Willow Tree
Linear Relationships
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...
University of Utah
Explore Proportional and Linear Relationships
Progress from proportional relationships to linear functions. Pupils first review concepts of proportionality covered in earlier grades. They then extend these concepts to linear functions, such as determining the slope of a...
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.
Mathematics Vision Project
Linear and Exponential Functions
Provide a continuous progression to linear and exponential functions. Pupils continue to work with the discrete functions known as sequences to the broader linear and exponential functions. The second unit in a series of nine provides...
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.
Teach Engineering
Applications of Linear Functions
It's not so straightforward — lines can model a variety of applications. Pupils experience linear relationships within the context of science, including Hooke's and Ohm's Laws. Class members got a taste of motion and speed from the...
University of Texas
A Library of Parent Functions
Don't think this lesson is for Mom and Dad; parent functions are all for your high schoolers. Flip through a presentation with a focus slide on each type of graph and its characteristics. Some examples are included but the...
Wordpress
Introduction to Exponential Functions
This lesson begins with a review of linear functions and segues nicely over its fifteen examples and problems into a deep study of exponential functions. Linear and exponential growth are compared in an investment task. Data tables are...
West Contra Costa Unified School District
Evaluating Functions Graphically and Algebraically
High schoolers evaluate functions graphically and algebraically. After completing that step, they write a statement describing the input and output.
CK-12 Foundation
Determining the Equation of a Line: Trip Functions
Let the function drive the activity. The interactive displays the odometer on a car for a trip. Pupils determine and interpret the slope of the situation. Then, they find a verbal description of the equation of the function.
West Contra Costa Unified School District
Graphing Family of Functions
Functions have families, too. Learners first graph the parent functions for linear, quadratic, and cubic functions, and then use vertical translations to graph families of functions.
EngageNY
Linear Equations in Two Variables
Create tables of solutions of linear equations. A lesson has pupils determine solutions for two-variable equations using tables. The class members graph the points on a coordinate graph.
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...
Flipped Math
Piecewise Functions
Break it up into pieces to solve the problem. Individuals watch a video on how to graph and determine the equation and values of piecewise functions. Viewers then work several exercises to practice evaluating a piecewise function at...
Rice University
Algebra and Trigonometry
Move on into trigonometry. An informative eBook takes the content of a College Algebra course and adds more relating to trigonometry and trigonometric functions. The content organization allows pupils to build upon their learning by...
University of Utah
Representations of a Line
Line up to learn about lines! Scholars discover how to express patterns as linear functions. The workbook then covers how to graph and write linear equations in slope-intercept form, as well as how to write equations of...
EngageNY
Modeling a Context from a Graph
Collaborative pairs develop functions that model a graph from a context using the modeling cycle. They then analyze their function models in order to answer questions about the scenario.
Benjamin Franklin High School
Saxon Math: Algebra 2 (Section 9)
Section 9 of the 12 linked Saxon Math sections introduces the young algebrist to graphing periodic functions, creating graphs from quadratic roots, working with inequalities, and rational equations. Common among all the lessons is the...
Virginia Department of Education
Transformation Investigation
Graph it! Investigate transformations with a graphing calculator. Pupils graph sets of linear functions on the same set of axes. They determine how changes in the equation of a linear function result in changes in the graph.
Illustrative Mathematics
Distance across the channel
Here you will find a model of a linear relationship between two quantities, the water depth of a channel and the distance across the channel at water level. The cross section of the channel is the shape of an isosceles trapezoid. The...
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,...
Illustrative Mathematics
Building a General Quadratic Function
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...
Virginia Tech
Unit Plan: Exponential and Logarithmic Functions
A six-day unit for algebra II on exponential and logarithmic functions builds upon Chapter 12 of Merrill Algebra II with Trigonometry; Applications and Connections. The text provides assistance in the depth of instruction...
EngageNY
A Critical Look at Proportional Relationships
Use proportions to determine the travel distance in a given amount of time. The 10th installment in a series of 33 uses tables and descriptions to determine a person's constant speed. Using the constant speed, pupils write a linear...