This problem involves addition of 1- and 2-digit numbers, and multiples of 5 and 10. Students are encouraged to see the efficiency of multiplication over repeated addition. Attributing number values to letters, and developing an efficient equation to represent the solution for solving the problem is early algebra.
Penina is playing with her name and with numbers. She lets all the consonants equal 10 and all the vowels equal 5. So the value of Penina’s name is
10 + 5 + 10 + 5 + 10 + 5 = 45.
What is the value of your name?
Can you find at least 5 names that have a value of 30?
Penina's name goes even, odd, even, odd, even, odd. What other names have an even, odd or odd, even pattern?
What is the biggest value that a name of six letters can have? What is the biggest value that you can actually find?
Penina writes an equation for her name: 3c + 3v = 45. What does she mean?
Write an equation for your name?
For what 5 names might this equation be true? 3c + 2v = 40
For what 5 names might this equation be true? 2c + 3v = 35
Have students write their own equation and find names for which it is true.
The value of student names will depend on those of your students.
A name with a value of 30 will have four letters two of which are consonants (eg. Fetu, Hana), have five letters one of which is a consonant (eg. Amaia,) or have six letters with no consonants (improbable).
Odd, even names will have a vowel, consonant pattern (eg. Elijah, Oliver). Even odd names will have a consonant vowel pattern (eg. Tane, Wiremu, Mila).
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.
The equation 3c + 2v = 40 will be true for names such as Ethan, Hazel, Rangi, Anika, Grace
The equation 2c + 3v = 35 will be true for names such as Tiare, Olive, Hoani, Aroha, Moana