Lesson Plan
Science and Mathematics Initiative for Learning Enhancement (SMILE)

Smile: Real World Applications Work Problems

For Teachers 9th - 10th
A lesson plan incorporating the use of real world work, rate, and time problems. Examples are provided and strategies for effective use of the lesson are included.
Activity
Cool Math

Coolmath: Fractional Exponents

For Students 6th - 8th Standards
This prealgebra tutorial explains fractional (rational) exponents.
Lesson Plan
Illustrative Mathematics

Illustrative Mathematics: N Rn: Rational or Irrational?

For Teachers 9th - 10th Standards
In each of the following problems, a number is given. If possible, determine whether the given number is rational or irrational. In some cases, it may be impossible to determine whether the given number is rational or irrational. Justify...
Handout
Purple Math

Purplemath: Graphing Rational Functions: Introduction

For Students 9th - 10th Standards
To graph a rational function, you find the asymptotes and the intercepts, plot a few points, and then sketch in the graph. Once you get the swing of things, rational functions are actually fairly simple to graph. This resources provides...
Handout
Purple Math

Purplemath: Graphing General Polynomials, Radicals, Rationals, and Piecewise Fun

For Students 9th - 10th Standards
This resource provides an overview of graphing, giving examples of general polynomial, radical, rational, and piecewise functions. Also includes advice on common mistakes made by students.
Handout
Purple Math

Purplemath: Solving Rational Inequalities

For Students 9th - 10th
Demonstrates the factor-table method for solving rational inequalities.
Interactive
Curated OER

Graphs: Online Calculator

For Students 9th - 10th Standards
This resource presents an online calculator which allows you to graph rational functions. Requires Java plug-in.
Activity
National Council of Teachers of Mathematics

The Math Forum: Ask Dr. Math: Definitions of Rational, Irrational

For Students 9th - 10th Standards
Math Forum definition and explanation of rational and irrational numbers, the definitions of mathematics is also addressed.
Whiteboard
ClassFlow

Class Flow: Radical Basics

For Teachers 9th - 10th
[Free Registration/Login Required] Using the product rule and rationalizing the denominator.
Handout
New Advent

Catholic Encyclopedia: Induction

For Students 9th - 10th
Excellent article that clearly explains the meaning and significance of "induction" in the history of philosophy. Relates the concept to philosophy of science as well as epistemology, demonstrating how the issues raised by induction are...
Handout
Purple Math

Purplemath: Factoring Polynomials: How To

For Students 9th - 10th Standards
Demonstrates the steps involved in factoring a general polynomial, including using the Rational Roots Test and synthetic division. Shows how to "cheat" with a graphing calculator.
Handout
Purple Math

Purplemath: The Rational Roots Test

For Students 9th - 10th Standards
Demonstrates how to use the Rational Roots Test to list possible fractional solutions for polynomials.
Handout
Purple Math

Purplemath: Solving Polynomials: How To

For Students 9th - 10th Standards
Demonstrates the steps involved in solving a general polynomial, including how to use the Rational Roots Test and synthetic division. Points out when using a graphing calculator can be very helpful.
Graphic
Curated OER

Oregon State University: Rational Functions

For Students 9th - 10th
A look at graphs of rational expressions, finding properties of the graph by using calculus. Formulas included.