Visualization is one way to better understand and apply math principles and concepts. Click on any of the concepts below to find illustrations, examples, and useful links.


Arithmetic Refresher

For a list of videos and practice exercises on a number of arithmetic topics, check out this pdf.

For more arithmetic help, be sure to also check out a wealth of other resources below.


When talking about fractions, the number on top is known as the numerator while the number on the bottom is referred to as the denominator.

As simple way to remember this is the mnemonic device: nUmerator Up, Denominator Down.

Alternatively, think "Notre Dame" (N before D, Numerator before Denominator).

For more information on fractions:

  • Visual Fractions helps you to understand fractions by manipulating visual pieces. You can learn about identifying, renaming, comparing, adding, subtracting, multiplying, and dividing fractions.
  • Math Drills offers fraction printouts and practice question worksheets.

Long Division

The steps involved in Long Division can be remembered through the simple mnemonic device: Dad, Mom, Sister, Brother, and Rover.

  1. Divide (Dad)
  2. Multiply (Mother)
  3. Subtract (Sister)
  4. Bring Down (Brother)
  5. Repeat (Rover)

Long Division: Step by Step

This short tutorial will walk you the necessary steps of Long Division:

Long Division: Step by Step (v2)

For more information and to practice your long division skills, please check out the following websites:

  • Math is Fun has a number of long division instructions with animated videos and practice questions.
  • Soft Schools offers practice questions with step by step instructions.

Order of Operations

It's easiest to remember the order in which components of an equation should be calculated by keeping in mind the mnemonic device: BEDMAS (Brackets, Exponents, Division, Multiplication, Addition, and Subtraction).

BEDMAS Illustration

For more information on order of operations:

  • Math Is Fun offers instructions with examples, practice questions, and an Order of Operations calculator.
  • MathFrog, from the University of Waterloo, offers a skill-testing order of operations game.


  • The Algebra Refresher provides links to a series of videos from the Khan Academy that will help reacquaint you with a number of algebra-related topics.
  • Michigan Virtual University has an Algebra tile activities that can help you visualize concepts, solve equations, and multiply or factor polynomials.
  • Utah State University provides a function plotter that graphs the line of a function. You can use their virtual manipulative to:
    • trace a point along the graph
    • vary function parameters
    • graph multiple functions
    • restrict the domain of a function
    • zoom in on a region of the graph


  • The Geometry Refresher provides links to a series of videos from the Khan Academy that will help reacquaint you with a number of geometry-related topics.


General Math Websites

  • is an online resource that provides printable worksheets on a number of fundamental math topics.
  • Math Interactives is a multimedia resource that covers the topics of numbers, patterns and relations, shape and space, and statistics and probability. The website includes games and instructions that relate mathematics to real world situations.
  • Math Is Fun offers a range of math-related instructions, practice questions, worksheets, and games.

Other Resources