Memorize the square of at least numbers 1 to 20 and you have an edge over any student who has not. Mathematician Dewayne Jones contends that a student should memorize facts through 25 or even 30. Jennifer Kreiseder, Math teacher and author of Perfect Squares Mnemonics, notes the incredible edge memorizing squares yields in the study of algebra. William Breitsprecher advises to read, say or write the material until it is memorized. Many tricks exist to arrive at squares without a calculator, but without a doubt, memorizing as many squares as possible gives a student the greatest advantage.
Quiz a Friend

With your chart of squares, take turns with a friend posing questions and responding. Allow the respondent to keep answering until he gets one wrong. Just for fun keep track of points.
Race Several Friends

Compete with your friends or classmates. Kreiseder claims this is a fun way to not only memorize squares, but to retain the information long term. Each person takes a sheet of paper and begins as the moderator says, "Go." Participant writes down all squares from 1 to 20. People should stand when finished. The person who finishes first, with the most correct answers, wins.
Create Mnemonic Device

A Mnemonic device is a trick used to memorize facts of many kinds, usually in a series. Generally the first letter of each word to be memorized is replaced with fun words that create a memorable sentence. Many people memorize the order of the planets with a mnemonic device such as "My Very Egregious Mutt Just Slipped Under Nick's Plate." Kreiseder developed a mnemonic game of sorts to memorize squares. She encourages students to use any play on words or pattern to memorize the squares. For example: 11 squared: two ones, separate them and place a 2 in the middle = 121. Breitsprecher also encourages the use of mnemonics where they are helpful.
Create Graphic Organizer

William Breitsprecher advocates the use of visual materials such as graphic organizers to memorize materials. In college, I took an Astronomy course that required memorization of every constellation. I developed a fill in chart that allowed me to memorize the entire list, but in smaller groups. I printed out several blank copies and filled them in whenever I had a few minutes. Within a week I had all 88 memorized. Prepare a simple chart with the numbers to be squared on one side and a blank box on the other. Separate the list into small groups of five or 10 numbers so it is less intimidating and print several copies. Fill it in whenever you have a few spare moments. Feel free to start with one section and only move on when you have mastered the first. Be sure to check yourself each time.
Flashcards

Flashcards, the old standby, are a favorite because they work. Print the number to square on the front and the answer on the back. Drill through the flashcards until you have them down. Breitsprecher contends, repetition is imperative.
References
 MathMagic.com; Squares; Dewayne Jones; 2004
 GMAT Hacks: Improve your GMAT Score; Estimating Square Roots; Jeff Sackman; 2010
 TeachersPayTeachers.com; Memorizing Squares 120  A FUN Approach!; Perfect Squares Mnemonics; Jennifer Kreiseder
 Breitlinks; William Breitsprecher; Memory Tips & Tricks; 2005
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