In this interactive game, Ms. Information is traveling the country trying to re-write history with her false information! Can you stop her? She has traveled to the Washington Monument in Washington, D.C. to change the story of George Washington's life. Use your knowledge of our first president to foil her plan once and for all!
This is a Jeopardy-style game on the American Revolution. It's super fun for classrooms, individuals, or small teams, and is totally customizable. Uncheck "teams take turns" to make it more exciting for kids.
This is a Jeopardy-style game on United States Founding Fathers. It's super fun for classrooms, individuals, or small teams, and is totally customizable. Uncheck "teams take turns" to make it more exciting for kids.
In this lesson, students will design an experiment to see if temperature affects the amount of dissolving of the sugar coating of an M&M.
Students will be able to identify and control variables to design an experiment to see whether the temperature of a solvent affects the speed at which a solute dissolves. Students will be able to explain, on the molecular level, why increasing temperature increases the rate of dissolving.
In this lesson, students will place isopropyl alcohol, mineral oil, and corn syrup in water to see if any of these liquids dissolve in water. Students will extend their understanding and definition of “dissolving” and see that certain, but not all, liquids can dissolve in water.
Students will identify and control variables to help design a solubility test for different liquids in water. Students will be able to explain, on the molecular level, why certain liquids, but not all, will dissolve in water. They will also be able to explain that the solubility of a liquid is a characteristic property of that liquid.
In this lesson, students will observe the dissolved carbon dioxide (CO₂) in a bottle of club soda. They will help design an experiment to compare the amount of CO₂ that stays in cold club soda compared to warmer club soda.
Students will be able to explain, on the molecular level, how a gas dissolves in water. They will also be able to explain why the gas comes out of the solution faster in warm water than in cold water.
In this lesson, students will feel the temperature change that occurs when a cold pack and a hot pack are activated. They will see that these temperature changes are due to a solid substance dissolving in water. Students will then compare the temperature changes that occur as four different solutes dissolve in water and classify these as either endothermic or exothermic. Students will be introduced to the concept that it takes energy to break bonds and energy is released when bonds are formed during the process of dissolving.
Students will be able to identify variables in an experiment to find out how much the temperature increases or decreases as each of the four solutes dissolves in water. Students will be able to correctly classify the process of dissolving as either exothermic or endothermic for each solute. Students will be able to explain that the temperature changes in dissolving are a result of the amount of energy released compared to the amount of energy used as “bonds” are formed and broken.
This informational material will introduce students to the concept of limits, including end behavior, asymptotes, and limit notation. When learning about the end behavior of a rational function, students described the function as either having a horizontal asymptote at zero or another number or going to infinity. Limit notation is a way of describing this end behavior mathematically. There is a corresponding video available. Practice questions with a PDF answer key are provided.
This online interactive will challenge students' knowledge of limits of functions using the following scenario:
You and your friend want to understand what the definition of a limit means. Here is an informal definition of a limit.
Notation and Informal Definition of a Limit of a Function
lim f(x) = L
x→a
means that as x approaches (or gets very close to) a, the function f(x) gets very close to the value L.
This video from Khan Academy on the CK-12 website will introduce students to the concept of limits by using two different functions as examples to demonstrate how to find the limits of a function.
This self-checking online assessment has 10 questions that will help students practice the skill of identifying limits of functions. There are hints available on the screen, and there is an online scratchpad that students can use to work the problems.
Humans thrive and survive within a narrow range of air pressures. When air pressures are out of this range, we have more physical problems. What happens when humans go into space? How have engineers made it possible to survive when air pressure approaches zero?
This informational material will relate the precalculus concept of limits of functions using a real-world issue--engineering astronaut spacesuits. There are embedded videos within the text.
In a previous read, students have learned what a limit is and how it is used to describe certain properties about functions. This interactive will challenge students to evaluate the limits of the function f(x) graphically.
In this interactive, the function f(x) will be represented by the green function.
Students will:
This self-checking online assessment has 10 questions that will help students practice evaluating limits using graphs of functions. There are hints available on the screen, and there is an online scratchpad that students can use to work the problems.
Finding limits for the vast majority of points for a given function is as simple as substituting the number that x approaches into the function. Since this turns evaluating limits into an algebra-level substitution, most questions involving limits focus on the cases where substituting does not work. How can you decide if substitution is an appropriate analytical tool for finding a limit?
This informational material will explain how to find a limit of a function using algebraic substitution and when this method is appropriate. There is a corresponding video available. Practice questions with a PDF answer key are provided.
This self-checking online assessment has 10 questions that will help students evaluate the limits of functions using algebraic substitution. There are hints available on the screen, and there is an online scratchpad that students can use to work the problems.
They're an important part of the ecosystem. They prevent disease and clean up carrion. Yet, they're also a nuisance to homeowners and a threat to livestock. Their population has recovered and grows at an incredible rate. At what point can we say that there are too many black vultures in America?
This informational material will apply a precalculus concept--limits of functions--to an environmental science issue--how biological and physical changes within an ecosystem can affect the population growth of a species. There are additional links provided for students to explore more about this issue.
Most functions continue beyond the viewing window in our calculator or computer. People often draw an arrow next to a dotted line to indicate the pattern specifically. How can you recognize these asymptotes?
This informational material will introduce students to the concept of vertical and horizontal asymptotes and explain how to identify asymptotes and the end behavior of functions from graphical representations. There is a corresponding video available. Practice questions with a PDF answer key are provided.
In this interactive lesson, students will explore how asymptotes appear on the graphs of functions. Students will move the red lines to lie on the vertical and horizontal asymptotes of the function.
This self-checking online assessment has 10 questions that will help students practice identifying the vertical and horizontal asymptotes of functions and identifying limits of functions. There are hints available on the screen, and there is an online scratchpad that students can use to work the problems.
Science fiction movies take it for granted that someday humans, or an alien race, will travel faster than the speed of light and build an intergalactic empire. Scientists aren't so sure that this is possible. It turns out that approaching the speed of light is very difficult. If Einstein's theories are correct, nothing that has mass can travel at the speed of light.
This informational material will apply a precalculus concept--limits of functions at infinity--to a well-known scientific theory--Einstein's theory of relativity. There is a video and links to additional information included.
This informational material will explain how to find all zeroes of a polynomial equation, including complex solutions. It will also introduce the concept of imaginary solutions. There is a corresponding video available. Practice questions with a PDF answer key are provided.
The Fundamental Theorem of Algebra tells us that any polynomial of degree n has n roots. At first, this may seem like a very convenient theorem but wait, what about counterexamples!? The function f(x) = x² + 1 clearly has no roots along the x-axis and we are told to believe that this function has 2. Does this mean that the Fundamental Theorem of Algebra is false?
In the interactive, students will:
This self-checking online assessment has 10 questions that will help students analyze polynomial functions to find possible zeroes. There are hints available on the screen, and there is an online scratchpad that students can use to work the problems.
The Story Map interactive includes a set of graphic organizers designed to assist teachers and students in prewriting and post-reading activities. The organizers are intended to focus on the key elements of character, setting, conflict, and resolution development. Students can develop multiple characters, for example, in preparation for writing their own fiction, or they may reflect on and further develop characters from stories they have read. After completing individual sections or the entire organizer, students have the ability to print out their final versions for feedback and assessment. The versatility of this tool allows it to be used in multiple contexts.
This free, interactive website helps middle and high school-aged students explore the effects of the Tennessee Valley Authority during the Great Depression and New Deal Era. The website includes videos, photographs, handouts, primary resources, and more.
This lesson provides information on the impact that the Tennessee Valley Authority had on the Tennessee Valley region during the Great Depression. Lesson plans are provided on the website including introductory activities and extension activities. Lesson plan powerpoints are also available. Full-length videos are provided on the website with video response questions as well as interactive graphics for student use.
This informational material will explain average and instantaneous rates of change by using the average velocity and velocity at a point using the slope of tangents. The article includes many examples of graphs related to this concept. There are corresponding videos available. Practice questions with a PDF answer key are provided.
Students will test their knowledge of average and instantaneous rates of change represented graphically with the following scenario:
Here you are given two points, C and D, which are located along the function f(x) = x2. If you draw a line crossing those two points, you will create a secant line. Now suppose you take point D and move it closer and closer to point C. What happens to the average rate of change as the two points get closer to each other?
In the interactive, students will:
In 1979 China introduced its one-child policy. Communist leaders hoped to raise the average annual income to $1000 a person. They felt that the rising population was holding back China's economy. Today, China's rate of population growth has slowed and its economy has soared. Did the one-child policy cause the change?
This informational material will apply a precalculus concept--the rate of change of a function--to a current issue in sociology--patterns of population change. There are links to additional information included.
This self-checking online assessment has 10 questions that will help students practice calculating and interpreting the average rate of change of a function. There are hints available on the screen, and there is an online scratchpad that students can use to work the problems.
Suppose you absolutely needed to know the value of the square root of 19 but all you had was pencil and paper, no calculator. Could you calculate it? With your current understanding of the derivative as the slope of a tangent line, you should be able to. Try computing √19 without a calculator; then compare your result with this concept's method of linearization and a calculator.
This informational material will explain how to create a linear representation of non-linear data, using technology and by-hand calculations. There is a corresponding video available. Practice questions with a PDF answer key are provided.
This video will explain the process of linearization and linear approximations. It will demonstrate how to create a linear representation of non-linear data.
How do pilots fly a plane when the autopilot isn't working? How do they quickly make the calculations necessary to stay on course and arrive safely at their destinations? By using linearization, a pilot turns a difficult calculation into a simple one and corrects his flight path.
This informational material will apply a mathematical modeling concept--linearization of a non-linear function--to the real-world problem of pilots creating flight paths. There is a video and links to additional information included.
This informational material will explain how to describe the relationship between two variables as either concavity or inflection using functions and graphical representations:
There is a corresponding video available. Practice questions with a PDF answer key are provided.
This video will explain how to solve functions to determine if the relationship between the variables shows concavity or inflection.
