Math 7, Lesson 7, Fall 2021, 11/07/2021

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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

Math 7, Lesson 6, Fall 2021, 10/24/2021

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1. Exam on chapter “Introduction to Algebra”

2. Home Work: 

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

Math 7, Lesson 5, Fall 2021, 10/17/2021

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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

Math 7, Lesson 4, Fall 2021, 10/3/2021

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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