What was I Trying to Find Out?In the world, problem solving has been selected to be the most relevant skills needed in order for human beings to survive dominantly on this planet in the future. Therefore, in this unit, we learned how to train your mind to think of deductive reasonings to find resolutions to various types of conflicts and understand the usage of them in the future. What did I Discover?After doing some random calculations, I have discovered that the answer for the first problem is 12, 17 and 8 because the rule of the problem is that the addition of the numbers in the squares should result in the numbers of the circles. Therefore, if you calculate all of the possibilities that can be the resolution to the problem, you will find out that adding the number 8, 17 and 12, will result to one of the numbers in the circle which are 20, 29, and 25. What Surprised me?What surprised me during this unit is that even though not always, in the future, deductive reasoning will be one of the most relevant skill you might need to accomplish because as technology improves, it may start to destroy human lives. Therefore, in case that happens, we need to be aware of what is the conflict and what is the best way to find the resolution to it. What was I Good at?During this unit, I think I was good at figuring out the possibilities which needs to be eliminated because I listed all the possibilities in my notebook and tried different equations by using it carefully to find the best solution to solve the problem without having any possible consequences. What do I still need to Practice?However, I think I still need to practice understanding the connections between patterns and deductive reasoning because deductive reasoning is a method to solve patterns, but if you don't understand about it, in the future, the knowledge you might be using to achieve your goals might be unbalanced for you to improve yourself. ConclusionFor conclusion, I hope everybody can understand the connection between patterns and deductive reasoning to make the world a better place in the future.
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What was I Trying to Find Out?What do you need to do to solve mathematical problems? Crate your equations? Know how to use operations appropriately in certain situations? I agree with you, but in every problems are patterns to be recognized. Most people don't notice about this. Therefore, in this unit, we tried to find out the definition of patterns and understand the usage of it. What did I Discover?After doing random equations and etc, I discovered that patterns are not only shapes, but numbers because as we check though interesting images about patterns, we realized that it is a subject which changes its formation, number, design, and etc repetitively forever with a certain type of rule. For example, if we want to figure out a challenging problem, we need to find out the pattern carefully to find the resolution of it much more easier. What Surprised me? What surprise me during this unit was that whether the pattern is difficult or easy, it can always turn itself into various types of equations which can give interesting resolutions. For example, when we were solving the rule of the pattern which Mr.Pug gave, I found the resolution easily with having the answer of X x 2 + 4 = Y. However, I could have also represent it in an algebraic way like this down below. 2X + 4 = Y What was I Good at?'I think I was good at using algebraic equations to solve rules of different patterns because I think I did a great job of that understanding the connections between them and use it for my advantage to solve more challenging problems. For example, if 2 is X and the Y is 4, the rule or an equation for this is multiply the X twice. What do I still need to Practice?However, I think I still need to work on solving rules of patterns in an easier way because when I was trying to find out equations of the patterns, even though it looks easy, I still had difficulties solving it due to thinking it to hard for myself. Therefore, I think next time, I should think of how many operations there are in the pattern and solve it carefully. What do I want to know now?Next time, I want to inquire though are there problems that doesn't have a pattern because even though it is dimensional, I don't know if it is relevant enough to form every problem you solve. That not only includes math problems, but also other important conflicts like moving forward to achieve our goals. ConclusionFor conclusion, I hope this had been an great experience to understand the usage of patterns to solve different problems. What are the Rules of Sudoku?The rules of Sudoku is that there are 9 rows which each row have 9 boxes with all of them having 9 different numbers with each other. As same as the rows, there are 9 columns which needs to have 9 different numbers in each box. Also, if you see carefully there will be 9 huge boxes. In each box, there needs to have small boxes with 9 different numbers as well. Furthermore, there are some missing numbers you need to fill to finish the game. Therefore, we need to use deduction to find missing numbers and fill it in boxes to create new rows and etc... How did I find the Solution?I figured this problem out by finding out missing numbers of one of the huge boxes which has many other small boxes with the numbers already filled in. The reason I used this trick is because if you find the missing numbers in the huge boxes first, you will soon be able to find out the unknown subjects of columns and rows one at a time until you discover all of them to accomplish this popular deduction game. Can I Think of any other Times I can use Deduction to find Missing Information?I can use deduction when I'm playing chess because the results depends on your decision making of how you move the chess into different positions. Therefore, you need to deduct using the rules of the game to take advantage of your location to capture the king. When do I use Patterns to find Missing Information?I use patterns to find missing information when I'm buying something with an interesting discount which is more unusual than any other prices because when you're calculating the prices of something with a discount, just like algebra, there is a pattern of using complement equations to find various answers. For example, to figure out the price of this something which costs $5,000 with a 50% discount, the solution would be 5,000 x 50% = 5,000 x 0.5 = $2,500. ConclusionFor conclusion, I hope this has been a great experience to check back to deduction skills to justify my claim much effectively. What was I Trying to Find Out?Have you ever got frustrated of measuring all the angles of a triangle using a protractor? I know you have because dealing with various angles using new equipment might be confusing to use. Therefore, in this unit, we learned about how can we measure 2 angles of a triangle and get 1 for free by testing out the tactic on triangle measurements we measured in the last unit called the 'world is formed with loads of triangles.' The reason we're doing this is to learn easy tactics to solve challenging geometry problems for others to solve. What did I Discover?The thing that I discovered during this unit is that instead of having hard time measuring 2 or all 3 angles of a triangle, you can measure only 1 angle and get 2 for free because if you're measuring the angles of the triangle which is split from the hexagon down below, you might notice it is an isosceles triangle, so the 2 angles of it is the same size. Then, if we measure the only angle which has different size than the other angles, it is 120°. Furthermore, the addition of the 2 angles which both has the same size would be 180° - 120° = 60°. Therefore, the 2 angles of the split triangle is 60° ÷ 2° = 30°. You can also do it this way by measuring one angle which has the same size with another and find the one missing angle. 30° + 30° + x = 180° 60° + x = 180° x = 180° - 60° x = 120° What Surprised me?What surprised me in this unit was that you don't need to spend a hard time measuring all 3 angles of a triangle because the only way to measure angles of these shapes is to use the protractor for every angles, but it turns out these dimensional shapes have the power to give the answer to the size of at least 1 angle for free. For example, for a scalene triangle, you need to measure 2 and get 1 for free due to the sides all different while for the isosceles, you can measure 1 and get 2 for free and finally, for the equilateral, you just need to know that every angles of it is 60°. What was I good at?In this unit, I think I was good at showing a good diagram of my thoughts into this project because in each important part to find the resolution, I did a specific label to let others understand what I'm saying and show others that I can turn this problem into an algebraic equation. For example, the equation I made to solve this problem and show others about it is 30° + 30° + x = 180° = 60° + x = 180° = x = 180° - 60° = x = 120°. What do I still need to Work On?However, I think I still need to work on how to write an equation of finding 2 unknown angles because the equation shown down below is an equation of finding only one unknown angle which I want to represent 2, so if people don't understand completely what my equation really means, they will get confused of whether this is right or wrong even though it is right. What do I want to know now?There were lots of new curiosities which I want to solve during this unit, but the most interesting one is finding 7 unknown angles while there is only one known angle from an octagon because it is one of the shapes which can be split into interesting and smaller shapes, so I wonder if I challenge myself and solve this problem, I can get interesting results which can create even more inspiring curiosities than the last one. For conclusion, I hope this has been a great challenge to look back to other units which I thought I have already mastered, but I'm not.ConclusionWhat was I Trying to Find Out?In this unit, we were trying to find out how do we figure out the area of various objects which is formed with different using triangles. The reason is that I wanted to justify our claim to everybody that triangles can form every polygons in various ways and we can use it in our future lives to construct new mathematical, scientific and technological ways to make our world a better place. For example, engineer new cities and etc. What did I Discover?From this unit, I have discovered that the area of the hexagon table down below has a volume up to 38,400.186 cm3 because if you split it up to simple shapes, there would be 2 triangles and 1 square. That means if you add the size of them all together, it would form the table again. Therefore, if you find the volume of those shapes, the 2 triangle's volume would be 139.8 cm(Length) x 39.6 cm(Width) ÷ 2 x 2 = 12,732.984 cm3 and the rectangle's volume would be 139.8 cm(Length) x 80 cm(Width) = 25,732.2 cm3. Then, if you add it all together, the volume would be 12,732.984 + 25,732.2 = 38,465.184 cm3. However, just like in the picture, there is a tiny hole on the table, so really the volume of the hexagon table is 38,465.184 - 3 x 3 x 3.14 x 2.3(Circle's Volume) = 38,400.186 cm3. What Surprised me?What surprised me was that all triangles can form all polygons because they are so dimensional that they can fit in even the most irregular and awkward polygon which is all around the world without leaving any gaps. For example, all polygons can be split into simple shapes such as rectangles and all rectangles can be split up to 2 or 3 triangles. Therefore, we can say that triangles form every polygons by being spliced into rectangles and it spliced into other unusual shapes. What was I good at?I think I was good at measuring and calculating the equation correctly and independently because during that time, my partner Tom was away to help his friend for his project. Therefore, I needed to do the hard work all by myself. However, even though there was nobody there to assist me, I still didn't gave up and measured, calculated the answer over and over again until I found the resolution. What do I still need to Practice?However, I think I still need to practice how to measure things by exactly knowing its formation because when I was measuring the hexagon table, I didn't notice there was a little hole on the middle which can also take up space. Therefore, I almost got the wrong answer by not subtracting the space the little circle can take out of the table. What do I want to know now?Now, I want to know how much triangles can fit in dozens of circles because circles are not polygons and it has only curved lines, so it is impossible to draw a diagram of how much triangles would fit in. However, they both have an area, volume and capacity, so if you divide the volume of the circles with the volume of the triangles, I think there would be an unusual result. What is Happening right now? Today, our class started a new math unit to keep on inquiring this amazing mathematical world. The unit we will be working for several weeks will be about unknown numbers which can be also called as Algebra. We are learning algebra not just because to prepare for school tests and to compete with other schools, but to know how to calculate challenging equations in certain situations like buying different things which have various costs. How am I going to Accomplish this?The way I'm going to accomplish this is to solve an equation using whole numbers which uses algebraic expressions in my math book and when I start to get comfortable with it, I can move on to challenging ones like fractions, decimals, square roots equation, and etc... For example, if you mastered how to solve 3x + 2, you can move on and solve 1/3x + 2, so on, and so forth. What things do I need to Learn?I think I need to learn how to solve an equation which contains division and multiplication operations with unknown numbers to accomplish this unit. The reason is, I already mastered how to solve equations which contains operations like addition and subtraction, so I need to move forward if I want to improve and stay away from my comfort zone. What kind of Skills do I need to use?I think I need to use the skill of solving various equations using complementary operations because algebra is all about figuring out the complementary state of other operations and use it to find resolutions. That means that I need to be logical of inquiring through different answers by solving various problems in complementary ways. ConclusionFor conclusion, I hope I can inquire and learn lots of things about algebra and use it in my life efficiently. It's about time we need to say good bye to our precious measurement unit. In this unit, there were things that worked out very well, new things that I should improve and effective curiosities from interesting videos, pictures and data. These are the things that happened during this unit.IntroductionThe things that I have improved is that I finally mastered how to convert measurements in different units because in the last few weeks, I have struggled figuring out the rule of converting measurements into kilo, centi and milli. Therefore, I kept on getting wrong answers, so I needed to solve it over and over again until I found the resolution. However, as I learned the milli, centi and kilo rule, I now, understand how to convert different measurements into various units.What things did I Improve and How?I find out converting time into different units is the hardest thing to do because there are no specific rules about them and it keeps on changing when you convert them into bigger or smaller units. For example, you can convert seconds into hours by keep on dividing it into 60, but as it get to days, you need to divide it into 24, 12 and many more.What was Difficult and why was it Difficult?I think the knowledge I can use on my life is that up to 11 years, I have used the computer for 1.7 years because technology is improving so fast that people are spending almost half of their lives on their devices without achieving anything that you motivated or interested at. However, by using this knowledge, I can tell myself that devices are good resources for your life, but if you use it too much, it can be a bad influence for me.How can you use this Math on my LifeI think the best way for me to improve my mathematical thinking is that I should keep measuring variety of subjects to find out interesting results because as I keep on discovering things that I want know about, there would be a new curiosity I want to research in mathematical ways. For example, how did scientists exactly calculated the location of where Neptune using math when technology didn't improve and if a person goes in a water tank which is filled up with water, the amount of water that you spilled as you went in the container is the exact volume of yours, so how water forms interesting results as you have an experiment with it. There are still lots of things that I need to know about this amazing world!!!What is the Best way for me to Improve my Mathematical Thinking?For conclusion, it has been an amazing experience to have experiments using different tools to find out interesting results and have a new curiosity which is related to it.ConclusionWhat were I Trying to Find Out?In this unit, there were lots of things that you could inquire about such as figuring out how much water can fit in your water bottle or be a huge thinker and solve how many dices can fill up the space of a soccer field. I and my partner, Nathan decided to find out if he was a rectangle, how many Nathans can fit in this classroom without leaving even one single gap. What did I Discover?After several calculations, we found out that if Nathan is a rectangle, --- Nathan can fit in the studio 5A classroom without leaving any gaps because the length, width and the height of the classroom is ---, so the volume would be ---. Furthermore, the volume of Nathan is --- having the length, width and height of ---, --- and ---. That means you can fit --- ÷ --- = --- Nathan can fit in this studio.What Surprised Me?Something that surprised me was that I thought Nathan had a volume at least higher than 10, but as his width, and his height is a decimal, as I multiply those numbers to find out the volume, the answer was 0.04... What were I Good at?I think I the thing I was good at was figuring out the precise answer because I used various math skills which I learned to figure out the volume, capacity and etc... of something. For example, this classroom is a trapezoid shaped room, so I found out the volume by figuring out the area of the trapezoid first and then, multiplied the height to earn the volume. What do I need to still Practice?I think I still need to practice measuring the area or the volume of something by exactly knowing the unit of the measuring equipment because when we were measuring this classroom, we thought the unit shown in the measuring tape was all formed of feet. However, as we found out that it wasn't, we needed to measure the entire classroom over and over again. Approximately 3 times. What do I want to know now?Now, I want to know how much A4 papers can fit in this classroom because I thought it would be interesting to find out how much of these flat things can fill up the space of the entire classroom and how much trees would be wasted to do that. For example, in my estimate, I think at least 1 million papers can fit in this classroom which is a waste of approximately 5,000 trees. If my statement is true, that would be an interesting fact. What were I Trying to Find Out?We lived on this planet for millions of years viewing the amazing world with our own eyes. With this kind of view and experience, human economy grew really fast. But, have you ever wondered what kind of things that we can't still see? Our human eyes can only see a little tiny part from what's there in the entire universe. Some of those things might be around you as you learn, cook or even drive. In this unit, we tried to answer some of those curiosities by watching the documentary below. From this, we have learned what's still out there far more to be discovered. What did I Discover? I have discovered that there are many things which are too fast, too slow, too small, and too big to see, but as technology improves over time, we would be able to discover the truths about these mysteries and keep on asking these questions of how did the world form. For example, depending on scientists, they say that one hydrogen atom created the universe by forming relevant things which have various features like invisibility. What surprised me was that the universe was formed with only several hydrogen atoms because these atoms have mysterious power to create this amazing world of human civilizations, the beautiful environment and even the multiverse. For example, when you separate uranium neutrons and protons apart, it will create a huge energy to destroy everything that is left in Earth.What Surprised me? What were you Good at?I think I was good at understanding the difference between the things that we can see and what we can't because I kept on my asking myself how is this too fast, too slow, too small and too big to see using the knowledge I already knew about these things. For example, as I saw ultraviolet in this video, I kept on asking myself how can't we see ultraviolet and as I already knew ultraviolet is a light ray, I guessed that it was a fast moving matter and I was correct. What do I need to Practice?I think I need to practice documenting new things I learned from a video, image and etc.. because if you don't record your learning, after having a good experience, you will forget about the new things that you learned which can be used to improve yourself. For example, when I didn't document my learning properly in my math book, I forgot about how can we treat cancer in the future using the technology of something to small to see which means I need to solve my curiosity again. What do I want to know now?Now, I want to know what is the smallest particle on Earth because since you never know what is the end of space, I wonder if there is a limit to how much small particles are. For example, around year 1900, scientists have discovered that there was something far smaller than atoms which are electrons, nucleus, protons, and neutrons. Answer these questions with reasons and examples.
What were you trying to Find Out?What did you Discover? What Surprised you? What were you good at? What do you still need to work on? What do you want to know now? What is Happening right now?How am I going to Accomplish this?What Things I need to Learn about? What Skills am I going to use? |