Fundamental Laws of Algebra

By Allen Reed, Douglas Jensen

Learners review the fundamental laws of algebra including the commutative law of addition, the commutative law of multiplication, the associative law of addition, the associative law of multiplication, and the distributive law. Examples are given.

Factoring by the Difference of Two Perfect Squares

By Roy Peterson

In this learning activity you'll factor problems using the difference of two perfect squares.

Karnaugh Maps

By Patrick Hoppe

Learners examine the Karnaugh map for a three-variable system. Several examples are given.

Solving Equations: Properties of Equality

In this interactive object, learners examine the properties of equality and use those properties to solve simple equations.

An Algebraic Word Problem Involving Motion: Case 2

By Kevin Ritzman

In this animated object, learners use an algebraic formula to solve the following problem: An airplane travels a certain distance with the wind in the same amount of time that it takes to travel a shorter distance against the wind. Given a constant wind speed, what is the speed of the plane without a wind?

Simplifying Square Roots

In this learning activity you'll simplify square roots involving the product of a numeric and variable term.

Gear Ratio Concepts (Screencast)

By James Bourassa

In this screencast, learners examine the concept of gear ratios. The number of teeth, diameters, and velocity relationships are discussed and calculated using linear ratio equations.

Excel: Determining the Square Root of a Complex Number

Learners view the steps for determining the square root of a complex number in Excel.

An Algebraic Word Problem Involving Motion: Case 1

In this animated and interactive object, learners use an algebraic formula to solve a problem involving distance, rate, and time.

Excel: Entering a Complex Number

Learners examine the complex number function to convert real and imaginary coefficients into a complex number.

Numerical Curiosities: Part 4

By Jeganathan Sriskandarajah

In this fourth part in a series, learners follow the steps of the “mathemagician” to examine three numerical curiosities: Be a Psychic by Predicting Birthdays, Predict a Card with Mind Reading, and Predict the Three Die Values Your Opponent Has Rolled. Learners will also study palindromic numbers and look at two alphametric puzzles.

Joint Variation

By Terry Lark

In this learning activity you'll practice calculating a joint variation problem.

Variation - Application Problems

In this learning activity you'll practice two variation application problems.

Identifying the Number of Significant Digits

By Ron Wallberg

Learners will identify the number of significant digits in practice problems.

Numerical Curiosities: Part 2

In part 2 of this series, learners follow the steps of the “mathemagician” to examine these numerical curiosities: The 189 Challenge; An Armstrong Number: What’s Special About 153? Is 495 Different or Indifferent? Is 6174 Different or Indifferent? It is always 618, and Beginning and Ending the Same.

Variation

In this learning object you'll review direct, inverse, joint, quadratic, and combined variations.

Quadratic Variation

In this learning activity you'll practice calculating a quadratic variation problem.

Excel: Complex Addition

Students view the steps to follow to add complex numbers in Excel.

Numerical Curiosities: Part 3

In this interactive object, part 3 in a series, learners follow the steps of the “mathemagician” to examine four numerical curiosities: What’s Special About 1089, Perfect Squares: 1089 and 9801, The Mathematical Significance of 1776, and The Calculator Number Game. The learner will also study six number patterns and look at one remarkable table. Immediate feedback is provided.

A Visual Approach To Simplifying Radicals

In this animated object, learners follow a process for simplifying radicals.

Direct Variation

In this learning activity you'll walk through a direct variation problem.

Combined Variation

In this learning activity you'll practice calculating a combined variation problem.

An Introduction to Algebraic Word Problems

In this animated object, learners follow the steps for solving word problems using algebra. An introductory example is explained.

Inverse Variation

In this learning activity you'll practice calculating an inverse variation problem.