Undo a function to create a new one. The inverse of a function does just that. An inquiry-based lesson examines the result of reversing the variables of a function, beginning with linear patterns and advancing to quadratic and...

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...

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,...

Going on up—and up and up! An open-ended task asks learners to model the movement of an amusement ride with parametric equations. They then analyze their equations to determine how the shadow of the ride's car moves as it rises at a...

Piece by piece ... dismantling a function can highlight interesting patterns. The task asks learners to slice functions in sections with the same vertical change. They then recreate the graph with these slices positioned horizontally....

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...

Scholars read and interpret a graph relating bacterial growth in a culture over time. They apply knowledge of derivatives, estimation, and graphing to the skill practice questions.

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...

Trigonometry teachers often go off on a tangent, and here's a worksheet that proves it! First, young mathematicians use a formula with tangent to prove a formula correct for area. Then, they draw conclusions about the area of a circle...

Construct yourself a winning geometry unit. A set of lessons introduces geometry scholars to constructions and proofs with compasses and straightedges. It also covers triangle congruence through transformations. This is the second of...

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.

Take a trip back in time to examine angular velocity. Using the revolutions per minute, learners calculate the speed of a point on a 33 record. They compare the speed of a point on the edge of the record to the speed of a point closer to...

Bring some concrete reasoning to the skills of multiplying and combining terms. Using various strategies, the six activities in the module provide practice for the skills of adding, subtracting, multiplying, and diving polynomials. The...

Model a bicycle chain with circles and tangent lines. Given the dimensions of the sprocket wheels, young scholars calculate the length of the chain that surrounds them. A second task has learners write a function for the length of a...

No need to change anything about the resource. The first of eight modules in the MVP Geometry unit focuses on transformations in the coordinate plane. It connects translations, rotations, and reflections to congruence, symmetry, and...

Class members have some catching up to do. Given a linear equation describing the distance of a runner, young mathematicians interpret the equation in terms of the context. They consider a general equation of the same form and describe...

Know thy calculator. Young mathematicians use their calculators to answer a set of questions. They consider how the number of digits the calculator displays affects the answers to calculations. They then find examples of computations...

Strive for gold with an informative resource. A short task challenges learners to investigate the thickness of a box made from a given volume of gold. The box must have specific dimensions, so setting up and solving a literal equation is...

Find the function that fits. Scholars first identify the graph of a function that looks the same after a horizontal translation. They must then find the equation of a function whose graph lies only in two adjacent quadrants.

Writing and sketching functions—what more could you want to do? Learners write and sketch functions that meet certain conditions as they complete a short task. They find a parabola that encompasses three quadrants of the coordinate plane...

One step at a time! A seemingly linear relationship becomes an entirely new type of function. Young scholars build their understanding of step functions by completing a three-stage activity that incorporates multiple representations of...

Controlling the efficiency of a greenhouse is a mathematical task. A collaborative project challenges learners to create an efficiency plan for a closed greenhouse. Using algebraic equations, they consider a set of constraints, design...