36
Lectures
30
minutes/lecture
1.
An Introduction to the Course
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 operations.
1.
An Introduction to the Course
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19.
Factoring Trinomials
Begin to find solutions for quadratic equations, starting with the FOIL technique in reverse to find the binomial factors of a quadratic trinomial (a binomial expression consists of two terms, a trinomial of three). Professor Sellers explains the tricks of factoring such expressions, which is a process almost like solving a mystery.
19.
Factoring Trinomials
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2.
Order of Operations
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 when you need to simplify algebraic expressions, making it critical to master them now.
2.
Order of Operations
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20.
Quadratic Equations—Factoring
In some circumstances, quadratic expressions are given in a special form that allows them to be factored quickly. Focus on two such forms: perfect square trinomials and differences of two squares. Learning to recognize these cases makes factoring easy.
20.
Quadratic Equations—Factoring
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3.
Percents, Decimals, and Fractions
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.
3.
Percents, Decimals, and Fractions
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21.
Quadratic Equations—The Quadratic Formula
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 to determine if a quadratic equation has no solutions.
21.
Quadratic Equations—The Quadratic Formula
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4.
Variables and Algebraic Expressions
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 language of problems (phrases in English) into the language of math (algebraic expressions).
4.
Variables and Algebraic Expressions
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22.
Quadratic Equations—Completing the Square
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 function is easily sketched.
22.
Quadratic Equations—Completing the Square
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5.
Operations and Expressions
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, making combining them relatively easy.
5.
Operations and Expressions
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23.
Representations of Quadratic Functions
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 upward "cup" or downward in a "cap."
23.
Representations of Quadratic Functions
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6.
Principles of Graphing in 2 Dimensions
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 y axes, and how to graph a linear equation.
6.
Principles of Graphing in 2 Dimensions
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24.
Quadratic Equations in the Real World
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 solution, graphing can often help.
24.
Quadratic Equations in the Real World
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7.
Solving Linear Equations, Part 1
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.
7.
Solving Linear Equations, Part 1
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25.
The Pythagorean Theorem
Because it involves terms raised to the second power, the famous Pythagorean theorem, a2 + b2 = c2, is actually a quadratic equation. Discover how techniques you have previously learned for analyzing quadratic functions can be used for solving problems involving right triangles.
25.
The Pythagorean Theorem
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8.
Solving Linear Equations, Part 2
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 number is a solution.
8.
Solving Linear Equations, Part 2
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26.
Polynomials of Higher Degree
Most of the expressions you've studied in the course so far have been polynomials. Learn what characterizes a polynomial and how to recognize polynomials in both algebraic functions and in graphical form. Professor Sellers defines several terms, including the degree of an equation, the leading coefficient, and the domain.
26.
Polynomials of Higher Degree
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9.
Slope of a Line
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, and undefined slope.
9.
Slope of a Line
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27.
Operations and Polynomials
Much of what you've learned about linear and quadratic expressions applies to adding, subtracting, multiplying, and dividing polynomials. Discover how the FOIL operation can be extended to multiplying large polynomials, and a version of long division works for dividing one polynomial by another.
27.
Operations and Polynomials
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10.
Graphing Linear Equations, Part 1
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 a graph and from a table of pairs of points.
10.
Graphing Linear Equations, Part 1
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28.
Rational Expressions, Part 1
When one polynomial is divided by another, the result is called a rational function because it is the ratio of two polynomials. These functions play an important role in algebra. Learn how to add and subtract rational functions by first finding their common divisor.
28.
Rational Expressions, Part 1
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11.
Graphing Linear Equations, Part 2
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 using the line and the line using the equation
11.
Graphing Linear Equations, Part 2
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29.
Rational Expressions, Part 2
Continuing your exploration of rational expressions, try your hand at multiplying and dividing them. The key to solving these complicated-looking equations is to proceed one step at a time. Close the lesson with a problem that brings together all you've learned about rational functions.
29.
Rational Expressions, Part 2
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12.
Parallel and Perpendicular Lines
Apply what you've discovered about equations of lines to two very special types of lines: parallel and perpendicular. Learn how to tell if lines are parallel or perpendicular from their equations alone, without having to see the lines themselves. Also try your hand at word problems that feature both types of lines.
12.
Parallel and Perpendicular Lines
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30.
Graphing Rational Functions, Part 1
Examine the distinctive graphs formed by rational functions, which may form vertical or horizontal curves that aren't even connected on a graph. Learn to identify the intercepts and the vertical and horizontal asymptotes of these fascinating curves.
30.
Graphing Rational Functions, Part 1
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13.
Solving Word Problems with Linear Equations
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 a linear rate?
13.
Solving Word Problems with Linear Equations
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31.
Graphing Rational Functions, Part 2
Sketch the graphs of several rational functions by first calculating the vertical and horizontal asymptotes, the x and y intercepts, and then plotting several points in the function. In the final exercise, you must simplify the expression in order to extract the needed information.
31.
Graphing Rational Functions, Part 2
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14.
Linear Equations for Real-World Data
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 descend to the ground floor.
14.
Linear Equations for Real-World Data
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32.
Radical Expressions
Anytime you see a root symbol—for example, the symbol for a square root—then you're dealing with what mathematicians call a radical. Learn how to simplify radical expressions and perform operations on them, such as multiplication, division, addition, and subtraction, as well as combinations of these operations.
32.
Radical Expressions
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15.
Systems of Linear Equations, Part 1
When two lines intersect, they form a system of linear equations. Discover two methods for finding a solution to such a system: by graphing and by substitution. Then try out a real-world example, involving a farmer who wants to plant different crops in different proportions.
15.
Systems of Linear Equations, Part 1
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33.
Solving Radical Equations
Discover how to solve equations that contain radical expressions. A key step is isolating the radical term and then squaring both sides. As always, it's important to check the solution by plugging it into the equation to see if it makes sense. This is especially true with radical equations, which can sometimes yield extraneous, or invalid, solutions.
33.
Solving Radical Equations
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16.
Systems of Linear Equations, Part 2
Expand your tools for solving systems of linear equations by exploring the method of solving by elimination. This technique allows you to eliminate one variable by performing addition, subtraction, or multiplication on both sides of an equation, allowing a straightforward solution for the remaining variable.
16.
Systems of Linear Equations, Part 2
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34.
Graphing Radical Functions
In previous lessons, you moved from linear, quadratic, and rational functions to the graphs that display them. Now do the same with radical functions. For these, it's important to pay attention to the domain of the functions to ensure that negative values are not introduced beneath the root symbol.
34.
Graphing Radical Functions
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17.
Linear Inequalities
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 frequently in business applications.
17.
Linear Inequalities
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35.
Sequences and Pattern Recognition, Part 1
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
35.
Sequences and Pattern Recognition, Part 1
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18.
An Introduction to Quadratic Polynomials
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.
18.
An Introduction to Quadratic Polynomials
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36.
Sequences and Pattern Recognition, Part 2
Conclude the course by examining more types of number sequences, discovering how rich and enjoyable the mathematics of pattern recognition can be. As in previous lessons, employ your reasoning skills and growing command of algebra to find order—and beauty—where once all was a confusion of numbers.
36.
Sequences and Pattern Recognition, Part 2
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18
Lectures
30
minutes/lecture
1.
Understanding Your Unique Intelligence
In this introductory lecture, students learn what intelligence is, how it reveals itself in multiple ways (including visual, spatial, interpersonal, and logical intelligence), and several characteristics that all great students share.
1.
Understanding Your Unique Intelligence
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10.
Delivering Dynamic Presentations
Develop an opening hook that takes advantage of a startling image or fact. Organize your speech or presentation the way you would organize a research paper. Make sure to use visual aids sparingly but effectively. These are just three of the many strategies students will find here for delivering dynamic presentations.
10.
Delivering Dynamic Presentations
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2.
Developing Effective Habits in Class
Students explore three keys to success in the classroom: preparing, participating, and taking good notes. How can they make preparing for class quick and simple? How can they participate in class without looking “dorky”? What are the best ways to take notes while still paying attention to what’s going on in class?
2.
Developing Effective Habits in Class
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11.
Taking Control of Tests
In this lecture, students find out what it takes to perform at their best when the stakes are high: taking tests. They’ll learn how to prepare themselves for various types of tests, focus their studying on what they need to know, combat test anxiety, attack tests with a clear strategy, learn from their wrong answers, and more.
11.
Taking Control of Tests
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3.
Working Cooperatively in Groups
Professor Geisen focuses on the techniques of effective group work. Students discover how to structure their group to use everyone’s strengths; how to avoid the dangers of insensitivity by communicating with tact; and how to reach a consensus using a variety of methods, including dot voting and weighted voting.
3.
Working Cooperatively in Groups
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12.
Finding Balance
Students learn the importance of maintaining balance in their lives. Professor Geisen’s pointed advice includes getting more efficient with their time, cutting back on things that prevent them from achieving their goals, and diving deep into a couple of activities they really love to do.
12.
Finding Balance
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4.
Managing Time and Organizing Spaces
By navigating their busy lives more effectively, students can free up more time and space for true learning—and things they really like to do. First, students will bust the myth that multitasking actually works. Then, they’ll develop strategies for planning and prioritizing activities. Finally, they’ll learn some secrets to keeping themselves—and their work—organized.
4.
Managing Time and Organizing Spaces
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13.
Managing Your Child’s Education
The most important teacher in a student’s life: his or her parents. Professor Geisen shows you how to become a true learner, why most learning happens outside the classroom, and how you can adapt to the continually changing landscape of 21st-century education.
13.
Managing Your Child’s Education
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5.
Taking Charge of Homework
Here, Professor Geisen gives students tips for creating the perfect study environment, offers them study techniques that fit with their unique learning style, and demonstrates ways to take truly effective notes.
5.
Taking Charge of Homework
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14.
Understanding How We Learn
Approach learning with wisdom from neuroscience and educational research. How do our brains assimilate information? What can you do when your student is out of his or her comfort zone on an assignment? How can you help your student embrace his or her learning style?
14.
Understanding How We Learn
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6.
Developing a Creative Mind
Students take a closer look at play, risk, trust, and other mind-sets needed for creative thinking, as well as practical techniques for brainstorming, using a different viewpoint, and changing their environment.
6.
Developing a Creative Mind
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15.
Helping with Homework
Discover how to create the perfect mood, space, and time for your student’s academic success; how to help your student with homework—and how much help to give; and what to do when you don’t have the answers.
15.
Helping with Homework
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7.
Thinking Critically
Students turn to the second half of thinking: critical thinking, where they decide what to do with all their ideas. They explore how to evaluate evidence, recognize bias, distance themselves from emotions, use logic and reasoning, and much more.
7.
Thinking Critically
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16.
Working with Teachers
Professor Geisen reveals the two foundations of a solid parent-teacher relationship, offers tips to improve communication, and provides options for effectively handling problems and complaints.
16.
Working with Teachers
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8.
Diving into Research
The ability to research effectively is a huge factor in students' success. Professor Geisen guides them through the process of pre-searching, searching, evaluating, and organizing. They’ll also get tips for working with the wide range of sources available to the 21st-century student.
8.
Diving into Research
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17.
Preparing for College and the Future
How you talk about and expose your student to college makes a huge difference in how he or she approaches this subject. Which post-high-school option is best for your child? What are colleges looking for in applicants? Find the answers to these questions and more.
17.
Preparing for College and the Future
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9.
Writing Well
Whatever kind of learning style students have, all it takes to strengthen and improve their writing is following a series of guidelines and techniques. They’ll discover the secrets to choosing powerful words, building effective paragraphs, organizing entire essays, spending the right amount of time drafting and editing their work, and more.
9.
Writing Well
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18.
Parenting with Balance
Professor Geisen offers you candid advice on being the best parent you can be—all from the perspective of his role as a teacher. You’ll find tips and exercises to ensure that you’re inspiring, not forcing, your child to learn and live a responsible life.
18.
Parenting with Balance
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