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...

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...

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...

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...

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. 

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...

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,...

It's time to show what they know! An assessment review concludes a five-part series about linear functions. It covers all concepts featured throughout the unit, including linear equations, graphs, tables, and problem solving.

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...

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...

There's no sorting hat here. A high school assessment task prompts learners to analyze different types of functions. They investigate graphs, equations, tables, and verbal rules for four different functions.

Let the graph tell the story! Adding context to graphs allows learners to analyze the key features of the function. They make conclusions about the situation based on the areas the graph is increasing, decreasing, or has a maximum...

I like algebra, but graphing is where I draw the line! Worksheet includes three multiple-part questions on interpreting and drawing line graphs. It focuses on the abstract where neither axis has numbers written in, though both are...

For this Algebra II worksheet, 11th graders solve nonlinear inequalities, graph the solution set on the number line, and write the solution in interval notation.  The one page worksheet contains thirty-eight problems.  Answers...

In this graphing and analyzing worksheet, 9th graders first state if each graph represents a linear or nonlinear relationship. Second, they create a difference table for each set of data presented and determine whether it represents a...

Rewrite a quadratic function to easily see the transformations involved. The instructional task takes a general quadratic function and rewrites it into a form that shows the translations and scaling of the parent quadratic function. The...

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....

How can you tell if number relationships are proportional? Mathematicians investigate proportional relationships. They compare and contrast functions and graphs to determine the characteristics of proportional relationships, as well as...

Determine the slope when the unit rate is difficult to see. The 17th part of a 33-part series presents a situation that calls for a method to calculate the slope for any two points. It provides examples when the slope is hard to...

In this system of equations worksheet, learners solve nonlinear systems of equations using the substitution method. An example of how to solve is given prior to the assignment. Twenty problems are available on this two-page worksheet.

It's all about lines when going around. Pupils graph the relationship between the length of a side of a square and its perimeter. Class members explain the origin in context of the side length and perimeter. They compare the graph to the...

Upper elementary or middle schoolers will explore non-linear functions, graphing, and the curve of best fit through real-life data collection and trial analysis. They explore the concept of half-life and radioactive decay using M&Ms,...