Free videos to help you learn and understand concepts in Algebra 1. #Algebra

I work through two examples of graphing systems of inequalities.  The first example involve linear inequalities and the second example has non-linear inequalities.

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

OVERSEAS

Graphing System of Linear Inequalities

I define Domain and Range and work through 3 graphs identifying the domain and range in each graph.

Determining the Domain of a Function from an Equation 
   • Determining Domain of Functions   Find free review test, useful notes and more at http://www.mathplane.com/

Identifying Domain and Range from a Graph

Examples at 0:44 9:20 12:48 22:20
Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Literal Equations Two or More Variables 4 Examples

I define Mathematical Quantities and explain the difference between constant and variable quantities.  Variables, Algebraic Expressions, and Numerical Expressions are also defined before working through many examples of writing algebraic expressions from phrases or sentences.  I include Addition (Sum, More Than), Subtraction (Difference, Less Than), Multiplication (Product), Division (Quotients), and when to recognize that parenthesis are needed.
EXAMPLES at 6:12 8:51 11:11 12:05 12:43 14:11 16:06 17:00 18:57 Application word problems at 20:46 25:08 26:16 29:30

PS. When I say that six feet tall is 62 inches...that would be 72 inches of course!!!

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Variables Defined & Writing Algebraic Expressions

If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob   I work through 6 EXAMPLES at 4:36 9:56 16:25 23:35 29:55 37:42 to try and help you understand how to convert word problems that you may see at the beginning of your Algebra 1 studies into equations.  NOTE: There is an annotation correction at 28:50 which you will not see without FLASH.  If you do not have FLASH you can watch this video to see the correction.     • Translating Problems into Equations 6...  

If you need help solving linear equations, please check out these lessons 
http://www.profrobbob.com/algebra/linear-functions-solving Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Translating Word Problems into Equations 6 Examples

If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  
 I work through 6 d=rt application problems.
Traveling in same direction.  How long for one person to catch another. 0:06
    In this first example at 9:30 I say that the time of 1 hour 15 minutes was Mary's travel time, but it was in fact Tom's travel time.  There is an annotation correction because I misspoke at the end of the first example.  t was defined at the beginning of the problem as Tom's travel time, I should have written that down.  So when I said "That is how long it is going to take Mary to catch up."... that is incorrect.  Tom was traveling that long so the time would be 2:45 when she caught up.  Sorry for misspeaking in the lesson:(
Traveling in opposite directions.  How fast is each person traveling 10:53
Two people sharing driving duties on a trip.  How long did each drive 20:41
Two people driving different speeds for the same amount of time, how fast did each drive? 27:46
Finding airspeed of a plane with information given about distance, equal times, and head wind and tail wind speed. 35:05
Finding speed driven for each portion of a round trip and average rate (speed) for entire trip 40:52 Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Distance Rate and Time d=rt 6 Examples PLEASE READ DESCRIPTION:)

I work through 5 examples of solving for missing sides of similar polygons.  Similar polygons have linear sides, the corresponding angles are congruent, and the corresponding sides are proportional.  The equal proportions, or constant ratios of the side lengths, are called the Scale Factor.  EXAMPLES at 3:15 6:46 12:17 15:21 17:34 22:24 Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Proportions and Similar Polygons / Similar Figures

I start by reviewing the Order of Operations (PEMDAS) and then work through 3 Arithmetic examples at 7:44 9:06 10:33 , 4 examples of Evaluating Algebraic Expressions 15:56 19:22  20:43 22:20 , 2 Application Examples 24:38 28:10 , and 1 Error Analysis example 32:57.  Another error in the last example is I spelled equivalent as equivalent(which is incorrect).

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Order of Operations Evaluating Algebraic Expressions

I introduce how to Add and Subtract Real Numbers, Adding and Subtracting Fractions, Adding and Subtracting Integers and Define Absolute Value.
Adding Numbers with the Same signs Examples 3:40 5:35 8:41
Adding Numbers with Different signs Examples 14:04 16:40 
Opposite Numbers defined 19:24
Inverse Property of Addition 20:24
Three more Examples involving Opposite Number 22:22 23:21 25:17 Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Adding and Subtracting Fraction Integers Real Numbers

I work through many examples of writing algebraic expressions from word problems.

A huge thank you to my friend Jigyasa for Close Captioning this lesson:)

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Writing Algebraic Expressions from Word Problems

I define and discuss Real Numbers their subsets of Rational Numbers, Integers, Whole Numbers, Natural Numbers, and finally Irrational Numbers.  I finish with Inequalities and the Number line at 23:53 Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Classification of Real Numbers, Inequalities, and Number Line

Identify Independent and Dependent variables at 2:22
Building a table of values to help develop the formula at 6:55
Graphing the Linear Function at 11:17  (If domain is restricted to Whole numbers the graph is just the disconnected points.)
How do we know a Linear Model is a good choice at 15:45
Applying the Linear Function to answer specific questions at 20:32 (Solving a two step equation and two step inequality)
Interpreting the slope, y-intercept, and x-intercept at 27:04
Use of TI-NSPIRE to find the intersection of 2 graphs at 31:54


Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/

Modeling Word Problems with Linear Functions Part 1

I introduce Direct Variation.  I then work through many examples of recognizing it with t tables, graphs, and equations.  I finish this video by working through three more examples of solving problems that involve direct variation. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Direct Variation

If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob   I work through 3 examples dealing with Percent of Increase or Percent of Decrease.  These types of problems are also called Percent of Change.
Example 1:  Applying a Percent of Discount and then adding the Percent of Tax at 1:56
Example 2: Calculating the Percent of Profit at 11:57
Example 3: Given the Percent of Change and Final Value, find the Original Value at 20:44 Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Percent of Change Increase and Decrease 3 Examples

If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob   Multiplying Numbers with the same sign: 0:58 2:48 8:22
Multiplying Numbers with different signs: 3:14 5:08
Simplifying Square Roots (3 Examples): 15:26
Dividing Real Numbers with the same & different signs 26:57
Dividing with Zero 31:12
Inverse Property of Multiplication (example includes mixed fractions) 31:36
Three more examples 35:51 37:56 40:47

Many examples involve fractions including improper fractions and mixed fractions. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Multiplying & Dividing Real Numbers and Fractions

Determining what will be the independent variable and dependent variable at 3:25
Determining a Linear Model will be appropriate given a table of values by calculating slope between multiple points at 7:03
Interpreting the slope at 10:47
Writing the equation of the line using a point and a slope at 17:07
Interpreting the y-intercept 22:36
Graphing the Linear Function at 24:16
Using the Linear Function to answer a question at 27:35

Modeling Real World Problems Linear Functions Part 1
   • Modeling Word Problems with Linear Fu...  
Regression Lines and Correlation with TI-84
   • Regression Lines and Correlation with...  
Scatter Plot, Linear Reg, Correlation & Residuals with TI-NSPIRE 
   • Scatter Plot, Linear Reg, Correlation...  

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/

Modeling Real World Problems Linear Functions Part 2

In this lesson I define Quadratic Functions in the form of y=ax^2+bx+c, identify the vertex, and graph a parabola using a t-table.  I also discuss the definition of a Polynomial and Degree.  We then identify Increasing and Decreasing Intervals, Domain and Range, End Behavior, and Absolute Maximum and Absolute Minimum 

Graphing a Parabola with a t-table at 14:40
Identifying Graphical Attributes at 24:56

Some of my other lessons involving Parabolas
Graphing Parabolas in Standard Form
   • Graphing Parabolas in Standard Form  
Graphing Parabolas w/ Vertex & Intercepts
   • Graphing Parabolas w/ vertex & interc...  
Parabola Applications Maximizing Minimizing Reflectors, etc 
   • Parabola Applications Maximizing Mini...  
Applications of Parabolas in Standard Form 
   • Applications of Parabolas in Standard...  
Optimization Calculus Problems Minimizing Lengths 
   • Optimization Calculus Problems Minimi...  

Negative Exponents and Power of Zero 
   • Negative Exponents and Power of Zero  

Check out www.ProfRobBob.com, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/

Defining Quadratic Functions & their Graphical Attributes

I define square roots and then work through examples.
Arithmetic Examples 7:32
Application Problem 1 15:12
Application Problem 2 24:10 Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Square Roots Defined and Examples

Sketching linear absolute value function using transformations and identifying domain and range examples at 11:07 15:00 18:00 23:20
Example highlighting difference between vertical stretch/compression and horizontal stretch/compression at 28:38  Thank you Rishana for letting me know that my segmented graph for example 5 is a relation and not a function.  I make silly mistakes like that even in my class sometimes.  My live students catch those immediately and help me out:)
Writing a function from a parent function given the transformations at 35:08
Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Graphing Absolute Value Functions with Transformations 6 Examples

If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob   I introduce the Distributive Property and then work through six EXAMPLES at 4:22 6:45 9:06 14:53 21:33 30:15  At 0:51 I call the variable "a" a term in the expression a(b+c), but it is factor.  Sorry about the error. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Distributive Property 6 Examples Algebra: Please read description

I take a system of linear equations and show you how to solve it with substition and then with linear combination.  I show how you could find one answer, no answer, or many answers.

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Solving Linear Systems with Substitution and Linear Combination (Simultaneous Equations)

I work through many examples of solving absolute value equations and inequalities. 
Example 1 and 2 at 2:32 7:28
Example 3 and 5 with coefficients and additions outside of absolute value 13:04 21:52
Example 4 variables on both sides 15:42



 "Separate" is misspelled on the initial chalk board, twice, sorry for the misspelling. 
If you have an equation or inequality with multiple absolute value functions check out this video    • 動画  

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Absolute Value Equations & Inequalities and the Number Line

I start by defining Compound Inequalities & explaining the difference between "and"  and "or" statements
Inequality to Number Line examples at 2:03 7:01 8:44
Number Line to Inequality examples at 11:01 14:19 16:55  These examples include Interval Notation.
Solving a Compound Inequality example "AND" statement at 19:19
Solving a Compound Inequality example "OR" statement at 24:48
Solving a Compound Inequality word problem at 33:41
Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Compound Inequalities 9 Examples including Fractions & Interval Notation

In this Algebra lesson I beginning reviewing how to graph inequalities on a number line.  I then work through 5 examples.
Example 1-3: Setting up single variable inequalities and graph them on a number line at 4:07 9:50 15:01
Example 4: Setting up and solving a multiple step inequality at 16:07
Example 5: Setting up and solving a more difficult multiple step inequality at 21:31
Modeling Word Problems with Linear Functions Part 1 
   • Modeling Word Problems with Linear Fu...  
Modeling Real World Problems Linear Functions Part 2 
   • Modeling Real World Problems Linear F...  
Translating Word Problems into Equations 6 Examples 
   • Translating Problems into Equations 6...  
Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class.

T-Shirt from www.SnorgTees.com Find free review test, useful notes and more at http://www.mathplane.com/
If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Solving Linear Inequality Word Problems

What is the Absolute Value at 1:09
Defining Linear Absolute Value Function at 7:14
Graphing a Linear Absolute Value Function with a T-table at 14:42
Identifying the Graphical Attributes at 22:01
     (Intervals of Increasing and Decreasing, Absolute Maximum or Minimum, Domain, Range)
Last Example at 29:04

Defining Quadratic Functions & their Graphical Attributes 
   • Defining Quadratic Functions & their ...  

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/

Linear Absolute Value Functions & Graphical Attributes

I define and discuss the following vocabulary:
Functions and the Vertical Line Test at 3:00
Relations at 8:01
Discrete Graphs at 11:35
Continuous Graphs at 13:20
Vertical and Horizontal Line of Symmetry at 14:38
Smooth Curves at 17:22
Increasing Function and Decreasing Function 21:45
Identifying Domain and Range from a Graph at 27:07

More on Functions vs Relations 

A Calculus lesson on Continuity & Types of Discontinuity 
   • Continuity On an Interval Open & Clos...  

Determining the Domain of a Function from an Equation 
   • Determining Domain of Functions   Find free review test, useful notes and more at http://www.mathplane.com/

Identifying Characteristics of Graphs

I introduce the concepts of Function and Domain.  I compare and contrast them with coordinates, graphs, and equations through many examples.
EXAMPLES at 5:14 11:02 16:05 18:12 21:33 23:05

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Function vs Relation

In this Algebra lesson I explain how to represent real world situations in a graph.
In this lesson I introduce the terms Increasing/Positive Slope/Positive Association that describe a graph when it is rising to the right, the terms constant/Slope of 0/No Association that describe a graph when it is horizontal, and the terms Decreasing/Negative Slope/Negatively Associated that describe a graph when it falls to the right.  I also define Independent Variable and Dependent Variable and explain how you can identify them in a word problem.  

I finish by working through 3 examples.  After reading a real world setting, we identify the Independent and Dependent Variables and then sketch a graph that can represent the given scenario.  EXAMPLES at 14:46 20:11 24:45 Find free review test, useful notes and more at http://www.mathplane.com/

Understanding Graphical Relationships between Variables

I start off by giving the definition of a linear function, slope and y intercept.  
At 6:15 I work through two examples of finding slope from 2 points.  
At 13:05 we look at a real world setting modeled by a linear regression line and interpret the meaning of the slope and the y intercept in this real life application.
At 21:16 I graph the equation from the previous word problem using the slope and y-intercept and with the x-intercept and y-intercept.  We then zoom in to the area of the graph that is appropriate to the word problem.
At 29:16 I discuss the attributes of linear graphs, like how can you identify if they will be increasing or decreasing, if there are any maximum or minimums, and horizontal and vertical lines.

Please check out my other lessons about Linear Functions:
Graphing Lines in Slope-Intercept form y=mx+b
   • Graphing Lines in Slope-Intercept for...  
Graphing lines using X & Y Intercepts
   • Graphing lines using X & Y Intercepts  
Standard Form of a Line
   • Standard Form of a Line  
Slope and Equations of Lines 
   • Rate of Change Slope & Point Slope Eq...  
Equations of Lines and Graphing
   • Equations of Lines and Graphing  
Equations of parallel and perpendicular lines
   • Equations of Parallel and Perpendicul...  
Regression Lines and Correlation with TI-84
   • Regression Lines and Correlation with...  

Check out www.ProfRobBob.com, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/

Linear Functions, their Attributes, & Interpreting Slope and y-Intercept

In this math lesson I define the Union and Intersection of Sets and set up Venn Diagrams to answer these questions.
Examples at 9:40 12:08 25:00
Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Union and Intersections and Venn Diagrams

I introduce the basic Properties of Real Numbers: Commutative Property of Addition and Multiplication, Associative Property of Addition and Multiplication, Identity Property of Multiplication, Identity Property of Addition, Zero Product Property,  and Multiplying by Negative One.  I also discuss how Counter Examples can be used to prove a mathematical statement is false where as we use Deductive Reasoning to prove a mathematics statement is true.

Now Closed Captioned thanks to my wonderful friend Jigyasa Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Properties of Real Numbers

I help you understand how to set up Linear Systems of Equations from word problems.  
First example 3:25
Second example 11:09
Third example 18:49
Fourth example 23:31  This is a d=rt system is solve through the Substitution Method
Solving LInear Systems by Graphing 3 Examples
   • Solving Linear Systems by Graphing 3 ...  
Solving Linear Systems by Substitution
   • Solving Linear Systems by Substitutio...  

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Linear Systems from Word Problems 4 Examples

I introduce the concept of Arithmetic Sequences and work through some examples.

For all my lessons so far on Sequences and Series go here:)
http://www.profrobbob.com/pre-calculus/intro-to-sequences-arithmetic-geometric

Check out http://www.ProfRobBob.com/, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Arithmetic Sequence Introduction

I define Function Notation and then work through 3 examples.
Example 1 is a word problem where we write a function that models the real world setting and then use it to evaluate a total cost at 6:55
Example 2 and Example 3 are substituting either a value or an expression into a function an then simplifying to a final answer at 16:37 and 23:07

More about Functions vs Relations at    • Function vs Relation  

More about graphing lines in the form of y=mx+b at    • Graphing Lines in Slope-Intercept for...   Find free review test, useful notes and more at http://www.mathplane.com/

Understanding Function Notation f(x)

Introduction to finding slope and graphing lines.

Please check out my other lessons about Linear Functions:
Graphing Lines in Slope-Intercept form y=mx+b
   • Graphing Lines in Slope-Intercept for...  
Graphing lines using X & Y Intercepts
   • Graphing lines using X & Y Intercepts  
Standard Form of a Line
   • Standard Form of a Line  
Equations of Lines and Graphing
   • Equations of Lines and Graphing  
Equations of parallel and perpendicular lines
   • Equations of Parallel and Perpendicul...  
Regression Lines and Correlation with TI-84
   • Regression Lines and Correlation with...  
Linear Functions, their Attributes, & Interpreting Slope and y-Intercept 
   • Linear Functions, their Attributes, &...  

Check out www.ProfRobBob.com, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  

Rate of Change Slope & Point Slope Equation of Lines

I introduce how to graph a line in slope intercept form.  I also discuss graphing vertical and horizontal lines.

Please check out my other lessons about Linear Functions:
Solving Linear Systems by Graphing 3 Examples
   • Solving Linear Systems by Graphing 3 ...  
Standard Form of a Line
   • Standard Form of a Line  
Graphing Lines with x-Intercepts and y-Intercepts
   • Graphing lines using X & Y Intercepts  
Slope and Equations of Lines 
   • Rate of Change Slope & Point Slope Eq...  
Equations of Lines and Graphing
   • Equations of Lines and Graphing  
Equations of parallel and perpendicular lines
   • Equations of Parallel and Perpendicul...  
Linear Functions, their Attributes, & Interpreting Slope and y-Intercept 
   • Linear Functions, their Attributes, &...  


Check out www.ProfRobBob.com, there you will find my lessons organized by class/subject and then by topics within each class.

Thank you Pigere Nicolas for the French Closed Captions.  BAM!!! Find free review test, useful notes and more at http://www.mathplane.com/ If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage    / profrobbob  