What Is x and y?

Hello, Everyone! How  R U?

I want to give U a math problem, high school algebra or college freshman algera level.

Let x and y be two unknown variables.

Question : If

x+y=7

x-y=3,

then,

what is x and y?

Solution:

x=___

y=___

Hint: solve it as system of linear equations.

If  U have forgotten about this level of math, please think about the question by guess: how many ways to have two numbers sum as 7, then find the pair of numbers with difference as 3.

for example,  7=7+0=6+1=5+2=4+3=3+4=2+5=1+6=0+7, I have told you 8 ways of sum to 7.

Solutions: x=5, y=2.

check:

5+2=7,

5-2=3. Thus solution is correct.

There are many ways of doing it, Doraz commented exactly how to solve it graphically, mathematically, or using methods of substitutions, cancellations. We can also solve it using graphing Ti-83 calculator…Any way. I give this question which is mediate hard, thus I prefer not to make it too abstract to majority readers. Let me know if you have questions!

Outstanding job, everyone who joined the fun! 15 of U did wonderfully in math computation on this one.

Complex Numbers

When it comes to complex numbers,

You may notice a strange guy,

Who and Why?

That guy is the imaginary number i.

Look at how i divides a pie

Into 4 pieces, as i, -1, -i, 1,

And i is i,

i squared is negative one, -1,

i cubed is opposite of i, -i,

i fourth is positive one, 1.

If you want to go further with the power of i,

You know i fifth is the same as i,

Because 5 is 4+1,

And i fourth power goes back to 1.

Thus the power of i is easy to simplify.

To learn more,

Divide any power of i by four, 4.

Complex solutions always come in pairs,

a+bi, a-bi are conjugate pairs.

Addition, Subtraction,

Multiplication, and Division,

All work the same wonders

In complex numbers

As they do in real numbers.

Make sure real parts go with real parts,

Imaginary parts join imaginary parts.

The final expression will always be  a+bi,

With a, b either a whole number or a fraction.

If b is a fraction,

Make sure i sits on top,

Otherwise,

Make 1 over i equal to negative i, -i.

Do you understand the function of i?

I like i,

Please don’t ask me why!

Math Is Cool, How About You?

I Remember when I was in second grade, my class went to market place of the town with everyone carrying a small abacus,  we were given unit price and the number of items assuming to buy, then each student was asked to calculate the total prices for each item, using multiplication method with our abacuses, I was the fasted to arrive a conclusion with correct answers most of the them. the math teacher was very impressed, and that made me smiling all the way back home.

As the subject becomes harder, I started to like some other subjects such as Transitional Proses,  Poetry, English, and Chemistry.  Chemistry is my strongest subject in High School because I found myself very good at solving chemistry problems during big tests. In general, students are given certain clues and required to figure out the substance implied in the problems. It is like finding solutions to riddles, I always wrote out all the give data on my papers and use logic and math skills to get a my answer. Mathematical thinking skills played a big role in my ability to excel in Chemistry, only those who have good patience, fast computing ability, and flexible analytic skills could stand out,  I am grateful to my early experiences and trainings in math.

Not being confident enough to major in math, and not really being  interested in becoming a professional in Chemistry,  I finished my college with a degree in Materials Management Engineering and got a job in power management company.

After coming to the U. S. A.,  I got a degree in Elementary Education  and in Pure Mathematics, and learned various math teaching and learning strategies. I realize that teaching mathematics is what I have always enjoyed in the past years, and it will be something I plan to continue doing  rest of my life.

Many people don’t enjoy this subject, they believe that they have No talent in it, which is not true. Math is learn-able and could be very fulfilling once you get it! I love math the way it is! There are creative ways to help students at all grade levels to master the concepts.

About five years ago, when I started to teach college freshmen Pre-Calculus, a little verse jumped into my mind,  and I have written it  down on board for my students, most of them liked it. and now I share it here,  you may replace math to anything you like most.

Math is cool,

If you know the rule;

Math is fun,

If you are its fan;

Math is tough,

If you don’t study hard enough,

…

Math is cool,

How about you?

 

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