March 30, 2009

March 30, 2009
scribe: Ryn Martin

classwork

DO NOT forget how to use the distributive property!

1. x/3 = 5/12
    12/12= 5 * 3 = 15/12 = 5/4

2. 3x + 1/5 = x/2
    next you are going to group like terms
    5x= 6x + 2
   -6x   -6x
    5x - 6y = 2
    -1x = 2
    -1    -1
     x = -2 

Tips to remember: 
These two examples are representing and using cross products property
with proportions you can NOT cross simplify

Test Aftermath

1. Reflect on your performance. Offer specific examples (using math vocabulary) of which areas you did well on and which areas you did poorly. Do Not tell me you were careless, tired, or did not study enough!

2. Select one problem you got wrong. Show me that you understand the problem by doing it or another problem like it from your notes or book correctly (site page number and problem number).

3. Select a topic that was not covered on the test. Show me you understand it by working a problem correctly.

A1 Homework

7.1 1-25 odd, 31-33

Common Mistakes When Completing The S...

Scribe: Kelsey Knight.
Common Mistakes When Completing The Square:
Forgetting to add (B/2)² on both sides.
Forgetting ± when taking the square root of each side.
Not Factoring Out the leading coefficients number.
Not finishing solving the equation for X after finding C.
Forgetting to move the constant to the other side of the equation before completing the square.
Fighting the temptations to deal with DECIMALS, learn to use FRACTIONS.

Questions:

-What to do after you multiply B by ½?
X² + 2X= 13
(2/2)² + X²  + 2X = 13 + (2/2)²     <- Add (B/2)²  to each side, in this equation (B/2)²  is (2/2)²
(2/2)² = 1
X² + 2X + 1 = 13 + 1
(X+1)² = 14
㊦(X+1)²= ㊦




14 <- Take the square root of each side.
(X+1) = ±㊦




14 <- Add A ± Sign.
X= 1+ ㊦14 OR
X= 1- ㊦14
There Are two answers because of the ± Sign.

-What to do if the x² coefficient is multiplied
by a number that is greater than 1?

A2 Homework

4/3 Internet Connect Activity!

3/24 Read pgs 302-303, find a video or web page that you think explains vertex form of a quadratic expression better for you than lesson 7.1. It is fine It is fine if the video is an excerpt of a longer video, just note what part I should look at. Your video or video clip should not be longer than 4 minutes. Once you have chosen your source please email it to me at Paideiamath@gmail.com Also, give me a paragraph explanation on why the video makes more sense to you than the book.

Thurs. 3/26 Do not leave your response on the blog. Write your answer on paper and then leave a colaborative answer under Daniel's notes on google docs.
1.) Given g(x) = 2x^2 + 12x + 13, write the function in vertex form. Give the coordinates of the vertex, the equation for the axis of symetry, then describe the transformations from f(x) =x^2 to g.

Thurs. 4/2 5.5 11-33 odd, 49-51

PLEASE DO NOT LEAVE HOMEWORK RESPONSES IN COMMENTS! ONLY QUESTIONS OR COMMENTS!

GTA3 Homework Assignments

3/23 Read p 109-117, create google doc video analysis on graphing sine function and the unti circle
3/24 Update the googledoc, Do 43-75 odd, read 118-20
3/31 3.1 1-17 odd, 21 collaborate on googledocs
4/2 3.1 6-10 even, 23-27 odd, 34, 36, google doc collabo on 3.2

A2 5.4 Completing the Square Cont'd

Last Nights Home Work

Complete the square: x^2+8x+11

Your finding where the parabola intersects on the x axis. (Solving for the variable)

You will have two answers for X

b/2 is a gift. It is always used to solve. (Add to BOTH sides)

When ever you complete your square you will always have a binomial times its self. (a perfect square)

To Solve: (x+4)^2= 5 (you need to fine the square root of both sides)

SR of x+4= SR of + or - 5
-4 -5
x= -4 + or - SR of 5


www.my.hrw.com (Professor Edward Burger)

Home work: 12-36 even

A2 5.4 Completing the Square

Scribe: Ari Paez 3/23/08

How do you slove for quadradtic equations:
1. Factoring
2. Graphing
3. Setting quadratic equation to zero and solving it.

HOMEWORK QUESTIONS
# 59 on 5.3
3x^2-5x=2
Subtract the two on both sides
3x^2-5x-2=0
a= 3 b=-5 c=-2
Do box method
1. put the a term in first box and in the diagonal box put the c term
2. multiply a X c-----> 3 X -2 = -6
3. find two numbers that multiply to each other to get -6 and add up to each other to get -6 and add up to each other to get b
Answer: -6 X 1= -6 and add up to each other to get -5

3x^2	-6x
1x	-2

4. find the greatest common factor
GCF for first two boxes on top ------>
-3x^2 and -6x is 3x
-then the second boxes----->1x and -2 is 1
- after find the GCF for the first columns
3x^2 and 1x is x
-then the second to columns----->
-6x and -2 is -2
5. The factor form of this is and set it to zero and solve
(3x+1)(x-2)=0
3x+1=0 or x-2=0
x= -1/3 x=2

5.4 Completing the Square

Completing the square: forces any quadratic expression to factor.
* used to solve quadratic equations.
* used to put quadratic equations into vertex form.
- vertex form is used to slove quadratic equations that are hard to factor

To Complete a Square: Ex. 1 x^2+ 6x-16=0

Step 1. move constant term (c) x^2+6x=16
to one side and every other term to the other

Step 2. factor out the leading coefficient "a" 1(x^2+6x)= 16
* will be more relevant when a ≠1 *

Step 3. Add (1/2 X b)^2 to side with a term 1(x^2 +6x (6/2)^2) =16 +1(6/2)^2
and b term.
* add a(1/2 X b) to side with constant term (c) (x^2+6x+9) = 16+9
* simplyfiy (x^2+6x+9)=25

Step 4. factor side with a and b terms (x+3) (x+3)=25
(x+3)^2=25


HW do x^2+8x=11

A1 6.3 Dividing Fractions

scribe= Ryn Martin
March 17,2009
6.3 Dividing fractions
The rules:
1. Copy-dot-flip
· Copy the numerator
· Write as multiplication
· Reciprocal of denom.
Homework for tonight
2-32 even 33,36,39,4

Trig Graphs and The unit circle

GTA3! Watch the following video and read lesson 2.1 pages 109-117 in your textbook. Answer the questions on google docs!

What were things that made sense in the video in relation to the text?

What were things that didn't make sense in the video in relation to the text?

Share your ideas (Sign Up for Google Docs) on areas where the textbook elaborated on vocabulary, examples, etc.

Give a try at drawing the cosine function on a graph.

March "Mathness" -What's the probabilty of picking a perfect bracket?

I have done a few brackets for this year's tournament!

1.) First Glance
2.) By Chance, flip of coin (random), then replace all #16 seed's wins with #1 seed teams.
3.) What I think, or sorry What I KNOW!

Help me math classes!

What is the probability of me picking a perfect bracket? Please site any sources that help you figure this out. Explain, how you get the percentage.


Who do you think will win and what are the chances of them winning?

By the way I have no idea what the answers are for this.

A2 5.3 Zeros of a function- any number

Zeros of a function- any number (r) that make f(x)=0

*distributing factors is like driving a car backwards

ZERO PRODUCT PROPERTY-

if p*q=0, then p=0 or q=o



EX 12: solve the following equation for x
x^2+5x+6=0 check:
(x+2)(x+3)=0 (-2)^2+5(-2)+6
*solve for x 4-10+6+0 (correct)
(x+2)=0, or (x+3)=0 check:
x can equal: (-3)^2+5(-2)+6
x=-2, or x=-3 9-15+6=0 (correct)

CAN'T SOLVE QUADRATIC EQUATIONS LIKE LINEAR EQUATIONS:
*5x+7=0
5x=-7
x=-7/5
when the y equals 0, we typically get one solution in linear equations because it only crosses the x axis once

*x^2+5x+6=0
(have to use factoring, can't solve it like the equation above)
when the y equals 0, we get TWO solutions for quadratic equations because the parabola crosses the x axis twice
EX 13: solve for x: 2x^2-11x=0
x(2x-11)=0
^ ^
p q
x=0, or x+11/2

*the box method does not work if you can factor out each term*

EX 14: solve 4x^2-24x+36=0
4(x^2-6x+9)=0
(now guess and check)
4(x-3)(x-3)=0
x=3, or x=3 (accept a parabola can't cross the x axis twice)
if the vertex lies on the x axis, you only have one zero

example <---

for quiz tomorrow: know how to factor, and know how to solve using zeros product property, and difference of squares

Oakley is now confused Oakley is trying to figure something out right now that he doesn't understand Oakley kind of sees how it works now, but is still somewhat dumbfound
Now Oakley is going to FOIL and check it
Oakley just said good job, because he foiled it and it worked

next scribe: ari paez

PORTFOLIO ACTIVITY NOTES BASKETBALL

Scribe:  Kelsey Knight

PORTFOLIO ACTIVITY NOTES  BASKETBALL

Quadratic functions are different from linear functions because the points are arched.

Literal equations have two or more variables in them.

Oakley’s frustration with his calculator was that the line wouldn’t perfectly fit on the point. (It estimated)

You find the maximum height achieved by pressing the maximum button. (Height is the Y)

You find a maximum if your parabola opens DOWN
You find a minimum if your parabola opens UP

5.3 Factoring Quadratic Expressions Cont'd

Scribe:  Madeline Babuka Black

Factoring ax^2+bx+c when a≠1:

HIGHLIGHTS OF BOX METHOD:
factor

6x	9x
2x	3

      2x            3
(right side is 3x on top and 1 on bottom)

1: two numbers that multiply to give you 18 and add to give you 11
2: use sign of whatever lead box would be

Factoring the difference of two squares: a^2- b^2 = (a+b)(a-b)
 
EX 9: x^2- 4 ---> (x)^2- (2)^2 ---> (x+2)(x-2)

EX 10: x^4- 121 ---> (x^2)^2- (11)^2 ---> (x^2-11)(x^2-11)

EX 11: 16x^4- 81 ---> (4x^2)^2- (9)^2 ---> (4x^2+9)(4x^2-9) ---> (4x^2+9) ((2x)^2+3^2) ---> (4x^2+9)(2x+3)(2x-3)

*you can sometimes use factoring to solve and equation and find all the zeros



 

Global Learning in Math Class/Factoring/The Box Method

So Factoring is the process of writing the sum of terms as a a product of terms. Most students taking Algebra must learn to factor at some point. It is never going to go away. There are different things mathematicians must recognize when factoring.

What type of expression are you factoring (perfect square trinomial, difference of squares, or some other type of polynomial.) Depending on the type of expression, we determine how we will proceed in factoring!

Ok, so the box method is probably best used for factoring trinomials with a leading coefficient great than 1.

Ex. 3x^2 + 5x + 12

It is not easy to "guess and check" here, so something we call the "box method" comes into play.

So, my Algebra 1 class left to go learn Factoring during the short term with Ansley Yoemans. They come back and aren't really that comfortable with factoring (no fault of Ansley's.) But, they LOVE this "box method" which brings them some comfort level with factoring. When they arrive, I am confused because I have never seen anything like this "box method" and Ansley forgot to give me the heads up that she taught it to them.

I, along with many other math teachers here at Paideia, have been teaching students to "Guess and Check" when factoring trinomials that are not perfect square trinomials! Well, darn it, now Ansley has thrown a wrench in my teaching with this "box method."

I decide to visit with Ansley and ask where she got this "box method" thingy and she says the internet! I thought she was a genius and had come up with it on her own. It turns out she simply used the internet to learn a new method and provide it to the class! Brilliant!

Since then, I have realized that we can become much better learners/teachers by using each other's pooled knowledge and by using the internet as a resource. Hopefully this blog will help us share some of our findings in our own math class as well as math classes across the world.

Here is the link that describes the "box method". We will be using it in class to factor quadratic equations with a leading coefficient greater than 1!

http://www.purplemath.com/modules/factquad2.htm

Please leave comments and/or questions.

Algebra 2 Scribe List

This is The Scribe List. Every possible scribe in our class is listed here. This list will be updated every day. If you see someone's name crossed off on this list then you CANNOT choose them as the scribe for the next class.

This post can be quickly accesed from the [Links] list over there on the right hand sidebar. Check here before you choose a scribe for tomorrow's class when it is your turn to do so.