WORDSWORTH

 To see information about the U. S. Presidents, click HERE.

"What's it worth?" is a common question in the business world to be sure. But what about a math classroom? The question of "What is the value of CAT or DOG?" certainly sounds intriguing to me and to elementary students I have taught. The idea becomes obvious if we give each letter its own value and we just add up the values of each letter to obtain the value of the word.

For starters, let's give the letters the value of their positions in the alphabet:

## A = 1, B = 2, C = 3, ... , Y = 25, Z = 26

Now, here is how things turn out for some common 3-letter words:

```	C =  3		D =  4		F =  6		F =  6
A =  1		O = 15		A =  1		L = 12
T = 20		G =  7		N = 14		Y = 25
24		    26		    21		    43
```

## Where's the Challenge?

Finding the value sums for three-letter words is, admittedly, not a great and difficult thing to do. So, why am I presenting this with such fanfare? It's because if we reverse things -- á la JEOPARDY -- and ask, "Can you find a word that is worth 50 points? Or 25 points? What word has the greatest/smallest value?" etc., then things become an experience in true problem solving. It's not so easy now, is it?

One sort of activity I have used is to ask the class, working as a team, to find words for each value number from some lower limit to some upper limit. For example, let's start out with 3-letter words. I have found word sums as low as 6 (CAB) and as high as 66 (WRY) -- and of course, every number inbetween.

As one begins such a project, it is convenient to just start putting down any 3-letter words that come to mind, compute their values, and compile an ordered list, leaving blank those numbers for which no value has been found so far. As spaces are filling up, soon you will start directing your attention towards the missing values. Then is when the fun -- and the challenge -- begins.

One suggestion would be to make a large poster on the bulletin board with a chart in this form:

 No. Word Expression Name Date 6 CAB 3+1+2 John S. Sept 10 7 BAD 2+1+4 Mary J. Sept. 11 8 CAD 3+1+4 Ann P. Sept. 12 9 DAD 4+1+4 Sue W. Sept. 10 10 BAG 2+1+7 Bill M. Sept. 11 ... ... ... ... ...

[If you are using cooperative grouping in your class, this would make a good activity for students working in this way. And for the independent individual, he or she can do this "all by oneself". In such structures, the chart is still a good recording strategy.]

### Trivia Fun

Sometimes as a large body of word values are compiled, you can find interesting equal-value-pairs. In my not very extensive collection to date, I have noted this nice pair: FOX and FUR, both words having a total of 45, and the words themselves have an obvious connection in the real world. You and your students can surely find additional cases like this one. This is definitely a case of "two heads are better than one"; when large word lists are compiled, more interesting gems can be discovered by cooperating together.

By way of introducing the concept and formal notation of inequality, we can make light-hearted statements such as

## CAT < DOG

[Lest I start receiving angry email from the cat lovers of the world, I offer the following inequality to put things in perspective:

### CAT < DOG < FOX

Okay?]

How about some numerical fun...

## SIX < TWO

### Go for FOUR

Of course, there's no rule that says you must limit yourself to 3-letter words; there are many more 4-letter words out there just waiting to be "valued"! My limit numbers so far go from 10 (BABE) to 79 (FUZZ).

And you say you want some trivia in this category? Here is one of my favorites: "MORE is less than LESS, MUCH is less than MORE and much less than LESS, whereas LOTS is lots more than all three of those." Show this to be true by finding their values and writing out the appropriate inequality statement.

And this one has a unique flavor all its own:

## SHOE + 1 = SOCK

Returning for a moment to our numerical case above, what sort of inequality should we write here for FOUR and FIVE?

And on it goes...

I'm sure you're beginning to see the possiblities for extending this activity as long as interest holds up. Contests could be on-going for extended periods of time for such ideas as

• the smallest value for 10-letter words;
• the largest value for 10-letter words;
• finding related words with the same or consecutive values;
• a short sentence (3 words or so) with equal-valued words.

The possibilities are limited only by one's own creativity.

Sample Word Lists:

```3-LETTER WORDS

6: CAB		19: EGG		32: RAM		45: FOX		58: TOW
7: BAD		20: AND		33: FIR		46: MIX		59: RUT
8: CAD		21: HID		34: OAR		47: NOR		60: TOY
9: DAD		22: AIL		35: RAP		48: WET		61: YOU
10: BAG		23: BAT		36: AWL		49: NOT		62: YUP
11: FAD		24: CAT		37: PAT		50: OWL		63: TRY
12: BEE		25: ALL		38: COT		51: POT		64: STY
13: HAD		26: DOG		39: FIX		52: SIX		65: TUX
14: BEG		27: SAG		40: TOE		53: ROT		66: WRY
15: FED		28: FOG		41: BOX		54: OUR
16: FEE		29: AWE		42: FUN		55: NUT
17: DID		30: DAY		43: BUT		56: ZOO
18: JAG		31: PAN		44: MOP		57: PUT

4-LETTER WORDS

10: BABE	28: BEAT	46: GIRL	64: SPIT
11: 		29: LAKE	47: SHOE	65: LOSS
12: BEAD	30: BEER	48: SOCK	66: LOTS
13		31: BELL	49: SING	67: TORN
14: DEAD	32: HIGH	50: FORK	68: XRAY
15: FACE	33: SAID	51: MORE	69: SOOT
16: CAGE	34: PALE	52: SHIP	70: SPOT
17: CEDE	35: GAVE	53: MANY	71: WAVY
18: HEAD	36: HAVE	54: LOVE	72: ROTS
19: BAKE	37: LIKE	55: LESS	73: MUST
20: FEED	38: NEAR	56: OVEN	74: MUTT
21: DICE	39: COAT	57: SORE	75:
22: BEAN	40: FIVE	58: TORE	76: PUTS
23: MADE	41: SAIL	59: VIEW	77: PUTT
24: BAIL	42: FISH	60: ROLL	78:
25: JACK	43: BOOK	61: MIST	79: FUZZ
26: BEAR	44: COOK	62: VOTE
27: HAND	45: MUCH	63: JAZZ
```

Footnote: Can you help me with the remaining blank spaces? I've been adding too much for this and my brain is tired. Just send me an
e-mail. Thanks.

Reference: Phyllis Zweig Chinn, Coding for fun and mathematics. The ARITHMETIC TEACHER, December 1976, pp. 597-600.

Update: 7/31/01

We have just finished researching the matter of applying this activity to the last names of the 43 Presidents of the United States. We feel we have found some interesting data worth sharing. Most of our data involves prime numbers.

First, there are 9 Presidents who numerical values are primes, ranging from Ford (43) to the two Roosevelts (131 each). The other 6 remaining prime totals are:

47, 61, 73, 79, 83, and 97
.

Can you connect each number with its corresponding President?

Second, if we add up the various individual totals from Washington up to another President, we get several more primes, in fact, this happens 7 times. Here are the results:

 241, up to Monroe; 811, up to Tyler; 2087, up to Roosevelt (Teddy); 2287, up to Harding; 2357, up to Coolidge; 2857, up to Kennedy; and finally, 3371, up to BUSH! (the newest one!)
[Note: Just so there is no confusion. Since Cleveland served 2 non-consecutive presidencies (22nd and 24th), his name is used twice to compute the totals.]

Finally, we'd like to mention two other interesting numbers that showed up. The squares of 64 and 121 are the values for Buchanan and Eisenhower, respectively.