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The Angle Game, Angles and Intersecting Lines, Geometry
A motivating activity is coupled with the use of algebra to explore the process of identifying the value of an angle. It feels like magic when Sal shows the solution to the final problem. Also, it would be worthwhile to consider using...
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A Clever Application of the Distributive Property to Solve a Multi-Step Equation
The instructor demonstrates how to use the distributive property to eliminate fractions in an equation. Remember to have learners plug their answers into the original equation to check their work.
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Similar Triangles, Similarity, Geometry
Although a rather complicated topic, this video clearly explains the concept of solving problems involving similar triangles. It employs problem-solving to determine whether two figures are similar triangles. In addition, it provides...
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Recognizing Direct and Inverse Variation
Sometimes, it is not always obvious which equations are direct variations and which are inverse variations. In this video, five different equations are considered. Each is manipulated and rewritten to determine whether there is a direct...
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Quadratic Formula (Proof)
This exciting video removes all of the mystery from the quadratic formula. By watching it, learners gain a deeper understanding of the formula and the process of completing the square. Sal shows step-by-step proof of how to get to the...
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Pythagorean Theorem II, Right Triangles and Trigonometry, Geometry
This lecture, the second in a series on the Pythagorean Theorem, delves into more complex problems. Primarily, it examines the process of finding the value of a hypotenuse. It is beneficial because the example problem is one in which the...
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Proof: A(logB) = log (B^A), log A - log B = log (A/B)
Here are the proofs for two logarithm properties. First, the Power Property of Logarithms is proved using the definition of a logarithm and the rules of exponents, and then the Quotient Property is proved in a similar fashion.
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Writing Equations in All Forms, Algebra I
Given two points on a line, this video shows how to write the linear equation in point-slope, slope-intercept, and standard forms. First, Sal reviews each of these forms, then calculates the slope, writes the equation in point-slope...
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Patterns in Sequences 2
This video again looks at finding the algebraic pattern in sequences. In the example, we are looking at a figure where a number of toothpicks (or lines) are added each time. You need to find how many toothpicks will be in the 50th...
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Part 2 of Proof of Heron's Formula, Perimeter, Area, and Volume, Geometry
Picking up where the prior installment in the series on HeronÕs formula ended, Sal provides a more detailed explanation.
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Part 1 of Proof of Heron's Formula, Perimeter, Area, and Volume, Geometry
This video is the first installment in a series devoted to exploring Heron's Formula. It is a high-level experience that delves into proof using algebra. It demonstrates a step-by-step process for finding the area of a triangle using...
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Parametric Equations 3, Parametric Equations and Polar Coordinates, Precalculus
Following his intuitive manner, Sal considers another set of parametric equations. This time, he looks at two equations using trigonometric functions and, using one of the basic trigonometric identities, removes the parameter from the...
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Parametric Equations 2, Parametric Equations and Polar Coordinates, Precalculus
In this well-presented video, Sal continues with the example of the car driving off the cliff and discusses how the time (t) should be bound based on the context of the problem. He then shows how to rewrite the set of parametric...
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Parametric Equations 1, Parametric Equations and Polar Coordinates, Precalculus
As an introduction to parametric equations, Sal solves the problem of finding the path of a car that drives off a 50-meter-high cliff while traveling five meters per second. He uses a pair of equations: x(t) = 10 + 5t and y(t) = 50 Ð...
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Parabola Focus and Directrix 1
In this video, starting with a point (focus) and a line below the point (directrix), Sal tries to find the set of all points (locus) central to the point and the line. Using the distance formula, he shows that we have a parabola equation.
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Overtaking Word Problem
These types of problems cause many people to be distressed over algebra. In this video, Sal looks at a problem where three people, each at set distances apart, are traveling at different constant speeds. We need to know how long it will...
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More Percent Problems
If Sal has fifty dollars in his pocket and everything at the store is 25% off the marked price, what is the highest marked-price item he can buy? He also demonstrates what would happen if he invested $100 and gained 25% the first year...
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Introduction to the Quadratic Equation, Quadratic Equations, Algebra I
Sal first solves some equations using the factoring method he has already taught. Next, he introduces the quadratic formula and demonstrates how to plug the numbers from the quadratic equation into the quadratic formula. He then solves...
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Introduction to Interest, Interest and Debt, Finance and Capital Markets
Here is a simple tutorial on the difference between simple and compound interest. In it, Sal describes interest and defines the vocabulary of principle and interest rate. He also models the amount of money owed under the different...
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Introduction to Functions
In this introduction to functions video, Sal intuitively defines a function and introduces the function notion f(x). He finishes the video by looking at a simple example of evaluating g(f(x)) without getting into the complexity of...
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Introduction to Conic Sections, Conic Sections, Algebra II
Here, parabolas, circles, ellipses, and hyperbolas are introduced by showing a general graph of each. By showing the intersection of a plane and a cone to create the different conic sections, one can see how these curves are related.
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Constructing and Solving a Two-Step Inequality, Linear Inequalities, Algebra I
This video highlights an interesting problem your pupils will find. Instead of solving an inequality for a value or set of values, this problem requires that the learner construct an inequality and interpret its meaning by abstract...
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Interesting Polynomial Coefficient Problem
This is an interesting problem that approaches higher-degree polynomials from a different perspective. Given a third-degree polynomial, two known zeros, and a y-intercept, find the value of the polynomialÕs coefficients. This problem...
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Constructing and Solving a One-Step Inequality, Linear Inequalities, Algebra I
This inequality word problem would make a good warm-up activity for a class studying single-variable inequalities. This video creates and solves an inequality based on a short-word problem about unit cost.