Cayley math contest

MATH CONTEST. ahhh. I did not expect this when I went into the cafeteria to take it. IT WAS SO HARD. well part A was really easy. I did it first so because i knew i would finish those fastest and then I would have more time to finish the harder ones knowing i had already finished some. Section B was pretty tough, it took time and thought. Every time I finished a question in section B it felt like a victory and i felt a little bit smarter.Then there was section c. IT WAS SO HARD. I didn't get any of them. I was disappointed that i didn't even do one of section c. When we were going over the question in class I felt kind of stupid. Mr Cheng made it look so easy. I found myself thinking HOW DID I NOT GET THAT many times. My favorite question of the contest was #10. There are 400 students at Pascal H.S., where the ratio of boys to girls is 3 : 2. There are 600 students at Fermat C.I., where the ratio of boys to girls is 2 : 3. When considering all the students from both schools, what is the ratio of boys to girls?

I liked this question because when i first looked at it I was confused. But after reading it a couple of times I saw that it wasn't so hard. This is what i did.
Pascal HS:
boys to girls: 3:2
# of students: 400
Fermat CI
boys to girls is 2:3
# of students: 600

What I did was try to find out how many student were for every "1" part of the ratio.
So for Pascal HS there are 400 students and together there are '5' parts of the ratio. So 400/5 = 80
That means each one part is equal to 80 students. Which means there are 240 boys and 160 girls. all equaling 400.
For Fermat CI there is 600 students. So 600/5= 120. Which means there are 240 boys and 360 girls.
Together from both school the ratio of boys to girls is 480: 520 or 12: 13

What does it meant to be good in math.

First of all, to be good in math I think that you have to love doing that. If you don't enjoy what you are doing or have no interest in it, how can you do a good at it.

After that.
3 trait that I think are most important for being good in math are
-patience
-thinking outside the box
-challenge yourself.

I think that patience is the one of the most important characteristics in math. In math you won't always get right answer right away. You have to be patient and keep trying. You will often get challenging question and you have to keep trying again again. You learn a little bit more each time.

Secondly, I think that in math you have to think outside the box. Sometime with some math questions, you have to be creative in the ways you solve the answer. There are so many different ways to solve something. If you don't think outside the box, you'll get stuck.

Lastly, I think that you must challenge yourself. If you don't challenge yourself in math you will not become better at it. You'll stay at the same level. After you learn something you should try something harder because you will be even better at what you learned before. If you can to the hard question, you can do the easy question.

PROBLEM SOLVING #2

Once again we have recieved another problem solving worksheet. They're actually really fun. The questions are chalenging and you feel smarter when you solve them. My favourite question this week was the following:

The pie chart shows a percentage breakdown of 1000 votes in a student election. How many votes did Sue receive?

okay so this question is super easy isnt it.
I know, IT IS!
but you know what.
when i first looked at this question i was confused! I dont know, why or how i was confused, but i was. I had to read it like 5 times to understand and then it clicked. wow. embarassing.
but anyways.
this is how you solve it.

there are 1000 votes.
45% of the votes went to jane
20% of the votes went to jim
and sue?

okay well.
out of 100%, Jane and Jim got 65% of the votes.
therefore. 35% of 1000 votes went to sue.
now. take thirty five per cent.
which means 35 per one hundred.
SOOO 35% of 1000 is 35.

BUT . we're dealing with 1000.
soooo 1000 is 100 ^ 10 correct?
THEREFORE. if you multiply 35 by 10, you will get the answer.
so the answer is 350
YAY.


that was the long way.
there are other ways to solve this question.
you could multiply .35 by 1000 which also gives you 350
OR .
find out how many votes the Jane and Jim got.
(1000 - (.20^1000)-(.45^1000)) which gives you 650
then just subtract that from 1000
which gives you 350.

so many ways to solve one question.

Solving Radical Expressions.

MONSTER QUESTION. ahhh.
okay.
When i first looked at this question I was so confused and I didn't know where to start.
So I remembered what Mr.Cheng says about taking it one step at a time.
and start with little and work your way up. This is what I did
1. The first thing I did was get rid of the negatives. You do this by flipping them.
2. You distribute the exponent outside of the brackets
3. You are left with a fraction exponent so you distribute those too on the numbers.
4. Then you distribute the fraction exponent of the variables and turn the squares and exponents of the numbers into a number.
5.The square roots of the variables cancelled each other out and the exponent can both be divided by 2.
and then you have your answer.
YAY. not so hard.

Problem Solving #1

My favourit question from this weeks problem solving sheet was question #10.

The sum on nine consecutive numbers positive integers is 99. The largest of these integers is
(a)9 (b)11 (c)19 (d) 7 (e)15

When i first looked at this question i thought that the only way to solve it would be trial and error but that would take a long.
One way to solve it is with an arithmetic sequence. Which is what we have been learning for the past week.
the sequence would be

x+1, x+2, x+3, x+4.... x+9 =99

from that sequence you can get the following formula

9x+45=99
9x=54
x=6

you then use 'x' and plug it into the 9th term.

x+9
6+9 = 15

so the largest of the integers is 15.

What I especially liked about this question is that it has so many other way to solve it. I find it amazing because with these other ways you can also check you answers. I enjoy having to think hard to find these alternate answers. Some of these alternate ways are the following:

x-4, x-3, x-2, x-1, x, x+1, x+2, x+3, x+4

9x+99
x=11

and
x+4 =15
11+4 =15

and there you have your answer.

At first i was anoyed because i didnt know how to solve it and i was applying what i know to solve the question. I learned that you have look deeper and use what you have learned to solve questions like that. Thats what being good math is all about.

Tower of Hanoi

describe the strategy and the formula for the puzzle Tower of Hanoi
Embed a screen shot of the completed puzzle with 5 dics

To some, The Tower of Hanoi puzzle may seem like just another, regular, for fun game but really it is a challenging math puzzle that involves skill and strategic thinking in order to be solved. During math class we got the chance to try it out. It harder than it seems.

The first time I tried doing this it took me over a hundred times. It was until Mr. Cheng explained that there was a strategy to it that I started to think. I had not even considered the option of there being a strategy to it.
The strategy I came up with throught out my various attempts at trying to do this puzzle is that is to pile the first 4 in the middle first then move the 5th disc to the other side and pile the 4 on top.