# James A. Sellers

### James A. Sellers >

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An Introduction to the Course

Episode 1 of Algebra I

Episode 1 of Algebra I

Professor Sellers introduces the general topics and themes for the course, describing his approach and recommending a strategy for making the best use of the lessons and supplementary workbook. Warm up with some simple problems that demonstrate signed numbers and…

Order of Operations

Episode 2 of Algebra I

Episode 2 of Algebra I

The order in which you do simple operations of arithmetic can make a big difference. Learn how to solve problems that combine adding, subtracting, multiplying, and dividing, as well as raising numbers to various powers. These same concepts also apply…

Percents, Decimals, and Fractions

Episode 3 of Algebra I

Episode 3 of Algebra I

Continue your study of math fundamentals by exploring various procedures for converting between percents, decimals, and fractions. Professor Sellers notes that it helps to see these procedures as ways of presenting the same information in different forms.

Variables and Algebraic Expressions

Episode 4 of Algebra I

Episode 4 of Algebra I

Advance to the next level of problem solving by using variables as the building blocks to create algebraic expressions, which are combinations of mathematical symbols that might include numbers, variables, and operation symbols. Also learn some tricks for translating the…

Operations and Expressions

Episode 5 of Algebra I

Episode 5 of Algebra I

Discover that by following basic rules on how to treat coefficients and exponents, you can reduce very complicated algebraic expressions to much simpler ones. You start by using the commutative property of multiplication to rearrange the terms of an expression,…

Graphing Linear Equations, Part 1

Episode 10 of Algebra I

Episode 10 of Algebra I

Use what you've learned about slope to graph linear equations in the slope-intercept form, y = mx + b, where m is the slope, and b is the y intercept. Experiment with examples in which you calculate the equation from…

Solving Linear Equations, Part 1

Episode 7 of Algebra I

Episode 7 of Algebra I

In this lesson, work through simple one- and two-step linear equations, learning how to isolate the variable by different operations. Professor Sellers also presents a word problem involving a two-step equation and gives tips for how to solve it.

Sequences and Pattern Recognition, Part 1

Episode 35 of Algebra I

Episode 35 of Algebra I

Pattern recognition is an important and fascinating mathematical skill. Investigate two types of number patterns: geometric sequences and arithmetic sequences. Learn how to analyze such patterns and work out a formula that predicts any term in the sequence.

Slope of a Line

Episode 9 of Algebra I

Episode 9 of Algebra I

Explore the concept of slope, which for a given straight line is its rate of change, defined as the rise over run. Learn the formula for calculating slope with coordinates only, and what it means to have a positive, negative,…

Principles of Graphing in 2 Dimensions

Episode 6 of Algebra I

Episode 6 of Algebra I

Using graph paper and pencil, begin your exploration of the coordinate plane, also known as the Cartesian plane. Learn how to plot points in the four quadrants of the plane, how to choose a scale for labeling the x and…

Solving Word Problems with Linear Equations

Episode 13 of Algebra I

Episode 13 of Algebra I

Linear equations reflect the behavior of real-life phenomena. Practice evaluating tables of numbers to determine if they can be represented as linear equations. Conclude with an example about the yearly growth of a tree. Does it increase in size at…

Solving Linear Equations, Part 2

Episode 8 of Algebra I

Episode 8 of Algebra I

Investigating more complicated examples of linear equations, learn that linear equations fall into three categories. First, the equation might have exactly one solution. Second, it might have no solutions at all. Third, it might be an identity, which means every…

Quadratic Equations - Completing the Square

Episode 22 of Algebra I

Episode 22 of Algebra I

After learning the definition of a function, investigate an additional approach to solving quadratic equations: completing the square. This technique is very useful when rewriting the equation of a quadratic function in such a way that the graph of the…

An Introduction to Quadratic Polynomials

Episode 18 of Algebra I

Episode 18 of Algebra I

Transition to a more complex type of algebraic expression, which incorporates squared terms and is therefore known as quadratic. Learn how to use the FOIL method (first, outer, inner, last) to multiply linear terms to get a quadratic expression.

Graphing Linear Equations, Part 2

Episode 11 of Algebra I

Episode 11 of Algebra I

A more versatile approach to writing the equation of a line is the point-slope form, in which only two points are required, and neither needs to intercept the y axis. Work through several examples and become comfortable determining the equation…

Quadratic Equations in the Real World

Episode 24 of Algebra I

Episode 24 of Algebra I

Quadratic functions often arise in real-world settings. Explore a number of problems, including calculating the maximum height of a rocket and determining how long an object dropped from a tree takes to reach the ground. Learn that in finding a…

Linear Equations for Real-World Data

Episode 14 of Algebra I

Episode 14 of Algebra I

Investigating more real-world applications of linear equations, derive the formula for converting degrees Celsius to Fahrenheit; determine the boiling point of water in Denver, Colorado; and calculate the speed of a rising balloon and the time for an elevator to…

Representations of Quadratic Functions

Episode 23 of Algebra I

Episode 23 of Algebra I

Drawing on your experience solving quadratic functions, analyze the parabolic shapes produced by such functions when represented on a graph. Use your algebraic skills to determine the parabola's vertex, its x and y intercepts, and whether it opens in an…

Linear Inequalities

Episode 17 of Algebra I

Episode 17 of Algebra I

Shift gears to consider linear inequalities, which are mathematical expressions featuring a less than sign or a greater than sign instead of an equal sign. Discover that these kinds of problems have some very interesting twists, and they come up…

Quadratic Equations - The Quadratic Formula

Episode 21 of Algebra I

Episode 21 of Algebra I

For those cases that defy simple factoring, the quadratic formula provides a powerful technique for solving quadratic equations. Discover that this formidable-looking expression is not as difficult as it appears and is well worth committing to memory. Also learn how…