Math 6A, Lesson 6, Spring 2017, 3/25/2017

1. Quiz: simplify algebraic expression and solve word problems using equations

2. 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
• 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

• Word problems involving ratios

3. Home Work:

• Handout one page
• Page 33: 1, 2, 3, 4

Math 6A, Lesson 5, Spring 2017, 3/19/2017

1. We continue working on how to construct/form linear equations to solve word 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

2. 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) = 

3. Home Work:

• Looking ahead: pop quiz next week on equations
• Show detailed steps for all HW problems
• Handout two pages
• Fun and challenge: Two pages are suggested. See email sent to parents to order the Math Contest books:

Math Contests, Grades 7 & 8 (and Algebra Course 1) Vol. 6

https://www.amazon.com/gp/product/0940805197/ref=oh_aui_detailpage_o01_s00?ie=UTF8&psc=1

Math Contests, Grades 4, 5 & 6, Vol. 6 (School Years 2006-2007 Through 2010-2011)

https://www.amazon.com/gp/product/0940805189/ref=oh_aui_detailpage_o02_s00?ie=UTF8&psc=1

Math 6A, Lesson 4, Spring 2017, 3/12/2017

1. 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

2. Review basic concert 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) =

3. Home Work:

• Show detailed steps for all HW problems
• Handout one page
• page 31: 23, 25
• Fun and challenge: one page each: 6th and 7th grade MATH CONTESTS problems

Math 6A, Lesson 3, Spring 2017, 03/05/2017

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

Keyword: 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.

2. Review Chapter 3.3 Writing Algebraic Expressions to Represent Real-World Situations:

• Concepts: algebraic expression, algebraic formulas, relationship between quantities, unknown variable
• Methods: translate the word problem into math language
• Keyword: translate, translate, translate. Translate the real-world problem sentences to math expressions

3. About 5-8 minutes talking about each student’s school vacation activities, anything NEW and CREATIVE?

4. Home Work:

• page 16: 6,7,8,9,10
• Page 17: 15, 19
• page 29-30: 11,12,13,14,15,16,17,18,19,20
• Fun and challenge: one page each: 6th and 7th grade MATH CONTESTS problems