Problem Set Number 3

Question: An equilateral triangle has a side length of 20. If a square has the same perimeter as this triangle, the area of the square is:
a) 25  b)400  c)225  e)100

An equilateral triangle means that the sides are all the same length. If one of these side lengths is 20, then the perimeter of the triangle is 60. (20+20+20=60) A square has four sides all the same length. If the perimeter of the square is 60, then each side is 15. (60/4=15) To find the area of a square, the formula is S^2 where S is the side length. 15^2=225. Therefore, the area of the square is 225 making the answer c.

I like this question because it is simple, but it is a good example of how different shapes with the same perimeter don't necessarily have the same area. We shouldn't just assume things. We might assume that the area of these two shapes is the same because the perimeter is the same. As shown in this question, the area can be very different.

I have learned that problem solving is much easier when you completely understand the question. If you do not fully understand a question, it is easy to assume things and make "silly" mistakes. It is also important to read and reread a question to make sure that you didn't miss anything.

JJXN

What I learned from the Workshop

In the workshop we worked on a page of problem solving. Some of the questions were easy, others were hard. I was almost finished all of them by the time we started to explain them to eachother. At the end of the workshop, some students shared their answers and their solutions. In this workshop, I learned that math is not only about the right answer to a problem, it is about the solution. You need to understand the solution, not just know the solution. You need to prove an answer in math; you can’t just give an answer with no solution. The solution is what proves your answer is correct so without a solution, you don't know if your answer is correct or not. I enjoyed this workshop and am glad we went on this field trip.

JJXN

What I learned from the Talk

The talk was very interesting and fairly confusing. I learned that math is about understanding the problem and understanding the answer and solution. In math, you need to prove the answer; you can’t just say the answer. He showed us how to prove the Pythagorean Theorem and how to prove that there are an infinite number of Pythagorean Triplets. Laws in math are true now and will be true forever. I found it interesting to see a mathematician prove a few things in math. The speaker was very intriguing and I enjoyed listening to him.

JJXN

10 things I Learned from the Math Field Trip

-I learned that it doesn’t only matter whether you get the correct answer, it matters how you get that answer.

-I learned that the laws in math, for example the Pythagorean Theorem will always be true. They are true now, and they will be true in a hundred years. The rule don’t change in math.

-I learned that many math theorems were proven by the Chinese hundreds of years ago.

-I learned that there are some very hard math questions that if you answer, you can receive a million dollars.

-I learned that a million dollars isn’t a lot of money.

-I learned that large numbers in math is not what makes some math questions hard. A math question can have large numbers and be very simple. A math question can have a few small numbers be very hard.

-I learned that you don’t only need to know how to get the answer, you need to understand how to get the answer.

-I learned that math is very important and is involved in our everyday lives.

-I learned that knowing how to make an educated guess is important. If there is a question with several answers and you don’t know the answer, then you should be able to single out the answers to make an estimate.

-I learned that math looks complicated and hard until you learn the solution. If I looked at some of the math questions that I am working on now a few years ago, then I would think that math must be hard in grade 10. But now that I am in grade 10, I am taught the solution and so the questions I see are easy. 

JJXN