Take a look in the window. Pupils watch a presentation to discover how to graph a polynomial using a graphing calculator and using the window to find the extrema. Scholars use their knowledge from previous lessons to gain a rough idea of...

Pupils rewrite expressions in equivalent forms to identify key features. They use the vertex and factored forms of quadratic expressions to identify the extrema and intercepts. To finish the installment of the Claim 1 Item Slide Show...

Gain an understanding of the test before taking your own. Scholars develop an understanding of how calculus concepts appear on the AP® exam. The six released questions come from across the curriculum and include particle movement and...

Get better prepared. Individuals use the six released AP® Calculus BC free-response questions to practice for the actual exam. The questions contain two calculator items and four non-calculator items. Topics include particle movement,...

Be integral to the learners in the classroom. Pupils use integrals, differentiation, and limits to solve the free-response questions from an AP® Calculus BC exam. Items cover topics such as area under a curve, particle motion, average...

It's time to put analytical applications to work. Learners use the eight questions of the mid-Unit 5 review to refresh their memories of the key points. Pupils apply what they have learned to use the Mean Value Theorem, find extrema...

How do you find the area of an irregular shape? Class members calculate the area of an irregular shape by finding the area of a random sampling of the shape. Individuals then utilize a confidence interval to improve accuracy and use a...

Make the most of your prom—with math! Pupils write and use a quadratic model to determine the optimal price of prom tickets. After determining the costs associated with the event, learners use a graph to analyze the break even point(s).

Instead of the typical function application problems, learners think a little deeper through these ten problems. Multiple types of functions are represented and the questions add a variety of thinking to practice their skills. 

Explore the mathematics of the paper snowflake! During the five lessons progressing in complexity from K through 12, pupils use spatial geometry to make predictions. Scholars consider a folded piece of paper with shapes cut out....

Beginning in 1851, Thoreau recorded the dates of the first spring blooms in Concord, and this data is helping scientists analyze climate change! The culminating instructional activity in the series of four has pupils graph and analyze...

Investigate the attributes of polygons. A thorough set of lessons presents problem scenarios for elementary through high school classes. The first lessons focus on basic characteristics of polygons, including the line of symmetry. As the...

What makes number pairs perfect? The resource provides five problems regarding perfect pairs of numbers, the definition of which changes in complexity with each task. Solutions require pupils to apply number sense and operations, as well...

If cubism were a religion, would you follow it? Lower-level tasks focus primarily on counting the number cubes in a structure and relating the number to surface area. As learners progress to higher-level tasks, isometric drawings and...

Math is all about finding solutions and connections you didn't expect! Young mathematicians often first discover nonlinear patterns when graphing quadratic functions. The lesson begins with the vocabulary of a quadratic graph and uses...

Graph A goes with equation C, but table B. The short assessment task requires class members to match graphs with their corresponding tables, equations, and verbalized rules. Pupils then provide explanations on the process they used to...

In this maximum and minimum of values activity, students solve 4 problems, two of which are word problems, related to determining values of a given variable. First, they find the maximum value of P subject to its constraints. Then,...

Students work collaboratively to create artistic renderings of digital photographs using a color value scale and grid techniques in this late-elementary school lesson based upon Ted Rose's book Discovering Drawing. The lesson includes a...

In this bar graphs worksheet, students read and interpret a bar graph on SAT scores by answering short answer questions. Students complete 7 questions total.

The midline of the mathematical model of the number of hours of sunlight is not 12 hours. Pupils use the modeling cycle to determine a function that will model the number of hours of sunlight at a location of their choosing. Using...

In the United States, most trains operate at a top speed of 100 miles per hour. Scholars use information on the distance and time of a train trip to determine if the train ever reaches a specific speed. They connect pieces of information...

Students are given a trigonometric function. They find the period of f, the maximum and ninimum values of f(x). Students compute the smallest positive value of x and the smallest positive value of x. They sketch the graph of the function.

In this math worksheet, students examine one equation and identify the maximum and minimum value of the equation. Using Excel worksheet, students graph the equation. There is one equation with three parts on this one-page worksheet.

In this graph worksheet, students interpret given line graphs. They determine the range, and identify the range in a set of data. This one-page worksheet contains approximately 14 problems.