Scribe Post for May 25, 2010

Today in math class, we learned about tangents of a circle. First of all, what is a tangent (of a circle)?

A tangent is:

-a line that touches a circle at exactly one point

-the point where the line touches the circle is called the point of tangency

We also learned how to use the tangent chord relationship to find the unknown lengths, given in the diagrams. We used the Pythagorean theorem (only if there's a right triangle).

for example:

-find the length of AB (if BC (diameter) is 14 cm, and AC (hypotenuse) is 20 cm)

solution:

Then we learned how to determine angle measures in a circle with a tangent line.

-find the measure of angles A,B,C

To find A

180°=A+42°+90°

180°-132°=A

48°=A

To find C

Since C, is subtended by the same arc as A, A could be divided by two, then you'll get 24° for C.

To find B. (A+B=diameter(which is always 180°)

A+B=180°

48°+B=180°

B=180°-48°

B=132°

After those two examples, we had another example using the tangent chord relationship, once again.

-find the measure of line DE

solution:

Today's homework are:

-10.3 textbook

-read

-CYU #2

-Practice (odd)

-Apply : ALL

-Extend 19&21

-Workbook, and Extra Practice

-journal

TEST ON FRIDAY

For Tuesday, June 1

hand in inside stash-its

-problems of the week (#3, and another)

-journal

-last test signed

Journal Entry

March 8, 2010

Today in class, we got our math test back. Then, we corrected some of the questions from the test that everyone had trouble with. Here's one question from the test: simplify by combining like terms:

(2c²+4)+(-c²-2)-(-3c²+4c-4)-(2c²+c+3)

c²+2+(3c²-4c+4)+(-2c²-c-3)

2c²-5c-1

Then we learned :

First

Outside

Inside

Last

It's FOIL which is used for multiplying binomials.

Here's an example:

That's all we did in class today. Now this is for homework:

-7-5 (blue sheet)

-write on your journal

-comment on the blog

Scribe Post for February 24, 2010

Hello 9-05! Today in class, we did many things. First of all, Mr. B asked us if we had any questions about the homework yesterday. The question was #25 from the textbook. Here it is:

a) 2w + s

b) w stands for the number of wins, s stands for the number of shootout losses

c)20-12-4=4 losses

d) 2w+s

2(12)+4

24+4

28

*Just replace the variables with the given numbers.

e) 2x5+18=28

2x9+10=28

*The combinations are for team B, and has to equal 28.

Then, we had a review about polynomials, their coefficients, variables, and exponents.

Here's a chart about that (we had to fill in the coefficients, variables, and exponents):

After that, Ms. Yoo, started us on unit 5.2. Which is equivalent expressions. But we talked about like terms first. What are like terms? Like terms are terms that differ only by their numerical coefficients.

*Variables, and it's power stay the same. Coefficients changes however.

examples:

3x and -2x

6y² and 3y²

-5xy and -2 xy

17 and 12

Here's are other examples featuring the variable x:

-1x=-x

+x= x

-x²=-x²

+1x²=x²

*Mathematicians are lazy, they don't like writing 1 in front of a variable.

Next, we had to identify like terms:

(like terms are colour coded, dark green, and blue)

a) 5b² 3bc -2b 7c 6b

b) 3x² 4xy -2x² 7x² 1/2 y

c) 3pq 11 -4q² -3 pq

Then, we were combining like terms. (the variables and coefficients are bolded, the constants are "slanted", while variables with higher power than 1 are left with regular font)

a) 4x-2x+3-6

2x-3

*4x-2x= 2x, +3-6= -3

b) 2x²+3x -1+x²-4x-2

3x²-x-3

c) k-2k²+3+5k²-3k-4

-3k²-2k-1

-Always start with the highest degree (power)

-Try to gather like terms first

After, we had to simplify like terms.

1) x²-(-3x) +4+7x²-8x-6

x²+7x²-8x+3x+4-6 (<= work should look like that)

8x²-5x-2

explanation: 7x²+x² is 8x², while -8x+3x is -5x, and 4+(-6) is -2

2) -x-5x+(-3x²)-9-2x+7

-3x²-8x-2

3) 4x³+6x²+6x-1+5x³-x²-(-9)

9x³+5x²+6x+8

That's all we did in class. Hope I covered everything. Here's the homework:

-5.2 Extra Practice

-5.2 Workbook

-2 sheets (double sided)

-journal

-textbook work (since we don't have class tomorrow because of the Tec Voc tour)

-5.2 Mathlink (Mr. B didn't assign this, so do it if you have time)

-COMMENT ON MY POST!

*By the way, Friday's scribe is Melanie (since there's no math class tomorrow)

Fortune Seeker

Rules/ Instructions:

1) First player spins the spinner.

2) If the spinner lands on an amount of money, the player then receives a card, which contains the same amount.

3) The player then tries to answer the question.

4) If the player gets it right, a token (pennies/dimes) is put on the board, on the same amount answered.

5) Then, it’s the other player’s turn, the cycle then continues.

6) If a player got his/her’s tokens 5 across, 5 down, or 5 diagonally, that player wins that set.

7) Some exceptions: if a player spins the spinner, and lands on “bankrupt” the player lose the highest amount they answered on the board. Then, the other player gets a bonus spot on the board.

8) If a player lands on “lose a turn” the player lost his/her turn, then it’s the next player’s turn.

9) When the player lands on the same amounts twice (on two spins), it’s the other player’s turn. When the board is filled, the person who has the most money wins.

10) When the board is filled, the person who has the most money wins.

Pictures of the game:

Mr. B

Hello Mr. B! How are you doing? Hopefully you and your family are alright. We ( I mean "The Class") really miss you. Thank you for helping us excel in Math and continue to be "The Class".

You're really a wonderful teacher. Why? Because, even though we students make mistakes, you're alright with that. Also, you're the only teacher that actually keeps on praising us and calling us "The Class". Then, there's our noise level, we're loud, and you actually don't mind, as long as we're doing our work. You're really one of the best teachers we ever had.

We really hope you come back soon Mr. B. Math class is not the same without you. Also all the mornings spent in 9-05, just finishing our math homework, isn't the same either. I know that life isn't all that wonderful, but what comes are challenges. And we'll always be there for you.

Always think positive, and remember that there's always hope.

Happy Holidays.

Scribe Post for December 14, 2009

Hello, 9-05. Today in class, we handed in our stash- it's. What should have been in it are your:

-self evaluation sheets

- foldable

- journal entry

-number line

- 3 point approach

- 2 tests that are signed by your parent/ guardian

We also did peer evaluation in other people's games. By the way, we were supposed to play 2 different games, and evaluate those games. We had to do the evaluation on a sheet that looks like this:

What you're suppose to write:

communication pieces- the name of the game, and the name of the person who owns the game

peer evaluator- write your name there (also on the spot that says "name:")

strengths (2nd column):

accuracy- if the math part on the game is accurate

logic- if the game makes sense (eg. if their rules makes sense)

clarity- is it clear

format- is it good (is it well made?)

other- any comments, or anything else you found special about the game.

suggestions (3rd cloumn):

-anything else that you would suggest to make the game even better

-comments

That was all we did in class. The only homework for math is those booklets (fractions, decimals). But we do have home work for other subjects in case you forgot:

-timeline, due tomorrow

-study science, test tomorrow

-mock trial assignments

By the way, if you're wondering why no one scribed on Thursday, and Friday, it's because we had a work period. I guess that's all. The next scribe is Shaneille. Please comment! :D

Question #15

Hi everyone! This is a post on question #15. The question is about patterns. The question is just basically saying to find three numbers, after the given numbers. Using patterns according to the numbers. So, it's really easy to do.




Here it is:

To do this first question, I changed the mixed numbers into improper fractions. Then, I found out the common denominator, for just the first two fractions. With those two fractions, I tried different operations, until I got to the pattern. Then you would have to see if the pattern actually works. so it's basically trial and error, for me.






On the second fraction, I did the same thing too. Except I only used the absolute value on the first fraction, to find out the pattern. This question, I had a longer time figuring out than the first one. Since the changing of signs (positive then to negative) caught me off guard. Then I remembered that a negative number, divided by a negative number is positive. Also a positive number divided by a negative number is negative. So the pattern must have been the number divided by a negative number. That gave me a clue. Sooner or later, I finally got it.

absolute value: only how far a number is from zero (eg. the absolute value of 6 is 6, and the absolute value of -6 is 6 also.

I guess that's it. I tried my best explaining this. I think that the easier question you get, the harder it is explaining it. Since there's nothing much to explain.

Have a good long weekend everyone! :D

AND:

Question #29

What's up fellow members of "THE CLASS"!! I hope you're having a good long week-end. So anyways this is a post about #29 from apply. The question was really easy. But, finding where to put the parenthesis is just trial and error.

The question was basically saying to put parenthesis in the equations to match the answer it had, for each letter.

* To solve the equations, remember to use:

The processes (known as PEDMAS), in order.

Parenthesis

Exponents

Division

Multiplication

Addition

Subtraction

a) 3.5x4.1-3.5-2.8=-0.7

b) 2.5+(-4.1)+(-2.3)x(-1.1)=4.29

c) -5.5-(-6.5)÷2.4+(-1.1)=-0.5

That's all you had to do for #29 Apply. Remember to finish all the homework, which is found on the homepage!

* Sorry if I haven't been commenting for the past 3 days or so, it's because of the language exam. Promise to catch up on commenting and many other things!

And don't forget to comment! :D

Rational Numbers

The next unit or chapter is about "rational numbers". What are rational numbers? What does the term rational numbers mean? I don't know most of these, so I read from the online textbook.

Rational numbers simply means numbers that can be written as a simple fraction. Example of a rational number is 8/4. The numbers in that fraction are the integers. Which is 8 and 4 (example). Rational numbers also means a ratio of 2 integers . One term we're all familiar with is integers, which we learned in grade 7, and grade 8. Integers are any whole number.

Irrational numbers are numbers that can't be written as a fraction. When you write it in decimal form, it goes on forever, without a pattern. An example of an irrational number is the square root of 7, or the value of pi. Both have decimals that go on forever, without a pattern. You also can't write both as a simple fraction.

Those are the major things I think we're going to learn in this chapter. Feel free to comment or add on to what I missed. :)

Question #11

Surface area is very important. We use it in many different kinds of things. Here are some examples on when and where surface area is important.

1) When you want to become a math teacher.

- You would need to use those surface area skills, in order to teach surface area to your students.

2) When you want to become a baker or you just like baking cakes!

-You would need to find the surface area of the cake. So, you know how much icing you're going to put.

3) If you work in a packaging company.

- You would need to know how much material (eg. cardboard) you're going to use in order to pack your items.

4) When you're painting your house.

- Of course, you would need to know how much paint you're going to use! You don't just go to home depot or whatever, to buy random amounts of paint!

5) When you're building a book case/desk.

- You would need to know how much wood you're going to use.

6) If you're painting the bookcase/desk you just built.

- Again, you just don't go and buy random amounts of paint!

7) When you're changing the shingles on your roof.

- You would need to know how many shingles you're going to buy.

8) If you're going to put insulation in your attic or basement.

- You would need to know the surface area in order to know how much insulation you're going to use.

9) When you want to put drywall over that insulation.

-You would need to know how much drywall you're going to use.

10) If you're tiling your bathroom.

-You would need to know how many tiles you're going to use.

11) When you're buying blinds.

- You would need to know how big your window is. So, you have blinds that actually fits your window.

12) If you're planning to have a garden.

-You would need to know how much soil and fertilizers you're going to use.

13) When you want a pool in your back yard

-You want to know if the pool is actually going to fit.

14) If you have a diving board for your pool, you would need stairs for that.

- You would need to know the surface area of the stairs. So you know how much paint you're going to use.Paint the stairs with those grip paints, rustoleum, or what ever.

15) When you're buying a new fridge.

-You would need to know the surface area. So you know if it actually fits through your doors, and the actual spot it's going to be in the kitchen.

16) If you're buying new tires.

-You would need to know if the tires actually fits your vehicle.

17) When you're going to be an architect.

-You would need those surface area skills, so you know if your building will actually fit on the lot.

18) When you buy a Christmas tree.

-You would need to know the surface area of that tree, so you know it fits your living room.

19) If you're wrapping Christmas gifts, or gifts.

-You would need to know how much wrapper you're going to use.

20) When you're buying a tablecloth.

-You would need to know the surface area of the table, so the cloth fits.

Elegant Algebraic Expressions for Finding Surface Area

I always wonder why we use those "elegant" algebraic expressions in math class. Well, I could probably answer my own questions. We use those formulas because, it's easier to understand (I think..) and when we write it out, it looks elegant, or beautiful, or whatever. I also think that we use those formulas because, mathematicians use it. We want to be like them!!!! :D

So, I'm here to blog about what formulas/ algebraic expressions are elegant for different kinds of shapes. Also to give examples on how to use them.


What is the most elegant algebraic expression...

for finding the surface area of a cube?

-A cube simply has 6 faces that are equal, so whatever length on one side is squared.

To find the surface area of a cube, you simply use this formula:


S.A.= 6s²

Just for an example on how to use that formula, I will find the surface area of the cube with a side length of 5.


S.A.= 6s²

= 6 (5²)

= 6 (25)

S.A.=150 u²

What is the most algebraic expression...


for finding the surface area of a rectangular prism?

-We already learned this last year, so I think you're familiar with the formula. A rectangular prism has 3 sets of 2 equal faces (each set), that equals to 6 faces in total.


In finding the surface area of a rectangular prism, you could use this formula:

S.A.+ 2(lw)+2 (hw)+ 2 (hl)



For example on how to use that formula for finding the surface area of a rectangular prism, I will use it, using the measurements shown above (in the picture).


S.A.= 2 (lw)+ 2 (hw)+ 2 (hl)

= 2 (7) (4) + 2 (10) (4) +2 (10) (7)

= 2 (28) + 2 (40) + 2 (70)

=56+80+140

S.A. = 276 cm²

* NEVER forget to put the unit (eg. cm)/ measurement and the squared sign (²) in your answers.

What is the most elegant algebraic expression...


for finding the surface area of a cylinder?


-We already learned this last year too. So, you're most likely to know this formula. You have to find the surface area of the 2 circles, then add the rectangle. The find the surface area of the rectangle, you multiple the height by the circumference of the circle.


To find the surface area of a cylinder, you use this formula:


S.A. = 2πr²+ 2πrh








I'm going to use the measurements above, in giving an example on how to use the formula.


S.A.=2πr²+2πrh

=2(3.14)(5²)+2(3.14)(5)(15)

= 2 (3.14) (25)+ 2 (3.14) (75)

= 2 (78.54)+2 (235.62)

= 157.08+ 471.24

S.A.= 628.32cm²


What is the most elegant algebraic expression...

in finding the surface area of a triangular prism?



-Triangular prisms also uses formulas. But, it's kind of mixed. You have to use the Pythagorean theorem, the formula for finding the area of the triangles, and finally, the formula for finding the area of a rectangle.





Area of 2 triangles= bh

= (10)(15)

= 150




Area of base= lw

= (10)(20)

= 200

*For finding the area of the roofs, most of the time, only one side is given. So you use the Pythagorean theorem to find the hypotenuse of the triangle, which is the unknown side. Then you multiply that by the side that is given (width).




a²+b²= c²

10²+15²=c²

100+225=c²

325=c²

√325=√c²

18.03=c





Area of 2 rectangles (roofs) = 2(lw)

= 2(18.03)(20)

= 2(360.55)

=721.11

Then, you add all of the areas together, to get the total surface area.

S.A.=Area of triangles+Area of base+Area of roofs

=150+200+721.11

=1071.11


What is the most elegant algebraic expression...



in finding the surface area of a composite object?


- There's no formula to use in particular. It all depends on what shapes are combined.

In this particular shape, I would use the formula for finding the surface area of a rectangular prism. I would have to use that twice (top and bottom). Add them together. Then, find the area of the overlap, then subtract.

S.A. (bottom)= 2(lw)+2 (hw)+ 2(hl)

= 2 (5)(2) + 2 (2)(2)+ 2 (2)(5)

= 2 (10)+2 (4)+ 2 (10)

= 20+8+20

= 48

S.A. (top)= 2(lw)+2(hw)+2(hl)

= 2(5)(1)+2 (2)(1)+2(2)(5)

= 2(5)+2(2)+2(10)

= 10+ 4+ 20

= 34

Area of overlap = (1)(5)(1)

= 5

S.A.=area (bottom)+ area (top) -area of overlap

=48+34-5

S.A. =77 u²

How does symmetry help us solve some of these surface area problems?

- Well, that's an interesting question. It's also an easy question to answer. Most solid shapes (eg. rectangular prism) has planes of symmetry in it. Planes of symmetry helps us how many faces are equal. Which helps us to know that when we see one side of that shape, the opposite side is the same. Planes of symmetry only applies to some shapes. So, it can't be like that for every shape.

What happens when a part of any of these shapes is missing? How do I find the surface area then?

-Simple! Most shapes have planes of symmetry. So if one side is missing, you will know that it's the same as the given part. That helps on finding the missing part of a shape, then calculating the surface area with the missing shape.

Hey! Feel free to comment on how great this post is! Also feel free to criticize this post! Or just comment! :D

Why use 360?

Most of us have been wondering why we use 360 degrees for a full circle. Well, blame the Babylonians. Just kidding! The Babylonians used 60 as their base. While, we, use 10 as our base. So, what the Babylonians did is that they multiplied their base (60) by 6 (the number of sides in a hexagon). This system is called the sexagesimal system.


I would say that we use 360 because, it has a lot of advantages. Like for example, it's one of the few numbers that have many factors. These are all the factors:1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360 . Having many factors makes 360 a very nice unit to divide a circle into equal parts. Also, we use it in calendars, and fractions. 360 is a very popular number.
This is an example: earth's revolution around the sun is approximately 360 days (Babylonians had 360 days a year).





So, I hope you understand a bit better of why we use 360. If I missed anything, or if you have any suggestions, fell free to comment. :)

Scribe for October 1, 2009

Hello, 9-05. Today in class, we had a math test. Some of the questions on that test was similar to the test last time. There are some questions I had trouble with on the test. Like, the one with a card (10 of diamonds). It was asking what type of symmetry is shown on the playing card, and explain. I was going to put it had line symmetry, but, I tried drawing lines of symmetry. Though, it didn't work. Then I remembered, it could have rotation symmetry. Here it is:



The image has an order of rotation: 2. The angle of rotation is 180 degrees. So, therefore it has rotation symmetry.


I'm going to show you another question from the test. Here it is:
Find the angle of rotation for the following image:

The angle of rotation is: 60 degrees.

Those are two of the questions that was on the test.

We had a few homework for today

1) Provide an algebraic formula for finding the surface area of a rectangular prism.

2) Provide a formula for finding the surface area of a cylinder.

*Then, when we come to class, we should be able to explain, make a net, and be able to talk about the symmetry of the shapes. (for rectangular prisms and cylinders)

3) Write in our journals.

4) Last but not least, comment on my post! :)

The next scribe is Aleiah. The homework is due. next class. So you better get going!