Dollar Words -- Alphabet Algebra with Addition

Discovering algebra with the alphabet is one of the most natural activities for children of any age. The most recognizable sequence for any child is the familiar alphabetic sequence: ABCDEFG....Z 

We use the standard valuation of letters: A=1, B=2, C=3, D=4, E=5 ......... Z=26. When we take a word like MATH, we add the values M + A + T + H = 13 + 1 + 20 + 8 = 42. We would call this a 42 cent word; not very interesting. 

Our objective here is to find Dollar Words; these are words that add up to exactly 100, like the word PUMPKIN. My best practice is for Mathletes to write the word vertically, write the number values vertically lining up the ones column and then adding with carries (see attached Dollar Word Example). The children love to try their own names, names of family members, favorite animal or sport, etc. There are close to 1,000 Dollar Words (see http://mathlair.allfunandgames.ca/onedollarwords.php). 

Mathletes also love to explore the number values of long words. They love SUPERCALIFRAGILISTICEXPIALIDOCIOUS, a 34 letter word that has a value of 379. One of my favorite long words is ANTIDISESTABLISHMENTARIANISM, a 28 letter word with a value of 307. The longest word in a work of Shakespeare, HONORIFICABILITUDINITATIBUS is , a 27 letter word meaning the state of being able to acheive honors, is worth 299.

It is fun to find Dollar Words that are mathematical in nature. Some of these include: THIRTY, QUARTER, MAXIMIZE, MIDPOINT, and PERCENTS. 

UPPER LEVEL DOLLAR WORDS

When you use a reverse valuation of letters: A=26, B=25, C=24, D=23, E=22 ......... Z=1. See the attached worksheet entitled Dollar Words Standard and Reverse Method. When we take a word like MATH, we add the values M + A + T + H = 14 + 26 + 7 + 19 = 66. When you add the reverse method value of 66 to the standard method value of 42 you get 108. Notice that this number is the fourth multiple of 27. Since the sum of the standard and reverse method valuation of a letter will always be 27, you can simply multiply the number of letters in the word (in the case of MATH, 4 letters multiplied by 27 gives you 108). This serves as a human calculator so you can check your work. 

Please encourage your children to work on Dollar Words everyday. It is a great way for them to connect things that they are learning about or enjoying with math.