Names and Numbers

The Problem

Gill, was playing with her name and with numbers. She let all her consonants equal 10 and all her vowels equal 5. So the value of Gill’s name is 10 + 5 + 10 + 10 = 35.

What is the value of your name?
Can you find a name whose value is 30?

Teaching sequence

1. Tell the students Gill’s story and let them find the value of some word, ROOM, say.
2. Make sure that they understand how you find the value of a word. Then send them off into their groups to find the values of each of their names. (That is, their first names and their other names.) Get their partner in their group to check that they have found the right value for all their names.
3. As the students solve the problem circulate asking questions that focus on their understanding of the addition of fives and tens.
   How are you adding these numbers?
   How do you know that you are correct?
   What can you tell me about the answers that you get? (end in 5 or 0)
4. The quicker groups can go on to try to find names with the value 30. You might ask them if they can find more than one answer here. And it would be good to have answers with different numbers of letters.
5. They can then tackle the Extension problem.
6. Get a few groups to report on what they have done.
7. Give all students time to write down something about the answers they got. This should help them to understand what is going on.

Extension to the problem

What is the biggest value that a name of six letters can have? What is the biggest value that you can actually find?

Solution

The answers that you get for the first part of the question will depend upon the names of the students in the class.

To get a name with a value of 30 it will either have four letters two of which are consonants, have five letters one of which is a consonant, or have six letters with no consonants. Here are some examples: Adam, Alan, and Emma.

Solution to the Extension:

With six letters the biggest value that you can get is 60. However, it is not very likely that they will be able to find a name that has no vowels that is six letters long. So 55 is perhaps the best that the students will be able to find. An example of this is Myrtle.

N.B. This problem gives lots of scope for exploration. You could find the biggest valued name, the smallest valued name, a name with value 100, names whose values are odd/even, etc.