In this video Paul Andersen explains how density measures the compactness of a material. You can calculate the density of a material by measuring the mass and dividing this by the volume. Water displacement is an effective way to...

In this video Paul Andersen explains how stoichiometry can be used to quantify differences in chemical reactions. The coefficients in a balanced chemical equation express the mole proportions in that reaction. These values can be used...

You’re probably familiar with the basics of magnets already: They have a north pole and a south pole. Two of the same pole will repel each other, while opposites attract. Only certain materials, especially those that contain iron, can be...

In this video Paul Andersen explains how the gravitational field strength is directly related to the mass of the object and indirectly related to the square of the distance from the center of mass. The equation for gravitational field...

What is matter, anyway? What does it have to do with math? And why aren't you made of Jesus? Delving deeper into the theory of (almost) everything - the Standard Model of particle physics.

In this video Paul Andersen explains how modeling instruction can be used in the science classroom. Instead of presenting a model for the students the teacher presents and experience or experiment and the students develop the model.

What is a differential equation, the pendulum equation, and some basic numerical methods

Consider the following sentence: "This statement is false." Is that true? If so, that would make the statement false. But if it's false, then the statement is true. This sentence creates an unsolvable paradox; if it's not true and it's...

The heat equation, as an introductory PDE.

In this video Paul Andersen explains why the slowest elementary step in a chemical reaction is the rate-limiting step. This step can be used to determine the overall rate law of the chemical reaction.

Mr. Andersen explains the concept of momentum. He also shows you how to solve simple momentum problems. He finally shows you how momentum is both conserved and relative.

Mr. Andersen explains the basics of balancing chemical equations. A visual guide shows you how to change coefficients to balance the atoms in reactants and products.

In this math video lesson, we will be finding the x- and y-intercepts of a linear equation written in standard form. The lesson begins by clearly defining each intercept: the x-intercept is the point where the y-value is zero, and the...

In this math video lesson, students learn how to write the equation of a line parallel to a given line when the original equation is written in slope-intercept form and a point on the parallel line is provided. An exemplar solution is...

In this math video lesson, students learn how to write the equation of a line that passes through a given point and is perpendicular to a given line. The visually modeled solution begins with a review of perpendicular lines, emphasizing...

In this math video, viewers are guided step by step through solving a problem where the first four terms of a geometric sequence are given and the goal is to write an equation for the nth term. The exemplar solution begins by introducing...

In this short math lesson, we’ll solve a quadratic equation step-by-step using completing the square. We follow 6 quick steps: 1️⃣ If necessary, “move” c to the right side of the equation. 2️⃣ If necessary, divide all terms by a. 3️⃣...

When I want to trick my students to solve a system of equations like this. Lucky for you there is a quick and easy way to overcome it. In this video I will show you how.

While this may look like two linear equations we are actually working with a linear equation and a reciprocal equation.

In this video we are going to explore a great question that many students struggle with in solving trigonometric equations.

How do you know when simplifying a rational expression if you have a hole or an asymptote? What does it look like algebraically and graphically?

When you need to find the distance between a point and a line there are two ways to look at it. First of all the easy approach is to plug it in to see if the point lies on the line. The second approach is to use a formula

When graphing piecewise functions there are some great tips that I want you to follow. This video will explain all.

Let's tackle how to factor a quadratic like this one. When you have a fraction as the middle term there are some things you need to know.