817 Math Blog

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HI! Mr. Harbeck told us to do a review post about adding, subtraction, multiplying and dividing proper, improper and mixed fractions.

Today, we were assigned to do another blog post. We have to put the definition of the word reciprocal, explain how it's used in mathematics and show 2 examples.

Reciprocal, also called multiplicative inverse, is a number that you multiply so that the result equals 1. The easiest way to find it is to just flip the fraction over.

We use reciprocal or multiplicative inverse in math because it is faster, quicker and easier to understand. it can be used in a ratio table.

Example:

3/4 divided by 3/5
This question means - how many groups of 3/5 are in 3/4?
The reciprocal of 3/4 is 4/3 and the reciprocal of 3/5 is 5/3.

The answer is going to be more than 1 because 3/4 is larger than 3/5.
The ratio table:


















3/5 divided by 3/3
This question means - how many groups of 3/4 are in 3/5?
The reciprocal of 3/5 is 5/3 and the reciprocal of 3/4 is 4/3.

The answer is going to be less than 1 because 3/5 is smaller than 3/4.
The ratio table:

Today in Math class, Mr. Harbeck gave us an assignment. He gave us a sheet of paper with word problems. You and a partner are supposed to answer all of the word problems and put it in Google documents, a picture or just blogger and send it to your partner. Here's our Google presentation:

In skills class, we were assigned to do another post about fractions. The question is: Are 2/5 of 3/4 the same as 3/4 of 2/5? We will find out by using pictures.

This is 2/5 of 3/4 :

To find out how to do this you need to multiply the fractions and to do that you have to multiply the numerators and the denominators.
numerators: 2 x 3 = 6
denominators: 5 x 4 = 20
So the answer is 6/20 or when simplified: 3/10


















This is 3/4 of 2/5:

numerators: 3 x 2 = 6
denominators: 4 x 5 = 20


















So, as you can see they're the same (:

In math class, we talked about subtracting fractions. To be able to subtract fractions, it has to have the same denominators. To get the same denominator you look for the lowest common denominator for example: 1/4 - 1/8, you can't subtract that because the denominators are different so you have to look for the lowest common denominator which is 8, you need to change 1/4 so the numerator is 2 and the denominator is 8. 2/8 - 1/8, is much better and you can now subtract. Mr. Harbeck also taught us how to subtract mixed fractions using two very effective techniques.

The first one is: turning it into an improper fraction, denominator x whole number + numerator = improper fraction. For example: 2 1/2 - 1 3/4 = ?, if you change it, it will be like this: 2 2/4 - 1 3/4. You can subtract 2 and 1 but you can't subtract 2 and 1 so you have to change it into an improper fraction: 10/4 - 7/4 = 3/4

The second one is: the borrowing technique, we use this when the numerator is too big. For example: 625 1/2 - 100 3/4 = ? or as an improper fraction: 1251/2 - 403 = ?, isn't that a bit more complicated? But, if you just borrow like this: ( 624 4/4 + 2/4) - 100 3/4 = ?, is much better because all you have to do is this:

Add 624 4/4 and 2/4 and the answer is 624 6/4. Then, you subtract 624 6/4 and 100 3/4 and the answer is 524 3/4.

Now, subtracting fractions are much easier whether it's improper, proper or mixed. (:

This week we learned about the Pythagorean Theorem. We were given an assignment where we have to explain what the given artifacts are and how we can use the given vocabulary to explain the artifacts.


Artifacts with the vocabulary explaining it: (The vocabulary is in red)



This is a right angle triangle (R.A.T.). It has one 90° internal angle (a right angle). The side opposite to the right angle is the hypotenuse; it is the longest side of the triangle. The other two sides are the legs (catheti) of the triangle.

*Hypotenuse-the longest side of the triangle and the opposite of the right angle.
*legs-shorter than the hypotenuse, comes out of the right angle and each triangle always has two legs.







This is a square. A square has four equal sides and four equal angles (90° angles which means that a square is 360 degrees).








This is the formula that Pythagoras made for the right angle triangle.







This is a bust of Pythagoras (father of numbers) a Greek mathematician who is best known for the Pythagorean Theorem. He is often revered as a great mathematician, mystic and scientist; however some have questioned the scope of his contributions to mathematics and natural philosophy.

*Greek- also known as Hellenes, are a nation and ethnic group native to Greece, Cyprus and neighboring regions who can also be found in a plethora of Omogenia communities around the world.

*Theorem- is a statement proved on the basis of previously accepted or established statements.



Pythagoras and the Pythagorean theorem is important to grade 8 math because this "guy" and this "theorem" started MATHEMATICS and the study of numbers. It's not important to only us grade 8's, it's important to everyone because math is a very important thing.

Pythagoras Problem:

#1 What is the perimeter of the orange triangle?











Solve:


* First you have to look for leg 2 = b.
* The hypotenuse is 914 and leg 1, a, is 17. ALL YOU HAVE TO DO IS SOLVE, BUT FIRST YOU HAVE TO FIND OUT WHAT THE FORMULA IS. YOU'RE LOOKING FOR THE OTHER LEG, leg 2 = b.





To find the perimeter of the orange triangle you have to...


* To get the perimeter you must add a, b and c.








So the perimeter of the orange triangle is 956 cm.

#2 This diagram shows the game plans for a game designed by Harbeck Toys INC. The board is made up of a square and four identical right triangles. If the central square has an area of 225 square centimeters what is the perimeter of the board game?


* The hypotenuse, c, is already given which is 225 cm squared. Since it's a square and all of the sides are equal you just need to find out the square root of 225 which is 15. Leg 1, a, and leg 2, b, is both 15 because all the sides are equal. To get the hypotenuse, you have to add a squared and b squared to get c squared. So 15 squared plus 15 squared is 450. Now, we have to find the square root of 450 which is 21.213. The hypotenuse, c, is 21.213. Now you have to find out what the perimeter is. To get the perimeter you have to first multiply 15, the legs, by 4 because there are 4 sides/triangles. And you will get 60. Then, multiply 21.213, the hypotenuse, by 4 because there are also 4 sides/triangles. And you will get 84.852. Add them together to get the perimeter. And the answer is 144.852.

The perimeter of the board game is 144.852 cm.

Here are some pictures of what we have been doing last week and this week for Pythagoras:











































Here's my Pythagoras video:

Today in math class, Mr. Harbeck taught us how to transpose algebra. We learned that to transpose algebra you have to:

On the last day of school we watched a movie called "Pay It Forward". The movie is about doing an act of kindness to someone and to ask them to 'pay it forward' to someone else. We are expected to do an act of kindness during our winter break. For that act of kindness me and Joysie decided to do something simple that would make someone special happy, babysitting, and we're going to do it for my dad's friends and their 4-year-old daughter, Dana.


How we payed it forward:
We decided to do this when I heard that my parents invited them to dinner after the Holidays. I thought it was the right time because it's dinner and my parents want them to have fun. I told them I will take care of Dana and they can just have fun. Me and Joysie looked out for her while her parents are eating, we fed her, which is very hard because she doesn't want to eat anything and played computer games, hide and seek and dollies with her.



What I felt after doing this:
After we did this I felt happy because I was able to help them even in a very small way. When they left our house they told me that they had a great time. Dana was sad because she doesn't want to leave and she wants to play more. One more reason is because Dana and her family just moved here to Winnipeg from Ontario. She said she misses all of her friends and that she has no one to play with because she's an only child. I told her that I will come over to her house more often to play with her. I asked Dana if she can 'pay it forward', of course I had to explain to her what I meant and after I did she said she will try.

Can one person make a difference?
I think one person can make a difference. No matter what it is, big, small or simple, a person can make a difference. Even if you're the only one, you can do SOMETHING to make a change.

Today in class we started learning about dividing integers. Mr. Harbeck and Mr. Backe (sorry if I spelt it wrong) taught us dividing positive integers. We flipped our 'barns' to the white side which is division.


We did the positive positive side (++).
The question is:
This question can be said in 2 ways.
1st way: (QUOTATIVE) How many 2s are in 6?
2nd way (PARTITIVE) How many equal parts are in 2 groups when we have 6?



ANOTHER WAY YOU CAN WRITE THIS QUESTION:







QUOTATIVE:










PARTITIVE:













Here's a video about dividing integers.




That's what we did in math today. Homework for Mr. Backe ( and again sorry if I spelt it wrong ): ) is to think about this question- ___x 2 = 6



I pick Gizzle to be the next scribe!

Adina and Jade are really good friends and today is they're birthday. Jade and Adina has a good life, they both do good in school and have lots of friends. Jade wanted a pony for her birthday and Adina wanted a dog but they're parents disagree they said those are,"the stupidest gifts ever". Adina and Jade always felt like nobody cares and loves them even they're parents,so they both decided to run away together.

They're adventure has begun.When they ran away they didn't know where to go and how to survive.
"What are we going to do Jade?", Adina said worried.
"Heck I don't know why are you asking me?", said Jade.
" I don't know why! I'm just really hungry and worried if we're going to survive", Adina said.
" Well you think I'm not worried and scared?!, wait a minute look what is that? it looks like a box", said Jade.
" I don't know lets go check it out, wait what if its food?", said Adina.
" Well then it's good, come one lets go!", said Jade rushing to see what's inside the box.

They both went to see what it is and what's inside . It was a box, when they both opened it a little person came out.
" Who are you?", said Jade.
" It doesn't matter who I am, I will help you and give you food", said the little person.
" Yeah, Jade don't ask because it doesn't matter his our angel, he will give us food and help us.", said Adina.
" Angel? I'm not going to help you just like that, there's a catch", said the little person.
" What catch?", both of the girls said surprisingly.
" The catch is to help me, I can't go back home unless I answer all 4 integer questions", said the little person.
" Sure we'll help you as long as you promise us that you will help us", said both of the girls.
" OK! I promise", said the little person.
"Oh! its +13, the answer is +13", said Jade. "Correct but now you have to explain or show how you got that answer"said the little person. "What?",said both of the girls surprisingly. "OK then we'll explain it", said Jade.

"CORRECT!", yelled the little person.

The girls we're cheering and they're ready to answer all of the questions.
" Very good", said the little man.
"Now the next question is... (-6)+(+3) and you have to explain it using a number line".

Third question is correct.
Last question is (-10)+(+3) =________ but you have to explain and show it using have and owe, number line and tiles.
" Are you kidding us, that's hard", said Adina
" Oh shut up Adina! it's the last question", said Jade.

"CORRECT AGAIN!, yelled the little man.
"YAY!, we're done, where's the food? you promised that you'd help us, remember?",said both of the girls.
"What? what promise?..oh, the help and food. I still remember come with me.", said the little man.
"Follow you where?", Jade asked.
"Over there.", said the little man while pointing at a mountain.

They walked and walked for days, then they finally got there.
"We're finally here",said the little man.
"So,where is the food you promised us?",asked Jade.
"Well, uuhmm.. the thing is that..there are 8 more questions left I'm not sure if you know how to solve them so I kinda tricked you I'm sorry",said the little man.
"Why didn't you ask us first we might know how to solve it?", asked Adina.
"Even I can't figure it out so how could two teenage girls solve it?",the little man said while looking at the two girls.
"What is it we might know", said Adina.
"Come on, we'll give it a shot", Jade said begging the little man.
"OK, OK I'll give you a chance",said the little man."The questions involve subtracting integers and adding and subtracting integers in standard form".
"Oh no problem I just learned that in math", Jade said happily.
"OK the questions are...",said the little man.
"Oh that's easy 1.) (-8)-(+2) is -6 because there is no such thing as subtracting integers you add the opposites to get a zero pair", said Jade." (-9)+(-3) is -12, (-10)-(-5) is -15, (-8)-(-3) is -5".
"OK! that's good. the next batch of questions will be about adding and subtracting integers in standard form",said the little man."And remember to put it in standard form".

Questions:
1.) 6+8
2.) -4-3
3.) 15-2
4.) 14+8

"I'll answer it!", said Adina.

Answer:
1.) is 14
2.) is -7
3.) is 13
4.) is 22

"It's all correct but how did you figure it out?",asked the little man.
"Easy, its same thing as adding or subtracting integers but with no diapers a.k.a. brackets",said Adina.
"You two answered all of the questions correct!, so as I promised I will give you food and help I will bring you two home to your parents but you have to promise me that you won't tell anyone about me", said the little man.
"We promise! Thank you very much!", both of the girls said happily.

So, they got back home to their parents and they learned they're lesson, They learned that running away is not a good idea even and never think that no one cares about you because you will always have god, your family and your friends by your side to love and care about you.