Problem Solving Set #3

7. In this diagram, square ABCD has side length 2, with M the midpoint of BC and N the midpoint of CD. The area of the yellow region BMND is. . .

It took me a few tries before I got the answer to this question, but once I realized what to do, it was pretty easy. First you have to find out the area of the triangle ABD. The formula for triangles is side time side divided by 2. So, just plug it in and you get 2 times 2 divided by 2. That gives you... 2! Yeah! So the area of triangle ABD is 2.


Now you have to find the area of angle NMC! Before you do this you have to figure out what sides NC and MC are. By reading the question again you see that N and M are midpoints; meaning that on each side of these points is 1... because 1 plus 1 equals 2! So now you know that MC and NC both equal 1. By knowing this we can plug it in and we get 1 times 1 divided by 2. This equals... 0.5! YAY!


Sadly we have not quite finished the question so we have to rap it all up by actually finding the shaded area. We take triangle ABD and triangle MNC and minus them from the entire square which is 4. This will look like 4 minus (2 + .5) = 1.5. There now you`re done. 1.5. That's all there is to it.


The area of the shaded region of BMND is (D) 1.5


Well actually the answer puts in in 3 over 2 form, but it's the same thing. 3 over 2 is the same as 1.5

Problem Solving Set #2

For this set of questions I will pick number 16 to show. I like this question because, you can use math or just common sense ! Here's the question.

16. On a rectangular table 5 units long and 2 units wide, a ball is rolled from point P at an angle of 45 degrees to PQ and bounces of SR. The ball continues to bounce of the sides at 45 degree angles until it reaches S. How many bounces of the ball are required?

The first thing I did was read the question a few times to make sure I knew what I was supposed to be looking for. Then I looked at the rectangle given and tried to figure out where to start. Then when you realized that each bounce is 45 degrees and it's starts at P I started drawing the path of which the ball would've taken. This is one answer.

Or you can mathematically deduct that each roll between the bounce off another wall will be 2 units, except for the end where there is not enough space. There is only enough room for 5 bounces, no more, no less.

So the answer = (D) 5

P.S. Everything in the picture that is black was given with the question. Everything in Red (or whatever that colour is) is what I drew to help figure it out.

Monster Equations!

When I first look at these questions, I think, yeah right, I can't do either one of these... but as soon as you start breaking them up into parts and looking at it separately, it becomes easier.

1a) First you put all of the negative exponents on the reciprocal top or bottom so that they are positive.
b) Spread out the 5 over 2 to the entire equation.
c) Solve each root separately.
d) Make sure they are in their simplest form!
Answer) Write down your answer and put it in a box so it is noticeable!

2a) Change the roots to x over y as exponents of the number.
b)Solve each section of the equation separately.
c) Take out any common numbers to put in simplest form
Answer) WRITE OUT YOUR ANSWER!

I don't know how to use the Word Equation something-something, so, I hope this helps anyways!

What does it mean to be good in math?

Today in Math class we were trying to find qualities that would make a person good at math!
We came up with a long list and now I have to pick three of the ones I think are the most important. These are the three - hard working , willing to learn and you must have perseverance .

You must be hard working because in order to solve a problem, sometimes you have to keep working at it - sometimes longer than you want to. When you don't understand something, you can't give up and forget about it, you have to keep trying to find the answer. Whether it's looking at the question in a different way, or going back to the basics of the question - you have to find it! Else it will bother you for the rest of your life!

Being willing to learn is a very important characteristic in math because there is ALWAYS more to learn. Math keeps going and you can't just want to stop after learning a certain amount... you have to want to learn more. You also have to be willing to learn from your mistakes. It's not a bad thing when you make mistakes because the next time you come across that question, you'll remember the mistake you made and you'll remember how to do it properly.

You also must have perseverance. This is obvious, because you can't just stop in the middle of a question because you don't know what to do - look back over your work, see if you did anything wrong or can do something differently

Problem Solving Set #1

On February the 9th my class recieved a worksheet to finish for homework. Sadly I did not get 100%, but they say that you learn from your mistakes, so if you never make a mistake, you won't learn.

So, the question I will go over is #11. Twelve balloons are arranged in a circle as shown. Counting clockwise, every third balloon is popped. C is the first one popped. This continues around until two unpopped balloons remain. The last two remaining balloons are: (A) B, H (B) B, G (C) A, E (D) E, J (E) F, K

Starting at C, you cross out every third balloon clockwise. It should be in a pattern like this: C, F, I, L, D, H, A, G, B, K. Once you get to K, you should only have 2 balloons left: E and J!

This is the only way I know to solve this problem and it's really easy too! When I was solving it I wanted to play MASH!

So, I hope now you understand this question and it all makes sense to you !

Tower of Hanoi

Describe the strategy and the formula for the puzzle: Tower of Hanoi

When I first played this game, I used the method of guess and check ... but after I got to 5 disks and couldn't find an answer, I got incredibly bored and frustrated .

Seeing as I couldn't find a mathematical solution , I'm still currently using the lovely method of guess and check!:)

My picture above proves to you that I have beaten 5 disks and if you can't do this then maybe my next piece of information will be helpful! All I've found out so far is, if you have an odd number of rings , you have to start by putting the smallest ring on the furthest pole and the second smallest ring on the middle pole. For an even number you would need to reverse this - putting the smallest ring on the middle pole and the second smallest ring on the furthest pole.

I don't know how else I can help except, don't give up, because it's problems like this that we're happy to solve! I can tell you I was... after looking at a few hints... But anyways, DON'T GIVE UP! One of the first rules in math, you are not allowed to say "I can't," because else we'll have to kick you out!