Combine simplifying trigonometric expressions with evaluating them! An open-ended question presents a trigonometric expression and numeric values for additional expressions. Learners must determine a value for the original expression by...

Writing a general rule to model a specific pattern is a high-level skill. Your classes practice the important skill as they write rules describing the solutions to a system of equations with variable coefficients. As an added challenge,...

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...

Combine geometry and algebra concepts to solve a modeling problem. Young scholars consider the effect surface area has on volume. They write a cubic function to model the possible volume given a specific surface area and then...

You'd be surprised what you can do with a string! The constraint is the length of string, and the task is to maximize area. Given a series of composite shapes, learners must create a formula for the maximum area for a specified...

And round and round the park we go! Given a description of an amusement park with the locations of three attractions connected by walkways, learners consider what happens when additional attractions join the mix by doubling the length of...

Let the resource take center stage in a lesson on population density. Scholars use provided historical data on the center of the US population to see how it shifted over time. They plot the data on a spreadsheet to look the speed of its...

What do a line and an ellipse have in common? Maybe zero, one, or two points! Learners consider the equation of an ellipse and a line to determine if their graphs have any shared points. They then write a system of equations, including...

Up the difficulty level by solving a system of equations with variable coefficients. Young scholars devise a plan to solve for x and y in terms of a and b. They represent their solutions as expressions and explain their...

Take a dive into a three-dimensional task. Given a specific surface area, individuals must maximize the volume of a cylindrical swimming pool. They combine their understanding of surface area and volume to create a cubic function that...

From linear to quadratic with a simple operation. An exploratory lesson challenges learners to find two linear functions that, when multiplied, produce a given parabola. The task includes the graph of the sum of the functions as well as...

The task is simple, but the solution is a little more complex. Learners must find the smallest number that results in a perfect square when multiplied by two and a perfect cube when multiplied by three. The task requires an analysis...

Are there some rectangles that are more square than others? A thought-provoking task asks individuals to create a formula that objectifies the square-ness of a set of rectangles. They then use their formulas to rank a set of...

How do you graph a sentence? Scholars do just that as they represent relationships between independent and dependent variables with a graphical representation. Given a sentence, they determine the pertinent relationship and create a...

Parent functions and their combinations create unique graphical designs. Learners explore these relationships with a progressive approach. Beginning with linear equations and inequalities and progressing to more complex functions,...

Is the gestation length of an animal a predictor of the average life expectancy of that animal? Learners analyze similar data for more than 50 different animals. They choose a data display and draw conclusions from their graphs.

What if a coordinate plane becomes a slope-intercept plane? What does the graph of a linear function look like? Learners explore these questions by graphing the y-intercept of a linear equation as a function of its slope. The result is a...

Just how durable could a hollow ball bearing be? Learners model the strength of the walls of a ball bearing as a function of the radius of its cavity. They use their models to make reasonable conclusions about the probability of failure...

Mathematicians typically reference eight different types of functions. Scholars learn about the requirements for graphing a function and must decide how many different functions fit. To finish, they define each specific function meeting...

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...

In Utah, one stretch of highway goes for 106 miles without a single gas station. Where should people build one? Scholars face the dilemma of where to place a new gas station between three cities. They consider distance and proximity to...

An English Language Arts Reading Comprehension Practice Test for Grade 10 asks scholars to read a poem and answer two multiple-choice questions about the poem. They finish the task by responding to an open-response essay question. 

Being able to recognize patterns, craft generalizations, and draw conclusions based on information in a text passage are essential critical thinking skills. Encourage learners to hone these skills with a learning exercise that asks them...

Run like a cheetah. A performance task challenges pupils to solve several different problems involving the speed of a cheetah. Given information for scenarios where the cheetah chases its prey, they determine if the big cat is fast enough.