Studying function means more than simply learning a formula. Learners must use functions to think through four problems and find solutions. Each task utilizes a different concept from a study of functions. Class members might...

Many phenomena in life are periodic in nature. A task-based lesson asks scholars to explore one of these phenomena. They collect data showing the sunrise time of a specific location over the period of a year. Using the data, they create...

Pupils design a fence for a backyard pool. Scholars develop a fence design based on given constraints, determine the amount of material they need, and calculate the cost of the project. 

Solids come in many shapes and sizes. Using geometry, scholars create two-dimensional cross-sections of various three-dimensional objects. They develop the lesson further by finding the volume of solids. The module then shifts...

Take a similar approach to three dimensions. Pupils develop the relationship between areas of similar objects and see how they relate to the ratio of the sides. Building upon area formulas, small groups put together volume formulas for...

Use right triangles for more than just mathematical problems. The first two lessons of a unit ask pupils determine distances between cities by using the Pythagorean Theorem and a map. To cement understanding, learners use trigonometric...

Have a popping good time. Using probability and statistics skills, learners determine which type of popcorn to buy based on the percentage of kernels popped. After analyzing corn and popcorn sales to make a prediction of future sales,...

Who knew there were pyramids in China? Learners apply surface area and volume formulas to several different real-world situations. They calculate the volume and surface area of an aquarium, an ice cream cone, and Egyptian and Chinese...

Twelfth graders solve problems using differential equations.  In this Calculus lesson, 12th graders analyze data regarding the spread of a flu virus.  Students use the symbolic capacity of the TI-89 to develop a model and...

Take a free look. Released free-response questions from the 2003 AP® Calculus AB exam show how questions cover different topics. Pupils and teachers review the topics of bounded regions, particle movement, rates, relationships between...

Differentiate between models. Pupils watch as the video works through three examples of creating a differential equation to model a situation. Scholars use their knowledge of proportional relationships to set up the equations and to...

Get the most out of released items. Teachers use the included materials to learn about test-takers' performance on released free-response questions. Pupils respond to the questions and compare their responses to sample scored responses...

Take a closer look at the exam. Released items from the 2001 Calculus AB exam allow teachers and pupils to view how the exam presents questions. Scholars use the questions to prepare for the test and compare their responses to the...

Help young mathematicians make cents out of the US currency system with this two-part math activity. Children first learn the names and values for each type of coin, before learning to count and compare the values of coins using the...

In this math worksheet, students answer 6 questions having to do with continuous and differentiable functions, falling bodies, and derivatives.

Using a 2002 California Gray David recall vote as an example, young statisticians  identify sources of bias in samples and find ways of reducing and eliminating sampling bias. They consider ways to select random samples from a...

Providing both review and practice problems, this worksheet prompts students to answer five questions having to do with slope, tangents lines, graphing, the Squeeze Theorem, differentiable functions and derivatives. This activity could...

Investigate the relationship between independent and dependent variables. Individuals begin by identifying independent and dependent variables from different problem situations. Then, using specific guidelines, they create posters...

No need to be exact every time. Pupils watch an engaging video on approximating function values. They see how to write the equation of a tangent line, use it to calculate approximations, and then determine whether it is an overestimate...

So many times the characteristics of triangles are presented as a vocabulary-type of lesson, but in this activity they are key to unraveling a proof. A unique attack on proving that an inscribed angle that subtends a diameter must be a...

Math and science come together in this cross-curricular astronomy lesson plan on planetary motion. Starting off with a hands-on activity that engages the class in exploring the geometry of circles and ellipses, this lesson...

Geometric design makes a fashion statement! Challenge learners to design a hat to fit a Styrofoam model. Specifications are clear and pupils use concepts related to three-dimensional objects including volume of irregular shapes and...

Double the dimensions, quadruple the surface area. Pairs build similar prisms and compare the ratios of their surface areas and volumes to the ratio of the heights. Given two similar cones, partners determine the ratios of the lateral...

Using the common errors and test taker responses, it's easy for teachers to see where to pinpoint instruction throughout the AP Calculus course. Pupils, using the released items, develop an understanding of how future exams assess the...