Time to study the most sensible function — rational functions! The seven-lesson unit develops the concept of a rational function through a connection to rational numbers and fractions. Scholars graph functions, solve equations, and...

It's all about location and size. With the aid of the interactive, pupils explore the relationship between the location and size of a circle and its equation. The learners use that relationship to determine the equation of a circle given...

Explore nonlinear systems through graphs and algebra. High schoolers begin by examining the different types of quadratic functions and their possible intersections. They then use algebraic methods to solve systems containing various...

How many things does one transformation tell you? Learners compare and contrast the graphs of different parent functions with the same transformation. Using a rational and absolute value function, pupils identify key features of their...

If at first you cannot graph, substitute. The lesson introduces the substitution method as a way to solve linear systems if the point of intersection is hard to determine from a graph. The 28th installment of a 33-part series finishes...

Larvae transportation on the New England seamounts is based on the density of the water. Scholars calculate density and graph salinity versus temperature to better understand the distribution of organisms in a water column....

Each form of a linear equation has its purpose — pupils just have to find it. Building on the previous lesson in the series, learners examine point-slope and standard form. Using point-slope form, pupils write the equation of a...

Bar or circle graph—which is best? Given a circle graph and a total amount of money earned, pupils calculate the amount of money in each category. Learners use the calculated amounts to create a bar graph and compare the two displays.

Take the road to a greater knowledge of functions. Young mathematicians graph an absolute value function representing a road connecting several towns. Given a description, they identify the locations of the towns on the graph.

The slope makes a difference. Given an equation of a circle and point, scholars determine the relationship of the slope of a line through the point and the number of intersections with the circle. After graphing the relationship, pupils...

Build conceptual understanding of graphs of quadratic functions with an out-of-this-world resource. An interactive lesson allows learners to manipulate a graph that models the launch of a UFO. The lesson focuses on the key features of...

The road to a greater knowledge of functions lies in the informative resource. Young mathematicians first graph a square root function in a short performance task. They then use given descriptions of towns and the key features of the...

Your knowledge of graphs is a function of how much you try. Young mathematicians work on a set of 12 questions that covers graphing functions, comparing functions, and rewriting functions in different forms to determine key features....

Everything you could possibly want to know about quadratic equations, all in one resource. Instructors demonstrate how to translate between different forms of quadratics (equation, table of values, graph, verbal description) and finding...

An interactive lesson helps individuals learn to graph inequalities in two variables. Scholars can adjust the interactive to present the inequalities in standard or slope-intercept form.

Read between the curves ... quadratic curves! Young scholars analyze the graphs of two quadratic functions by writing their own function whose outputs are between the two given. They then consider intersecting quadratic functions and...

Working with imaginary numbers — this is where it gets complex! After exploring the graph of complex numbers, learners simplify them using addition, subtraction, and multiplication. 

Discover another way to interpret multiplication. Using an interactive, learners slide points (representing the factors of multiplication) along the x-axis of the graph of y = x^2 and observe changes in the line segment connecting the...

We seem to keep missing each other. A short task provides pupils with a quadratic function, as well as a linear function with a missing coefficient. They must determine the value of the coefficient for which the graphs do not intersect.

Vaccinations prevent disease, but do they impact anything else? Some may not realize they also have an economic impact. A set of questions from College Board asks learners to consider what, exactly, that impact is. Other practice prompts...

Keep moving along a curve. Two items in the set of released free-response questions from the 2010 AP® Calculus BC exam involve movement along a graph. One involves particle motion along a polar curve while the other uses a squirrel...

Ninth graders identify and describe the x-intercept as the place where the line crosses the x-axis as it applies to football. They create their own differentiations to reinforce the distinction between the x-intercept and the...

Seventh graders discuss the importance of being able to represent scientific data in the form of graphs. They comprehend the differences between a bar graph and a line graph. Students identify the type of data with which each graph...

In this graphing worksheet, students graph 10 equations using the following methods: slope-intercept form, x- and y-intercepts, or by using a table. Students check their work using a graphing calculator.