It's all in the cards. Using cards to simulate a disease's attack on the immune system, pupils develop an understanding of how the immune system and pathogens react to each other and why at times the pathogen wins. Groups play a game to...

There's value in using a video to analyze a table of values. Pupils learn how to find the limit of a function from a table of values in the fourth of 18 lessons in Unit 1 - Limits and Continuity. An engaging video gives a tutorial on how...

Be instantly transfixed by the idea of instantaneous rates of change. Scholars watch an informative video that introduces the fathers of calculus, Newton and Leibniz. They then learn about instantaneous rates of change by first...

How vulnerable are you to COVID-19? High school mathematicians use the Pandemic Vulnerability Index to create models that help them collect and analyze data about the risk factors associated with COVID-19. After investigating four groups...

Young scientists use exponential growth and logarithms to model how a virus spreads through a population. Pupils watch a news clip about the 2012 outbreak of Ebola. Scholars then manipulate inactive graphs to see how various factors...

Data can tell us a lot about celestial objects that are just too far away to study otherwise. Learners examine data on the brightness of an asteroid to predict its rotation rate. Graphing the data reveals a periodic pattern that allows...

Supernovas burn for a short time but can give scientists extensive information about the universe. Learners analyze given data about the change in the light magnitude of a supernova. They look for patterns in the data and use them to...

Let's see what the class learned! The last installment of the 23-part Pre-calculus module consists of nine assessment questions designed to measure a specific portion of a standard in the unit. Learners demonstrate their understanding of...

Stay composed while solving problems. Learners put their knowledge of compositions to solve problems. To connect with the concept, scholars compose equations to answer questions from real-world situations. Finally, pupils practice using...

Get close to your favorite line. Scholars use end behavior to help find horizontal asymptotes. With the understanding of domains of rational functions, learners find vertical asymptotes and then use graphing calculators to verify the...

Find out when rational expressions are closed. Pupils review adding, subtracting, multiplying, and dividing with rational numbers to make the connections to operations with rational expressions. Using specific examples, learners notice...

Visualize the nth roots of unity. Pupils calculate the nth roots of unity and find all n roots. Learners plot the solutions in the complex plane and observe that they are the vertices of a regular n-gon inscribed in the unit circle....

Obviously, a sturdy bridge is the desired outcome. Pupils select from one of four different types of truss bridges, then construct a model of the bridge from craft sticks and glue, making sure that it satisfies certain constraints. They...

Join together to investigate truss joints. Scholars learn how to analyze forces at truss joints to determine the strength of truss bridges. They apply the "method of joints" in calculating the tension and compression forces at each joint...

Just how old is it? The 22nd portion to a 23-part Precalculus unit uses radiocarbon dating and other exponential modeled real-world problems. Learners use the inverse relationship between logarithms and exponentials to solve the problem...

But what if the function cannot be inverted? Pupils continue to work with inverses of functions using tables, graphs, and algebraic equations. They restrict the domain of non-invertible functions to make them invertible. Using...

Undo the functions. Learners refresh their knowledge of inverses of functions from Algebra II in the 19th section of a 23-part Precalculus unit. Pupils look at inverses in tables and graphs. They then add to their understanding of...

Combine functions for the first time. Pupils investigate composition of functions using a function table and then function machines in the 17th installment in a 23-part Precalculus series. Scholars learn the two notations for composition...

Put everything together in a picture. Scholars take what they learned in the previous three lessons in the 15th segment of a 23-part unit to graph rational functions. They find the end behavior, the horizontal and vertical asymptotes if...

Connect end behavior to previous learning. Pupils connect finding the end behavior of rational functions to finding end behavior of polynomial functions. The 13th segment in a 23-part unit starts with finding the end behavior or power...

Make a connection between rational expressions and rational functions. Pupils review simplifying and performing operations on rational expressions and recall what it means for two rational expressions to be equivalent based on their...

Take a slice out of life. The ninth section in a series of 23 introduces classmates to Cavalieri's principle using cross sections of a cone and stacks of coins. Class members participate in a discussion using pyramids and how Cavalieri's...

Escape to investigate hyperbolas. Pupils take a look at what happens to the elliptical orbital path of a satellite that exceeds escape velocity as the opener to the eighth lesson in a unit of 23. Scholars analyze basic hyperbolas and how...

Move all rational functions—well, maybe. Learners investigate the graphs of the reciprocals of power functions to determine a pattern between the graph and the power. Pupils graph rational functions where transformations are clearly...