Today is our review day as we will have the midterm exam next week.

First, we went over the making square part (Ch 12.4) that the substitute teacher did not get to finish last week. In particular, we talked about how to derive the general formulae for solving a generic quadratic equation ax^2 + bx +c. I hope every student really understands this.

Some students missed last week’s homework because they didn’t see it in my last post (I posted two articles last week, the first one with homework, the second one didn’t). If so, please get it this week and do it. It will help you prepare for the midterm exam.

We then went over what we learned so far this semester, mainly Chapter 10 and 11, plus 12.4 (making squares).

For homework, please do the Chapter 11 standarized test in the book. This is to help you prepare. You should also look back to Chapter 10’s test to help you review as well.

Sorry that I miss the school today due to Lexington Town business.

The material covered today are the following:

Ch 11.7 on dividing polynomials; Ch 11.8 on rational equations.

It is important to remember that when solving rational equation, always check your answer and throw away any that makes any denominator zero.

We also cover Ch 12.4 on conpleting squares. This is to let students learn how to derive the general solution for a quadratic equation of ax^2 + bx + c = 0

For homework, visit the link below:

http://blog.newtonchineseschool.org/wangweidong/files/2012/03/Math7_Spring_HW_L6.pdf

We started the topic of rational expression operation today. A rational expression is a fraction with either numerator or denominator or both being a polynomial. As such, all rules for dealing with factions apply.

A rational expression is simplified if there is no common factor between the numerator and denominator (other than 1 or -1).

We covered rational expression multiplication and division, followed by addition and substraction. The goal is to reach a rational expression in its simplified form after the operation.

Homework link can be found with the link below:

http://blog.newtonchineseschool.org/wangweidong/files/2012/03/Math7_Spring_HW_L5.pdf

Sorry I could not go to school to teach today, as I had two important campaign events to go to.

As some of you know, I am running for Lexington Housing Authority and Town Meeting Member this time and the election day is coming Tuesday 3/6. This weekend is the last weenend before the election.

So, if you are a Lexington resident, I hope you will go out to vote on Tuesday and vote for me.

That said, here is the material covered today by a substitute teacher:

Section 11.1 on Ratio and Propertion, two important properties to remember:

1. Reciprocal Property: if a/b = c/d, then b/a = d/c if they exist

2. Cross Product Property: if a/b = c/d, then ad = bc

Section 11.2 on Percents: number being compared to base = percent of base number

Section 11.3 on Direct and Inverse Variation:

The variables x and y vary directly if for a constant k, y/x = k or y = kx, k not equal to 0.

The variables x and y vary inversely if for a constant k, xy = k, or y = k/x, k not euqal to 0.

Here is the homework:

http://blog.newtonchineseschool.org/wangweidong/files/2012/03/Math7_Spring_HW_L4.pdf

We spent more time on factorization today, as we really want the students to get good at. We did more classroom exercises.

For homework, it is to take the Chapter 10 Stanaridized Test:

http://blog.newtonchineseschool.org/wangweidong/files/2012/02/Math7_Spring_HW_L3.pdf

Note:

I won’t be able to come in to teach next Sunday. There will be a substitute teacher. We will start Chapter 11.

Today we continued to cover the content of factorization, with focus on factoring ax^2 + bx + c.

If it can be factored, then we can write the following:

ax^2 + bx +c = (mx + p) (nx + q) = mnx^2 + (mq+np)x + pq

Then we have:

a = mn

b = mq + np

c = pq

That is, we want to find two factors m and n from a, so that a = mn, we want to find two factors p and q from c, so that c = pq, and such that the mq + np = b.

If you list m, n, p, q the following way:

m        p

X

n        q

It is the sum of the cross-product, m * q + n * p that must equal to b.

We also talked abut factoring by group. For example:

x^3 +2x^2 +3x +6 = x^2(x+2) + 3(x+2) = (x+2)(x^2 + 2)

Factorization takes time to get good at and only practice can get you there. So here is the homework:

http://blog.newtonchineseschool.org/wangweidong/files/2012/02/Math7_Spring_HW_L2.pdf

Today we started the Spring 2012 semester. For new parents/students, please refer to my teaching plan to know what we will cover in this semester.

After spending a little time on the exam, we continued from where we left off before the exam. We talked about a polynimial in factored form, and how to solve an equation already in factored form by using the zero product property.

We then focused on doing factorization for quadratic equation with the form of x^2 + bx + c = 0 (notice there is no “a” in front of x^2 term). This is the simplified version of a quadratic equation.

Basically for a quadratic equation of form x^2 + bx + c = 0 to be able to factor into (x + p)(x + q) = 0 form, then

p + q = b   and pq = c

So you start with the factors from c to pick out two so that their product is c, then you check if their sum is b. If so, you got it.

This needs practice to be good at and it really helps to be good at factorization. It will make your life with quadratic equations much easier. So do your homework below:

http://blog.newtonchineseschool.org/wangweidong/files/2012/02/Math7_Spring_HW_L1.pdf