So on Thursday, October 21, we went to UBC to watch a game show called, Who Wants to be a Mathematician. It was a lot of fun cheering on Kathleen as she did a lot of very hard math questions, and even though she didn't win, it was still awesome to root for her and watch her do these mind-boggling problems. We also attended a seminar and a workshop teaching us more about the world of mathematics. Ten things that I learned about math are:
1. Math is a lot harder than I thought.
2. Math has a lot of practical applications in everyday life.
3. Math can make you a millionaire.
4. Doing math all day is actually a job.
5. Math is more than just calculations and numbers.
6. Math can be a lot of fun when you work with others.
7. A lot of people like math.
8. Watching people do math is entertaining!
9. People did complicated math thousands of years ago.
10. Math can bring people together.
The seminar, "And a Millionaire, too..." was really interesting. The speaker was humorous and knew a lot about math. He showed us how to prove the Pythagorean Theorem and told us that this theorem was probably already discovered by Chinese people. He also did a whole bunch of other complicated equations that I didn't quite understand, but it was still fun to see all those numbers being put together into something that made sense. The speaker explained how you could become a millionaire by solving one of the Seven Millenium Questions, and that it is better to be a mathematician than a millionaire, because a millionaire is just someone with a lot of money, and a million isn't that much, really.
During the last part of the day, we went to a university classroom and took part in a math workshop where we worked with each other on some math questions while UBC students helped us. It was a lot of fun working with my friends on the problems, although some of them were quite difficult and took more than 10 minutes to solve. The UBC students were very helpful and friendly and gave us a lot of help whever we needed it. This workshop helped me with my future learning by showing me that it is easier to learn with other people around you and that with a little patience and perseverance, you can do solve almost any math problem!
Sunday, October 24, 2010
Friday, March 26, 2010
Qualities of a GooooD Mathematician
Mr. Cheng wrote a blog post about good qualities of a mathematician. He asked us to write about the three characteristics that I find most important. The qualities that I think are most important are: never giving up (perseverance), willing to learn, and teamwork.
I think it is important to have perseverance because sometimes, even the best mathematician makes mistakes and gets questions wrong. If he/she has perseverance, they will keep trying the question and uses different techniques.
Another quality that goes well with perseverance is being willing to learn. If you don't get the question, you should be willing to learn how to solve it. People who are willing to learn more are the people who strive to do well in school.
The final quality that I find essential is teamwork. You should have good communication skills and be able to work well with others. In math, and the jobs that require math, you have to work with the people around you. If you do that well, you will succeed at what you do.
I think it is important to have perseverance because sometimes, even the best mathematician makes mistakes and gets questions wrong. If he/she has perseverance, they will keep trying the question and uses different techniques.
Another quality that goes well with perseverance is being willing to learn. If you don't get the question, you should be willing to learn how to solve it. People who are willing to learn more are the people who strive to do well in school.
The final quality that I find essential is teamwork. You should have good communication skills and be able to work well with others. In math, and the jobs that require math, you have to work with the people around you. If you do that well, you will succeed at what you do.
Friday, March 5, 2010
Pascal Contest
Recently, I completed the 2006 Pascal (grade 9) Contest for fun. This was a question that looked really hard when I first read it, but I figured it out really quickly. Let me show you!
19. The sum of ten consecutive integers is S. Ten times the smallest of these integers is T. What is the value of S-T?
A.) 45 B.) 55 C.) 10 D.) 9 E.) 66
To solve this question, I made an equation of it. First, let the smallest integer be x. This will be what the first equation looks like: x+(x+1)+(x+2)+..........(x+9) = S In total, that would be: 10x+9=S. T would be 10 times the smallest integer, and T would be 10x. To figure this out, you just take away (10x+9) - 10x. Simply the answer would be D.) 9. My reflection on this contest and the problem solving was that it was quite easy, partly because I am in grade 10 and this is a grade 9 contest, but also because I have improved a lot since the last time. I have done a lot more different problems and figured out more different ways to solve them. I feel that now I can solve almost any problem.
19. The sum of ten consecutive integers is S. Ten times the smallest of these integers is T. What is the value of S-T?
A.) 45 B.) 55 C.) 10 D.) 9 E.) 66
To solve this question, I made an equation of it. First, let the smallest integer be x. This will be what the first equation looks like: x+(x+1)+(x+2)+..........(x+9) = S In total, that would be: 10x+9=S. T would be 10 times the smallest integer, and T would be 10x. To figure this out, you just take away (10x+9) - 10x. Simply the answer would be D.) 9. My reflection on this contest and the problem solving was that it was quite easy, partly because I am in grade 10 and this is a grade 9 contest, but also because I have improved a lot since the last time. I have done a lot more different problems and figured out more different ways to solve them. I feel that now I can solve almost any problem.
Math Contest!
Last Monday, we took part in a Canadian Math Competition. At the beginning, it was quite nervous and people were chatting anxiously. When we received our answer sheets and booklets, I felt more relaxed as I started to do the math. The first few questions were quite simple, but as I worked on, they got harder and harder. I managed to complete most of the questions with some confidence. I thought I did really good at the beginning, but not so good at the end. I tried not to guess any questions, but some of them I wasn't sure about. I felt that I did really good and it was easier than I thought, but when we went over a question I was confident about, I discovered that I got it wrong. I will show you one question that was on the contest that I liked and how I solved it:
12. The price for each item at the Gauss Gadget Store has been reduced by 20% from its original price. An MP3 player has a sale price of $112. What would the same MP3 player sell for if it was on sale for 30% off its original price?
A.) $78.40 B.) $100.80 C.) $89.60 D.) $168.00 E.) $98.00
First, to solve this problem, you have to figure out how much the MP3 player cost at full price. Because I forgot how I solved this problem two months ago, I will use the tried and true guess-and-check method. You just multiply a number by 0.8 until you get 112. First, I plugged in 150 and got 120. Then, I tried 145 and got 116. Eventually, I got 140. From here, solving this problem is easy. You just multiply 140 by 0.7 and you will get your answer, which is E.) $98.00.
I did pretty good this time around and hope to do better next year!
12. The price for each item at the Gauss Gadget Store has been reduced by 20% from its original price. An MP3 player has a sale price of $112. What would the same MP3 player sell for if it was on sale for 30% off its original price?
A.) $78.40 B.) $100.80 C.) $89.60 D.) $168.00 E.) $98.00
First, to solve this problem, you have to figure out how much the MP3 player cost at full price. Because I forgot how I solved this problem two months ago, I will use the tried and true guess-and-check method. You just multiply a number by 0.8 until you get 112. First, I plugged in 150 and got 120. Then, I tried 145 and got 116. Eventually, I got 140. From here, solving this problem is easy. You just multiply 140 by 0.7 and you will get your answer, which is E.) $98.00.
I did pretty good this time around and hope to do better next year!
Thursday, February 25, 2010
Solving Rational Expressions
HEY YOU. Time to be rational! LOL. So I am back again to write an entry that was due ages ago. A while back, when we were still doing rational expressions, Mr. Cheng gave us two equations and challenged us to solve one of them. That is what I will be doing/trying to do today.
Alrighty! So here goes nothing. At first glance, this question looks quite long and very difficult. But don't be scare! There is nothing afraid. You just need to break down this equation into little tiny pieces and it is as easy peasy, lemon squeezy. I will now give step-by-step instructions as to how I will solve it.
1. First, to make this equation a lot easier, I will move x^-2 to the bottom and y^-4 to the top, thus removing the negatives from the equation.
2. Next, I will multiply the exponent 5/2 to everything in the equation. So for 81, you would put the denominator 2 on the outside and you can square root 81 to get 9^5, which is 59049, a pretty big number.
3. Then you multiply y^4/1 by 5/2, making it y^20/2 or simplified y^10.
4. You repeat steps 2 and 3 with the bottom terms, and getting 16807 and x^5 as a result.
There you have it! Rational expressions in a nutshell. And if you still don't get it, feel free to ask me how. (NOT!) ;)
Problem Solving #2
This is one of my favorite questions from the second problem solving sheet that I got:
10. If x + y + z = 25 and y + z = 14, then x is:
A.) 8 B.) 11 C.) 6 D.) -6 E.) 31
This question was actually quite simple. Because you know that y and x are equal to 14, you can plug that into the first equation. You can replace (y+z) with 14 to get this equation:
x + 14 = 25
From there, you can easily solve the equation and get the answer B.) 11. One year ago, I wouldn't have been able to solve this question. But now that I have learned to use equations to solve equations, it is much easier. Another way you could solve this problem is guess and check, but that would take forever. I really enjoy problem solving because you never know what kind of problems you are going to get. There are thousands of problems out there just waiting for you to solve them. I especially like problems that you can apply in real life because they are very useful and the skills you pick up are essential. I hope to do more problem solving and get better at it!
10. If x + y + z = 25 and y + z = 14, then x is:
A.) 8 B.) 11 C.) 6 D.) -6 E.) 31
This question was actually quite simple. Because you know that y and x are equal to 14, you can plug that into the first equation. You can replace (y+z) with 14 to get this equation:
x + 14 = 25
From there, you can easily solve the equation and get the answer B.) 11. One year ago, I wouldn't have been able to solve this question. But now that I have learned to use equations to solve equations, it is much easier. Another way you could solve this problem is guess and check, but that would take forever. I really enjoy problem solving because you never know what kind of problems you are going to get. There are thousands of problems out there just waiting for you to solve them. I especially like problems that you can apply in real life because they are very useful and the skills you pick up are essential. I hope to do more problem solving and get better at it!
Problem Solving #1
I love math(sort of). Math is cool. This is a math problem that I did:
3. The value of 2 1/10+ 3 11/100 + 4 111/1000 is
(A) 9. 321 (B) 9.111 (C) 9.123 (D) 9.111111 (E) 9.11081081
The first step in solving this equation is to make the three denominators the same. To do that, you should multiply 2 1/10 by 100 to make the denominator 1000, resulting in 2 100/1000. Secondly, you multiply 3 11/100 by 10 to make it 3 110/1000. After that, you can add the three numbers together and the answer will be 9 321/1000. Finally, you change the number into a decimal. The final answer is A- 9.321. :)
3. The value of 2 1/10+ 3 11/100 + 4 111/1000 is
(A) 9. 321 (B) 9.111 (C) 9.123 (D) 9.111111 (E) 9.11081081
The first step in solving this equation is to make the three denominators the same. To do that, you should multiply 2 1/10 by 100 to make the denominator 1000, resulting in 2 100/1000. Secondly, you multiply 3 11/100 by 10 to make it 3 110/1000. After that, you can add the three numbers together and the answer will be 9 321/1000. Finally, you change the number into a decimal. The final answer is A- 9.321. :)
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