赵一兵

Today, students studied the new contents in solving quadratic equations with the coefficient of quadratic term not equal to 1. It is definitely harder than the case as the coefficient of quadratic term is 1. Factorization is the one of 4 methods that students are studying in solving quadratic equations. Building up the sense to number computing is helpful in order to figure out the way of factoring. Besides, the sum of quadratic solutions (roots) and product of the solutions (roots) have relations with the coefficients and constant in a quadratic equation. However, students need to clearly know the rule of the coefficient of quadratic term in the relations. These features provide more tools in solving/analyzing quadratic equations and writing equations from these information.
The more practice, the better skills. Here is the assignment for today’s contents:
P.298, 10.2.2, 10.2.4, 10.2.5

P.307, 10.3.1, 10.3.3

P.311, 10.4.1, 10.4.2, 10.4.6

In the class, students reviewed the parallel lines and transversal system, and the properties and relations of all angles in the system. By studying a couple of examples, students learned to use the knowledge to solve the angle problems in the parallel lines/transversal system, most importantly, learning the statement/reason procedure in geometry.

Here is the homework covering the class contents:

Workbook 8A
Ch. 7,
1, 2, 12.(a)(b)(e), 13.

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

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

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

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

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.

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

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

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.