This problem solving activity has an algebra focus.
Gill is playing with her name and with numbers.
If A = a, B = 2a, C = 3a, D = 4a, E = 5a, F = 6a, G = 7a and so on, the value of Gill’s name is 7a + 9a + 12a + 12a = 40a.
What is the value of your name?
Change the rules so that the value of your name is 100a.
This problem, in which students substitute values into their own names, is about powers of 2. 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; Go Negative, Level 4; and Doubling Up, Level 5.
Gill is playing with her name and with numbers. If A = a, B = 2a, C = 3a, D = 4a, E = 5a, F = 6a, G = 7a and so on, the value of Gill’s name is 7a + 9a + 12a + 12a = 40a.
What is the value of your name?
Change the rules so that the value of your name is 100a.
Can you get your name to have a value of a + b? How about 3a – 4b?
Solutions will depend upon the names of the students in the class.
To make a value of 100a with a name such as Harry: Use any values for H, A and R and then choose Y to make up 100a. There are many ways to do this.
The same approach will work if there are two different names in a group. Give all of the letters that are in common with both names some arbitrary values. Then make up the values for the other letters so that the name values both come to 100a.
With Gill, for example, let G = a, I = b. This would mean that L would have to equal 0.
For 3a – 4b, let G = 1, I = 2a and L = -2b. Many other combinations will work.
Have your students create their own variations to this problem.
Printed from https://nzmaths.co.nz/resource/multiples at 7:03pm on the 20th April 2024