Math 7A, Lesson 3, 2/26/2012

Weidong Posted in Homework, Spring 2012, Teaching info
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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.

 

Math 7A, Lesson 2, 2/12/2012

Weidong Posted in Homework, Spring 2012, Teaching info
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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

Math 7A Spring 2012, Lesson 1, 2/5/2012

Weidong Posted in Homework, Spring 2012, Teaching info
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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