Scrabble Algebraic Method, Ascending and Most Frequent Value

Last week, I introduced how mathematicians use algebraic symbols to represent numbers. We used the ascending value method where A=1, B=2, C=3 …. Z=26. One way to connect language and math is to have children convert words to numbers using several different letter valuation methods. The children were asked to add the value of each letter. I encouraged them to add the ones column first by grouping 10s and 20s and then adding that answer to the tens column. I have been working with the children to group 10s using a method I call “bracketology;” for example, by connecting 4 and 6 or 3 and 7. Another strategy is to connect 8, 8 and 4 to generate 20. 

Children analyzed the famous game: Scrabble. The Mathletes were asked why Scrabble values the 100 letters pieces as it does: the letters worth 1 point are A, E, I, L, N, O, R, S, T, and U. All other letters have greater values. This is another algebraic method.

The children made conjectures that these letters are the most common letters used in the alphabet and easier to make words. The inventor of Scrabble, Alfred Mosher Butts, analyzed the English language by hand while now computers do the work. Using the Oxford English Dictionary’s analysis of the most common letters, I developed an algebraic method called the Most Frequent Value Method where the most common letter E is equal to 26, the second most common letter is worth 25 and so on until the letter Q, the most rare letter is worth 1 point. 

I gave the children a glossary of 450 of the most common math terms and asked them to value some of these words using three algebraic valuation methods. The youngest Mathletes used the Scrabble Value Method to add up the value of words. I gave some of them a challenge to use the Ascending Valuation Method to try to get to 100.

The older Mathletes were asked to use the Most Frequent Valuation Method and compared these values to the same words under the Ascending Valuation Method. They first made conjectures that the Most Frequent Valuation Method would yield higher values and then sought to prove this. For the most part, they were correct.

The attached pdfs include the math glossary and worksheets for the children to value words under each of the three methods.