Math 6A, Lesson 12, Spring 2021, 5/9/2021

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1. Percentage: a percentage is a fraction with 100 as the denominator

  • Meaning of percentage: “per cent” means “by the hundred” or divided by one hundred. The term “percentage” is derived from the Latin per centum, meaning “per hundred”.
    • 38% = 38/100 = 0.38
    • 100% = 100/100 = 1
    • 0% = 0/100 = 0
  • Decimals, percentages and fractions and how to express a number in each form
  • Express one quantity as a percentage of another
  • Compare quantities using percentage
  • Word problems involving percentage

2. Home Work:

  • Handout:
    • Two pages
  • Workbook:
  • Page 39: 1, 2, 3, 4, 5
  • Page 40: 6, 7

Math 6A, Lesson 11, Spring 2021, 5/2/2021

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Exam on ratio, rate, average rate, speed, uniform/constant speed and average speed, and Conversion of units.

Math 6A, Lesson 10, Spring 2021, 4/11/2021

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1. Average Rate

Rate involves two quantities and it is usually expressed as one quantity per unit of another quantity.

  • $/oz, mile/gal, words/min, $/sq.ft, $/hour

2. Speed, uniform/constant speed and average speed

  • Speed = (distance traveled) / (time taken)
  • Average Speed =  (Total distance traveled) / (total time taken)

3. Conversion of units

  • km/hr → m/s → miles/hr
  • $/inch → $/ft
  • $/ticket → euro/ticket

4. Home Work:

  • Handout:
    • Three pages
  • Workbook:
  • Page 34: 5, 6, 7, 8, 9, 10
  • Page 35: 11, 12, 13, 14, 15, 16, 17
  • Page 36: 18, 19, 20, 21, 22

Math 6A, Lesson 9, Spring 2021, 4/4/2021

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1. Ratio

  • Meaning of ratio – Given any two similar quantities, a and b, the ratio of a to b (denoted by a:b) is defined as a:b = a/b, where b != 0
  • The quantities have to have same/similar unit.
  • Simplification of ratios: a:b = (ma): (mb) =  (a/m): (b/m), where m !=0

2. Ratios of three quantities: the ratio involving three quantities cannot be written as a fraction. However, it can be simplified by multiplying or dividing each term by the same constant.  For example, a:b = 5:6, b:c = 8:11, find a:b:c. Recall LCM, we convert each ratio to an equivalent ratio where the new value of b is the LCM of the original values of b:

  • a:b = 5:6 = 5*4 : 6*4 = 20:24
  • b:c = 8:11 = 8*3 :11*3 = 24:33
  • hence , a:b:c = 20:24:33

3. Word problems involving ratios

4. Home Work:

  • Handout:
    • three pages
  • Page 33:
    • 1, 2, 3, 4

Math 6A, Lesson 8, Spring 2021, 4/3/2021

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Continue on Chapter 5.4 Forming Linear Equations to Solve Problems

1. Midterm Exam: all about equations

2. Constructing/Forming Linear Equations to Solve Problems

The steps involved in problem solving with linear equations are:

  • Step 1. Read the question carefully and identify the unknown quantity
  • Step 2. Use a letter to represent the unknown quantity (e.g. x)
  • Step 3. Express other quantities in terms of x
  • Step 4. Construct/Form an equation based on the given information
  • Step 5. Solve the equation
  • Step 6. Write down the answer statement

Math 6A, Lesson 7, Spring 2021, 3/28/2021

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Continue on Chapter 5.4 Forming Linear Equations to Solve Problems

1. Quiz – and quiz go over

2. Constructing/Forming Linear Equations to Solve Problems

The steps involved in problem solving with linear equations are:

  • Step 1. Read the question carefully and identify the unknown quantity
  • Step 2. Use a letter to represent the unknown quantity (e.g. x)
  • Step 3. Express other quantities in terms of x
  • Step 4. Construct/Form an equation based on the given information
  • Step 5. Solve the equation
  • Step 6. Write down the answer statement

3. Homework:

  • Handout
    • Two pages
  • Workbook:
    • Page 31: 21, 22, 23, 24, 25
    • Page 32: 26, 27, 28, 29

Math 6A, Lesson 6, Spring 2021, 3/21/2021

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Newton Community Vigil for Victims of violence and hate crime

Math 6A, Lesson 5, Spring 2021, 3/14/2021

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Chapter 5.3 Simple Fractional Equations

Chapter 5.4 Forming Linear Equations to Solve Problems

1. Fractional equation: when the variable of an equation is in the denominations of a term, the equation is called fractional equation

6 /(x – 2) = 3

1/(x + 3) = 2/x

Note: it is important to check the solutions, that they can’t be those values that make a denominator of the original equation zero.

2. Constructing/Forming Linear Equations to Solve Problems

Two pages handout of teaching material. The steps involved in problem solving with linear equations are:

  • Step 1. Read the question carefully and identify the unknown quantity
  • Step 2. Use a letter to represent the unknown quantity (e.g. x)
  • Step 3. Express other quantities in terms of x
  • Step 4. Construct/Form an equation based on the given information
  • Step 5. Solve the equation
  • Step 6. Write down the answer statement

3. Review basic concept of “open parenthesis”

  • 2(3x+y) – 5(0.2x-0.6y) =
  • -2(3x+y) + 5(0.2x-0.6y) =
  • -2(3x-y) + 5(-0.2x-0.6y) =
  • 2(3x-y) – 5(0.2x+0.6y) =

4.Homework:

  • Handout
    • Three pages
  • Workbook:
    • Page 30: 15, 16, 17, 18, 19, 20

Math 6A, Lesson 4, Spring 2021, 3/7/2021

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Chapter 5.2. Equations involving Parentheses

1. We apply the distributive law of multiplication over addition to help us solve equations involving parentheses.

Recall a(x + b) = ax + ab

Solve equation 9(x + 1) = 2(3x + 8)

2. When working with equations, always apply the same action to both sides of the equation.

Solve equation 5(2x – 9)/3 -8 = 2x

Solve equation (3x + 2)/5 = (4x – 7)/6

3. Rewriting equations

Giving the formula A = ½ * (a + b)h, find the value of a when b = 13, h = 9, and A = 90.

4. Homework:

  • Handout
    • Two pages
  • Workbook:
    • Page 27: 4
    • Page 28: 5
    • Page 29: 11, 12, 13, 14

Math 6A, Lesson 3, Spring 2021, 2/28/2021

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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