Curated OER
Composition of Functions
In this composition of functions worksheet, students solve and complete 7 different problems related to various functions. First, they define a function, its domain and range, and also the composition of functions. Then, students solve...
Curated OER
Matchstick Math: Using Manipulatives to Model Linear, Quadratic, and Exponential Functions
Playing with matches (unlit, of course) becomes an engaging learning experience in this fun instructional unit. Teach pupils how to apply properties of exponential functions to solve problems. They differentiate between quadratic and...
Shodor Education Foundation
Two Variable Function Pump
Use a function to operate on two variables. Pupils look at operating with complex numbers as a function of two variables. The interactive squares the input and adds a constant to it. Learners visualize the resulting output and its...
Curated OER
Numeral Analysis: Introduction To Fixed Point Iteration
In this fixed point iteration learning exercise, students use given theorems to determine converged functional iteration. This six-page learning exercise contains five problems. Explanations and examples are provided.
CK-12 Foundation
Newton's Method
Does the accuracy of the first guess make a difference down the line? Learners investigate the effects of the iterative process of finding roots, using Newton's Method. By moving the initial guess of a root on a graph, pupils observe the...
5280 Math
Aquarium Equations
Take a look at linear functions in a new environment. A three-stage algebra project first asks learners to model the salt concentration of an aquarium using linear functions. Then, using iterations, pupils create a set of input-output...
Agile Mind
Transforming Graphs of Quadratic Functions
In the activity on this webpage, learners use interactive graphing technology to investigate transformations of graphs. In the first part of the task, they look at the graph of a quadratic function with coordinates of a few points...
Howard County Schools
Exponential Decay Exploration
How can you model exponential decay? Explore different situations involving exponential decay functions and decreasing linear functions by performing activities with MandM candy, popcorn kernels, and number cubes.
Curated OER
Strong Arm Iteration
Young scholars solve exponential functions and inequalities. In this algebra lesson, students find the roots of equations and use it to graph and evaluate exponential functions. They simplify exponents using the law of exponents.
Curated OER
The Mandelbrot Set
Students explore the concept of Mandelbrot sets and Julia sets. In this Mandelbrot and Julia set lesson, students use a function integrator applet to investigate two-variable function iterations. Students use Julia set and Mandelbrot set...
Curated OER
Complex Analysis: Complex Variables
In this complex variable worksheet, students use functional iteration to find the fixed points of a function. This two-page worksheet explains the functional iteration, the Julia Set and the Mandelbrot set. Four problems are included.
Curated OER
Sequences and Series
In this sequences and series worksheet, 11th graders solve and complete 10 different problems that include identifying various sequences and series. First, they find the first six terms of each sequence. Then, students determine the...
Curated OER
Numerical Analysis: Nonlinear Equations
In this nonlinear equations instructional activity, students use iterative methods for solving systems of nonlinear equations. This four-page instructional activity contains eight multi-step problems.
Curated OER
Introduction to Fractals: Geometric Fractals
Middle schoolers study and observe the patterns made by the areas of the Sierpinski Triangle. Students use the computer to draw two or three iterations to discover the number patterns. Middle schoolers complete worksheets based on...
Curated OER
Iterating the Function over Real Numbers
Students use a spreadsheet to find sequences of numbers. In this algebra lesson, students find the values for c of a quadratic written in standard form. They relate the behavior of the graph to the values of the equation.
Curated OER
Iterating the Function and Complex Numbers
Students identify the end behavior of polynomial graphs. In this algebra lesson, students factor and solve quadratic and complex equations. They factor out negative roots and identify the real and imaginary parts of an equation.
Curated OER
Iterating Linear Functions
Learners use a spreadsheet to investigate data. In this algebra lesson, students collect and graph data on a coordinate plane. They explain properties of a linear equation both algebraically and orally.
CK-12 Foundation
Newton's Method
Use an iterative process to find an approximation of a square root. Pupils use the interactive to find an approximation to find the positive root of a quadratic function with Newton's method. With the graphs, learners position the...
Trash For Teaching
The Light-House Project
Groups work together to design a lighthouse, from designing and drawing the wiring diagram, to creating prototypes of the switch and circuit, to envisioning and building a scale model along with a blueprint. By including different...
Curated OER
Two-Variable Function Pump Exploration Questions
Guiding students through two variable (complex) functions, this learning exercise helps them perform complex arithmetic on 6 expressions. They iterate several functions with given starting points, determining whether each is a prisoner,...
Curated OER
The Mandelbrot Set
Students are introduced to the notion of a complex number and function iteration in order to motivate the discussion of Julia sets and the Mandelbrot set.
Curated OER
Numerical Analysis
In this math worksheet, students practice analyzing iterative methods. Then they use the reading to practice problem solving focusing upon convergence.
Curated OER
What are Fractals?
Middle and high schoolers identify and analyze fractals and research information using the Internet to locate information about them. They look at fractals in relation to nature and other real world situations. Pupils create several...
Teach Engineering
Take Off with Paper Airplanes
Let's go fly a kite ... oops, a paper airplane! The 13th segment in an aviation unit of 22 relates the parts of an airplane to paper airplanes. Pupils learn the functions of the control surfaces of a plane to really make their knowledge...