Go Negative
Perform calculations with negative fractions.
Devise and use problem solving strategies mathematically. This problem uses be systematic and draw a picture strategy.
Although this problem is ostensibly about addition of decimal numbers, it is really a precursor to algebra. The students are substituting values into their own names and so laying the groundwork for later algebra work.
More generally this exercise links numbers and letters of the alphabet. This is the basis of algebra as it seeks to generalise number.
The lesson we’re dealing with here is the fourth of a sequence of six dealing with the same theme. These develop from Level 2 to Level 5. In the process they involve number concepts at the various Levels and will gradually involve algebraic concepts too. The lessons 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, was playing with her name and with numbers. She let 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 = ½ = 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 let them find the value of some word, ROOM, say.
- Make sure that they understand how you find the value of a word. Then ask them to find the values of their names. (That is, just their first names.) Get their partner in their group to check that they have found the right value for their name.
- As the students solve the problem circulate asking questions that focus on their understanding of the addition of fractions and negative fractions.
How are you adding these fractions?
Is your answer reasonable? How do you know? (estimation)
How do you know that you are correct? - Then ask the students to 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.
- In groups, the students could then find some way of ending up with a negative number. Can they arrange for both members of their group to have the same negative value? They could be asked to find more than one way to get negative answers.
- The quicker groups can go on to tackle the Extension problem.
- Get a few groups to report on what they have done.
- 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
Using Gill’s original substitution, what is the biggest and smallest value that you can find using names in your class?
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 should not be too hard. For instance, if their name is Mark, then they might let M = 1/8, A = -7/8, R = 1/8 and K = 1/8. The thing here is to use arbitrary values of the first four letters and then use whatever is needed for the last letter. Of course the trick here is to make sure that the first four letters don’t have too big a sum.
| Attachment | Size |
|---|---|
| GoNegative.pdf | 49.26 KB |
| GoNegativeMaori.pdf | 55.31 KB |
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