Dollar Words Ascending Values = 100 Algebra with Addition and Multiplication

This week we introduced algebra to the children with an exercise I call Dollar Words. Algebra uses letters and symbols to represent numbers. The Dollar Word challenge ascribes values to each letter by its position in the alphabet in ascending order. A=1, B=2, C=3 … Z=26. If the sum of all of those values equals exactly 100, it is a Dollar Word. 

There are close to 1,000 individual Dollar Words in the English language out of a total of 250,000 words. Therefore, 1 out of every 250 words is a Dollar Word, or less than a half of one percent of all words. This is what makes it so challenging.

There are many ways to calculate the value of words. Until the children become masters of this process, I would like them to use the following process:

1. Use the attached ascending value worksheet.pdf
2. Write the word or phrase vertically down the left side of the page in all capitals
3. On the worksheet, it has the values of each letter. Write the value to the right of the letter being careful to put the 10s place on the left and the 1s place on the right.
4. First, add the tens column and write the value on the bottom of the column and circle it.
5. Then group the 1s column numbers by complements of 10 and 20 (e.g., 1 and 9, 2 and 8, 1 and 6 and 3, and so on). 
6. Add up the total 1s column and add this total to the tens column and you have your value.

My objectives for the children are as follows:

1. Think about numbers in an abstract way. 
2. Choosing words or phrases that have high letter values to add up to 100.
3. Listing numbers vertically by place value 10s and 1s.
4. Adding tens.
5. Grouping by complements of 10 and 20.
6. Finally, coming up with the total value of the word.
7. Strategically thinking of ways to add prefixes or suffixes to the words to make 100 (for example, the word WIZARD is worth 81 and if you add the letter S = 19 it is 100.

Each age group will reach certain levels of the above objectives. Some K/1st graders may only be able to work up to Number 4 above. The 5th and 6th graders may try all of the challenges on the attached pdf. The file has examples of my method with short Dollar Words such as Turkey and Pumpkin. It also shows how to find the value of a long word which greatly exceeds 100.  Show me all of your attempted words.

For the older children, I introduced the concept of multiplying letters that are horizontally next to each other. These were very challenging and utilizes the commutative property of mulitiplication.