AOPS Algebra 1 Course, Lesson 17, 01/19/2020

Today, I started the new chapter, quadratic equations, basic nonlinear, but very important, expressions and equations. I introduced the basic concepts of quadratic expression and equations, and the methods to solve the quadratic equations with coefficient of quadratic term being 1. The first method introduced is factoring quadratic expression, the process of inverse of the distributive to the product of two binomials. Through the factor form of quadratic equation, you can find the solutions of the quadratic equation easily.
Here is the homework reflecting the contents in today’s class,

P.292, 10.1.1, 10.1.2, 10.1.3, 10.1.4, 10.1.5, 10.1.6

P.298, 10.2.1, 10.2.3

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AOPS Algebra 1 Course, Lesson 16, 01/12/2020

Today, students continued to study the linear inequality, solving one variable inequality, three ways to represent inequality solution, inequality notation, interval notation, and number line; For two-variable inequality, graphing is used to present the solutions because the solution is zone bordered by a straight line from the inequality. The method of drawing the two-variable inequality and inequality system was introduced in the class.
Here is the homework for today’s class
P.268, 9.3.1, 9.3.2, 9.3.3, 9.3.4

P.271, 9.4.1, 9.4.2, 9.4.3, 9.4.4

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Singapore Math 8th Class, Lesson 16, 01/12/2020

Today, students finished congruence and similarity study and started to work on parallel lines and transversal. In the similarity, one of the transformation, the enlargement, was introduced. The center of enlargement and scale factor are two key information to determine the transformation of enlargement. Scale factor is the ratio of length of side of image to that of corresponding side of object, as well as the ratio of the distance from center of the enlargement to the image to the distance from center of enlargement to the corresponding point in object. In the parallel lines and transversal, three types of angles were discussed, corresponding angles are equal, alternate angles are equal, interior angles are supplementary.

Here is the homework for the similarity section

workbook 8A
Ch. 6, 12, 26, 27

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AOPS Algebra 1 Course, Lesson 15, 01/05/2020

Today, we resumed the class and students started to study inequality, the basic rules, and the application of those rules in the number comparisons and solving linear inequalities.
Homework for today’s class:
P.259, 9.1.1, 9.1.2, 9.1.3, 9.1.5P.264, 9.2.1, 9.2.2, 9.2.3, 9.2.4

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Singapore Math 8th Class, Lesson 15, 01/05/2020

Today, we had the first class in 2020. Students continued to work on “congruence and similarity”, the transformations like translation, rotation, and combinations. In similarity, students learned relations between object and image in terms of the ratio of corresponding sides and corresponding angles.

Here is the homework for today’s class:

Workbook, 8A
Ch. 6
8 (a)(c), 9, 10, 17, 18, 19, 21, 22, 23, 24.

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AOPS Algebra 1 Course, Lesson 14, 12/15/2019

In today’s class, students reviewed the method of writing line equation, the slope-point, furthermore, writing line equation using two given points; In addition, students learned the different line form, slope-intercept form and conversion between standard form and slope-intercept form. In the section of relations between two lines, intersection, perpendicular, parallel, overlap were introduced; and the relations are associated with the solutions of two linear equations that students studied before. Simply speaking, overlap and parallel show the same slopes, but difference in the treatment in y-intercepts, overlay showing the same intercept; but parallel showing the different intercepts. Using those knowledge to write line equation is another practice for students to enhance their skills in writing equations.
Here is the homework for today’s class

P.232, 8.4.5 (c) (d)

P.237, 8.5.1, 8.5.2, 8.5.3, 8.5.4, 8.5.5

P.244, 8.6.1, 8.6.2, 8.6.3, 8.6.4 (a) (b), 8.6.5

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Singapore Math 8th Class, Lesson 14, 12/15/2019

Today was the last class of 2019 in NCLS, as well as our math class. In today’s class, students continued to study word problems in fraction section. In order to help students to overcome the barriers in solving word problems, I suggest students to set all variables if necessary, and translate the words from sentences to sentences in math expressions and equations. Writing as many variables as equations, then eliminating non-used variables and only saving the variable you want to find out.

In the new chapter, congruence and similarity, the definitions and properties of congruence, reflection, and translation were introduced. The most important part is to represent different figures in coordinate plane, including the operation of reflection and translation.

Here is the homework for today’s class:

workbook 8A
Ch. 5,

6.a,c,e,g
7, 9, 10, 17
Ch. 6
1, 3, 4, 5.a,d, 6, 13, 14.a, 15, 16

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Singapore Math 8th Class, Lesson 13, 12/08/2019

Today, students continued to study the fractional expression operation, addition and subtraction, or called representing fraction expression in single fraction form, primarily the skill of finding least common multiple in algebraic expression way. The knowledge of simplification of fraction expressions and operations of fraction expressions is the basics to support the knowledge of solving fractional equations. In solving the equation, two rule of thumb are changing fraction form to equation with fractions; and checking the solutions through “division by zero” to validate results and reject the invalid. In the fraction word problem, students again touched the approach of setting variables, writing expressions and building equations. in other words, using math language to represent the words in the questions.

Here is the homework for today’s class:
Workbook 8A
Chapter 5
4, 5, 8(a)(c)(e), 14(a)(c)(e)(g)(i), 15(a)(c)(e)(g)(i), 16(a)(c)(e), 26, 28, 37.

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AOPS Algebra 1 Course, Lesson 13, 12/08/2019

Today, students continued to work on coordinate plane and straight line. Students studied the distance between two points in the coordinate plane through the Pythagorean theorem, midpoint coordinates between two points, slope of straight line passing through two points, and meanings of slopes. Writing linear equations through two given points, or slope and a point is a practice of line equations in coordinate plane. This method is called “slope-point” way, that means to form equation through slope definition. Besides, students need to figure out the relation of standard form of straight line equation and the slope-point form of straight line equation.
Here is the homework assignment:

P.214, 8.1.3, 8.1.4

P.224, 8.2.1, 8.2.4

P.228, 8.3.1, 8.3.2, 8.3.3

P.232, 8.4.1, 8.4.3, 8.4.5 (a) (b)

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AOPS Algebra 1 Course, Lesson 12, 11/24/2019

Today, students continued to study the word problems associated with “rate”, driving from one place to another, average speed, working rate, rowing boat in downstream and upstream. The most challenging part is in the working rate, and people are involved in the work. In the practice class, students finished a few of rate questions and they should understand more about solving the questions by creating equations. In the new chapter, graphing lines, number line and Cartesian plane (coordinate plane) were introduced. ordered pairs are defined to represent the points in the coordinate plane.
Here is the homework related to today’s contents
P.202, 7.4.1, 7.4.2, 7.4.3, 7.4.4, 7.4.5, 7.4.6P.214, 8.1.1, 8.1.2

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