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...
CK-12 Foundation
Function Rules for Input-Output Tables: Whats My Rule?
What's the rule that makes it true? A virtual function machine generates output values as learners submit the input values. Their job is to analyze the inputs and outputs for a pattern and write a function rule.
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...
CK-12 Foundation
Input-Output Tables for Function Rules
How does changing a graph affect the function? Learners watch the changing input-output table as they adjust the location of the line graph. Questions prompt them to complete a table of values and determine the function rule.
Education Development Center
Creating a Polynomial Function to Fit a Table
Discover relationships between linear and nonlinear functions. Initially, a set of data seems linear, but upon further exploration, pupils realize the data can model an infinite number of functions. Scholars use multiple representations...
CK-12 Foundation
Function Rules for Input-Output Tables: Function Machine 1
Challenge your classes to find the pattern of a double function machine. After recording the outputs of both machines, learners identify the pattern and the corresponding function. Both patterns involve adding/subtracting a constant.
CK-12 Foundation
Input-Output Tables for Function Rules
Make the abstract a bit more concrete with an interactive that asks learners to slide an input value through a function to determine the output. Changing the slope and y-intercept allows them to see the how the output values change.
Curated OER
Graphs and Functions
Middle schoolers describe plotting functions on the Cartesian coordinate plane. They solve functions on paper and using an online tool to plot points on a Cartesian coordinate plane creating lines and parabolas.
EngageNY
More Examples of Functions
Discrete or not discrete? Individuals learn about the difference between discrete and non-discrete functions in the fourth installment of a 12-part module. They classify some examples of functions as being either discrete or non-discrete.
Curated OER
Introduction to Functions
Students explore functions, function rules, and data tables. They explore terms of linear functions. Students use computers to analyze the functions. Students write short sentences to explain data tables and simple algebraic expressions.
CK-12 Foundation
Function Rules for Input-Output Tables: Soda Sugar Function Table
Examine the relationship between the input and output variables in a table of values. As learners build an input-output table using online manipulatives, they begin to identify patterns. They answer questions about these patterns...
Curated OER
More Complicated Functions: Introduction to Linear Functions
Students explore the concept of linear functions. For this linear functions lesson, students translate linear functions from tables to graphs to equations. Students use an applet to write a function rule for a linear function in...
Mathematics Vision Project
Module 6: Quadratic Functions
Linear, exponential, now it's time for quadratic patterns! Learners build on their skills of modeling patterns by analyzing situations with quadratic functions. The sixth module in the Algebra I series has pupils analyze multiple...
Curated OER
Linear Functions
Students solve and graph linear equations. In this algebra lesson, students collect data and plot it to create a linear function. They identify the domain and range of each line.
College Board
Beginning the Year with Local Linearity
Local linearity isn't the first thing that comes to mind to start off an AP® Calculus course. A scholarly article discusses one possible beginning to the AP® Calculus course: investigating and introducing derivatives through activities...
Curated OER
Properties of Logarithms
Students explore the concept of logarithms. In this logarithms lesson, students discuss the logarithm properties. Students use linear functions as a basis to develop the logarithm properites by substituting log b and log a...
K20 LEARN
Didn’t We Already Learn That Pattern? Functions/Arithmetic Sequences
Just how many toothpicks does the pattern take? After watching a video of someone building a pattern with toothpicks, groups create methods to find the number of toothpicks needed to accomplish that task. Groups either use explicit...
101 Questions
Styrofoam Cups
How many cups does it take to reach the top? Learners attempt to answer this through a series of questions. They collect dimension information and apply it to creating a function. The lesson encourages various solution methods and...
SHS Algebra
Linear vs. Exponential Functions Tasks
Your algebra learners will enjoy the real-life application of the three tasks presented here. They complete a table and a graph comparing the two options presented. One option is linear, while the other is exponential. After coming up...
Mathematics Vision Project
Quadratic Functions
Inquiry-based learning and investigations form the basis of a deep understanding of quadratic functions in a very thorough unit plan. Learners develop recursive and closed methods for representing real-life situations,...
Curated OER
Cramer's Rule ID: 8793
Mathematicians are introduced to Cramer’s Rule and use it to solve three systems that have one solution, no solutions, and an infinite number of solutions. High schoolers use TI-Nspire to graph the systems to verify their answers...
West Contra Costa Unified School District
Writing Exponential Functions Based on Data
Give your class a concrete example of exponential growth and decay using this hands-on activity. These Algebra II lessons allow for the exploration of exponential growth and decay models, as well as the discovery of the patterns of...
EngageNY
Integer Sequences—Should You Believe in Patterns?
Help your class discover possible patterns in a sequence of numbers and then write an equation with a lesson that covers sequence notation and function notation. Graphs are used to represent the number patterns.
Virginia Department of Education
Greetings
Welcome learners to the world of algebra. Use a lesson that poses a situation involving the profit from creating greeting cards to teach about algebra. It requires scholars to use linear functions and inequalities to solve problems.