Math 6A, Lesson 3, Spring 2018, 2/11/2018

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Chapter 5.1 Simple Linear Equations in One Variable

1. Quiz on  algebraic expression and manipulation: variables, constants, terms, like-terms, regrouping, combining like terms, simplifying expression, factoring.

2. Starting chapter 5. Solve simple linear equations in one variable:

  • Concepts: equation, variable, solution/root, linear equation (ax+b=c, where a,b,c are constant and a != 0), LHS, RHS, balancing.
  • Methods: subtract, add, divide or multiply to both sides by the same number.

3. Introduce concepts and methods of “isolate”, “move items to other side and change of sign”, “plug the answer/solution back in the equation”.

Key word: isolate, isolate, isolate. The key to solving many equations is to get the variables alone on one side of the equation. To solve a linear equation with one variable, we isolate the variable by following a few simple steps:

  • simplify both sides of the equation by combining like terms on each side;
  • move all the terms with the variable to one side and all the constants to the other using addition and subtraction, or just moving them to other side with change of signs;
  • after simplify the equation that results from the previous step, multiply by the reciprocal of the variable’s coefficient to solve for the variable.
  • you can always check your answer by plug the solution back to the variable in the equation, both sides should be equal. if not, go check your calculation.

4. Home Work

  • handout:
    • two pages
  • Workbook:
    • page 27: 1, 2, 3
    • page 28: 6

 

Math 6A, Lesson 2, Spring 2018, 2/4/2018

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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

 

Math 6A, Lesson 1, Spring 2018, 1/28/2018

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Math 6A, Lesson 1, Spring 2018, 1/28/2018

Simplification of Linear Algebraic Expressions

1. The distributive law is applicable when moving parentheses in an algebraic expression. Examples in class:

  • 2(3x + 4y) =
  • -4(5a – 3b) + 7a
  • a(2x + 7y + 5z)
  • (2p + 3q -4r)(-6b)
  • 2[x- 5(3-x)]

2. Express each of the following as a single fraction in the simplest form. Recall LCM of denominators.

  • -p + p/3 +(3p)/5
  • (3p + 10)/4 -2
  • (3x – 4)/4 + (2x+5)/3
  • (1 – 2x)/3 + (3x + 1)/5 + (4x -3)/6

3. Home Work:

  • Handout:
    • two pages
  • Workbook: correct last week’s HW problem of
    • page 21: 3, 4, 5
    • Page 23: 11, 12, 13, 14, 15
    • Page 24: 21
    • Page 25: 22, 23

 

Math 6A, Lesson 16, Fall 2017, 1/21/2018

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Distributive Law, Addition and Subtraction of Linear Algebraic Expressions

1. Hand out the report card for Fall 2017

2. 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

3. 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)

4. 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 2017, 1/14/2018

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Like Terms and Unlike Terms

1. Go over the exam problem one by one.

2. 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

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

4. 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

5. Home Work:

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

 

Math 6A, Lesson 14, Fall 2017, 01/07/2018

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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 2017, 12/17/2017

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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 2017, 12/10/2017

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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 2017, 12/03/2017

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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

6. Extra: What is Super Moon? What are King tides? When does it happen?

 

Math 6A, Lesson 10, Fall 2017, 11/19/2017

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1. Exam

2. No homework, no class next week. Happy Thanksgiving break.