“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:
|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.]
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
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 possibilities 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:
1. 241, up to Monroe;
2. 811, up to Tyler;
3. 2087, up to Roosevelt (Teddy);
4. 2287, up to Harding;
5. 2357, up to Coolidge;
6. 2857, up to Kennedy; and finally,
7. 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.
The $1 Word Game
To learn more about another related activity, HERE.