MATH+as+AOK

Math as an Area of Knowing
With the Moon as our starting point to link the Ways of Knowing (WOK's - Think PERL) and the Areas of Knowing (AOK's - Think IB Hexogram - Math / Natural Sciences / Human Sciences / Arts / History) we will a) make sense of some of the Math questions raised in our Moon Perception exercise and b) have fun interpreting some quotations about Math as an AOK.

Copy the following onto your Math page and add your thinking:

A. Record here 3 Math Questions raised in class that interest you. Then under each write your answer/s and reflect on your process for expanding your knowledge in that area.

Q1. **How many moons would fit inside the Earth? ORBIT? WEIGHT?**



Moon's Orbit

About 50.

The moon is about 238,900 miles (384,000 km) from Earth on average. The moon is 221,460 miles (356,410 km) at its closest approach and 252,700 miles (406,700 km) at its farthest approach from the Earth. The moon revolves around the Earth in about one month (27 days 8 hours). It rotates around its own axis in the same amount of time and the same side of the moon always faces the Earth.

The moon's mass is (7.35 x 10 22 kg), about 1/81 of the Earth's mass.

Q2. **Does the distance between the moon and earth change overtime?**

The Moon's orbit is expanding over time as it slows down. A billion years ago, the Moon was much closer to the Earth (roughly 200,000 kilometers) and took only 20 days to orbit the Earth. Also, one Earth 'day' was about 18 hours long (instead of our 24 hour day). The tides on Earth were also much stronger since the moon was closer to the Earth.

Q3. **How many craters are there in a moon?**

Approximately 300,000 craters (with diameters down to 1 km) are visible from ground-based telescopes; high-definition photographs from lunar probes reveal millions of craters; extreme close-ups show countless microscopic craters.  There are estimated to be roughly 300,000 craters wider than 1 km on the Moon's near side alone.

B. Read the following Math quotations (some you may have heard before) and below three of them, write your interpretation of what you believe the author is trying to say.


 * <span style="font-family: 'Comic Sans MS',cursive;">"Mathematics is neither physical nor mental, it's social." Reuben Hersh, 1927- **

<span style="font-family: 'Comic Sans MS',cursive;">It means that math is not physical and mental but it brings people together in the sense that we communicate our ideas through sharing what we know to others.


 * <span style="font-family: 'Comic Sans MS',cursive;">"The useful combinations (in mathematics) are precisely the most beautiful." Henri Poincare, 1854-1912 **

<span style="font-family: 'Comic Sans MS',cursive;">This tells us that that we can see the beauty of math if we use the different concepts that we know about it and compile it together to make use of it.
 * <span style="font-family: 'Comic Sans MS',cursive;">"A mathematician is a machine for turning coffee into theorems." Paul Erdos, 1913-96 **
 * <span style="font-family: 'Comic Sans MS',cursive;">"A mathematician is a machine for turning coffee into theorems." Paul Erdos, 1913-96 **

<span style="font-family: 'Comic Sans MS',cursive;">It only means that the mathematicians are needed to influence other people on what they know about math and they are responsible for turning it into theorems or formulas.

<span style="color: #843aa6; font-family: 'Arial Black',Gadget,sans-serif; font-size: 330%;">Phases of the moon

<span style="font-family: 'Comic Sans MS',cursive;">

<span style="color: #800080; font-family: Impact,Charcoal,sans-serif; font-size: 250%;">Math helps me understand the world :)

Whenever we hear the word Math, the first question that comes to our mind is, “Why do we need to learn it?” This question is very common to everyone especially to teenagers who are not interested in Math. Math as an area of knowing give us the tools that we need to understand the world more. It can be represented as numbers, shapes, and lines. As a student, I would say that the concepts in Math that we learn from school are like pieces of puzzle that we put together to acquire new knowledge. The idea behind it is that Math is something that you construct from the basic knowledge that you know. Annoying equations, exaggerated formulas and inhuman values, these are the common negative comments about mathematics. A lot of people find it hard to study this particular field of science. But in reality, mathematics, though difficult //at first//, is the fundamental ingredient of our existence and of world’s harmonious beauty. It can be complicated and misunderstood at times but it doesn’t mean that it makes difficult for us to comprehend what the world is about.

Most of the teenagers think that Math is not that important to learn especially if you won’t consider a career in the future that is a math or science related field. But I don’t believe that Math is only for those people who are interested in taking up courses that are related to it. In some time of our life, we will need it and we never know when. But when that time comes, all the knowledge that we know would be helpful for us to deal with everyday life.

Math encompasses everything from the large-scale measurements of celestial bodies down to the balanced symmetry of biological creatures. Our everyday life reflects the basic but vital applications of math. A good example is time. They say that time is of the essence, thus the use of abstract numerals in expressing the moment of the day makes math valuable in the flow of life. Another application of math is currency. We take our money for granted, but in fact, math is the bottom line of the existence of monetary units. Simple transactions, complex exchange rates, daily allowance and anything of like that involves money, all these have one common denominator, which is math.

In conclusion, Math helps me to understand the world better because it builds us the ability to think more logically. Math should not be taken for granted because it was there in the creation of the world, math is here in class, and math will be in our lives forever. It’s simple yet complex function to humanity and to earth is incomparable. We should appreciate the beauty within math, because mathematics makes the world go round.

<span style="font-family: Arial,Helvetica,sans-serif;">“Mathematics starts with counting. It is not reasonable, however, to suggest that early counting was mathematics. Only when some record of the counting was kept and, therefore, some representation of numbers occurred can mathematics be said to have started.” Write a letter to the text book company explaining:

<span style="font-family: Arial,Helvetica,sans-serif;"> · what you think this means to you in terms of math <span style="font-family: Arial,Helvetica,sans-serif;"> · what, if anything, does this say about learning or knowledge in general <span style="font-family: Arial,Helvetica,sans-serif;"> · whether you agree with it or not. Give real life examples.

<span style="font-family: Arial,Helvetica,sans-serif;">Dear Sir O'Connor and Sir Robertson,

<span style="font-family: Arial,Helvetica,sans-serif;">My name is Pamela S. Victorino and I am currently studying in Harbor Secondary School. I would like to say that your textbook has a lot of information that made me realize that Math was not that complicated before until it was developed. Math started off using texts as a guide to develop their ideas about its different areas such as geometry, trigonometry, algebra, and science. I believe that the idea of Math began to expand when it became necessary to count. We all know that humans understand things by naming them, categorizing them or labeling them in a way that other people can understand the concept. Math has changed as different cultures found out different formulas to use for calculations. Mathematicians proposed formulas that would help us to understand the world better. But before that, numbers were discovered and it became the representation of Math. As people needed to count more and more, algebra came into play just as a way to organize bigger numbers. Algebra encompasses relationships, the use of symbols, modeling, and the study of mathematical change. Algebra uses notations or what we called “variables” which serves as a representation of a number. Most people would say that Algebra is not necessary to learn as long as you know the basics in Math but I would say that the knowledge that you’ll get from it would also benefit you in the future. Whenever you need to problem solve a situation that involves money, time, distance, perimeter, volume of something, prices when you shop and rentals, you will probably need algebra.

<span style="font-family: Arial,Helvetica,sans-serif;">As math was altered, it became a part of our everyday life. It serves as a tool to understand the world better. When numbers were developed, people started to appreciate Math in the sense that it has been useful for us. For instance, when you went out with your friend and your mom asked you to be home at 6.30ish, the numbers in your watch would help you to determine what the time is. Another example is when you are traveling from Thuwal to Jeddah and you want to know how far would it take you to be there. The numbers that are shown in each post will help you determine the distance between Thuwal and Jeddah.

<span style="font-family: Arial,Helvetica,sans-serif;">I therefore to conclude that Math have started when numbers were used as a representation because it became easier for us to deal with our everyday life and it also helped us to understand the world better through the use of different notations.

<span style="font-family: Arial,Helvetica,sans-serif;">Yours truly, <span style="font-family: Arial,Helvetica,sans-serif;">Pamela

<span style="font-family: 'Comic Sans MS',cursive;">Can a mathematical statement be true before it has been proven?

<span style="font-family: 'Comic Sans MS',cursive;">a) a statement of your thoughts in response to the question. b) examples that back up your thinking

<span style="font-family: 'Comic Sans MS',cursive;"> and add at the bottom: any other questions or ways of looking at the question that occur to you
 * <span style="font-family: 'Comic Sans MS',cursive;">YES. **

<span style="font-family: 'Comic Sans MS',cursive;">Based on my own perspective, I believe that a mathematical statement can be accepted as true before it has been proven. Consider the three types of triangles that we know such as isosceles, equilateral, and obtuse. As we all know, isosceles triangles have two equal sides, equilateral triangles have the entire length sides equal, and obtuse triangles doesn’t have any equal sides. If we have given numbers, we can prove if the statement is true or not. But I would say that some mathematical statements just like this example could be true without being proven because of the knowledge that we know about it and another reason could be maybe someone else discovered it a long time ago.

<span style="font-family: 'Comic Sans MS',cursive;">Some mathematical statements can be proven and at the same time can be accepted as true without being proved. For instance, we all know that complementary angles form a right angle and it add up to 90. So if we are given two angles, let’s say, we have 60 degrees and 30 degrees, we can do the math to prove that it is complementary but even if you didn’t prove it, you will still know that if it is complementary or not because of the shape of the angle.

<span style="font-family: 'Comic Sans MS',cursive;">In some cases, I think that we mostly depend on our own perception rather than being reasonable that’s why we consider our knowledge as the truth.