It's a scrabble
Letters have different values in Scrabble - how are they decided upon? And would the values be the same for other languages?
Problem
Here's a sort of code you may have seen before:
| A, E, I, O, U, L, N, R, S, T | 1 |
| D, G | 2 |
| B, C, M, P | 3 |
| F, H, V, W, Y | 4 |
| K | 5 |
| J, X | 8 |
| Q, Z | 10 |
If you exchanged each letter of your name for a number, what would the code be?
Mine is Lynne so my code is 1 4 1 1 1 . The numbers add up to 8 which is not much!!
What is your name worth using this code?
Try some other names - what names are worth the most and which are worth the least?
Are longer names always worth more?
Can you work out why certain letters are worth a lot and why others are only worth one?
Student Solutions
We had nearly $50$ solutions and ideas sent in for this challenge. Georgina from GISC in Malaysia, Tallulah, Danyal, Devraj, Anna, Aishwarya and Jessica from Salcome Prep School in England, Briana from the International Community School of Addis Ababa in Ethiopia sent in the values of names.
Suruchi from Salcombe in the United Kingdom wrote this;
What is your name worth using this code? My name is worth $12$.
Try some other names - what names are worth the most and which are worth the least? The names that are worth the most are: Elizabeth and Zack. The names that are worth the least are P: Ben and Maya. The names which have the letters Q and Z are worth the most because they have the highest value of $10$.
Are longer names always worth more? Longer names are not always worth more. This is because they may not always have the high value worth letters like : Q,Z,J and X.
Can you work out why certain letters are worth a lot and why others are
only worth one?
The commonly used letters for names like a,e,i,o,u are worth less. The very rarely used letters like q,j,z and x for names are always worth more.
Alya, also from Salcombe wrote,
The different values are decided on how often the letter the is used. The letters that are used the most get the lower values and the mose rare ones get the highest values.
Other languages would be judged the same - most often letters lower values and rare higher values.
Longer names don't have to be worth more because they might have very common letters. But if they don't, they will be worth quite alot. Shorter names might have rare letters and be worth more than a longer name with more common letters.
Thank you for all these contributions and to everyone who sent in their name as a value.
Teachers' Resources
Why do this problem?
Some children may recognise that the 'code' is based on the values of the Scrabble tiles. Those values are based on the frequency of letters in written English and so this activity is a gentle introduction into the sort of data analysis which underpins much code breaking.
Possible approach
If this is your first code-related acivity you may wish to use the task 'What's in a name?' first.
Display the table or show this PowerPoint slide. Ask the children to write down their own name and work out what letters would represent it using the code. What do they notice?
Draw up an alphabet table on the board, and tell the children you are going to collate the letters from each child's name (using a five bar gate, or whatever way of recording is familiar to the children). Ask the children to predict what they think will happen.
| Letter | Frequency |
| A | |
| B | |
| C etc |
Once complete, compare their predictions with the actual table. Unless you have a lot of non-English names in your class, the frequency distribution is likely to mirror the Scrabble table.
If they haven't already spotted it, make connections to Scrabble and how the Scrabble values were derived. If you have a Scrabble set in the classroom, children could check that the table is correct.
Ask the children to add up the numbers in their names: whose name is worth the most/least?
Can they work out a short, high value name?
What about a long, low value name?
Let the children explore other sorts of words - can they make some short, high value words and some long, low value ones?
Key questions
Which letters do you think will have the highest frequency?
Why?
Are long words always worth more than short ones? Why or why not?
Possible support
If you have some Scrabble tiles they can be used to support children who need to manipulate the letters. You can download a set of blank alphabet tiles for children to make their own Scrabble set.
Possible extension
Use some of the texts familar to the children and ask them to analyse a short section to see if the frequencies are the same.
Here are some translations of the same text into other languages ( courtesy of Google Translate). How do these frequency tables compare?
Scrabble was invented in 1938 by Alfred Mosher Butts and was originall called 'Criss-Crosswords' The letter values were then worked out from a frequency analysis of the letters used in lots of different places, including the New York Times. In 1948 the right to publish the game was bought by James Brunot and it was then renamed.
In an English-language set the game contains 100 tiles, 98 of which are marked with a letter and a point value ranging from 1 to 10. The number of points of each lettered tile is based on the letter's frequency in standard English writing; commonly used letters such as E or O are worth one point, while less common letters score higher, with Q and Z each worth 10 points. The game also has two blank tiles that are unmarked and carry no point value. The blank tiles can be used as substitutes for any letter; once laid on the board, however, the choice is fixed. Other language sets use different letter set distributions with different point values.
Source: wikipedia