Joseph's Journal Entry

Monday, February 22, 2010

Hey, 9-05! Well, today was the second class of our Polynomials Unit. *yaaay* We started off class by getting our stash-its back! *For anyone in hope of handing in part of your stash-it... or if you were planning on trying to hand in your mathlinks for bonus marks (like me)...you're to late.

Afterwards, we started reviewing our Chapter 4 Unit Test! Nicky pointed out that the test was in fact out of 47 instead of 48! The question that I think most people had difficulty on would probably be question #28.

28. You have been asked to design new placemats for use in the community hall. The placemats are to be hexagonal in shape. They need to be 15cm across between any two opposite sides. Create a scale drawing of your design, using a scale factor of 2 : 5.

First of all, you need to find the distance between each side in your drawing. We'll call it "x".

We will be using a scale of 2 : 5

We know the distance between to opposite sides are 15cm in the actual, so it goes with the 5.

"x" Is part of the image, so it will go with the 2

To get from 5 to 15, you multiply 5 by 3

In order to keep it proportional, you must do the same to the other side. So 2 x 3 = 6

The length between to opposite sides will be 6cm.

The next thing we needed to do was to draw the hexagon. We know that a hexagon has 6 sides, and what Mr. B told us last week is that the number of sides a regular polygon has, is the amount of equivalent and equiangular triangles the polygon is made up of. To find the angles of these triangles, we need to divide 360° by 6, since that is how many triangles we will be using. That gives us triangles with 60° angles. Since you know all that information, all you then have to do is draw the straight horizontal line measuring 6cm, the diagonal lines using a 60° angle between the lines, and lastly connect the sides. Sorry if you didn't quite understand that, if you need any help just ask in class.

After going through our test, we had 7 questions to answer. Sorry, I do not have the exact wording for the questions, since I did not exactly knwo I would be scribe in advanced, but I will try my best.

1) Give an example of a monomial.

(-2x)

2) Write an expression with 3 terms. Name it.

x² + y + 4 It is a Trinomial.

3) Write an expression with 2 terms. Name it.

3x² - 2 It is a Binomial.

4) Use 4 terms and make sure each term is at least one degree of a term larger than the following one.

4x^5 + 3x^4 + 2x^3 + x^2

5) What is the degree of a polynomial in the following: 3x^3 + 3x^2 + 3x + 3

The degree is 3.

6) What is a term?

-an expression formed in the product of a variable and/or a co-efficient.

7) What is a constant?

-something that never changes. eg. y + 4 The y could be changed with a different letter or number, but the 4 has to stay a 4.

HOMEWORK

- 5.1 Extra Practice

- 5.1 in the workbook

- Journal

Oh yeah, sorry for there being no color in this post, my computer is not letting me change the colour at the moment....It just changes everything.. Anyways, the next scribe is LINDA! (:

Scribe Post: Thursday, January 28, 2010

Hey 9-05! Anyways, today in math we started off by reviewing what we should have learned from yesterday's homework.

From our homework, we should have learn two important words: Angle & Side.

* The sum of all interior angles should equal to 180°

You should know 3 different ways to write an angle.

For example, we will try to say the 90° angle in the bottom left corner of the triangle.

It

may be written as:

∠B or ∠ABC or ∠CBA

*Remember to put the "Fancy" angle symbol

Next, we talked about naming sides, in 3 different ways.

For example we'll use side "C" or the "slanted side."

It may be written

as:

AC or CA or b

I know, you're thinking what? Why "b"? Well it's for a simple reason actually.

*Opposite angles name the line, in other words; The side that is opposite of the angle, is named after that angle remember it

*MAKE SURE IT IS WRITTEN IN lower case LETTERS

1:56 pm: We went to get our textbooks

After getting our textbooks, we reviewed some questions people were stuck on.

2:10 pm: We looked at question 6 on the giant paper with all the rectangles (Activity Sheet 6.2)

6) If the ratio of the lengths of two similar rectangles is 5 : 1, what will be the ratios of the areas?

You need to find the area of each square using the formula: A = S² Then, compare the areas.

A = S²

A = 5²

A = 25 u²

A = S²

A = 1²

A = 1 u²

The ratio of the area is: 25 : 1 *Ratios don't have unit values

2:14 pm: Aleiah asked an "Aleiah Question."

A few minutes later, we were given a question.

In the expression 1 : 8 what does the 1 stand for?

• One thing (image) on the scale will be 8 times bigger

What does 5 : 2 mean?

• 5 units will be 2 units

Where do you see enlargements and reductions in real-life?

• Billboards
• Blueprints
• On your television
• And a lot more!

Find "x".

1) Find out how 1.2 got to 3.96

2) Multiply how 1.2 got to 3.96 by the number on the other side (330).

3) Right down the product

I find this to be the easiest way, but there is another way you could solve this by.

Multiply 3.96 by 330 = 1306.8

Divide the product by 1.2 = 1089

x = 1089

HOMEWORK:

• Journal (everyday)
• Study for our test which is supposedly TOMORROW!
• There will be 16 questions on the test
• There will be 1 "hard" triangle question
• The test will also include scale diagrams, enlargements, and reductions (Chapter 4.1 & 4.2)
• Leave a comment (:
• WEAR GREEN OR YELLOW TOMORROW!

Finally, the next scribe will be......T..R...A..C..E...Y..! Tracey! Good Luck(:

Rational Racers
This is a game for 2 or more players.
*Take out all Jokers, Kings, Queens, and Jacks from the deck of cards.

Step
1) Each player must pick up two playing cards.
2) Each player must make the greatest fraction possible using their two cards
3) The player with the greatest fraction flips a coin (player x)
4) Heads = positive Tails = negative
5) Player X then rolls the dice
6) Player X then goes forward or backwards on the game board, depending on if the number is positive or negative.
7) If you land on a tile with a number on it. Go backwards or forwards depending on the number’s value.
8) Repeat from step 1, until someone reaches the end. (Tile number 64)

Question #14

Hey 9-05! Today I'll be showing you how to answer question #14.


First of all you need to read the information given to you and pick out key words:

Li and Ray shared a vegetarian pizza and a Hawaiian pizza of the same size. The vegetarian pizza was cut into eight equal slices. The Hawaiian pizza was cut into six equal slices. Li ate two slices of the vegetarian pizza and one slice of the Hawaiian pizza. Ray ate two slices of the Hawaiian pizza and one slice of the vegetarian pizza.














a) Who ate more pizza?
-To find out who ate more pizza you need to add the sized pieces they ate together
-Li ate two slices of the vegetarian pizza (out of 8) and one slice of the Hawaiian pizza (out of 6)
-2/8 + 1/6=




-When adding fractions you must have a common denominator
-Add the numerators, leave the denominator as it is
-Simplify if possible

-This means Li ate 10/24 of the pizzas


-Ray ate two slices of the Hawaiian pizza (out of 6) and one slice of the vegetarian pizza (out of 8) -2/6 + 1/8=





-When adding fractions you must have a common denominator
-Add the numerators, leave the denominator as it is
-Simplify if possible
-This means Ray ate 11/24 of the pizzas




11/24 is larger than 10/24 so that means Ray ate more pizza.


b) How much more did that person eat?




-Since there are already common denominators,
all you need to do is subtract the numerators




Ray ate 1/24 more pizza than Li.

c) How much pizza was left over?

-There was a total of 2 pizzas (2/1)
-Li ate (10/24) of the pizzas
-Ray ate (11/24) of the pizzas
-The answer is how much pizza was left after they ate



There was 1 1/8 pizza left over.

Woot! That's it! Please COMMENT if I made any mistakes, you don't understand something, or if you just feel like commenting. ^__^

Question #28

Extend Question #28

Hey 9-05! We were all assigned a question which we're supposed to make a post and explain how to solve the question. Well I was assigned #28. Red=question and Orange=Value of Variable

Evaluate the following:

a) 3.6 + 2y, y= -0.5

1) They tell you the value of the variable so, you must fill that in (y= -0.5)

2) Follow PEDMAS: First multiply 2 with -0.5

3) A positive + a negative sign side by side = a negative sign

4) Add the addends together and recieve the sum

















(m - 1.8) (m + 1.8), m=1.7

1) Fill in the values of the variables.

2) Answer the questions in the brackets

3) Multiply the answers from each bracket together

4) Recieve the answer.











4.5/q - q/4.5, q=-3.6

1) Fill in the Variables

2) To add/subtract fractions, they must have a Common Denominator. To create a common denominator. Simply add one the fraction by a an eqiuivalent fraction of 1. (eg. -1.25/-1.25) Now both of the denominators in every fraction is 4.5 .

3) Subtract the numerator by numerator. Yet don't do anything to the denominator.

4) You have your answer. If asked, reduce it to lowest terms.

October 21, 2009 Scribe Post

Hey 9-05! *cough, The Class* Today in class we did some more learning about Rational Numbers.

Can you prove that pi is an irrational number? Well, that's one thing that we learned in class today. On your calculator put in: π then =. You should get 3.141592654. Now divide π by 100000000. *gasp* Did you get pi as an answer? That's because there are a limited amount of characters on your calculator and it can't calculate the full number.

Today we also learned about Equivalent Fractions. Equivalent Fractions are fractions that mean the same thing. In other words have the same value in decimal form. An example of an equivalent fraction is 10/20=1/2=5/10=100/200=0.5

Sometimes when we see something written differently we almost automatically think that they are different from each other. There are many different ways to write the same fraction. So, next time you compare fractions..check to make sure they aren't equivalent.

Example:











REMEMBER: The sum of opposites=Zero. Why? Because they are Zero Pairs, which means they cancel each other out. 365+(-365)=0


WATCH THIS VIDEO IF YOU HAVE ANY PROBLEMS:

HOMEWORK:

• Mr.Backe gave us a package of papers a few days ago. We need to complete Section 2.1 Extra Practice(2 pages)


• In the homework book. Chapter 2.1 (pages 16-17)


• And remember to Journal everyday we have class.
  

By the way, if you're planning on buying a new calculator..Casio fx-300Es is the best one for Grade 9. hmm...The and the next scribe is........Dean S...!!!!..gets a longweekend..

Okay, well this is the end of my scribe..I hope I didn't miss anything. Please leave a commment for any reason.

Rational Numbers

Rational Numbers are any numbers that can be written as a ratio of two integers.
Rational came from the word ratio and integers are numbers.
eg. 5 is a rational number because it can be written as 5/1.
1.75 is rational because it can be written as 7/4.

Irrational Numbers numbers that are not rational. ( They can't be made of a ratio of two integers)
eg. The square root of 2 is an irrationable number because it can't be written as a ratio of two integers.

Remember an integer is a whole number. Such as 1, 2, 3, 150687, -45, -4651387

The Most Elegant Algebraic Formulas

Happy Thanksgiving to everyone!

The most elegant formula to find the total surface area of a cube is TSA=6s². That's basicly saying the length of one side squared, multiplied by 6 (because there are 6 faces on a cube).

Eg.

TSA= 6s²

TSA=6(2²)

TSA=6(4)

TSA=24u²

The most elegant formula to use when finding the TSA of a rectangular prism is
TSA=2(=lw+hl+hw). Luckily you only have to find the area of 3 different sides, thanks to symmetry. When you know one side, you know the opposite side. (Only for Rectangular Prisms)

Eg.

TSA=2(lw+hl+hw)
TSA=2(4x2 + 6x4 + 6x2)

TSA=2(8+24+12)

TSA=2(42)

TSA=84u²

The most elegant formula to find the toal surface area of a cylinder would be TSA=2πr²+2πrh.
2πr² is to find the to circle shaped tops of a cylinder. Then when you add the 2πrh, it's the area of the rectagular net (tube of cylinder). h is the height of the cylinder. 2πr is to find the circumference. (2r x π is equal to πd).

Eg.

TSA=2πr²+2πrh
TSA=2(3.14)(2²)+2(3.14)(2)(10)

TSA=2(3.14)(4)+2(3.14)(2)(10)

TSA=25.12+125.6

TSA=150.72u²

Finally, time for the total surface area of a composite. Sadly, there is no certain formula for TSA's of composite figures. That's only because composite shapes are all different. A composite shape is one big shape made by combining little basic shapes. To find the TSA for these typesof shapes, simply cut the shape into the basic shapes, and then REMEMBER to subtract the area of overlap, from both shapes connecting. (for 3D shapes)

Eg.

O___O What's that shape?....if you think about it, you can turn it into a square and two right angle triangles. Let's give side length of the square 5 and length a (verticle) of the triangle=2.5, with b=6. Usually you would need to find length "c", but since there are two symmetrical triangles it will make a rectangle. So that means you find the area of a square and a rectangle with the dimensions of a triangle.

Area of square= s²

Area of square= 5²

Area of square= 25u²

Area of Rectangle=lw

Area of Rectangle=2.5x6

Area of Rectangle=15u²

TSA=40u²

Why are there 360° in a Circle?

Why 360°?

Dear rooms 9-05 and 9-06,

we have 360° in a circle because of 3 main reasons.

1) The Babylonians used a sexagesmal number system. That means that instead of using a base of 10, they used a base of 60. We go up to 9 and then we put a 1 followed by a 0 (10). A base of 60 meant that they would go up to out so called "59", then the would combine their numbers to make a "60".

2) 360 is a very easy number to divide. There are 24 factors for the number 360. Those numbers include 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360.

3) Did you notice that there are about 360 days in a year? Meaning that it takes about 360 days for Earth to make a full rotation (orbit) around the Sun. Remember, the Babylonians had 360 day years.

I hope you understood my post and it helped. I have one thing for you to think about. Did you ever notice that there are 60 seconds in a minute and 60 minutes in an hour? 24 hours in a day? 12 months in a year? Almost everything is a factor of 360. Please comment if I missed anything or if you have any ideas.