Minggu, 06 Mei 2012

How to Develop Teaching Learning Process in Junior High School


The Practice of Teaching Learning of Mathematics
Title: How to Develop Teaching Learning Process in Junior High School

 I.            Lesson Plan
Lesson plan is a direction and purpose (grounding) teachers to teach in accordance with the law (PP No. 19 of 2005 on the SNP, Permendiknas No. 41 of 2007 on the Standard Process). In Indonesia lesson plan is called RPP. Lesson plan includes the syllabus and learning implementation plan that includes at least the purpose of learning, teaching materials, teaching methods, learning resources, and assessment of learning outcomes. Lesson plan is an important part in the implementation of education in schools. Through a good lesson plan, teachers will be easier to implement and student learning would be more helpful and easy to learn. Lesson plan developed in accordance with needs and characteristics of students, schools, and subjects. Lesson plan in Junior High School is arranged by subject. Need for lesson plan is intended to achieve improved learning undertaken with the following assumptions:
a.       To improve the quality of learning should begin with a lesson plan that is manifested by the presence of instructional design,
b.      To design a learning need to use a systems approach (conventional or computerized),
c.       Lesson plan refers to how students learn to be independent,
d.      The lesson plan should be based on objective and directed by the ease of learning
e.       Lesson plan which involves learning the variable conditions, variables methods and learning outcomes.
The steps to make a lesson plane:
a.       Make lesson plans identity
b.      Understanding basic standards of competency and competency
c.       Determine indicators
d.      Make a plan to implementation it, choose materials
e.       Determine learning goals
f.       Determine learning materials
g.      Determine learning method
h.      Arrange the steps to develop students' activity
i.        Determine the reference and source
j.        Determine the evaluation system (assessment)
There are any obstacles to implementation lessons and weakness plane, but lesson plan has many benefits.
a.       The obstacles to implement lesson plane are:
need extra time.
b.      Need more teachers’ skill.
c.       Almost any teacher feel troublesome to make it
Whereas the advantages of Lesson Plane are:
a.       Make a systematically learning
b.      Becomes more regular learning, etc

II.            Small Group Discussion
Small group discussion is one of students group that have the purpose to give a chance for students to exchange their ideas, share opinion, or other interaction between them then discuss the problem then solve it together. The steps to develop small group discussion are:
a.       Teacher should provide a problem or students’ work sheet and give a direction to discuss it.
b.      Distribute the problems.
c.       Give a chance for students to solve the problem in their group.
d.      Teacher guide students work and help them if they have any problem.
Many kinds of small group discussion that useable in Junior High School, mentioned below, there are three example of small group discussion:
a.       Debate Method
Learning Materials is choose and elect to be pros and cons package. Student divide to several group, each group consist of 4 students. In a group, two students in pros side and the other in cons side. They will debate about one topic that given by their teacher.
b.      Group Investigation
Teacher divided students in a class to small group that consist of 5 until 6 students in a group. Each group is given subtopics from different are of common problems. But first, teacher gave overview about the subtopic. Then students in group have to analyze and synthesize the subtopic.
c.       Method Jigsaw
Teacher divided general information to smaller components. Then student made small group consist of 4 until 5 students. Each member of group have to responsible for each subtopics, then each student who has a subtopic make a new group that has a same subtopic with him. After that, he/she back to their first group and explain to the other member about his subtopic.
                                                                  
III.            Various Method of Teaching
Teaching method is a teachers’ way to develop their learning become a meaningful learning and to explain material learning so students can understand what teacher mean. Teaching method is important in the learning process because it affect of successful learning. Teachers in Junior High School should use various methods so students are not bored. As we know that students in Junior High School have different characteristic, so teacher should use various methods to explore it. Many kinds of teaching method that useable in Junior High School, mentioned below there are 4 example of teaching method:
a.       Guided inquiry Approach Method
Guided inquiry Approach Method is inquiry approach that teacher guide the student to do activity with give first question and direct to discussion.
b.      Recitation method
Learning recitation method is a method of teaching requires students to create a resume with your own sentence.
c.       Methods Study Tour (tour of Work)
Methods Study tours is a method of teaching by encouraging students to visit an object of knowledge and further expand the students create reports and discuss and record the results of those visits, assisted by educators.
d.      Methods of Teaching Team
Teams learning method is a method in which educators teach more than one person, each of which has one of task. Usually educator appointed as coordinator. The way the test, every educator create questions, and then merged. If an oral examination that tested each student should immediately be faced with a team of educators.
Nothing the best method for teaching, but I select guided inquiry approach method to teach of mathematics in Junior High School, because in Junior High School that degree of development student still at transfer phase and student not experience learned with guided inquiry approach method and student still in learn degree scientific process, such that guided inquiry approach method suited for applicable in Junior High School.

IV.            Various Interaction
Teaching and learning process is a process of interaction between two human elements as the party which students learn and teachers teach. Interaction is a communication between someone with others. In managing the interaction of teaching and learning in Junior High School, teachers must have the ability to design courses, mastering the subject matter, capable of creating conditions conducive class, skilled use of media and select the source, understand the ways or methods used have the skills to communicate the program and understand the foundations of education as a basic act.
In the process of interaction is a required supporting component (characteristic of educative interactions) that is the goal, procedure, special construction materials, student activities, teacher as guide, discipline, time limit, elements of the assessment.
In order for an interaction of good teaching and learning, there are several factors that must be met, that is the basis of teaching and learning interactions ¬ base consisting of:
a.       Interactions are instructive.
b.      In the interaction of behavioral changes in students as a result of learning and teaching.
c.       Proper role and position in the process of teaching and learning interactions.
d.      Interaction as a learning process.
e.       Means of teaching and learning activities are available, which help to achieve the interaction of teaching and learning effectively and efficiently.
According to the role of teacher in teaching and learning interactions, among others:
a.       As a facilitator, which provides a situation ¬ situation required an individual to learn.
b.      As a supervisor, is to give students guidance in learning interactions, so that students can learn well and work effectively and efficiently.
c.       As a motivator, this gives encouragement to students willing and keen to learn.
d.      As an organizer, this is organizing the learning activities of students and teachers.
Teaching and learning interactions are characterized by the presence of student activity, because in principle to learn is to do. Do to change behavior, so do the activities. There is no learning if there is no activity. That is why the activity is the principle or principles are very important in the interaction of teaching and learning.
In the class, there are three parts of various interactions that are whole class interaction, small group interaction, and individual interaction. Whole class interaction is an interaction between someone, for example teacher with all students in the class. Teacher explain the material in front of class which is intended to all students other example is teacher give a chance for students to share their idea in front of class. Students’ reflection is included in whole class interaction.
From the whole class, teacher can divide class into small group then distribute some problems and let students to discuss and solve it. In small group discussion, there is an interaction between students with others. They can share their idea and express their opinion then discuss together to solve the problem that have been distributed by teacher. In the small group discussion, teacher offer something that is needed by students and identify difficulty one so an interaction between students in group and teacher is occurred. In individual interaction, the interaction can be a communication between teacher with a student when ask question or interaction between a student with one student. The advantages when teacher use various interactions in the learning are:
a.       make a learning become an interesting learning
b.      increase students’ spirit in the class
c.       help students to appreciate others’ opinion

V.            Various teaching aids/media
Media is goods or other that can be use to support teaching learning process in Junior High School. Media help students easier to understand learning. Teacher must use various media, so students in Junior High School not bored because media make students interest the learning. Teaching aids are supporting goods in the learning so the learning becomes easy understand.
Steps to expand various media are:
a.       Understanding Standard competency and basic competency
b.      Prepare all thing that needed in learning process
c.       Explain how to use it.
The kind of Various Teaching Media:
a.       Electronic Media
Electronic media is media that uses electronic or energy.
b.      With Tools
Procure learning to use tools, will facilitate students in understanding a case.
c.       Print Media
For example is book. The student can learn the material with reading the book.

VI.            Cognitive Scheme
Cognitive scheme is students’ thinking ability concept. Cognitive scheme encourage teacher to construct students’ knowledge and skill so students get new understanding by themselves. It will become a meaningful learning so students can easy to remember it, to construct it and to apply it in the learning to solve problem learning. Cognitive scheme can said as a way to construct students’ knowledge structure. It can start with basic knowledge then students know more difficult material, teacher give stimulated so increase students’ level understanding. The purpose of developing cognitive scheme is students have good understanding structure so they can receive knowledge easily. The steps to developing cognitive scheme are:
a.       Teacher prepares teaching content.
b.      Teacher explains material from easy to hard.
c.       Teach material in simple form.
d.      Choose a correct method so student can understand what teacher mean.
e.       Teacher says the advantage of the material that is being learned.
Cognitive scheme consist of motivation, attitude, knowledge, skill, and experience.

VII.            Student’s Worksheet
Student's worksheet is a media to facilitate students in Junior High School to improve their understanding or find some formulas, so we can conclude that student's worksheet use to support the learning process in class. Student's worksheet, consist of problem which make student try to solve it and get a solution then make a conclusion about that. Student's work sheet can apply in group or individual.
Know, student worksheet that teachers made is collection of questions. It is wrong, because student worksheet is the media and preparation that student use it to find the formulas. In others word student worksheet can use to construct mathematics concept. The function of student's worksheet:
a.    Improve students’ competency by themselves
b.   Help students construct their mind by self so the knowledge can last longer on their mind
c.    Can be a problem, example, exercise, or other material that can improve students’ thinking ability.
d.   Students will more easily to understand the material that being taught
A good student's work sheet is, consist of hints or clues which can make students apply their knowledge and find a conclusion in the end. Teachers have to develop student's work sheet according the student's ability. Teachers can guide students to identify and solve the student's work sheet.
How to develop student's work sheet?
a.       Teachers must understanding student's competency
b.      Difficulty level of student's work sheet is appropriated with student's ability, basic competency, and the material that being studied
c.       Teachers prepare to make a student's work sheet.
d.      Teachers distribute it to all students (in the group or individual).
e.       Give a chance for student to solve the problem.
f.       Discuss together in the class.
As a media to develop students’ knowledge, students’ work sheet has some obstacles:
a.       Teacher needs extra time to develop it.
b.      Need teachers’ skill to make it.
c.       Require other facilities to develop students’ work sheet.
The last is the advantages of students’ work sheet, there are:
a.       Can be a media to construct students’ mind.
b.      Train students to be an active student.
c.       Students have been accustomed to solve problem, etc.

VIII.            Student’s Presentation
Student presentations are very useful in the learning process in Junior High School, because with the presentation of the student can develop a sense of responsibility on himself and responsibilities toward others. For example, after discussion in group, students tell their discussion result and reflection it together. Then students presentation it, share and present the knowledge that they have gained from discussion. From reflection and presentation students can perform in the best and trained to explain their knowledge with their friends and their friends get new knowledge from them. One of the advantages of students’ reflection and presentation is train students to more confident.

IX.            Student’s Conclusion
Student's conclusion is a part of student's activities in learning process. Students make a conclusion from their experience. Students resume the knowledge that have been got then colligate it in a new knowledge. Teacher help student to find the conclusion, so teacher as a facilitator try to provide anything that can help student to find conclusion.
The steps to build up student's conclusion:
a.             Divide whole class into small groups.
b.            Distribute problem to each group.
c.             Give a chance to discuss the problem.
d.            Students present their discussion result.
e.             Students create a conclusion with teacher guidance.
f.             Students justify the conclusion so it will be a true conclusion and become new knowledge.
The obstacle when develop students’ conclusion are:
a.             Need teacher creativity to make various problems.
b.            Need teacher skill to develop it.
c.             Need extra time to apply it.
d.            Students have different potency so difficult to make problems with same difficulty.

X.            Classroom Based Assessment
Assessment is used to determine what a student know or can do. Assessment can called as a process of documenting knowledge, skills, attitude, and beliefs of students. Assessment emphasize on the process, not on final exam. Because it is not fair if student has bad value on the report card because he or she can’t do the exam well because of sick, but in the class he or she is an active student and a smart student. Different with evaluation that is assess students from the final exam. Assessment is a record process of lesson from the lesson begins until it ends. Steps to develop assessment are:
a.       Prepare and make a plan.
b.      Use various methods so students expand their potency.
c.       Record all students’ activity from the lesson begin until end.
d.      Evaluate all students’ activity.



Sabtu, 14 April 2012

#3 English Task (Reflection For Video English Math Tutor)


Basic Mathematics Lesson : 4 (Properties of Numbers)
With host: Luis Anthony Ast (The Video Math Tutor)
Welcome to Basic Mathematics Lesson number 4, properties of numbers.

A special Note
For explain properties, I would use variable ABC, to present my numbers or my variables or other my variable expression.
Now I’ll choose say number.

A.      Properties of numbers
1.       The Reflexive Property of Equality
A number is equal to itself.
So, symbolically is about meaning what that A is equal to A. Its self. And how ways is like thing 2 same 2, 3 same 3. This is simple. So it’s good to know this.

2.       The symmetric Property of equality
If one value is equal to another, then that second value is the same as the first.
Symbolically, we can just say if A equal to B, then this B equals to A, that like symmetrical.
The word problem its look like this, 3 equals X, that’s fine. But to this usually for finally answer you wanted  x to be the other side, so x is equal to 3.

3.       The Transitive Property of Equality
If one value is equal to a second, and the second happens to be the same as a third, then we can conclude the first value must also equal the third.
Symbolically if A equal to B and B is equal to C, so that A is equal to C.

4.       The Substitution Property
If one value is equal to another, then the second value can be used in place of the first in any algebraic expression dealing with the first value.
If A is equals B, then B can be substituted for A and A can be substituted for B.

5.       The Additive Property of Equality
We can add equal values to both sides of an equation without changing the validity of the equation.
To see this rule, now we can use A equals to B. We can add the same thing to both sides of an equation without changing. So I can actually A plus C equals B plus C. We also change this to C plus A equals C plus B.

6.       The Cancellation Law of Addition
We can subtract the same thing in the equation. if we look like this A+C=B+C, so we can subtract each side with C. and then this is gonna be A=B.

7.       The Multiplicative Property of Equality
We can multiply equal values to both sides of an equation without changing the validity of the equation.
If A equals to B, I can multiply both sides equation with C. And then A times C equals B times C we also can change this to be C times A equals C times B.

8.       The Cancellation Law of Multiplication
If we want to cancel the equation like this A times C equals B times C, we can divide both sides with C. so that can be A equals B.

9.       The Zero Factor Property
If two values that are being multiplied together equal zero, then one of the values, or both of them, must equal zero
If A times B equals zero, what we can calculate this situation? A is equal to zero or B is equal to zero, or both of them is must be zero, to make this situation true.

B.      Properties of Inequalities
1.       The law of Trichotomy
For any two values, only ONE of the following can be true about these values:
They are equal.
The first has a smaller value than the second.
The first has a larger value than the second.
Given any numbers A and B. so that ca be A=B or A<B or A>B.

2.       The transitive Property of Inequality
If one value is smaller than a second, and the second is less than a third, then we can conclude the first value is smaller than the third.
 If A is less than B and B is less than C, so we can transit so that A less than to C.

C.      Properties of Absolute Value
For number one |A| is greater than and equals to zero. Number two, the absolute value of negative A is equals to the absolute value of A, like this |-A|=|A|.
Number three |AB|=|A||B|. You can multiply the numbers in sides the absolute value or you can check of the number absolute value in the right side and multiply together. Number four |A/B|=|A/B|. The denominator is not equal to zero. So you can divide the absolute value in the left side or you can check the numbers of the absolute value in the left side and you can divide it.

D.      Properties of Numbers (Closure)
1.       The Closure Property of Addition
When you add real numbers to other real numbers, the sum is also real. Addition is a “closed” operation.
A plus B is equals a real number. If A is real number and B is real number, then the answer will gonna be a real number.

2.       The Closure property of Multiplication
When you multiply real numbers to other real numbers, the product is a real number. Multiplication is a “closed” operation.
Symbolically with multiplication, A times B is equal to a real number. So A is real, B is real, and the result is real.

A special Note
Like this data, the real numbers or closed with aspect addition or multiplication, if the problem is real numbers so the result also real numbers.
For example 3 is natural number and 5 is natural number too. Then three minus five is negative two. and negative two is not part of the sets of the natural numbers, so is not closed. If want to be “closed” the all sides must a natural numbers.

E.       Commutativity
1.       The Commutative Property of Addition
It does not matter the order in which are added together.
For example A plus B is the same thing of B plus A.

2.       The Commutative Property of Multiplication
It does not matter the order in which numbers are multiplied together.
Of this property, if A times B is exactly same with B times A.

F.       Associativity
1.       The Associative Property of Addition
When we wish to add three (or more) numbers, it does not matter how we group them together for adding purposes. The parentheses can be placed as we wish.
(A+B)+C , I can associate for group this together, two the term (A+B) and about the third term C. or I can show this with the different way, like this A+(B+C).

2.       The Associative Property of Multiplication
When we wish to multiply three (or more) numbers, it does not matter how we group them together for multiplication purposes. The parentheses can be placed as we wish.
(A.B).C, I can associating the first two term (A.B) and then the third term C. or I can associate the group with different way, like this A.(B.C).

G.     Identity
1.       The Identity Property of Addition
There exists a special number, called the “additive identity.” When added to any other number, then that other number will still “keep its identity” and remain the same.
Symbolically A plus zero equals to A. And if I put zero first plus A is equal to A.

2.       The Identity Property of Multiplication
There exists a special number, called the “multiplicative identity.” When multiplied to any other number, then that other number will still “keep its identity” and remain the same.
A times one is equals to A, if I exchange to 1 times A is also equals to A.

A special Note
Zero is the unique additive identity. And one is the unique multiplicative identity. Don’t confuse.

H.      Inverse
1.       The Inverse Property of Addition
For every real number, there exists another real number that is called its opposite, such that, when added together, you get the additive identity (the number zero).
Symbolically if A plus the inverse of A is equals to zero. And if negative A plus A then the answer is zero.
2.       The Inverse Property of Multiplication
For every real number, except zero, there is another real number that is called multiplicative inverse, or reciprocal, such that, when multiplied together, you get the multiplicative identity (the number one).
Symbolically we can say the number (A) times its multiplicative inverse (1/A), so that the result is one. And then the multiplicative inverse (1/A) times a number (A) is also equals to one.
By the way
There is one number it doesn’t have the multiplicative number, it is zero. For example, if we divide one by zero, the result is undefined. So, zero has no multiplicative number.

I.        Distributivity
1.       The Distributive Law of Multiplication Over Addition
Multiplying a number by a sum of numbers is the same as multiplying each number in the sum individually, then adding up our products.
First example, look at this thing 5(7+3). Simplify this, so I can choose 7 adding 3 is equal to 10. Then, 5 times 10 is equal to 50. I will check 5 times 7 is 35 plus 5 times 3 is 15. And then you added, so we get 50. The result is same. What happen in both parts? Look at this five times seven and seven with the three, I am distributing. The number is in the bracket. The answer is same. The answer is same.
Symbol like we can see A(B+C)=AB+AC. A times the B plus A times the C is equal to AB+AC. So A goes times the B then A goes times the C.
We have (A+B)C=AC+BC. I can distribute it like this, C times A is AC and C times B is BC. So it is easy.

2.       The Distributive Law of Multiplication Over Subtraction
The distributed property occurs in addition and subtraction. You can symbolic like this, A(B-C)=AB-AC. A times B is equal to AB and A times C is equal to AC, so you can subtract it.

3.       The general distributive property
If we have 2(1+3+5+7), so I can distributed two to the 1, 3, 5, and 7. We will get this 2 times 1 is 2 plus 2 times 3 is 6 plus 2 times 5 is 10 plus and 2 times 7 is 14. And we get the answer is 32.
Suppose we have a(b1+b2+b3+…+bn). I can distributed ‘a’ with b1, b2, b3, and so on until bn.

4.       The negation distributive property.
If you negate (or find the opposite) of a sum, just “change the signs” of whatever is inside the parentheses.
For last property, we have –(A+B) is equals to (-A)+(-B) and then we can simplify this so that -A-B.

Answer to Quiz Questions
1.       The question number one, you wanna find the additive inverses. Let’s going to that the inverses -5 will be 5, 2/3 would be -2/3, -1 is 1 and the additive inverse 0 is just say 0.
2.       The questions number two we want to find multiplicative inverses. Let’s going to that the multiplicative numbers of -5 is -1/5, 2/3 would be 3/2, -1 it’s actually itself -1, and the multiplicative numbers of 0 it doesn’t have (none).
3.       The question number 3 ask, what is additive identity. Yes the answer is of course 0.
4.       The equation number 4, what is multiplicative identity. It is 1, of course.
5.       The question number 5, do all numbers have an additive inverse, the answer is yes.
6.       Number 6 ask, do all numbers have an multiplicative numbers, and the answer is no because 0 does not.
7.       The question number 7, I will completely each the equation. I will fill in the box, so the first line that –u plus u will gonna be 0. For eight times seven, we can use multiplication property. Its round, so the answer will gonna be seven times eight. 5(w-y), I can distributed it, and then I get 5w-5y. -3+(6+2), I will using associative property, the answer will gonna be look like this (-3+6)+2.
8.       The next one, I want to answer about property of equality. So, Z is equal to Z. If a is not less than b, a is not equal to be therefore a is greater than b.
9.       Identify first line here there is m times 1/m equal to one. So this is numbers times inverse property multiplication.
10.   The next one, since square root of three and e are real numbers, so this is square root of three plus e. And the answer is the real number. It is a closure property of addition.
11.   2 plus x square equals x square plus two, it is the commutative property of addition.
12.   (Z+7)+2=Z+(7+2), This is a associative of property addition.
13.   Y times 1 is y, this is identity property of multiplication.
14.   If x=y and y=5 then we conclude x=5 , it is the property of equality.
15.   The next one, square root of two plus zero is equal to square root of two. It will the same identity property of addition.
16.   For the last one, -(x+2)=-x-2 look the sign, so this is the negation of distribution property.
17.   Square root of three times (2 plus x) equal to square root of three times (x plus two). this is a commutative property of addition.
18.   (ab)c=(ba)c. this is a commutative property of multiplication.
19.   [z+(x-1)]y=2y+(x-1)y. this is a distributive property.
20.   (1/x^2+4)(x^2+4). It is the inverse property of multiplication.
21.   (x+y)+z=z+(x+y). it is commutative property of addition.
22.   (1)(1)=1. This is inverse property of multiplication.
23.   5+w+(-w)=5. This is inverse property of addition.
24.   (2a)(bc)=2(ab)c. this is associative property of multiplication.
25.   |-2/3|=|-2|/|-3|=2/3. This is a property of absolute value.
26.   (x+1)(y+2)=(x+1)(y)+(x+1)(2). We can distributed (x+1) to y and also (x+1) to 2. So this is the distributive law of multiplication.
27.   1(y-2)=y-2. We can calculate with 1 times y minus 1 times 2. So this is distributive law of multiplication over subtraction.
28.   x+5=5+x, so this is a commutative property.
29.   p times q so that q times p.
30.   2y+8=8+2y. so this is the same thing as y times 2 plus eight. And then 8+y(2).
31.   2-ab=2-ba.
32.   3+(w+z)=(3+w)+z, so this is the associative property.
33.   3(wz)=(3w)z.
34.   -2(x+3) ia equal to -2x+(-2)(3), next equals to -2x-6.
35.   –(2y-9), so we can multiply the sign (-) to 2y and to nine. So that -2y-(-9), and then we get -2y plus nine.
End of Quiz. And this is the end of the lesson. If you have the question, you can ask me in Luis-Ast@VideoMathTutor.com.

Minggu, 01 April 2012

#2 English Task (Reflection for Math Song and Mathematical Content Video)


1.      Reflection for Math song
Mathematics felt so difficult or so easy depend on our method to learn or teach. March 19, 2012 I study English education in my class with my friends and Mr. Marsigit as my lecturer. Mr. Marsigit shows the video about the song of math in my class. He said if we can teach a lesson on mathematics with song of math, it can make mathematics so fun and then the student also enjoy at the moment of study mathematics. I think it’s good idea, because up till now I am still hear the student felt mathematics so difficult and very boring.
The first song is “the math song parody.” This video is talking about function and relations. I am happy when I watch this video, because song of this video is often I hear. This video can make me interested and also amuse me so that I enjoy watching this video.
The second song is “that’s mathematics by Tom Lehrer.” This video is talking about many topics of mathematics in daily life. Rhythm in this song is so fun and makes me enthusiasm.
The third song is “mean, median, and mode.” The video tell us about how to find mean, median, and mode. I’m very amused because in this video there is funny picture. And also rhythm of this song makes me enjoy.
The fourth song is “what you know about math.”  I think actor in this video is very enthusiasm. This video put in my of mathematics formula.

a)      “The Math Song (The Lazy Song – Bruno Mars) Parody”
Today I don’t feel like doing anything
I just wanna focus on Math
Domain and range and rate of change
It all makes me go insane
Today I don’t feel like doing anything
Now let’s sketch graphs
Try to figure out how to represent relations
Ordered pairs and tables are destination
Learn about this function notation
I’ll be graphing linear function
And interpreting relations
Did you know that y=mx+b?
So in Math class, I’ll get good grades
Oh yes, I know, I know
I said it cause I know
Today I don’t feel like doing anything
I just wanna focus on Math
Domain and range and rate of change
It all makes me go insane
Today I don’t feel like doing anything
Now let’s sketch graphs
Tomorrow I’ll wake up
And do some more graphing
Gonna ace my test and stop all that slacking
And I’m gonna out “I did great!”
I’m gonna walk around
And show all my friends
I bet my old man will be so proud of me
Don’t worry pops, I’ll keep doing great
Oh yes I aced it, I aced it
I aced it cause I can
Today I don’t feel like doing anything
I just wanna focus on Math
Domain and range and rate of change
It all makes me go insane
Today I don’t feel like doing anything
Now let’s sketch graphs
Oh I know all the definitions
 And I know what a function is
One element of the domain goes with the range
There are different types of variable
The dependent and independent
The relationship between two sets of things
Today I don’t feel like doing anything
I just wanna focus on Math
Domain and range and rate of change
It all makes me go insane
Today I don’t feel like doing anything
Now let’s sketch graphs


b)      That’s Mathematics by Tom Lehrer
Counting sheep, when you’re trying to sleep
Being fair, when there’s something to share
Being neat, when you’re folding a sheet
That’s Mathematics
When a ball, bounces off of a wall
When you cook, from a recipe book
When you know, how much money you owe
That’s Mathematics
How much gold can you hold in an elephant’s ear?
When its noon on the moon, then what time is it here?
If you could count for a year..
Would you get to infinity? or somewhere in that vicinity?
When you choose, how much postage to use
When you know, what’s the chance it will snow?
When you bet, and you end up in debt
Oh try as you may, you just can’t get away From Mathematics!
Andrew Wyles, Gently Smiles, Does his thing and voila!
QED we agree and we all shout “ hurrah!”
As he confirms what Fermat, Jotted down in that margin, which could’ve used some enlarging
Tap you feet, keep in time to a beat
Of a song, while you’re singing along
Harmonise, with the rest of the guys
Yes try as you may, you just can’t get away
From Mathematics!


c)       Mean, Median, and Mode Math Learning Upgrade
Mean, median, and mode
How do you find the mean?
Add up the numbers in the data sheet
Divide the total by the number of items
The answer is the mean or average
 Mean, median, and mode
How do you find the median?
Arrange the numbers in order, from the lowest
To the highest values
The middle number is the median for an
Odd number of items
Mean, median, and mode
Mean, median, and mode
How do you find the mode?
Just find the number that repeats most often
Ad the number is the mode
Of you find no number that repeats most often,
Then there is no mode
Mean, median, and mode
Mean, median, and mode
Mean, median, and mode



d)      What you know about Math
What you know about Math
What you know about Math
What you know about Math
Hey don’t you know I represent math league when I add Shorty subtract
Freshman backpack where I holdin’ all my work at
What you know about Math
What you know about Math
What you know about Math
 I know all about Math
Answer’s 44 it’s real easy cus it’s sig figs
You got 45 your answers high you rounded too big
What you know about Math
What you know about Math
What you know about Math
I know all about Math
TI-80 silver edition know I’m shinin’ dog
Extra memory on the back to do my natural log
You know we multiply while memorizing pi
Take limits to the sky be sure to simplify
Graphing utility it’s trigonometry 100 our Math B
Don’t you cheat off me
Distance is rate times time
The sign graph ain’t no line
Exponential decline
But your score can’t beat mine
We’re memorizing rate for our math league states
Against the math league greats
Not getting many dates
I got to find mate but girls just play a hate and always make me wait
Can’t even integrate
Don’t you know I represent math league when I add shorty subtract
Freshman backpack where I holdin’ all my work at
What you know about Math
What you know about Math
What you know about Math
I know all about Math

2.      Reflection for mathematical content video
a)      First Video
It is about how to solve word problems.
Word problems can be very challenging to many students and some of the basic thing is to think about when we trying to solve the word problem is to figure out what are the facts and what is being outs for. Here’s an example.
A college student plans to spend $420 on books for one semester. He also plans to spend $20 per week on pizza. The fall semester is 18 weeks long. How much will he need for books and pizza?
Solution:
Basically we have the fact here. A student going is to be spending some money.

He’s spending $420 on books and he’s spending $20 per week on pizza.
We need add $420 and $20 per week. Looking for the other fact to the fall semester is 18 weeks long. So we’re going to take $20 he’s spending each week and multiply 18 the number of weeks. So he is spending $360 on pizza for the semester and $420 on books for the semester. If we one to know how much he need for the books and the pizza, we need add $360+$420. And of course, he will need $780 for books and pizza.
This is help to solve a word problem.

b)      Second Video
The second video is talking about solving puzzles and riddles (otherwise known as word problems) using two variables.
Example 1 :
A first number plus twice a second number is 23. Twice the first number plus the second number is 31. Find the numbers.
Solution:
Let the first number is x and the second number is y. We need to write two equations.
The first equation is x plus twice a second number so that would be 2y, equals to 23. Second equation is two times x plus the second number is y and equals to 31. We can solve each equation with substitution.
From the first equation, we can find the value of x with subtract the right side and left side with -2y, such that the value of x is 23 – 2y. And then we put the value of x from the first equation for 2x in the second equation. So,  2(23-2y)+y=31. And we can calculate this.

So, it can be 46-4y+y=31. Then, we can subtract variable of y, so -3y+46=31. Then, you can add the left side and right side with 3y and you can subtract with 31. The result is 15=3y. And then you can divide the right side and left side with three and you can get the value of y is 5.

After you get the value of y, you also can find the value of x with x=23-2y. And you can put the value y in this equation, x=23-2.5. So, the value of x is 13.

Then, you can check your answer with put the answer to the equation. Like this, x+2y=23 so, 13+2.10=23 and it’s true. 2x+y=31 so, 2.13+5=31 and it’s also true.
So, the numbers are 13 and 5.

Example 2 :
The sum of two numbers is 16. The first number plus 2 more than 3 times the second equals 18. Find the numbers.
Solution:
Look for a first and the second number. Suppose, first number is x, and second number is y.
Alright, so we have x and y.

The sum of two numbers is 16, so that x+y=16.
The first number plus 2 more than 3 times the second number equals to 18, so that x+(3y+2)=18.

We can simplify the second equation to be x+3y=18-2 so that x+3y=16.
Next step , we can eliminate both of equation.
The first equation is x+3y=16, and the second function is x+y=16 . Then we must multiply the second equation with minus one, so that –x-y=16. Then, we can add both of equation.
x + 3y = 16
-x – y =16
Such that 2y = 0, and the values of y is 0. Because x+y=16, so the value of x is 16.

Alright, let’s check!
x + y =16, so 16+0=16. It’s true.
x +(3y+2)=18, so 16+(0+2)=18. It’s also true.
So, the numbers are 16 and 0.
We finish.

c)       Third Video
The third video is talking about logarithm.
Basically, if you have logarithm the base b, so log b of x equals y.
This formula same with b to the power of y equals to x. It is the first information about logarithm that we should to know.
The second one is notation of logarithm.
If we have log base 10 of x, we can simplify into log x , without 10.
And also for log base e of x (e is equals to 2.71…).
We can rewrite ln of x (ln x). That is we call natural logarithm.

For example log the base ten of one hundred equals to x. You can use the basically formula. So that ten to the power of x equals to one hundred. Be careful for the value of x, it’s not multiplication but its exponent. And the value of x is two, because ten to the power of two equals to one hundred.

Next example is log the base two of x equals to three. You can change the logarithm to be exponential, so two to the power of three equals to x. Finally the value of x is two times two times two equals to eight.

Then, next example suppose we had log the base seven of one over forty nine equals to x. we can change the logarithm to be seven to the power of x equals to one over forty nine. You know forty nine is seven squares, so that seven to the power of x equals to one over seven squares.  And then, seven to the power of x equals to seven to the power of negative two. Such that the value of x is negative two.

Next, you have log the base b of m times n, it is equals to log the base b of m plus log the base b of n. Then if you have log the base b of m over n is equals to log the base b of m minus log the base b of n.  And the last, if you have log the base b of x to the power of n then simplify to n times log the base b of X.

For example suppose you have log the base three of x squares times y plus one over z cubic. You must see the logarithm formula, so the problems equals to log the base three of x squares times y plus one minus log the base three of z cubic. Then you must expand again, so log the base three of x squares plus log the base three of  y plus one minus log the base three of z cubic. And last step, two times log the base three of x plus log the base three of y plus one minus three times log the base three of z.