AOPS Algebra 1 Course, Lesson 10, 11/10/2019

Today, students continued to study ratio in the application problems. In addition, students learned the definition of percent and standard formulas for percentage, increasing percent and decreasing percent.
Here is the homework assignment:
P.166, 6.2.5, P.172, 6.3.1, 6.3.3, 6.3.4, 6.3.6, P.176, 6.4.1, 6.4.2, 6.4.3, 6.4.4, 6.4.5, P.182, 6.5.1, 6.5.2, 6.5.4

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AOPS Algebra 1 Course, Lesson 9, 11/03/2019

In today’s class, students continued to work on word problems since it is a challenging section in Algebra for most of the students. The summary of strategy to write the algebraic expressions and equations is useful for students to master the skills. A new chapter including ratio was introduced as well in the class. Students should grasp the keys of finding the relation of ratio and actual numbers, individual and whole.
Here is the homework covering today’s contents:
P.141, 5.4.4, 5.4.5P.161, 6.1.1, 6.1.2, 6.1.4P.166, 6.2.1, 6.2.2, 6.2.3, 6.2.4

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AOPS Algebra 1 Course, Lesson 8, 10/27/2019

Today, students continued to study the method of solving two-variable linear equations, elimination. In general, the methodology of solving multi-variable linear equation is to reduce two variables to one variable. Not all two-variable linear equation system has solution. One solution is only when two equations are absolutely distinct. When two equations are the same, there are infinitely many solutions. When coefficient of each variable in two equations are the same, but the constants are different, the system has no solution. In two variable word problem, the procedure is exactly the same as what students learned in solving single variable word problems. So far, word problem is still challenging to some students, especially in writing expressions and equations.
The homework for today’s class:
P. 136
5.3.1, 5.3.2, 5.3.3
P. 141
5.4.2, 5.4.3
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Singapore Math 8th Class, Lesson 8, 10/27/2019

Today, students continued to explore the quadratic expression factorization ax^2+bx+c when a=1 and other than 1. Factorization is one of four methods in solving quadratic equations. When a quadratic equation is factorized, using factorization in general is considered first. Therefore, it is critical to grasp the skills of factorization.

The homework to cover the contents above
Workbook 8A
Ch. 4
1. c,d,e,f
2.
3. a, b, c, d
6. a, d, e, f, g, j
7. a, c, e, g, j
11. a, c, d
15. a, b

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AOPS Algebra 1 Course, Lesson 7, 10/20/2019

In today’s class, students reviewed linear expression/equations and studies a few examples of word problems to understand the key points and general strategy in solving the word problems in math. In the two-variable linear equations, students learned the idea of equations of solving multi-variable linear equations, and studied the first method to solve the two-variable linear system, called “substitution”. The key using substitution method is to solve one of the equation in order to represent one variable in terms of another variable, then to substitute the same variable in another equation.
Here are practice questions
P.92, 3.3.2, 3.3.4, 3.3.5, 3.3.6
P.126, 5.1.1
P.130, 5.2.1 (a), (d), 5.2.4
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Notice of Midterm test in Singapore Math 8th Class

This class will have midterm on Nov. 3. For more details, please contact Zhao Laoshi at yz32@yahoo.com

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Singapore Math 8th Class, Lesson 7, 10/20/2019

In today’s class, I guided students to work on factorization of algebraic expressions, especially the special expression factorization, such as a^2+2ab+b^2, a^2-b^2, etc.
In the quadratic expression factorization, students learned the definition of quadratic expression and the standard form, special quadratic expression factorization, and the method of factoring quadratic expressions with leading coefficient of 1.

Here is the homework to practice the factorization

Ch. 3
2. b, f, h
7. d, h
8. c, e
9. a, b, c, d
10. a, c, e, f, g
11. a, c, g, h
13. a, b, c, g, h
15.
18. a, b, c, e, f

Ch. 4
1. a, b

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AOPS Algebra Course, Lesson 6, 10/13/2019

Today, students continued to work on Algebra 1, the linear equations. Students understand what the linear expressions, linear equations are. The solutions to one-variable linear equations are one solution, no solution and infinite solutions. In addition, students learned the procedure of dealing with word problem, such as setting variable(s), writing expressions, writing equation, and solving equation.
Here is the homework for today’s class:
P.82, 3.1.1, 3.1.2, 3.1.3, 3.1.4
P.88, 3.2.1, 3.2.2, 3.2.3
P.92, 3.3.1
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Singapore Math 8th Class, Lesson 6, 10/13/2019

In today’s class, students studied expansions of Algebraic expression, especially the method of handling “sign” in algebraic expressions. A few special products were introduced that are so important in the quadratic expression section. By using those special products, we are able to compute some type of numbers without calculator. In addition, reverse applications of those special products are helpful in the factorization of certain types of algebraic expressions, such as some quadratic expression factorization. Limited class practices should be good guidance for students to deal with more questions.

Here is the homework assignment for the contents that students studied today.

Workbook 8A

Ch.3
1. b, c, g, h, j
2. a, c, e, g, i
3. a, c, e, g, h
4. a, c, d, f, h
5. b, d, e, f
6.
7. a.b.c.f.g
8.
9. e, f, g, h,j
11. b,e, h
12, a, b, d, e ,g, h

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AOPS Algebra Course, Lesson 5, 10/06/2019

In the new content section, students learned algebraic fractions, simplification of algebraic fractions, addition, subtraction. The key to implement simplification is factoring the expressions of numerator and denominator correctly, and cancellation can be only done in the form of factors; In the addition/subtraction of fractions-making a single fraction, finding least common denominator is critical.
The homework for the contents above:
P.73, 2.4.1, 2.4.3, 2.4.4, 2.4.5, 2.4.6
P.118, 4.4.1, 4.4.2, 4.4.3, 4.4.4
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