Ike, 2.3, Solving a Mixture Problem

Today was relatively brief in its lesson as due to a technical failure (?) of homework from the previous night. We did cover how to SOLVE A MIXTURE PROBLEM!, though, and so I shall review over this amazingly fun and wildly interesting material for you. Yay!

MIXTURE PROBLEM:
James has 20 ounces of a 20% salt solution. How much salt should he add to make it a 25% solution?

Step One: Set up a table for salt.

	original	added	result
concentration
amount

Step Two: Fill in the table with information given in the question.

John has 20 ounces of a 20% of salt solution. How much salt should he add to make it a 25% solution?

The salt added is 100% salt, which is a 1 in decimal form.
Then you can go ahead and change the rest of the percents to decimal form for easier simplifying. I mean, you dont HAVE to, but thats how i know how to do it. Great!

Then let x= amount of salt added. You get 20 +x.

	original	added	result
concentration	0.2	1	0.25
amount	20	x	20 + x

Step 3: Multiply down each column.

	original	added	result
concentration	0.2	1	0.25
amount	20	x	20 + x
multiply	0.2 × 20	1 × x	0.25(20 + x)

Step 4: original + added = result

0.2 × 20 + 1 × x = 0.25(20 + x)
4 + x = 5 + 0.25x

Isolate variable x
x – 0.25x = 5 – 4
0.75x = 1

Answer: He's got to add 4/3 ounces of salt. YAY!

um.. next scribe... amelia? I dont know! aaahhh dont hate me.

Verbal expressions:

Addition:

Sum

More than

Plus

Added to

Increased by

Subtraction:

Less than

Minus

Decreased by

Subtracted from

Difference between

Multiplication:

Times

Multiplied by

Of

Twice

Product

Division:

Quotient

Divided by

Ratio

Jared Section 2.3

 When class began, we learned how to solve a percent problem.  There are six different steps to solving a percent problem.  They are as followed: 


Read the problem  
Assign a variable  
Write an equation from the given information  
Solve the equation 
 State the answer  
Check 

We also learned how to solve an investment problem.  The steps for solving a percent problem also apply for solving an investment problem.  Following this was a daily quiz to conclude our class.  

Fact about Percents!

The word percent, comes from the latin phrase "per centum"( per 100). This is because a percent = x/100. Today we use % as the percent symbol.

http://www.mathgoodies.com/lessons/vol4/meaning_percent.html

Christine, 2.3 For Yesterday and Today!

MONDAY:

Yesterday in class, we discussed translating words into mathematical expressions. A few examples of this for addition would be:

6 more than a number

3 plus a number

the sum of two numbers.

An example for subtraction would be:

2 less than a number

a number decreased by 12

the difference between two numbers.

An example of multiplication would be:

2/3 of a number

twice a number

the product of two numbers

An example for division would be:

the quotient of a number

a number divided by.

It was really helpful to see math in words instead of numbers! It made it much easier to figure out problems and helped me understand better! This showed up in last nights homework in the form of word problems.

TUESDAY:

Today in class, we related math to real life by looking at the scribe posts that everyone had come up with and seeing things that you can change. Also, JoJo talked to us about the importance of doing homework because it will pay off later in life. We went over the homework problems that many didn't understand, especially number 27. 27 was difficult to most because it made you show every single step and not everyone fully understood it. It REALLY helps doing work in steps because it stops you from messing up! Why wouldn't you do the steps if you could get a 100? I have problems showing the steps and it does show in my homework, you just need to take the time to really disect the problem and go through all of the steps ON PAPER!

The next scribe will be Jared

If one is once and two is twice is three thrice?

someone in class (sorry I can't remember who) asked: so if two is twice, is three thrice?

Three would be thrice, but four would be "four times".

Reply to Why is M used for the Slope in Linear Equations

I had to post my comment as its own post because it wouldnt let me comment on Noa's post.
M is the slope or the slant of a linear equation. I was wondering why it used to be called Modulus and was also wondering if M was always used to represent the slope in linear equations.
Amelia

Why M is Represented as Slope!

Slope, was once named "Modulus of slop". "Modulus" once being represented as the number used to measure.

http://wiki.answers.com/Q/Why_is_slope_represented_by_the_letter_m

Math Stories & Poems -PoP

On The Road To Wonderland
Originally uploaded by Disney Resort

Write a story or poem that includes verbal mathematical expressions and/or equations. Write the actual mathematical expressions or equations underneath your story.

Remember, all things must have values if they are represented in a mathematical expression or equation. Use elements that you can measure with numerical value.

Good Example : number of something
Bad Example: a feeling or emotion (unless of course you assign it a value)

Math Formulas -PoP

Math formulas up the wall
Originally uploaded by trindade.joao

Write a short paragraph summarizing what you have learned in the exercises on Page 71 (1-5) as well as something new you learned in your group work on Thursday!

Scribe Post, Amelia 22/7

Today in class we went over how to solve different kinds of linear equations, equations with distributive property, linear equations with decimals and linear equations with fractions. We also went over the steps used to solve the linear equations and did lots of examples. At the end of class we did a daily quiz. Todays class helped me to understand solving linear equations with fractions because I had forgotten how to do that.
The steps to solving a linear equation
1. If there are any frations or decimals the first thing you do is clear the fractions or decimals.
2. distribute
3. group like terms
4. combine like terms
5. Isolate variable
6. check
Other Important things to do
What you do to one side of the equation you must do to the other side of the euqation.
Solving Equations with Distriburive Property
Example:
2(k-5)+3k=k+6
2k-10+3k=k+6 Distribute
5k-10=k+6 Group like terms
5k-10-k= k+6-k What you do to one side of the equation you must do to the other side.
4k-10=6 Combine like terms
4k-10+10=6+10 What you do to one side of the equation you must do to the other side.
4k=16 Combine like terms
4k/4=16/4 Isolate variables
k=4
Check by plugging back into the equation
2(4-5)+3(4)=4+6
2(-1)=12=10
10=10
True
K=4
Solving Linear Equations with Decimals
Because each decimal number is in the hundreths, multiply each side of the equation by 100.
.06x+.09(15-x)=.07(15)
100(.06x+.09(15-x)=.07(15))100 Multiply by 1oo
6x+9(15-x)=7(15) Distribute
6x+135-9x=105
-3x+135=105 Group like terms
-3x+135-135=105-135 What you do to one side of the equation you must do to the other
-3x=-30 Combine like terms
-3x/-3=-30/-3 Isolate variable
x=10
Check by plugging back into the equation
.06(10)+.09(15-10)=.07(15)
.06(10)+.09(5)=.07(15)
.6+.45=1.05
1.05=1.05
True
x=10
Solving Linear Equations with Fractions
2p/7-p/2=-3
14(2p/7-p/2=-3)14 Elemanate the fractions
14/1(2p/7)-14/1(p/2)=14/1(-3/1) Distribute
28p/7-14p/2=-42
4p-7p=-42 Combine like terms
p=14
Check by plugging the number back into the equation
2(14)/7-14/2=3
2(20/1-14/2=3)2
8/2-14/2=-3
-6/2=-3
-3=-3
True
p=14
The next scribe will be Christine

Test Aftermath Instructions

Reflect on your performance mathematically (do not talk about non-math related things like sleep, breakfast, or study skills). Talk about math!


(1 point)
1. Offer specific examples of some areas you did well on the test (use math terms to describe, not numbers of problems from the test.)


(2 point)
2. Offer specific examples of some areas you did poorly on the test (use math terms to describe, not numbers of problems from the test.) Tell specifics about the problem that caught you up...(wording, computation, comprehension, etc.)


(3 points)
3. Select one problem you got wrong. Show me that you understand the problem by doing another problem like it correctly.  This can be one problem from the test, as long as I did not write the answer during corrections.  Please avoid correcting small errors.


(3 points)
4.    Select a topic that was NOT covered on the test, but was covered in class or the book. Show me you understand it by working a problem correctly.

Scribe Post, Danielle 9/14/10 Chapter 1

Today in class we went over Daily Quizzes #4 and #5. The class was mainly review.We reviewed rational numbers, irrational numbers, and what real numbers are.
Rational Number- A number that has a terminating or repeating decimal
Irrational Number- Decimal Numbers that dont terminate or repeat
Real Number- A number thats either rational or irrational

Rattional Numbers can't be written as an integer
Irrational Numbers can be expressed as a fraction

We also went over what an additive inverse is.
Additive Inverse- For any real number a , the number -a is the additive inverse of a

Number Lines were giving us trouble today also .Always remember that numbers on a number line should be in order and the dashes that you put the number on should be equally spaced apart.

Below, is what the number line should look like.

Jonathan September 13th

Today in Jojo's class we went over our homework in groups. Then we asked jojo about questions we had on our homework. We went over a question that was fairly simple. We got it wrong because we didnt follow pemdas.

-25(-4/5)+ 3^3 - 32 / sqrt 4

using order of operation you do exponents first

-25(-4/5)+ 27 - 32 / sqrt4

Next we would multiply and get

20 + 27 - 32/ 2

Now this is were we got it wrong instead of following pemdas and divide we added and we got

47-32/2

15/2

we should of did

-32/2

47-16

31

This is what pemdas means:
P erenthesis

E xponents

M ultiplication

D ivide

A dding

S ubtraction



The scribe for tommorow is Danielle

Notes on How To Prevent Careless Mistakes!

1. Show each and every step ( Do not use mental math!)

2. Write every problem clearly

3. Check every answer and ask yourself if the answer you got make any sense

4. Write out all the given information from the problem

5. Be organized and stay relaxed!

( All ideas contributed by students in class today)!

Hope this helps on our next test!

Tyler, September 10

On Friday we talked about and took notes on additive inverse, set notation, and distributive property (JoJo's favorite property). Then, as a class, we went over the homework for that day which was 1.4 1-59 odds. Here are some additive inverse, set notation problems, and rules we discussed.

additive inverse

if a=-1 then |-1|= -a 

set notation

x= { 2, 4, 6, 8 ...} open set

x= { 2 ,4, 6, 8 ...298}

The product of two numbers with the same sign is positive

The product of two number with different signs is negative

The reciprocal of a non zero number is 1 over the number. (ex. a= 1/a )

Karen, September 9th

Hello there! Well, today we started off by taking Daily quiz #4 just to practice our use of exponents. After that we went over problem #89 on the homework from Tuesday night and realized we used a fraction symbol instead of division which did in the end determine our final answer. This is what the book wanted us to do originally:

(V × .5485 - 4850) ÷ 1000 × 31.44

Which is working from left to right.

And this is what we made a mistake on in class:

(v × .5485 - 4850)

_______________

1000 × 31.44

Which is using the fraction symbol in replacement for the division symbol.

We were thinking that it is the same exact thing but when you work from left to right like the book wanted us to, we divide 5000 by 1000 and THEN multiply it by 31.44.

But the other way we did two separate equations and THEN divided them by each other.

Next off, we went over Daily Quiz #3 from yesturday.

One main point we covered was that if you are adding two numbers with the same symbol,

you add the absolute values of each number and then on your final answer you return the symbol you were originally working with. here is an example:

5+8=

|5| + |8| = 3

But if you are adding with two numbers of different symbols,

you take the absolute value of the bigger number and subtract it from the smaller number. Here is an example of this type of problem:

-5 + 6=

|-5| + |6| = 11<---- this is where you return the original symbol to ultimately get: -11

And that's practically all we went over hope you enjoyed pretty colors! =]

For the next scribe I think Tyler should do it.

Blogging on Blogging -Reflections -BoB Chapter 1

There is a BIG difference between learning and just being there. Learning is an interactive sport; not a spectator sport. There has to be a conversation between us, back and forth, as we work through the material. Learning doesn't happen when I talk and you listen; learning happens when you have a conversation -- with me and with each other.

I am going to offer you up to 5 bonus points on your test with completion of a simple assignment.  I would like you to post your reflections on the material covered so far.  Just comment on this post.  To get that bonus on your test, the kind of post I'd like you to make should have one or more of these characteristics:

• A reflection on a particular class (like the first paragraph above-how did that class enhance your learning?).
• A reflective comment on your progress in the course.
• A comment on something that you've learned that you thought was "cool".
• A comment about something that you found very hard to understand but now you get it! Describe what sparked that "moment of clarity" and what it felt like.
• Have you come across something we discussed in class out there in the "real world" or another class? Describe the connection you made.

Scribe Post Jonathan - September 8th

Today in math class we basically went over what we learned yesterday. We started of the class by taking our daily quiz. Today we talked about square roots with exponents. Basically A^n/m = n/A^m. For example if its 2/25^1 is 5^2. We also learned that any term being multiplied by an expression including addition and subtraction you use the distributive property.

Ex: X^-1 - y^-1/x-y = -1/xy
1/x - 1/y/ x-y
xy(1/x - 1/y) =xy/x - xy/y= x-y

This works because xy distributed gets you xy/x - xy/y then you cross multiply and you get rid of the x and the y then cancel eachother so your left with x-y.

The coolest thing to me is when we learned the equation that allows us to find property taxes.the equation is that (v x .5485- 4850) / 1000 x 31.44 this will help you latter on in life so that you dont get screwed over by the government when they come to collect your property taxes.

Scribe poster for tommorow is karen.

Scribe Post 9/7/10

William has already been the scribe before, so I am going to do the post for today instead.

Today in class we learned about section 1.3 which is about exponents. At the beginning of class, we went over the orders of operation also known as PEMDAS. PEMDAS stands for: parentheses, exponents, multiplication, division, adding, and subtracting. Multiplication and Division are changeable, so in an equation you would just do the operations from left to right, same with Addition and Subtraction. Also today we learned about the properties of exponents.

Properties of Exponents:

a∧n=A power of a

a=the base

n= the exponent

a∧0=1

a∧-n=1/a∧n (take the reciprocal of the power)

Today we also learned about all of the different rules of exponents, these rules are really important to remember, so make sure you know them before the quiz!

Rules of Exponents:

a∧m a∧m= a∧m+n *you can do this only if the bases are the SAME

a∧m/a∧n= a∧m-n *again, you can only do this if the bases are the SAME

(a∧m)∧n= a∧mn (Multiply the exponents together)

(ab)∧m= a∧m b∧m (Distribute the exponent) ***CAUTION: you cannot do this with an equation such as: (a+b)∧m it is not the same thing

(a/b)∧m= a∧m/b∧m (Again, you distribute the exponent to everything inside of the parentheses)

Another thing that JoJo taught us today was that you always put variables in alphabetical order. One more rule that we learned was when you have a∧m/n it is equal to n√a∧m. A new thing that I learned today was that a square root symbol is called a radical, and the number inside of the radical is called the radacan. At the end of class we did a few examples and one big example at the end, at first the last example seemed really hard, but it made much more sense after JoJo showed us how to do it. It was a great day in math, and we learned a lot!

For the next scribe, I choose Jonathan.

**This symbol means raised to an exponent (∧), sorry I wasn't sure how to do it on the computer!

Properties of Exponents

Power to a power: Multiply the exponents.

Example: ( x^n)^m = x^mxn
Power of a Product: Distribute the power.
Example: (xy)^2 = x^2 y^2


Power of a Quotient: Distribute the power.
Example: (x/y)^2 = x^2/y^2


Product of Powers: Add exponents.
Example: x^m* x^n = x^m*n


Quotient of Powers: Subtract the top exponent from the bottom exponent.


Example: x^3 over x^2 = x^m-n
Negative Exponents: Take the reciprical and change the sign of the exponents.
-n n
Example: x^-n = 1/ x
Zero Power: Any base with zero as an exponent equals one.

Example: x^0 = 1


Sorry if you were confused the exponents are above the example and the base is on the line bellow.
Amelia

Order of Operations

The order of operations are PEMDAS. Parentheses, exponents, multiplication/division, addition/subtraction. This means that you have to do whatever is in the parentheses first then exponents, multiplication/division then add or subtract.

Ex. (3+2)+4•2=
(3+2)+4•2=
(3+2)+4•2=
You would add 3+2 first (5), then multiply 4•2 (8), then add 5+8 which is 13.

Subtrahend- Minuend.

Subtrahend- The number being subtracted.

Minuend- The number not being subtracted.

Example- 24-23= 1.

24 is the Minuend and 23 is the Subtrahend!

Source:http://encarta.msn.com/dictionary_1861716631/subtrahend.html- Subtrahend
http://encarta.msn.com/dictionary_1861630342/minuend.html- Minuend

Emma's Scribe Post - 9/2/10

Today in class we started to go over Section 1.2.
We studied for about five minutes and then we had our second benchmark quiz.
We talked about the different ways to add and subtract negative numbers.
Positive amounts or adding on a number line moves you in right/positive direction.
Negative amounts or subtracting moves you to the left.
Ex. Adding two negative numbers:
-12 + (-8) = 
-(12+8) = 
-(20) =
-20
Ex. 2 Adding numbers with different signs:
-17 + 11 =
| -17 | - |11| =
17 - 11 =
-6
Subtraction:
a - b = a + (-b)
[Subtrahend] <- what does that mean?

JoJo put two rings in front of Amelia, then took one away and said that he was adding one to his negative account. So taking away one from her positive account.
I thought that that was an interesting take on subtracting.
Over all, today was a good day in math.


The next scribe will be William!
^_^ Emma
Don't forget to do your homework!

Brigid's Scribe Post 9-1-10

Today was a really fun day in Jojo's math class. Since yesterday we took pictures, we looked over all of the pictures, (that were tagged correctly...) we watched the slideshow of the math pictures and commented on them. We could correct anything that incorrect, like definitions or things like pictures we thought would better represent another term. Hopefully all of our comments were helpful and encouraging!
After we finished with our Flickr assignment we sat down for our first benchmark quiz. It was four questions to finish in five minutes or so. So everyone make sure you are ready for those in the future!
Being able to see the terms, like elements and additive inverse, out of the book was really cool. This way we can remember what the pictures looked like and that will help us remember the definitions in the future. It will help us remember because we can associate the term and picture.
Anyone who hasn't uploaded their pictures onto Flickr should do that ASAP! Also, anyone that didn't do the units of measurement PoP remember to do that.
The next scribe is Emma!