Bob Jones Pre-Algebra & Algebra 1 Videos!

Bob Jones Pre-Algebra and Algebra 1 -- over 200 videos on YouTube!
http://www.youtube.com/user/MsBetsy9
They're not in an exact order, so my advice is to save them in order yourself -- maybe on youtube playlists a few chapters per playlist (They can be rearranged if saved out of order), or bookmark them by chapter(s) in folders.
This is simply awesome! =D

If someone does make youtube playlists, and if you don't mind sharing, please leave a comment and a link!
That would be wonderful!  =)

Triangle Trick!

I love this.  =)

When you have a simple formula where one variable or value equals a fraction, and you need to rearrange it so that you find a different value, this triangle trick might just be what you need.  =)

velocity = distance/time

9:20-10:42 from this video.

Isn't this awesome!?! =D

Factor/Label Method

I wish I had seen this video when I was editing the Physical Science Module 1 post!
It is added to that post now, but I'm posting it here for those that may have missed it.  Or still need a bit more clarity on the Factor/Label method, or need a bit of review, or are just curious about this awesomely simple, but so logical video!  =)

A bit loud, so you may want to turn it down.  =)

Factoring Trinomials using the Berry Method

Before using this method, I recommend that you fully understand how to FOIL and how to factor trinomials. (See math tab for more posts about polynomials and trinomals).

►Accompanying worksheet for this video.


►Accompanying worksheet for this video


YayMath.org has more videos, worksheets, and online quizzes.
YayMath is also on facebook.

Translating English phrases into Algebraic Expressions

As always, it's a good idea to have pencil and paper handy.  After you understand the concept being taught, pause the video to see if you're able to work the problems before the answers are shown.

A variable is a letter that is used to express an unknown number.

"Less Than" and "Subtracted From"
The phrases "less than" or "subtracted from" indicate that the first variable or number mentioned is being taken from the second number or variable mentioned.
So when you see these phrases, you will know that the expression will be written in the opposite order as they are mentioned in the sentence.

Examples:
►If you have $85.00 and I have $10.00 less than you, I have $75.00.
If I were to express this in an English phrase (or word phrase), I might say,
10 less than y
But I would not write 10 - y; instead I would write y - 10.

►Suppose I say, "$267 was subtracted from my bank account!"
I will use b for the bank account, and write b - 267 

(1)  Intro to algebraic expressions



When you see the phrases product of, sum of, quotient of, or difference of, there will be at least 2 terms to be calculated.
The product of 6 and a number
The sum of 3 and 9
The quotient of 28 and a number
The difference of 23 and 16

(2) Professor Perez and Charlie introduce this ↑ concept, then show how you can apply this knowledge to longer algebraic expressions.
At 4:35, he shows how to go from algebraic expressions back to English phrases.  This really helps in understanding the key phrases.  Very good!



(3) More Practice.
►At 0:50 there is a chart with phrases that can be used to indicate the 4 operations of multiplication, division, addition, and subtraction.  (such as more than, in addition to, greater, etc.)
It might be useful to pause the video and write these down to keep on hand.

►At 1:10, instruction begins.
He refers to "less than" and "subtracted from" as switch phrases.
He goes rather quickly,  but you should be able to understand these problems if you watched the first two videos.
Pause the video if you need to think it through.  Write down any examples you find helpful.

"John has twice as many quarters as dimes."  Should this be 2q = d or q = 2d?



(4) Even More Practice
Again, at the beginning of this video, there is a chart with phrases used to indicate the 4 operations.  Check to see if there are any additional phrases to the ones in the previous video.
►Pause at 1:20 to see some words and phrases used in place of the = sign.
►At 4:00, there are a few word problems.




"Algebraic Expressions" vs. "Algebraic Equations."
• An expression is like a phrase - incomplete.  There is no = sign, no answer.
• An equation has the = sign.

►The equals sign is like a verb: "is"     5x = 10.  5x is 10.
Words without a verb can be phrases, or in algebra, expressions.
An algebraic expression has no verb.  No "is."

These videos in this blog post are teaching how to write algebraic expressions.
That probably means you'll be learning equations next.  Yay!  

I L♥ve algebra!  =)

Algebraic Expressions and Equations

(1) Writing expressions and equations from phrases and sentences.
Very good explanation of the phrase/sentence parts.



(2) Expressions and Equations with Prof. Perez and Charlie
At 1 minute he notes a common mistake that students sometimes make.



(3) Basics of writing expressions and equations;
Writing algebraic phrases and sentences.

Polynomials - what kind, what degree

A variable is a letter that represents a number.
Since it can represent different numbers at different times and will not always represent the same number, it is called a variable.

A variable with a zero power equals 1.
xº = 1
When a number is written without a variable, the invisible variable has a zero power.
So 8 is the same as 8xº which is the same as 8 x 1.

Variables written without a visible exponent are understood to have the exponent of 1.
x = x¹
This does not equal 1 unless the variable is equal to 1.
The value of this term, or monomial, is whatever the value of x is.
If x = 7, then x¹ will equal 7.

Watch these videos first:
Embedding on these videos was disabled, so you'll need to click on the links to view.
►Degrees and Types of Polynomials, part 1 , part 2
►Degree of a polynomial if the terms have more than one variable.

A little more advanced in this video, but very well explained.

►Interactive lessons -- may be best to do after viewing the videos here.

Click Unit 5, Lesson 22, Play Lesson, Introduction to Polynomials.  

You may read along with the lesson in the left sidebar.

Note:  Lesson does not seem to work in Safari browser.

Adding and Subtracting Polynomials

(1) Adding polynomials


(2) Adding polynomials with multiple variables




(3) Subtracting Polynomials


(4) Subtracting Polynomials with multiple variables



(5) Adding and Subtracting Polynomials - very good video

►Interactive lessons -- may be best to do after viewing the videos here.

Click Unit 5, Lesson 22, Play Lesson, Adding and Subtracting.  

You may read along with the lesson in the left sidebar.

Note:  Lesson does not seem to work in Safari browser.

Factoring Polynomials - Solving for x

(1) Solving Polynomial Equations for x
She gets two answers.  In this case, if you plug either of those back into the original equation, they both work.  Sometimes, one will not work, and you throw it out as a possibility.


(2) More on Trinomials - solving for x  (Trinomials are a type of polynomial.)
►Accompanying worksheet for this video.

Introduction to Factoring Trinomials - reverse of FOIL

YayMath.org  "Factoring means turn it into pieces you can multiply." 
►Accompanying worksheet for this video.



A trinomial has 3 terms.   x² + 2x - 63
A binomial has 2 terms.   x - 7
The 2 factors of a trinomial are binomials, and each can be written in parentheses.
(x + 9)(x - 7)  They are called binomial factors.
When these binomial factors are multiplied, they will equal the trinomial.

After checking for a greatest common factor and factoring it out, then you can factor the trinomial.

To easily determine signs when factoring trinomials:

1.  If the sign of the last term in a trinomial is negative, such as x² + 2x - 63
the signs between the terms in the binomial factors will be one positive and one negative.
Example 1:  
x² + 2x - 63
(x + 9)(x - 7)

Example 2:
x² - 2x - 63
(x - 9)(x + 7)

Do you see the difference?
• In the first example, only the last term in the trinomial was negative.
• In the second example, both the last term and the middle term were negative.
• So no matter what the middle term is, if the last term in a trinomial is negative, the signs between the terms in the binomial factors will be one positive and one negative.

So what does the sign of the middle term in the trinomial tell us?
It is what you use to determine which of the binomial factors will be positive, and which will be negative.
• In the first example, the middle term of the trinomial is positive (+2x), showing that the 9 in the binomial factors should be positive since it is greater than 7, because if you combine +9 and -7, you will get +2.
• In the second example, the middle term of the trinomial is negative (-2x), showing that the 9 in the binomial factors should be negative, because if you combine -9 and +7, you will get -2.


2.  If the sign of the last term of a trinomial is positive, the signs between the terms of the binomial factors will either be BOTH positive or BOTH negative.
• If the last term in the trinomial is + 63, the terms in the binomial factors will either be 
( __ - 7) and ( __ - 9), or they will be ( __ + 7 and ( __ + 9).
• Then the sign of the middle term of the trinomial will determine what they both will be.

Example 3:
x² + 2xy + y²
(x + y)(x + y)

Example 4:
x² - 2xy + y²
(x - y)(x - y)

If you use the FOIL method and multiply the Inner and Outer terms (from the binomial factors), you will get either both positive terms or both negative terms to add together, equaling the middle term of the trinomial.
In example 3, +xy and +xy will give you +2xy.
In example 4, -xy and -xy will give you -2xy.


►Found this video at Virtual Nerd: Determining Signs when Factoring a Trinomial

Multiplying Polynomials - FOIL and more

• Monomial - 1 term
• Binomial - 2 terms
• Trinomial - 3 terms
• Polynomial - more than 1 term

(1) YayMath.org - Foil method
►Accompanying worksheet for this video.
►Online quiz.


(2) Multiplying a binomial by a polynomial


(3) Multiplying vertically - I like this method!

Rules for Exponents

There are a lot of videos here!  About 35 minutes total, so I suggest taking more than one day to watch these, and taking notes as you do. The first several videos are shorter.

►Interactive lessons -- may be best to do after viewing the videos here.

Click Unit 5, Lesson 20, Play Lesson.  Click on the lesson titles on the left.

You may read along with the lesson in the left sidebar.

Note:  Lesson does not seem to work in Safari browser.

(1) Product Rule


(2) Quotient Rule


(3) Power Rule


(4) Using the rules


(5) Simplifying fractions with exponents


(6) Exponents, powers of base 10


(7) Level 1 Exponents, part 1 - the "why" of some of the above, and a few new concepts.


(8) Level 1 Exponents, part 2

In the last example, he leaves "3 to the negative 36th power." 3^-36, (since I can't write exponents on here except for °²³).  I have been taught and have seen taught in various videos online that you should try to not have a negative exponent in your answer.
In the 5th video, she showed how to get rid of negatives by moving the negative exponent to either the top or bottom of a fraction.  So the last answer could be written as a fraction: 1/3^36.  "1 over 3 to the 36th power."

Dividing Polynomials

YayMath.org
►Accompanying worksheet for this video.

Algebra 2 - Dividing Polynomials from Yay Math on Vimeo.

Systems of Equations: Inconsistent/Consistent; Independent/Dependent

When graphing systems of equations, you can figure out whether they are consistent or inconsistent.
If they are consistent, you then see whether they are independent or dependent.

(1) The differences


►If the lines are parallel to each other:
•there is no solution (There is no place of intersection - which would have been the solution, therefore no solution.)
•and they are inconsistent (have no points in common)
►If lines intersect:
•they have a solution such as (2, -4) or where ever they intersect, and that is what you write. "(2, -4)"
•they are consistent (have at least one point in common)
•and they are independent (of each other -- they go their own direction)
►If lines land in the same place, on top of one another:
•the solution is along the entire line - any and all points on the line will work as the solution, so you would say "entire line" or "infinite."  There is an infinite number of possible points along the entire line.
•they are consistent (have at least one point in common)
•they are dependent (do not go their own direction)

(2) Using substitution to tell the difference

Graphing Linear Inequalities

To understand these videos (some go pretty fast), you must fully understand how to solve and graph linear equalities.  You must also know how to solve linear inequalities. 

You must be familiar with slope-intercept form (y = mx + b), and understand which numbers in the equation are m and b, and how to graph them.  Mark b on the graph, then graph the slope (m) from that point. 
Inequalities are very similar, with only a few differences:

• It's not a line of solutions as in a linear equation; it is a solid or dashed boundary line that shows on which side all the solutions are.
• Shade above or below the boundary line, showing on which side all the solutions are.
• Change the direction of the inequality (>, <) if you divide by a negative number.

►These differences are explained in the fourth video.  It is fast, and it is good to pause the video to read the text on the board.
►Check your work by using (0,0) as a test point.  This will help you know if your answer is correct, and if you forgot to change the direction of the inequality.
These videos cover the same topic, but go about solving in slightly different ways.  I watched all of them, and gleaned a little more from each one.

(1) from YourTeacher.com - graphing using a table



(2) boundary line


(3) graphing using slope-intercept form, y = mx + b


(4) graphing using slope-intercept form.  He is fast, so pause and read the text on the board.


(5) graphing using slope-intercept form

Solving Linear Inequalities

(1) from YourTeacher.com


(2) from PatrickJMT
Accompanying worksheet for this video.

Direct and Inverse Variation (finding the constant - k)

Direct Variation - as one value goes up, the other goes up accordingly.
Inverse Variation - as one value goes up, the other goes down.
►Accompanying worksheet for this video.

Algebra 2 - Direct and Inverse Variation from Yay Math on Vimeo.

At Virtual Nerd
►How Direct Variation looks on a graph Very good!!!
►What is Direct Variation or Directly Proportional? 
►Constant of Variation - table
►Solving a word problem - has a fraction

Solving Systems of Equations (graphing, substitution, elimination/addition)

The reason for solving systems of equations is to find at which point will they intersect on a graph.
A "system" of equations is 2 equations where the x's in each equation equal the same number, and the y's in each equation equal the same number.
When you find what x and y equal, they are written in parentheses as an ordered pair like this:  (-3, 5) with the x always being written before the y.  If you graph the (-3, 5) -- use the slope-intercept form "rise over run" -- that is where the two graphed equations (lines on the graph) would intersect.

►After graphing, if lines are parallel they will not intersect.  The answer to this kind of problem is "no solution."  There is no point on the graph at which the lines will intersect.

►If the lines end up graphing as the same line, on top of one another, the answer is "infinite solutions" or "entire line."  In other words, ANY of the points on the entire line will work in both of the systems of equations.

►If the lines do intersect, the point at which they intersect is your answer.  You will write the answer as an ordered pair, such as (-2, 5).

A. Solving Systems of Equations by Graphing

(1) Solving Systems by Graphing (YayMath.org - my favorite math videos!)
►Accompanying worksheet for this video.



(2) Solving Systems by Graphing



(3) Solving Systems by Graphing [y-intercept (b) is zero]






B.  Solving Systems of Equations by Substitution

(4) YourTeacher.com - Solving Systems by Substitution



(5) YayMath.org - Solving Systems by Substitution
►Accompanying worksheet for this video (only do the Substitution method problems for now).






C. Solving Systems of Equations by Elimination

(6) YayMath.org - Solving Systems by Elimination/addition.
►Accompanying worksheet for this video.

"To 'eliminate' may make you think of the Terminator. But in Algebra, it's a method of solving two or more equations at the same time."  ~Yay Math!


(7) YayMath.org - Solving Systems by Elimination/addition.
►Accompanying worksheet for this video (use the last problem -- this is the rest of the video from #5 above).  Full video here.

Graphing Linear Equalities using slope-intercept form (Rise over Run)

A steep hill has a greater slope than a gradual incline.
A steep roof may rise UP 10 inches to every 120 inches across ACROSS.  This would have a slope of 10/12.  In other words, it "rises" 10 inches as it "runs" 12 inches.  This would be an extremely steep roof!  
♦ The slope is 10/12, and to make the line on a graph, you would use rise over run.  You would start at 0 in the center of your graph having an x and y axis (see videos below), and rise 10, then run 12.  Draw a point here, then draw a line connecting this point to 0 on your graph.
♦ A more gradual incline (a less steep roof) might have a slope of 5/12.
This slope is called the pitch of the roof.  You must know what pitch you need when ordering tresses for a roof.

(1) YourTeacher.com - graphing a slope


(2) YourTeacher.com - graphing slope-intercept form
At this stage, you are not asked to identify what x and y specifically equal.  They actually equal all points along the line that was graphed.  
To determine specifically what x and y equal, you would need 2 equations, called a system of equations.  Where the 2 graphed lines intersect will be your answer.


(3) YourTeacher.com, converting to slope-intercept form; graphing


This method is called Slope-Intercept because it is graphed by first finding the point where the line will intercept the y-axis, and then finding the slope of the line using "rise over run" -- the number beside x in the equation.


►YourTeacher.com's Demo Lesson just happens to be about slope-intercept.  =)  These slopes are already graphed, and you learn how to figure the slope.
Click on Demo Lesson under the video.  The explanation is fast, but there is a help button. 

There are 4 videos for 4 example problems.
Then click on the buttons for the practice problems, and see if you know the answers.
Below the practice problem buttons, you can click to see a hint, or the answer, as well as show an explanation.
The volume icon gives an oral explanation of the practice problem you are on.
There is also a self-test. Click the problem number 1.  Click on MC to see the multiple choice answers.  Choose A, B, C, or D.
If you click on the wrong answer, you can click on the Notepad icon for an explanation.

Graphing Linear Equalities using a table

(1) Graphing Linear Equations, Part 1, Mr. Perez & Charlie
In the first problem, when the line is graphed, you notice that the line crosses the y-axis at (0,5), and crosses the x-axis at (5,0).  The points at which the line crosses the axes (pl. of axis) are called the x-intercept and the y-intercept.


(2) Graphing Linear Equations, Part 2, Mr. Perez & Charlie
Problem 2 continues in this video, and you can see the line crosses the x and y axes.
The x-intercept is at (3,0) and the y-intercept is at (0,-2).
Problem 3 shows the x-intercept at (6,0) and the y-intercept at (0,-4).