Continue a study of calculus by using a slideshow to introduce the concept of continuity. After defining the term, the presentation provides examples of functions that are discontinuous and introduces different types...

Two for one—create an invertible and non-invertible function from the same data. The task presents a function table with missing outputs for the class to use to create two functions. One of the functions should have an inverse while the...

Going up and down makes a more exciting ride. Pupils recall what they know about continuity and limits of functions. Working in groups, classmates design a skateboard ramp that meets a given set of criteria, using at least three...

Create a shift in TV viewing habits. The interactive presents a cosine model of an individual's TV viewing habits during a year. Class members move the model to reflect given conditions. Finally, they determine key features from the...

The sky's the limit of what you create when combining functions! The module begins with a review of transformations of parent functions and then moves to combining different function types using addition, subtraction, and...

Differentiable or not, that is the question. An informational website gives two theorems on the differentiability of piecewise functions at their endpoints. It goes on to apply the theorems to present two solution methods to a past AP®...

Get the class to take an extreme look at functions. The interactive presents a function on a closed interval with a movable tangent line. Using the given function, pupils determine the extrema, critical points, and points of...

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...

Middle and high schoolers collect and analyze data from four different activities. The activities include information about classmates, tallying colors of cars in a parking lot, stem and leaf plots, and making a histogram from...

Positioned inside the framework of linear and exponential functions, this lesson is more of an investigation into the effects of changing variables and constants inside an expression. The author takes familiar formulas, those for...

Tie up everything in one differentiable bow. Pupils work through 20 problems to review the concepts from the unit. The problems range from finding the average rate of change to finding the derivatives of various functions that require...

Students access how to collect, classify and display data involving statistics. The concepts of quantitative, discrete and continuous data is covered in depth within the lesson. They practice with a scenario of James filled with...

High schoolers concentrate on discrete quantiative data. They are shown that the vertical line diagram as a more appropriate way to present discrete quantiative data then bar charts. Students work as a group to help with the...

Trying to find a linear transformation is like finding a needle in a haystack. The second lesson plan in the series of 32 continues to explore the concept of linearity started in the first lesson plan. The class explores trigonometric,...

Build a patio from toothpicks and marshmallows to analyze functions! Learners look for patterns in the data as they create different size patios. As they discover patterns, they make connections between the different representations of...

Give classes a sneak peek at an upcoming test. Scholars work released items from the AP Calculus AB test to prepare for their own exams. The resource consists of six items, two graphing calculator items, and four non-calculator items....

Build a function to solve problems rooted in archeology. A comprehensive set of five lessons presents problems requiring individuals to use functions. The initial lesson asks learners to find the possible number of dinosaurs from a...

In this algebra worksheet, students solve word problems involving money. They calculate the interest earned over a period of time given the formula. There are 28 questions.

Read between the lines to find a solution. Budding mathematicians analyze a situation to solve a problem. They view a video presentation of the problem, brainstorm important information to gather, and write linear equations to find...

Good things happen when algebra and geometry get together! Continue the exploration of coordinate geometry in the third lesson in the series. Pupils explore linear equations and describe the points of intersection with a given polygon as...

Examine trends in student-to-teacher ratios over time. Building from the first task in the two-part series, classes now explore the pattern of student-to-teacher ratios using a non-linear function. After trying to connect the pattern to...

Develop a graph to represent the distance between two cars. The assessment task presents a scenario in which two cars are traveling at constant speeds with one faster than the other. Pupils develop graphical representations to show the...

Graphs, functions, symbols, and more! Use these strategies to model everything from the flow of a river to the number of cars passing a toll booth. Presented differently but solved similarly, learners consider five different scenarios...

Learners explore patterns involving objects or figures and geometric shapes. They identify the missing shapes in patterns and discuss what would come next in the pattern, analyze patterns using different objects, and complete a...