Functions are special types of relations, but what makes them so special? Pupils use an interactive to slide a vertical line across six different graphs. Ten challenge questions then assess understanding of functions.

How does an input affect an output? Assess your learners' ability to answer this question using this pre-test. Scholars answer questions about the basics of a function. Topics include determining if a table or statement represents a...

Define, explore, compare, and analyze functions with the fourth chapter of a 10-part eighth-grade workbook series. After encountering the definition of a function, pupils begin to explore linear and nonlinear functions. They then...

How do you combine linear and nonlinear functions? You piece them together! The lesson begins by analyzing given linear piecewise functions and then introduces nonlinear parts. Then the process is reversed to create graphs from given...

Sixth graders interpret linear and nonlinear graphs. They create graphs based on a problem set. Next, they represent quantitive relationships on a graph and write a story related to graphing.

Time to show what you know about functions! The review concludes a series of nine lessons on the basics of functions. The problems included are modeled from the previous lessons. Pupils determine if a table represents a function,...

Roller coaster cars traveling along a graph create quite a story! The lesson analyzes both linear and non-linear graphs. Learners determine the intervals that a graph is increasing and/or decreasing and to locate maximum and/or...

How do letters and numbers create a picture? Scholars learn to create input/output tables to graph functions. They graph both linear and nonlinear functions by creating tables and plotting points. 

Explore linear and nonlinear models to help your class build their function skills. In a continuation of the previous activity, learners continue to analyze and sketch functions that model real-world situations. They progress from linear...

Time to move on to nonlinear functions. Scholars create input/output tables and use these to graph simple nonlinear functions. They calculate rates of change to distinguish between linear and nonlinear functions.

Explore nonlinear systems through graphs and algebra. High schoolers begin by examining the different types of quadratic functions and their possible intersections. They then use algebraic methods to solve systems containing various...

How well does your garden grow? Model the growth of dahlias with nonlinear functions. In the lesson, scholars build on their understanding of mathematical models with nonlinear models. They look at dahlias growing in compost 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...

Scatter plots tell a story about the data — you just need to be able to read it! Building from the previous lesson in the series where learners created scatter plots, they now learn how to find associations in those scatter plots....

Introduce your algebra learners to linear and quadratic functions. Learners compare the differences and relate them back to the equations and graphs. Lead your class to discussions on the properties of a function or a constant slope...

Give your class a chance to show how much they've learned in the module with an end-of-module assessment task that covers all topics from the module including linear and non-linear functions and volumes of cones, cylinders, and...

Explore the graphs of functions and equations with a resource that teaches scholars how to graph functions as a set of input-output points. They learn how the graph of a function is the graph of its associated equation.

There's just something special about lines in algebra. Introduce your classes to linear equations by analyzing the linear relationship. Young mathematicians use input/output pairs to determine the slope and the slope-intercept formula to...

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...

Examine trends in student-to-teacher ratios over time. Building from the first task in the two-part series, classes now explore the pattern of student-to-teacher ratios using a non-linear function. After trying to connect the pattern to...

Show learners the power of mathematics as they model real-life designs. Pupils graph a periodic function by comparing the degree of rotation to the height of a ferris wheel. 

A function is like a machine that has an input and an output. Challenge scholars to look at the eight given points and determine the two functions that would fit four of the points each — one is linear and the other non-linear. The...

Your learners can approach this task algebraically, geometrically, or both. They analyze the building of a linear function given two points and expand the concrete approach to the abstract when they are asked to find the general form of...

Model situations with graphs. In the fourth installment of a 16-part module, scholars learn to qualitatively analyze graphs of piecewise linear functions in context. They learn to sketch graphs for different situations.