24
Lectures
30
minutes/lecture
1.
Addition and Subtraction
This introductory lecture starts with Professor Sellers’ overview of the general topics and themes you’ll encounter throughout the course. Then, plunge into an engaging review of the addition and subtraction of whole numbers, complete with several helpful tips designed to help you approach these types of problems with more confidence.
1.
Addition and Subtraction
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13.
Exponents and Order of Operations
Explore a fifth fundamental mathematical operation: exponentiation. First, take a step-by-step look at the order of operations for handling longer calculations that involve multiple tasks—complete with invaluable tips to help you handle them with ease. Then, see where exponentiation fits in this larger process.
13.
Exponents and Order of Operations
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2.
Multiplication
Continue your quick review of basic mathematical operations, this time with a focus on the multiplication of whole numbers. In addition to uncovering the relationship between addition and multiplication, you’ll get plenty of opportunities to strengthen your ability to multiply two 2-digit numbers, two 3-digit numbers, and more.
2.
Multiplication
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14.
Negative and Positive Integers
Improve your confidence in dealing with negative numbers. You’ll learn to use the number line to help visualize these numbers; discover how to rewrite subtraction problems involving negative numbers as addition problems to make them easier; examine the rules involved in multiplying and dividing with them; and much more.
14.
Negative and Positive Integers
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3.
Long Division
Turn now to the opposite of multiplication: division. Learn how to properly set up a long division problem, how to check your answers to make sure they’re correct, how to handle zeroes when they appear in a problem, and what to do when a long division problem ends with a remainder.
3.
Long Division
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15.
Introduction to Square Roots
In this lecture, finally make sense of square roots. Professor Sellers offers examples to help you sidestep issues many students express frustration with, shows you how to simplify radical expressions involving addition and subtraction, and reveals how to find the approximate value of a square root without using a calculator.
15.
Introduction to Square Roots
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4.
Introduction to Fractions
Mathematics is also filled with “parts” of whole numbers, or fractions. In the first of several lectures on fractions, define key terms and focus on powerful techniques for determining if fractions are equivalent, finding out which of two fractions is larger, and reducing fractions to their lowest terms.
4.
Introduction to Fractions
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16.
Negative and Fractional Powers
What happens when you have to raise numbers to a fraction of a power? How about when you have to deal with negative exponents? Or negative fractional exponents? No need to worry —Professor Sellers guides you through this tricky mathematical territory, arming you with invaluable techniques for approaching these scenarios.
16.
Negative and Fractional Powers
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5.
Adding and Subtracting Fractions
Fractions with the same denominator. Fractions with different denominators. Mixed numbers. Here, learn ways to add and subtract them all (and sometimes even in the same problem) and get tips for reducing your answers to their lowest terms. Math with fractions, you’ll discover, doesn’t have to be intimidating—it can even be fun!
5.
Adding and Subtracting Fractions
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17.
Graphing in the Coordinate Plane
Grab some graph paper and learn how to graph objects in the coordinate (or xy) plane. You’ll find out how to plot points, how to determine which quadrant they go in, how to sketch the graph of a line, how to determine a line’s slope, and more.
17.
Graphing in the Coordinate Plane
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6.
Multiplying Fractions
Continue having fun with fractions, this time by mastering how to multiply them and reduce your answer to its lowest term. Professor Sellers shows you how to approach and solve multiplication problems involving fractions (with both similar and different denominators), fractions and whole numbers, and fractions and mixed numbers.
6.
Multiplying Fractions
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18.
Geometry—Triangles and Quadrilaterals
Continue exploring the visual side of mathematics with this look at the basics of two-dimensional geometry. Among the topics you’ll focus on here are the various types of triangles (including scalene and obtuse triangles) and quadrilaterals (such as rectangles and squares), as well as methods for measuring angles, area, and perimeter.
18.
Geometry—Triangles and Quadrilaterals
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7.
Dividing Fractions
Professor Sellers walks you step-by-step through the process for speedily solving division problems involving fractions in this lecture filled with helpful practice problems. You’ll also learn how to better handle calculations involving different notations, fractions, and whole numbers, and even word problems involving the division of fractions.
7.
Dividing Fractions
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19.
Geometry—Polygons and Circles
Gain a greater appreciation for the interaction between arithmetic and geometry. First, learn how to recognize and approach large polygons, including hexagons and decagons. Then, explore the various concepts behind circles (such as radius, diameter, and the always intriguing pi), as well as methods for calculating their circumference, area, and perimeter.
19.
Geometry—Polygons and Circles
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8.
Adding and Subtracting Decimals
What’s 29.42 + 84.67? Or 643 + 82.987? What about 25.7 – 10.483? Problems like these are the focus of this helpful lecture on adding and subtracting decimals. One tip for making these sorts of calculations easier: making sure your decimal points are all lined up vertically.
8.
Adding and Subtracting Decimals
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20.
Number Theory—Prime Numbers and Divisors
Shift gears and demystify number theory, which takes as its focus the study of the properties of whole numbers. Concepts that Professor Sellers discusses and teaches you how to engage with in this insightful lecture include divisors, prime numbers, prime factorizations, greatest common divisors, and factor trees.
20.
Number Theory—Prime Numbers and Divisors
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9.
Multiplying and Dividing Decimals
Investigate the best ways to multiply and divide decimal numbers. You’ll get insights into when and when not to ignore the decimal point in your calculations, how to check your answer to ensure that your result has the correct number of decimal places, and how to express remainders in decimals.
9.
Multiplying and Dividing Decimals
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21.
Number Theory—Divisibility Tricks
In this second lecture on the world of number theory, take a closer look at the relationships between even and odd numbers, as well as the rules of divisibility for particular numbers. By the end, you’ll be surprised that something as intimidating as number theory could be made so accessible.
21.
Number Theory—Divisibility Tricks
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10.
Fractions, Decimals, and Percents
Take a closer look at converting between percents, decimals, and fractions—an area of basic mathematics that many people have a hard time with. After learning the techniques in this lecture and using them on numerous practice problems, you’ll be surprised at how easy this type of conversion is to master.
10.
Fractions, Decimals, and Percents
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22.
Introduction to Statistics
Get a solid introduction to statistics, one of the most useful areas of mathematics. Here, you’ll focus on the four basic “measurements” statisticians use when gleaning meaning from data: mean, media, mode, and range. Also, see these concepts at work in everyday scenarios in which statistics plays a key role.
22.
Introduction to Statistics
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11.
Percent Problems
Use the skills you developed in the last lecture to better approach and solve different kinds of percentage problems you’d most likely encounter in your everyday life. Among these everyday scenarios: calculating the tip at a restaurant and determining how much money you’re saving on a store’s discount.
11.
Percent Problems
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23.
Introduction to Probability
Learn more about probability, a cousin of statistics and another mathematical field that helps us make sense of the seemingly unexplainable nature of the world. You’ll consider basic questions and concepts from probability, drawing on the knowledge and skills of the fundamentals of mathematics you acquired in earlier lectures.
23.
Introduction to Probability
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12.
Ratios and Proportions
How do ratios and proportions work? How can you figure out if a particular problem is merely just a ratio or proportion problem in disguise? What are some pitfalls to watch out for? And how can a better understanding of these subjects help save you money? Find out here.
12.
Ratios and Proportions
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24.
Introduction to Algebra
Professor Sellers reviews the importance of math in daily life and previews the next logical step in your studies: Algebra I (which involves variables). Whether you’re planning to take more Great Courses in mathematics or simply looking to sharpen your mind, you’ll be sent off with new levels of confidence.
24.
Introduction to Algebra
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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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