Scholars model the height of water in a container with an exponential function and apply average rates of change to this function. The main attraction of the lesson is the discovery of Euler's number. 

Find the how long it has been raining based upon the amount of rainfall. Scholars analyze a table of the amount of rainfall as a function of time. Pupils first determine whether the function is invertible, then they find and interpret...

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...

Don't lose the chance to use the task. Given three diagrams of curved pieces of wires, young mathematicians must explain whether it's possible to conclusively match the wires as representing cubic, exponential, or quadratic functions....

In this graphing quadratic equations worksheet, students find the vertex and graph the parabola for 24 quadratic equations. The final four are factored into binomials to increase accuracy of the x intercepts.

Build on pupils' understanding of inverse functions by connecting logarithmic functions to exponential functions. This activity allows individuals to see graphically the inverse relationship between an exponential and logarithmic...

Work out to Algebra II with the 50-question worksheet that practices different types of functions. Multiple choice questions focus on topics such as rational, radical, and logarithmic functions. The resource comes with a printed answer...

Use a triangle area formula that works when the height is unknown. The eighth installment in a 16-part series on trigonometry revisits the trigonometric triangle area formula that previously was shown to work with the acute triangles....

Explore linear functions! In this Algebra I lesson, mathematicians graph data in a scatter plot and use a graphing calculator to find a linear regression and/or a median-median line. They use the model to make predictions.

Challenge scholars to show what they know about properties and addition and subtraction formulas for trigonometric functions. The resource provides a mid-unit check on the progress toward mastery of trigonometric concepts. The areas...

Challenge your scholars to show what they know about the Law of Sines, Law of Cosines, and inverses. The six-question assessment is the last in a series of 16. Pupils find the area of triangles and show that the Law of Sines and Law of...

Grab the wheel in learning about functions. A short performance task challenges young mathematicians to develop a function that describes the cars eight people drive. They consider whether the inverse of the function exists. If not, they...

In this algebra worksheet, students validate continuity of a graph by a defined interval as well as determine continuity of a piecewise function.

Turn your first graders into adding machines! This is a fun way to practice single-digit addition, and scholars complete 25 equations. Each machine has a function; five numbers go into the machine, are added to, and emerge on the other...

Viruses can spread like wildfire, and mathematics can model the speed of infection. Given a function, scholars analyze it to describe the spread of a disease within a stadium. Learners find the initial number infected and the maximum...

Learners investigate average rates of change for linear functions and connect the concept to slope. They then determine average rates of change in quadratic and exponential functions.

Determine the location of a point on a moving wheel. The task challenges groups to determine the horizontal and vertical locations of a point on the edge of wheel that is moving. Teams first determine a function that will model the...

It's time to check the mail! The task is to determine the most cost-effective way to mail a packet of information. Young scholars write an equation that models the amount of postage as a function of the number of sheets mailed and...

What will that cost in the future? The scenario provides pupils with a growth as a Consumer Price Index. Learners create functions for a given item to determine future prices and graph them. Class members then compare their functions to...

Many organizations put on barbecues in order to make money. In a real-world math problem, the money allotted to purchase steak and chicken at this barbecue is only one hundred dollars. It is up to your potential chefs to figure out how...

Here's a resource that models rising water levels with a linear function. The task contains three parts about the level of water in a cylinder in relationship to the number of golf balls placed in it. Class members analyze the data and...

Scholars crave practical application. Let them use the different models of a quadratic function to plan the size and shape of a school playground. They convert between the different forms and maximize area.

It's a sign! Scholars analyze sine functions for patterns in their periods. The exploration advances beyond a simple function to the combination of two functions with even and odd coefficients. Their goal is to find a pattern between the...

Compose yourself! Learners first use given graphs of functions f and g to graph the composition function f(g(x)) and identify its value for a specific input. They then consider functions for which f(g(x)) = g(f(x)).