PBL Pathways
Death Project
Verify the rule of thumb for finding the time of death. The project-based learning task asks pupils to determine when the rule of thumb process of finding the time of death is appropriate. Learners develop a function for the rule and...
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...
Inside Mathematics
Picking Apples
Getting the best pick of the apples depends on where to pick. The short assessment presents a situation in which class members must analyze a real-world situation to determine the cost of picking apples. The pricing structures resemble...
Curated OER
Is There a Limit to Which Side You Can Take?
Calculus young scholars find the limit of piecewise functions at a value. They find the limit of piecewise functions as x approaches a given value. They find the limit of linear, quadratic, exponential, and trigonometric piecewise...
Curated OER
Functions
Students explore a variety of functions. They recognize and describe functions and use linear functions to describe situations. Students find the domain and range of linear functions and graph rational expressions.
Curated OER
Reviewing the First Unit
In this linear function worksheet, students explain how the linear function relates to direct proportionality. They answer questions dealing with slope fields, rate equations and illustrate Euler's Method. After answering six...
Intel
Pedal Power
Show your classes the importance of mathematics in something as simple as bicycle design. The final lesson in the six-part STEM series has each group research a different aspect of the bicycle. Learners use mathematical formulas, linear...
PBL Pathways
Medical Insurance
Design a plan for finding the best health insurance for your money. Learners compare two health plans by writing and graphing piecewise functions representing the plan rules. Using Excel software, they create a technical report...
PBL Pathways
Medical Insurance 3
Create a technical report explaining the components of a medical plan through a function. The project-based learning activity gives a medical insurance scenario that young mathematicians model using piecewise functions. Their analyses...
Curated OER
Evaluating Functions
In this evaluating functions instructional activity, 11th graders solve and complete 24 various types of problems. First, they evaluate the functions for the given values. Then, students graph each of piecewise functions. They also write...
Curated OER
Linear Graph
Students solve linear equations and graph the different functions. In this algebra lesson, students graph piecewise functions using the slope and y-intercept and the given restrictions on the domain of the line. They discuss rate of...
Mathalicious
XBOX Xpotential
Touchdown! This is an exponentially insightful lesson that explores the growth of football games with different video game consoles. Class members discuss whether the increase of mergahertz can be described as linear or exponential. The...
EngageNY
Analyzing a Graph
Collaborative groups utilize their knowledge of parent functions and transformations to determine the equations associated with graphs. The graph is then related to the scenario it represents.
Balanced Assessment
Bagels or Donuts
Explore business problems through mathematical analysis. The task has individuals write and graph a linear system to determine the best business model. They use their models to answer a series of questions that help to make a conclusion.
Curated OER
The Function Elevator
Students solve and graph functions. In this precalculus lesson plan, students use piecewise function to relate real life scenarios. They analyze the graphs and identify the vertex and intercepts.
PBL Pathways
Medical Insurance 2
Make an informed decision when choosing a medical insurance provider. An engaging lesson asks your classes to write piecewise models to represent the cost of different medical plans. The project-based learning activity is a variation of...
Curated OER
Functions and the Vertical Line Test
Students explore the concept of functions. In this function lesson, students determine if the graph is a function by using the vertical line test. Students use an applet to explore the vertical line test on a variety of graphs.
Curated OER
Piecewise Modeling with Multiple Functions: Federal Debt
Students analyze data on debt and write an equation. In this statistics instructional activity, students are given data from different time periods, and are asked to graph and analyze the data. They work in groups, and are assigned...
Curated OER
Position and Piecewise Velocity
Young scholars solve piecewise functions. In this precalculus lesson, students model real life scenarios using velocity and piecewise. They create velocity graphs and find the beginning and end position of an object.
EngageNY
End-of-Module Assessment Task - Algebra 1 (Module 3)
Looking for higher-level thinking questions? This assessment provides questions that challenge young mathematicians to think and analyze rather than simply memorize. Topics include piecewise functions, linear modeling, exponential...
Curated OER
Slope Fields and Euler's Method
For this slope field worksheet, students use a slope field for a rate equation. Using Euler's Method, they identify the piecewise linear function approximating the solution of the initial value problem. This four-page worksheet...
Curated OER
Successive Approximations and Euler's Method
In this Euler's method worksheet, students compute the successive approximations for a given function. They compute the piecewise linear function to produce the approximation to the solution of the initial value problem. This four-page...
Curated OER
Rate Equation
In this rate equation learning exercise, students use Euler's method to estimate the value of rate equations. They use the piecewise linear function approximation to determine the solution of an initial value problem. This two-page...
Flipped Math
Calculus AB/BC - Connecting Multiple Representations of Limits
It's time to put it all together. Viewers of an informative video learn to connect multiple representations of limits. Given algebraic, tabular, and graphical representations of a linear piecewise function, they determine whether a limit...