Pay It Forward Reflection

Pay it forward describes a good theory, but the theory is just one of the possibilities, it cannot be real. I think it is impossible, unrealistic, and utopian. A lot of people might be influenced by Pay It Forward, but a lot of people do not mean all people. The standard of each people is different. The movie wants to explain and describe the message which is our world will be peaceful if people help other people. I think we already know it, and why we do not act it even if we know the theory is humans are different, selfish, and egoists. If you read an ethical or philosophical book, all authors will emphasize it. Unless Jesus comes here and becomes a king of the world, it is impossible that all opinion of all people to make one way. Mr. Simonette referred the prediction of adults in the world to students in seventh grade. I liked the sentences because literally adults can predict everybody cannot be elites for the society because they have met a lot of people in their life and finally got the result. It means that they had to accept that everybody cannot be same. The end of the movie is Trevor is killed by other students, and his friends, family, and the people who are influenced by Pay It Forward praise for Trevor. If Pay It Forward is possible, Trevor would not need to be killed. The people saw his possibility, and it became evidence abouhis utopia. Of course, we cannot guess the future about if he is alive. A few, no. A lot of people are influenced by Pay It Forward. However, I cannot be sure if it is really possible while we are living in the world which the different people are living in.

Week 15 in Math 10

What we learned in week 15 in Math 10 is about a formula to get slopes and kinds of forms. The formula to get the value of a slope is pretty interesting for me. If the coordinates are (x1, y1) and (x2, y2), the formula is y1 – y2 over x1 – x2, so it means, we can the value of slope easily if we know ONLY the two coordinates on the line. A slope is the most important part of these units, and the forms are no exception. We learned two new forms in this week excepting Slope-Intercept Form which we already know. One of them is Pretty General Form, easily, the numbers must exist on only one side. It must consist of integers, it means there is NO fractions and decimals. Also, it must contain more positive numbers. For example, there is – x + y – 1 = 0, x – y + 1 is better. Another form is Point-Slope Form. The form is used when we know a coordinate and the slope. If we know the coordinate (x1, y2) and the slope is m, the formula of this form is y – y2 = m(x – x1).

For example,

1. When the two coordinates of the slope are (3, 7) and (5, – 13), the value of the slope.

  • The formula of a slope is y1 – y2 over x1 – x2.  We can substitute the coordinates on the formula, then, it is – 13 – 7 over 5 – 3. – 20 over 2 can be divided by 2, so it is – 10.
  • So, the slope is – 10.


  • The slope is 4
  • The y-intercept is 2
  • The formula of the line is y = 4x + 2, so the formula of Pretty General Form is 4x – y + 2 =0.
  • We know a coordinate (1, 6) and the slope 4. The formula is y – y2 = m(x – x1). We should substitute the coordinate and slope. So, Point-Slope From is 4(x – 1) = y -6.

Week 14 in Math 10

What I learned week 14 in math 10 is about a slope.

The slope of a line segment defines and describes a measure of the steepness of the line segment. The most important part to get a value of the slope is a rise and a run. A rise defines the change in vertical height between the endpoint, and a run is a change in horizontal length between the endpoints. It is difficult to memorize with those meaning because my English skills are weaker, so I decide understanding meanings instead of memorizing. Easily, a rise is a connection with y value and a run is a connection with x value. The rise and run are used to make a ratio to get a value of the slope. The ratio is the rise over the run (rise/run). The rise is POSITIVE if we count UP, NEGATIVE if we count DOWN and the run is POSITIVE if we count Right, and NEGATIVE if we count LEFT.

For example,

  • a = it counts UP and RIGHT, so its slope is POSITIVE. The rise is 6 and the run is 2, so the fraction is six over two and it can be divided by 2.
  • So, the slope is 3.
  • b = it counts UP and LEFT, so its slope is NEGATIVE. The rise is – 9 and the run is even 9, so the fraction is nine over nine and it can be divided by 9.
  • So, the slope is – 1.
  • c = it counts DOWN and RIGHT, so its slope is NEGATIVE. The rise is – 2 and the run is 6, so the fraction is negative two over six and it can be divided 2.
  • So, the slope is – 1/3.
  • d = it counts DOWN and LEFT, so its slope is POSITIVE. The rise is – 3 and the run is – 5, so the fraction is negative three over negative five it can be divided by – 1.
  • So, the slope is 3/5
  • e = it counts DOWN and RIGHT, so its slope is NEGATIVE. The rise is – 1 and the run is 8, so the fraction is one over eight and there is no GCF (Greatest Common Factor) which can divide them.
  • So, the slope is – 1/8

Week 13 in Math 10

We started to learn Relations and Functions Unit this week. It might be the most difficult unit for me in math 10.

I learned about an independent variable and a dependent variable firstly. An independent variable is usually called x, and a dependent variable is usually called y or f(x). A dependent variable is changed by an independent variable in a functional formula. We can get x and y-incepts, a domain, and a range using those variables. When we should get a value of the x-intercept, we must substitute 0 for the y (x-intercept, 0), in contrast, how to get a value of the y-intercept is similarly substitute 0 for the x (0, y-intercept). A domain is the set of all of numbers for the independent variable (input x) in the relation, and a range is almost same as a domain excepting to change the independent variable to the dependent variable (output y). A relation is a comparison between two sets of elements and has connections more than one. A function is same as f(x) and has only one connection.

For example,

1. The cost of jellies is related to the weight

  • The cost is a dependent variable, to output, a range, and y.
  • The weight is an independent variable, to input, a domain, and x.
  • It is a function.


  • It is a functionf(x) is same a function, and 2/3 x2 – 6 is a notation.
  • x-intercept is to substitute 0 for y, 0 = 2/3 x2 – 6. So, the x-intercept is equal to 3 and -3.
  • y-intercept is to substitute 0 for x, y = 2/3 * 02 -6. So, the y-intercept is equal to -6.
  • A domain is the set of all of numbers for the independent variable in the relation. So, the domain is {-3 ≤ x ≤ 3, x ∈ R}
  • A range is the set of all of numbers for the dependent variable in the relation. So, the range is {-6 ≤ y ≤ 3, y ∈ R}

Week 11 in Math 10

What we learned Week 11 in Math 10 is to factor when the degree of a polynomial is more than 2. (for examples 4, 6, et cetera.) The bases of factoring polynomials are C, D, P, E, and U.

C has used the polynomial which can be divided into common factors.

3x2 + 6x = 3x(x + 2)

D is differences of squares, it is used when the polynomials are perfect squares.

16 – x2y2 = (4 – xy)(4 + xy)

P is to find the pattern of the polynomial.

x2 + 6x – 7 = (x + 7)(x – 1)

E is used by easy polynomials which can be used the easiest pattern.

x2 + 4x + 4 = (x + 2)2

U is used by ugly polynomials. (We usually use a square to factor.)

6x2 + 13x + 6 = (2x + 3)(3x + 2)

We can use the bases and solve the polynomials which degree is bigger than 2. We also learned the pattern about a degree. When the degree is bigger than 2, other exponents of x must be half of the degree if there are not any common factors, and it cannot be factored if it is not.

For an example, 32x4 – 2 can be divided by 2 (Greatest common factor) and it becomes 2(16x4 – 1). 16x4 and -1 are perfect squares, we can use D. 2(16x4 – 1) = 2(42 + 1)(42 – 1). 42 – 1 is even perfect square which can be used D, but 42 + 1 is not because the binomial must have ONE minus sign. 2(42 + 1)(42 – 1) = 2(42 + 1)(2x + 1)(2x – 1). So, the answer is 2(42 + 1)(2x + 1)(2x – 1).

Week 10 in Math 10

What I learned this week in Math 10 is to factor trinomials easily. It seems more difficult, but trinomials that can be factored if we find and use the pattern, it is similar to simplify polynomials. I could find the pattern of factoring other trinomials. It is not different to find and divide trinomials by the greatest common factor (GCF) on trinomials from simplifying polynomials.

Factoring with Common Factor: find greatest common factor and divide the trinomial by GCF.

Example: 3x+ 6x + 9 = 3(x+ 2x + 3)

Factoring the square binomials: the terms in binomials are perfect squares.

Example: 9x– 4 = (3x + 2)(3x – 2)

BUT, it is impossible => 9x+ 4

Factoring simple trinomials: find the factors of last term and add them, and find a pair which is become a number of middle term (coefficient of x)

Example: x+ 4x +3 = (x+3)(x+1)

Factoring UGLY trinomials:

The most important term in the trinomial in the picture is the first term that is the coefficient of xand the term that is just a number. After he coefficient of xand the last numbers are multiplied, we can find the factors of the multiplied number. (1, 24), (2, 12), (3, 8), and (4, 6). The numbers are added by their pair (1+24 = 25), (2+12 = 14), (3+8 = 11), and (4+6 = 10) and we can find the middle term (the coefficient of x, 11) 3+8 = 11. Factors of 6 are (1, 6) and (2, 3). Factors of 4 are (1, 4) and (2, 2). 1×3 (= 3) + 4×2 (= 8) = 11.

So, 6x2 + 11x + 4 = (3x + 4)(2x+1)

Complex and Compound-Complex Sentences

She was a famous writer of popular novels and she was preparing to write a new novel.

Although she was an author of famous novels, it was not easy to create stories and write her imagination on papers until the sky turned dark.

Unless an interesting or special situation happened to her, it seemed impossible to write her own story even if she focused on only making a story for a few days.

When she did not have any ideas before, she walked around her town and talked neighborhoods.

Meeting people was interesting to her because she thought their talk might help or be an idea of her story.

When she prepared to go outside, she realized the outside turned dark a long time ago and there was nothing including a small movement.

She tried to go outside whether there was something or not, but she felt the just cold atmosphere and went back to her study again.

Although a few pieces of fire woods on the stove were still burning, she felt colder than outside.

She gave up writing new stories and just started to read her favorite novels in the study because her will was still staying in cold outside and she should try to forget the cold.

Another word of imagination was isolation because she thought reading a book is same to make another world in a human head.

While she concentrated on books, it was being easier to forget her anxiety including a problem of her people.

She decided to become a writer by attraction to books, and she hoped to make other medicine of forgotten stress while she read books.