Go Negative
This problem solving activity has a number focus.
Gill, is playing with her name and with numbers.
She lets all her consonants equal 3/8 and all her vowels equal –5/8.
So the value of Gill’s name is 3/8 – 5/8 + 3/8 + 3/8 = 4/8 = 1/2 = 0.5
What is the value of your name?
Change the rules so that the value of your name is negative.
- Perform calculations with negative fractions.
- Devise and use problem solving strategies mathematically (e.g. be systematic, draw a picture).
This problem, in which students substitute values into their own names, focuses on the addition of positive and negative fractional numbers. To successfully work with this prolem, your students should have knolwedge of operating on negative integers and fractions.
It is a precursor to algebra which seeks to generalise number.
Other similar Number problems are: Points, Level 1; Names and Numbers, Level 2; Make 4.253, Level 3; Multiples of a, Level 3; and Doubling Up, Level 5.
The Problem
Gill, is playing with her name and with numbers. She lets all her consonants equal 3/8 and all her vowels equal –5/8. So the value of Gill’s name is 3/8 – 5/8 + 3/8 + 3/8 = 4/8 = 1/2 = 0.5
What is the value of your name?
Change the rules so that the value of your name is negative.
Teaching Sequence
- Tell the students Gill’s story and have them to find the values of their own first names.
- Have a partner check that they have found the right value for their name.
- Have students put themselves into groups all of whom has the same value. Get them to think about their names to see if there is a good reason why they are all in the same group.
- As students then work in groups to find some way of ending up with a negative number, ask:
How are you keeping track of your ideas?
Can you arrange for members of your group to have the same negative value?
Can you find more than one way to get negative answers?
Ask questions that focus on their understanding on the addition of fractions and negative fractions. You could also ask students to simplify the fractional value of their name, or convert it into a decimal, as Gill did with her name. - Have a few groups report on what they have done.
- Pose the extension problem when appropriate.
Extension
Using Gill’s original substitution, what is the biggest and smallest value that you can find using names in your class?
Attribute different fractional values to vowels and to consonants.
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 negative value, students should choose arbitrary values for each of their letters. For example, if their name is Mark, then they might let M = 1/8, A = -7/8, R = 1/8 and K = 1/8. The choice of value for the last letter should ensure a negative value, if the first four letters don’t have too big a sum.