Dollar Words: Descending Value and the Rule of 27

I was very excited to see how many words the children were able to value using the ascending method of dollar words. They were very clever. For example, one student found the value of LANDSCAPE was worth 75; he removed the E worth 5 and added ING worth 30; a DOLLAR WORD. Many students attempted the very long words I gave as challenges. I showed them that if they were within 5% of the actual value, they were almost ALIEN STATUS. Just so you understand my language, since all humans make mistakes, when they get difficult problems correct, they are “ALIENS.” Of course, they like alien status. To demonstrate 5%, we took the actual value (for example, PNEUMONOULTRAMICROSCOPICSILICOVOLCANOCONIOSIS is worth 560), 10% is just one place value less at 56 and 5% is half of that value, or 28. So if the student calculated 540, they were only 20 from the actual answer and less than 5% off. 

THE DESCENDING METHOD VALUATION (a=26, b=25, c=24 ... z=1) IS MORE DIFFICULT SINCE WE ARE USED TO THE ABC SONG. I HAD THE CHILDREN SING THIS VERSION:

"ZYXWVUTSRQPONMLKJIHGFEDCBA, NOW YOU KNOW YOUR ZYX'S, NEXT TIME IT WON'T YOU GO TO TEXAS.” AND, “…DRIVE A LEXUS.” They did great with the song while looking at the letters but then, of course, I removed the letters and it was quite the challenge; even for me. 

I gave them Descending Value Worksheets and a challenge sheet with 23 hints to Dollar Words such as When looking for "dollar" words, don't look to far. How ironic that the word “DOLLAR” is worth 100 in descending value. I also gave them a list of over 1300 words that are dollar words using this method. Of course, they should practice using my method. Please make the additional copies.

My objectives for this week are as follows:

1. Letters and symbols can be given any value as long as we are consistent.
2. The descending value method will allow shorter words to be close to 100 since vowels are very popular.
3. I want to reinforce the concept of place value or tens and units digits (ones values).
4. Add the tens column first and circle your subtotal. 
5. Then group the complements of 10 or 20 and write a 10 or 20 and circle each of these.
6. Then add the tens and ones subtotals for a grand total.
7. Given the hints, can the children solve these puzzles and check their answers by valuing their chosen word.

For some 3rd and all 4th, 5th, and 6th graders, I introduced a very interesting connection. Since the sum of each letter in ascending and descending value is always 27 (for example, A is 1 or 26, B is 2 or 25), if you multiply the number of letters in the word by 27, that product will be equal to the sum of the Ascending Value and Descending Value. For example, my name, DAVID is worth 40 in Ascending Value and has 5 letters. Multiplying 5x27=135, I know for sure that my Descending Value will be the difference between 135 and 40 = 95. Then I check my work on the Descending Value worksheet and sure enough it is 95. This can be done with even the longest words. The formula is 

A + D = (n)(t) where A = Ascending Value for whole word; D = Descending Value for whole word, n = number of letters in the word, and t = 27, the constant.

Although this can seem advanced for even middle school or early high school students, surprisingly, a large number of students got the concept. Another object of mine was to introduce distributive property to these students who were asked to multiply by 27. I asked them to separate 27 into (20 + 7) and multiply each part by the number of letters and then add those parts together.