EngageNY
Comparing Linear Functions and Graphs
How can you compare linear functions? The seventh installment of a 12-part module teaches learners how to compare linear functions whose representations are given in different ways. They use real-world functions and interpret features in...
EngageNY
Linear Functions and Proportionality
Connect linear equations, proportionality, and constant rates of change to linear functions. Young mathematicians learn how linear equations of the form y = mx + b can represent linear functions. They then explore examples of linear...
Charleston School District
Graphs of Linear Functions
What does a slope of 2/3 mean? Develop an understanding of the key features of a linear function. Pupils graph the linear functions and explain the meaning of the slope and intercepts of the graphs.
EngageNY
Graphs of Linear Functions and Rate of Change
Discover an important property of linear functions. Learners use the slope formula to calculate the rates of change of linear functions. They find that linear functions have constant rates of change and use this property to determine if...
Mathematics Vision Project
Module 1: Functions and Their Inverses
Nothing better than the original! Help your class understand the relationship of an inverse function to its original function. Learners study the connection between the original function and its inverse through algebraic properties,...
EngageNY
Graphs of Simple Nonlinear Functions
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.
EngageNY
Graphs of Functions and Equations
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.
Balanced Assessment
Garages and Phones
Examine and compare a linear and step function. The task provides two scenarios, one modeled by a linear function and the other a step function. Pupils create a graph for each and explain how each compares to the other.
Inside Mathematics
Functions
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...
Charleston School District
Tables of Linear Functions
Don't forget the tables! The previous lessons in this five-part series examined the linear equation and graph relationship. The current lesson adds tables to the mix. At completion, individuals should be able to create a table of values,...
EngageNY
Nonlinear Models in a Data Context
How well does your garden grow? Model the growth of dahlias with nonlinear functions. In the lesson plan, scholars build on their understanding of mathematical models with nonlinear models. They look at dahlias growing in compost and...
Mathematics Vision Project
Module 1: Functions and Their Inverses
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...
Charleston School District
Review Unit 4: Linear Functions
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.
Charleston School District
Pre-Test Unit 3: 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...
Concord Consortium
Function Project
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...
Virginia Department of Education
Nonlinear Systems of Equations
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...
CK-12 Foundation
Linear and Non-Linear Function Distinction: Domain and Range of a Function
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.
West Contra Costa Unified School District
Shifting Linear Equations in Function Notation
Time for a shift in thinking! Learners examine translations of linear functions. They use function notation to describe the translation and make connections to the graph.
EngageNY
Wishful Thinking—Does Linearity Hold? (Part 1)
Not all linear functions are linear transformations — show your class the difference. The first lesson in a unit on linear transformations and complex numbers that spans 32 segments introduces the concept of linear transformations and...
Mathematics Vision Project
Features of Functions
What are some basic features of functions? By looking at functions in graphs, tables, and equations, pupils compare them and find similarities and differences in general features. They use attributes such as intervals of...
Curated OER
Parent Functions Review Sheet
No laundry or cooking dinner here: these parent functions are all about math. Every graph you could think of from basic linear functions to the hyperbolic arccotangent function are included. With 40 parent functions, the worksheet...
EngageNY
Comparing Linear and Exponential Models Again
Making connections between a function, table, graph, and context is an essential skill in mathematics. Focused on comparing linear and exponential relationships in all these aspects, this resource equips pupils to recognize and interpret...
EngageNY
Relationships Between Quantities and Reasoning with Equations and Their Graphs
Graphing all kinds of situations in one and two variables is the focus of this detailed unit of daily lessons, teaching notes, and assessments. Learners start with piece-wise functions and work their way through setting up and solving...
Mathematics Vision Project
Connecting Algebra and Geometry
Connect algebra and geometry on the coordinate plane. The eighth unit in a nine-part integrated course has pupils develop the distance formula from the Pythagorean Theorem. Scholars prove geometric theorems using coordinates...