

1. Exam on chapter “Introduction to Algebra”

2. Home Work: 

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

Section 1: 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

Section 2: 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

The use of letters in algebra

Quiz-2 today.

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