Hey, It's the Halloween scribe post. ooooooooh.

Hey guys, it's me, Sirus again. I'm only doing this because Gaberiel isn't gonna be at his home until like 2:00 AM, so yeah. It's me.

Anyway, our POD.

Our POD was to write 11101 in base 10.
OK, so the way to figure this out follows.
To solve base 2, you go from right to left. So the last 1, in 11101, stands for 2 to the zeroeth, so 1. The zero is a place holder, and the 3rd digit, another 1 stands for 2 to the second, or 4. If you continue to do this, you will end up with 16+8+4+0+1, which equals 29. Since 29 is in base 10, 11101 in base 10 is 29.

After this, we practiced with some more binary, or base 2 numbers.

For example, 42 in base 2 is 101001.
40= 101000
53= 110101
55= 110111

Try finding 82 in base 2.

Next, we practiced turning base 2's into base 10's, with problems that we made up.
Gaberiels was 11110110, which turns into: 128+64+32+16+0+4+2+0, or 244. At least, that's what Gabe has on his paper of notes.

The last thing we learned was how to find the GCF, or Greatest Common Factor using factor trees. The steps were thus.

1) Find prime factors of each number.
2) Write the prime factors of each, writing out the exponents.
3) Circle all of the common factors.
4) Choose one row/set of the circled numbers.
5) Multiply the numbers.

One of our examples was 18 and 44.
The prime factorization of the two were:



Don't make fun of my picture, my wordperfect was on the fritz, so I just used paint.
Next, circle one 2 from each, as those are the only common factors. Next, multiply them.
You will find that the GCF is 2.

Another was 220 and 56, which if you will look:


The Homework was to read pages 164-166, and to do problems 17-29 (?) odd. Don't quote me on that. It might have been 17-31. For some reason, Gaberiel didn't write that down, but I'm not blaming him. Anyway, Mr. A said that he probably wouldn't collect the homework.

I pick (drum roll please) Karol to be the next scribe.

Tuesday, October 30th

This is Austin, telling you what we did in class today.

The POD was the prime factorization of 224.

224
/\
2 112
/ /\
2 2 56
/ / /\
2 2 2 28
/ / / /\
2 2 2 4 7
/ / / /\ \
2x 2x2 x 2x2x7 = 2 to the 5th power x 7

2 more problems including prime factorization:

392= 2 to the 3rd power x seven to the 2nd power
-78= -2 x 3 x 13
then we did factoring expressions completly.

10x to the 2nd power = 2 times 5 times x times x times x

-48xy to the 3rd power= (-1) times 8 times 6 times x times y times y times y

-56ba to the 2nd power=(-1) times a times a b times 2 times 2 times 2 times 2 times 3

H.W is read Pg. 159-161. complete Pg. 161 #s 3, 13-39 odd.

we also learned that ato the 0 power is 1

1 example of expanded base 10 form is:

23=2 bundles of 10 and 3 bundles of 1
23=(2 x 10) + (3 x 1)
23=(2 x 10 to the 1st power)+ (3 x 10 to the 0 power)


1=10 to the 0 power 10=10 to the 1st power 100= 10 to the 2nd

346= (10 to the 2nd power x 3)+(10 to the 1st power x 4)+
(10 to the 0 power times 3)

4,003=(10 to the 3rd power x 4)+ (10 to the 0 power x 3)


computers use the base 2 form(bianary code).

1=on 0=off

Example:
21=10101

I choose Gabriel to be the next scribe.

Monday's Math Class, a la Sirus, the Scribe

Hi! This is the Scribe post for Monday, the 29th of October.

Our POD was thus:

Simplify:


As Paint and upload image are as of yet unfathomable concepts to a mind such as my own, I will explain here.
STEP 1 is the problem stated.
STEP 2, according to PEMDAS is to go inside the brackets, [ ] and do whatever is inside them. Within that, there are parentheses, but you cannot do anything with them, so you turn to the E, or exponent. 2x^2 is equal to 2*2*x*x, or 4x^2.
STEP 3 is rephrasing 2*2*x*x as 4x^2.
STEP 4 is distributing the -3 to the 2 and the -4x^2.
STEP 5 is simplifying, as the 6's cancel out.

Now for the Lesson.

Today, most of our focus was on Prime Numbers. For those of you who were absent, or who have forgotten, a prime number is one that has ONLY TWO factors, 1 and itself. Its opposite, if you will, composite numbers, are those that have more then two factors.

One of the problems that we had to solve was to find all of the primes between 1 and 20.
The following numbers are not prime because of the number in front of it, or in front of the colon. Thanks Gabriel, for this method.

If you'll notice, we don't have to check for 4, because if it is divisible by 2, then it is divisible by 2. We don't have to check 6 because if it is divisible by 2, then it is divisible by 6, and so on.

Also, the numbers themselves are not included, as they will go into themselves 1 time.

2: 4, 6, 8 ,10, 12, 14, 16, 18, 20
3: 6, 9, 12, 15, 18
5: 10, 15, 20
7: 14

Once you cross out the numbers that are shown here, the only primes from 1 through 20 are: 3, 5, 7, 11, 13, 17, and 19. (1 is not a prime, because it only has 1 factor, itself.)

If you use the same method for 60-70, you should come up with 61 and 67, although you would use the factors of 2, 3, 5, 7, and 11. This is because no numbers within this range are divisible by 13, as it skips the whole set.

The next fun thing was Prime factorization, which is when a number is expressed as a product of primes and their exponents.

For example, the prime factorization of 10 would be 5x2, as both are prime numbers and 5x2=10.
Another is 12, which would be 2^2x3. This is because 12=2x2x3, but we can shorten that.
One can use a factor tree to find the prime factorization.
For example, let's find the Prime Factorization of 16.
16
/\
8 2
/\
4 2
/\
2 2

There was no Homework. Except for me.
The next Scribe is to be Austin. BUH BUH BUH!
ok im done.

HELLO!!!!

Problem of the Day!!!!

n	1st n odd intergers	Sum of the 1st n odd intergers
1	1	1
2	1,3	4
3	1,3,5	9
4	1,3,5,7	16
5	1,3,5,7,9	25
6	1,3,5,7,9,11	36
n	1,3,5,7,9,11,n

How did we figure it out??? Look Below!!!

Number of people giving	Number given	exponent
1	5x5=25	5 to the 2nd power
5	5x5x5=125	5 to the 3rd power
25	5x5x5x5=625	5 to the 4th power
125	5x5x5x25=3,125	5 to the 5th power

In Class Problems

1-) Word Problem: A square field has sides that are 30m long, use exponents to calculate the area of the field.

30m

2-) Word Problem: A building is as long as it is wide as long as it is tall. The building is 50ft tall. Use exponents to calculate the volume of the building.

Volume: How much space an object takes up or how much an object can hold inside of it. It also means to times length times width times height.

50ft

50ft

50ft

50ft

50 times 50 times 50 which is the same as:

Also today in class we went over a practice sheet that gave us information on exponents. It told us what a power, base and exponent are and examples of what they those words mean.

Our homework today was the work sheet that Mr. Alcantara gave to us this morning. It was all on exponents!!!

The scribe now is Ali Pieri

Friday's Math Class

Hey Guys! Here are some things that we covered in class on Friday.

POD.

Promblem: Complete the table

x	4x	4 to the x power
1
2
3
4

Answer:

x	4x	4 to the x power
1	4	4
2	8	16
3	12	36
4	16	64

Use the table to guide your thinking when answering the following questions:
Why do we have exponents? How aer they useful? What general affects do exponents have?

Answer:

• simplify the promblem "Shorten the promblem"

• used for volume and area

• general effects:

• make numbers grow rapidly. Thats why we use them

• also an efficient way to communicate

Something to note: Dustin Short- he can tutor you Friday after school for those who need it in this class, it costs $10.00



Evaluate if a=2 b=4 c=-3

1. ac to the 3rd power = 37

2. 3a + b to the third power = 70

The homework for this weekened is read page 153 - 155 and on pg. 156 29 47 odd and 49 -57 all.


I choose Sirus to be the next person for the blog.

Todays POD was this:Given that 3/4 x 4=3

i)Write an arguement stating why 3/4 is or isnt a factor of 3.

ANSWER:no it is not a factor of 3 nor is it a factor of anything.3/4 is not an integer.(answer buy sirus han)

ii)write an arguement stating why -1 is or isnt a factor of 3.

ANSWER:yes -1 is a factor of 3 becaus -1 is an integer.(answer by margo wilson)

DIVISIBILITY:

• is 8 divisible by 3?
• is 1338 divisible by 6?

DIVISIBILITY RULES:

NUMBERS

2 if number is even

3 if sum of digits is divisable by 3

4 if last 2 digits form a # divisable by 4

5 ?

6 if divisable by2 and 3

9 if sum of digits is divisable by 9

10 if ones digit is 0

rules for 7-8 may come later

home work for wednesday:

r:148-149

pg.151

17-29 odd

49

i choose the next scribe to be charlotte

Math pre-algebra

Hey guys, its Gabriel with the scribe of the day.

This was our “pod” of the day:

a) Use graphing paper to draw as many rectangles as possible that enclose on an area of 36 square units. (Each little square on the graphing paper counts as 1 square unit.)
b) List the dimensions of those rectangles.

Answer) you will get 5 rectangles of the following areas:

All of these numbers are factors of 36: 1,2,3,4,6,7,9,12,18,36

Then Mr. A asked us to give him what we think a “factor” is. We weren’t very accurate. His definition for factor was: A factor of a number “A” is an integer “B” that divides “A” with a remainder of zero. IF YOUR NUMBER DOES NOT HAVE A REMAINDER OF ZERO IT IS NOT A FACTOR.

According to Mr. A, the definition for a factor in our text books is too simple. Two or more numbers that are multiplied together to form a product, are called factors. That was the definition in your text books.

Then he asked us to list all the factors for 24. 24 factors are 1,2,3,4,6,8,12,24. Factors can be negative and positive (-, +).

I pick Afik to be the next scribe

Oh! And by the way we didn’t have H.W. (homework)

Scribe Post Evaluation Form

Here is a copy of the form that I will fill out and return to you after you make your scribe post. Use this post and the scribe post instructions (see sidebar) to guide you in writing your scribe post.

Scribe, Oct 19, 2007

Hello class, this is Lilly with the scribe of today.

Today we practiced solving equations using DPE, MPE, APE and SPE.

Our pod was the following: Write and solve an equation to answer the following problem.
* Wilfred bought 2 tennis racquets and 5 cans of tennis balls at a total cost of $263.75. The racquets cost $130 each. How much did each can of tennis balls cost?

First we made a variable which in this case was c=cost of 1 can of tennis ball. Then we made an equation which was 130+5c=263.75 then we used MPE to do 130•(2)+5c=263.75. After that you use SPE to do 260-260+5c=263.75-260.00, after that you use DPE to do 5c÷5=3.75÷5 and we got the answer which was c-75 cents.

After this we practiced solving x:
1.) 5x-(3+x)=9 to solve it we did 5x-3-x=9 then we combined the like terms to do 4x-3=9 after this we used APE to do 4x-3+3=9+3 which gave us 4x=12 and then we used DPE to get the answer by doing 4x÷4=12÷4, and that gave us the answer of x=3.

2.) -3(2x-4)+8x=0 to solve it we first distributed to get -6x+12+8x+(-20)=0 then we combined like terms to get 2x+(-8)=0 after that we used APE to do 2x+(-8)+8=0+8 which got us to 2x=8, after this step we used DPE to do 2x÷2=8÷2 which gave us the answer of x=4.

3.) x+4÷2=2(x-3) and we first distributed to get x+4÷2=2x-6 after this we used MPE to do 2•(x+4÷2)=(2x-6)•2 and then we used SPE to do x+4-x=4x-17-x which gave us 4=3x-12 and then we used APE to do 4+12=3x-12+12 which gave us 16=3x and the answer was x=16/3.


We had optional HOMEWORK: page #148, numbers 7-19 odds and 23-25 all. page #142 numbers 10-21

Ill see you all Monday, enjoy your weekend and i nominate the next scribe to be Austin.

Scribe, Oct 18, 2007

Hello Class!

Today we did practices of DPE, MPE, SPE, and APE.

Our POD was the following: 1. x÷8-4=5 and 2. 8÷x-4=5
For question number one we used APE to change x÷8-4=5 into x÷8=9 (adding 4 to each side) Then we used MPE to change x÷8=9 into x=72 (multiply 8 to both sides)
For question number two we used APE first to change 8÷x-4=5 into 8÷x=9 (adding 4 to both sides) then we used MPE to change 8÷x=9 into 8=9x (multiplying both sides by x) then we used DPE to change 8=9x into x=8 over 9 (fraction)

Then we solved a story problem that Luanna made yesterday.

The story is the following:
Margo had 5 rings. Lilly gave her some more. Then Austin gave her twice as many as Lilly gave her. Margo, deservedly or not =] ended up with 26 rings.

To answer the problem we made it into an equation. 26=5+x+2x.(x=number of rings Lilly gave Margo.)
We combined Like Terms. Which gave us 26=5+3x. Then we subtracted 5 from 26, 5 and 3x. Which gave us 21=3x. Then we divided both sides by 3. Which gave us 7x. Then we had to multiply the answer by 2, because Austin gave Margo twice as many rings. Which gives us the final answer. 14 rings.

HOMEWORK: Finish worksheet Mr. A gave us in class today.

*Test On Monday*

See you all tomorrow in class. =] I nominate the next scribe to be Lovely Lilly....
-Margo

WHAT WE DID IN CLASS

HI,
Today Mr. Alcantara collected our homework from yestarday, which was to finish the practice sheet. The POD that we did is the followin:
A lodge charges $70 per night plus $9 for ech person. A group of people rented the cabins for 1 night, they paid $151. How much
people rented the cabins?
n=the amount of people
70 + 9n= 151
70 - 70 + 9n= 151 - 70 (SPE)
9n= 81 (DPE)
9 9
n = 9 people
We worked on making one-step equation and two-step equetions. And solving them. We also work on our books on page 125. Read the page and then complete problems 1 and 2.
We work on solving equations but ignoring SADMEP, for example:

5c - 8= 17
5 5 5 DPE
c - 8 + 8 = 17+ 8
- - - -
5 5 5 5
25
c= 5 c=5

****QUIZ ON MONDAY!!!!!!!!!!!!!
*Solving one-step equations & two-steps equations
*Writing equations from word descriptions
*Solving word equations
*Algebraic properties
-APE, SPE, MPE, DPE
***HOMEWORK:***
Read pages 120-122, page 123 # 13-27 odd and 47,49

what we did in class

Hello students, today i will talk or remind you about what we did today in class about math.

1. when solving two step equations use reverse pemdas.
The first step will be eather + or- .
The second step will be eather multiplication or :

One of the problems we did today in class was:
1. I have a #
2. Multiply by 4
3. subtract 6
4. I get 34
What is my #

4x-6=34
+6 +6
4x:4=40:4
x=10

Thank you all for remembering how to do this math problem, and i hope you all rememberd to do your homework that we got for math today. See you all tomorow at school.
And the next scribe for tomorow will be kar0l.

Scribe List

Pick someone whose name has not been crossed out.

Scribe, Friday 10/12

Hi guys! Sirus here with the lesson from today.

OK. First point. The main point of today's lesson was to solidify our knowledge of the four main algebraic properties, the multiplication, division, addition, and the subtraction properties of equality.

The properties are stated thusly:
Multiplicative: If a = c, then ac = bc.
Division: If a = c, then a/c = b/c.
Addition: If a = c, then a+c = b+c.
Subtraction: If a = c, then a-c = b-c.

We also explored how writing about math helps you to understand it. These were the problems that we had to write about.

1) Explain how to undo multiplication in algebra.

2) What does x/2 signify?

3) Explain how solve for x and how to check x/3 = 4.

4) Come up with three algebraic equations for each property. You must use at least one negative number for each property, not for each equation.

5) You have two choices for this one.

1: If you aren't too familiar with the properties yet, try to solve the equations you created in number 4.
2: If you are familiar, write a word problem for each property.

Some of the problems that we came up with follow. Try them! (Be sure to define your variables)

1. There were a certain number of bees in the hive, until 3 left. After the 3 left, only 7 remained. How many bees were in the hive before the 3 left?

2. Bob had 144 skateboards. Now he only has one quarter as many as he did before. How many skateboards does he have now?

3. Mark had a certain amount of money. As he was walking to the store, a mysteriously heavy bag of money fell on his head, knocking him out and nearly concussing him. When he came to, somehow there was only $4 in the bag. If he now has $14, how much did he have before the bag fell on his head?

There is no homework. Since only 3 other people have at the moment accepted the invite, I nominate Marco to be the next Scribe.

Scribe Post Instructions

You will be responsible for posting a summary of the day's lesson. Your post must appear on the blog by 8:00 pm on the day that you are the scribe.

Scribe Post Requirements:

1. Title the post as a scribe post with the day's date.
   
2. Briefly explain the major concepts or skills.
3. Provide copies of the problems & their solutions.
4. Highlight any important issues associated with the problems. (These might include key steps, likely errors, connections to previous material, tips for understanding or memorizing, etc.)
5. List new homework assignments, and provide reminders for any upcoming assignments, quizzes, or class schedule changes.
6. Pick the next scribe(s).

Tips for success:

• COME TO CLASS EVERYDAY!
• Check the blog the night before to see if you are the next scribe.
• Read and practice the night before you are the scribe. Make sure that you understand and have practiced the most recent skills that we have learned.

Thursday's Class 10/11/07

Today we just practiced solving equations that had multiplication and division.

Remember: Use Inverse Operations!!!!!!!!!!

When an equation has addition or subtraction AND multiplication or division, take care of the addition/subtraction first.

HW: READ pgs. 115 - 117, pg. 117 # 1 - 3 All, 17 - 37 odd, 45


Practice, practice, practice!

See you tomorrow.

Wednesday 10/10/07

Howdy Bloggers!!

Today we took a super easy quiz and then practiced solving equations that involved multiplication and division.

The trick was to use two new properties:

• MPE - The Multiplication Property of Equality
• DPE - The Division Property of Equality

Try these two:

1. -3x = 12
2. -x/4 = -20

If you think you can solve them, add your solution as a comment to this post. (Click below where it says "comments")

Feel free to start your own post. Just be sure to keep it to math, keep it positive, and stay respectful to each other. If you need help; you can ask for it on the blog.

HW: Finish the practice Sheet


See you tomorrow :)

10/5, 10/8, 10/9

Friday's class:

• We practiced simplifying expressions.
• When adding or subtracting negative integers be sure to choose a technique: absolute value rules, number lines, or using additive inverses. If you take the time to work it out, you do not need to guess.

Monday's class:

• We started solving simple equation using pieces of paper to represent variables and numbers. By adding and removing papers from both sides of the equal sign we were able to isolate x (solve the equation).
• See pgs. 108 - 109 for examples

Tuesday's Class:

• We compared solving equations by moving pieces of paper with solving equations using just symbols.
• KEY IDEA: Cancel operations using their inverses (addition cancels subtraction, subtraction cancels addition)
• We learned the Addition Property of Equality (APE) and the Subtraction Property of Equality (SPE). We used these to justify making changes to equations.

Homework: Read 110 - 112, pg. 113 # 15 - 35 odd (this was assigned long ago)

Reminder: Quiz Tomorrow

• Operations with +/- integers
• Simplifying expressions (including distributive property)
  
• Evaluating expressions
  

10/4/07

Today: More practice with simplifying algebraic expressions.

The new trick is to use empty boxes to represent the terms. Keeping the operation signs separate from the terms should help alleviate some of the issues with negatives.

HW: Finish the problems from the practice sheet: 12-20, 28, 30, 31, 33.

Do the other problems if you want more practice.

Remember, quiz coming up on Wednesday.

Wednesday 10/3/07

Today we practiced simplifying algebraic expressions.

HW: pg. 105, # 7 - 27 odd

Check your answers in the back.

If you are having trouble, be sure to read the pages before the assignment.