Your AP Calculus learners probably have their ID numbers memorized, but have they tried graphing them? Pique your pupils' interest by asking each to create a unique polynomial function based on their ID numbers, and then analyze the...

Within collaborative groups, scholars factor a degree six polynomial. They can factor the polynomial using many different strategies — a great way to prompt mathematical discussion.

Patterns in polygons lead to patterns in polynomials. Presented with a series of polygons, individuals create polynomial expressions to represent their patterns. The algebra project consists of nine problems that incorporate polynomial...

Birthdays are a time for celebration, and now they're a time for calculation! An AP calculus lesson uniquely explores relationships between a polynomial function and its derivative. Learners create a cubic function based...

Control the computer processing speed with mathematics! Scholars use a computer program to graph color-changing functions. Using complex polynomial functions slows the speed of the program, but simplifying the expression allows the...

These four problems will guide your class through the idea behind the Fundamental Theorem of Algebra, which states that a polynomial of degree n has exactly n roots. Use the division algorithm and the definition of a zero/root of a...

Factoring polynomials is an essential part of writing equivalent expressions and algebraic problem solving. Here is a card game that serves an engaging activity for reviewing factoring of polynomials.

Your algebra learners explore the values of two types of functions in order to compare growth rates in this short cooperative task. Two types of solutions are given, using a table of values and an abstract argument.

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...

Functions behaving badly: the squaring function and the absolute value function are both zero at x=0. Yet when you divide each by x, different things happen. Here, your class will explore each scenario as a means to adding depth to their...

This activity uses the division algorithm and the definition of a zero/root of a function to guide your class to see the relationship between zeros and factors of a general quadratic, which can later be generalized to the Remainder...

Examine trends in student-to-teacher ratios over time. Building from the first task in the two-part series, classes now explore the pattern of student-to-teacher ratios using a non-linear function. After trying to connect the pattern to...

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...

This activity highlights the use of the remainder theorem to solve for the unknown coefficient of a specified polynomial when given one of its factors. Use this single problem as a warm-up exercise, a quick check-in at the end of a...

Practice evaluating polynomial expressions at the same time you find Pythagorean Triples. Look for patterns and find examples when the "formula" does and doesn't work. Finally, verify the formula by proving the identity true.

Calling all subscribers! Model revenue based on individual cell phone subscribers. The project-based learning activity presents a challenge to scholars from a cell phone company. Individuals model data provided to them from the company...

Practice simplifying complex fractions and long division of polynomials with this brief exercise. These four questions make a challenging warm-up activity or a short, but comprehensive, follow-up after a detailed lesson on algebraic...

Patterns, patterns, everywhere! Young scholars examine the multiplication table to identify patterns. Their exploration leads to an understanding of the difference of squares and sum of cubes by the completion of the algebra project.

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.

How can baseball and skeet-shooting be modeled mathematically? Sports lovers and young mathematicians learn how to use quadratic equations and systems of equations to model the flight paths of various objects.

The Egyptians used unit fractions to describe all other fractions. Your class will rewrite rational expressions in order to deduce information about rational numbers. The activity starts with specific fractions, guides you through a few...

An upper-level treatment of what is often presented as a basic concept (the right angle of an inscribed circle on the diameter), this activity really elevates the mathematical thought of the learner! Expected to develop formulas...

Forty-four problems present a variety of practice adding, subtracting and multiplying polynomials. They are given with each step to the solution cleverly revealed one at a time. You can work each step of the problem then click the "View...

Hotmath provides 20 practice problems that relate to polynomial and rational functions. Each of the practice problems include a step-by-step guide for solving.