PBL Pathways
Doctors and Nurses
How many nurses does it take to support one doctor? A project-based activity asks learners to analyze state data to answer this question. Classes create polynomial functions from the data of doctors and nurses over a seven-year period....
Kenan Fellows
Attack of the Aphids!
Insects threaten the food production industry, and aphids are one of the big players! Analyzing data of aphid populations gives insight into their behaviors. Learners model the population data of an uninhibited population with an...
Curated OER
Multiplicity of Zeros of Functions
Pupils identify the multiplicity of exponents as they graph polynomials. They write equations for a function given the zeros of the function and work backwards from solving equations.
Curated OER
Exploring Power Functions 1
Learners describe the end behavior of polynomial functions. Pupils relate the behavior of the graph to the exponent of the graph. They differentiate graphs with odd-exponent and graphs with even exponents.
Curated OER
Exploring Power Functions 2
Young mathematicians learn to write algebraic equations. They solve and graph different polynomial functions with different powers. They then graph radicals and identify the domain and range.
Curated OER
Arithmetic Complex Numbers
Students convert quadratic functions from standard form to vertex form. In this algebra lesson, students solve polynomials using synthetic and long division. They derive and apply the remainder theorem and factor theorem.
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
Classifying Functions
Eleventh graders sort different types of functions including rational, periodic, exponential, polynomial, quadratic, logarithmic and linear using "function cards." The functions are displayed in multiple representations including...
Mathematics Vision Project
Module 4: Rational Functions
Time to study the most sensible function — rational functions! The seven-lesson unit develops the concept of a rational function through a connection to rational numbers and fractions. Scholars graph functions, solve equations, and...
Inside Mathematics
Quadratic (2009)
Functions require an input in order to get an output, which explains why the answer always has at least two parts. After only three multi-part questions, the teacher can analyze pupils' strengths and weaknesses when it comes to quadratic...
Inside Mathematics
Sorting Functions
Graph A goes with equation C, but table B. The short assessment task requires class members to match graphs with their corresponding tables, equations, and verbalized rules. Pupils then provide explanations on the process they used to...
Mathematics Vision Project
Module 8: Modeling With Functions
Sometimes there just isn't a parent function that fits the situation. Help scholars learn to combine function types through operations and compositions. Learners first explore a new concept with an introductory activity and then follow...
Curated OER
Exponential Functions
Analyze functions by their shape and equation and identify decay and growth based on the equation given. Learners graph their exponential functions and differentiate it using the logarithmic versus the exponential function.
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...
Curated OER
Exponential Growth versus Linear Growth II
Your algebra learners discover that exponential functions, with a base larger than one, outgrow linear functions when the inputs increase sufficiently. Their analysis includes using a graphing calculator to produce tables.
Curated OER
Math Handbook: Calculus
If only there was a reference that listed all the formulas covered in calculus. Luckily, there is. This comprehensive 197-page handbook provides formulas and explanations for all topics in AP Calculus or in a standard college calculus...
Virginia Department of Education
Transformational Graphing
Find relationships between the structure of a function and its graph. An engaging lesson explores seven parent functions and their graphs. Learners match functions to their graphs and describe transformations.
Curated OER
Applying Trigonometric Functions To Real Life
Students examine where trigonometry exists outside the classroom. In this trigonometry lesson, students create trigonometric functions to match the data provided and to solve word problems relating to the real world.
Curated OER
Worksheet 23
In this math worksheet, students find two power series solutions to Airy's equation. Then they find the radius of convergence for the solutions.
Curated OER
Calculus
Students make an inquiry with the aid of technology into the concept of functions. The emphasis of the lesson is on the interplay between the geometric and analytic information.