This problem solving activity has a number focus.
Gill is playing with her name and with numbers.
If A = 1, B = 2, C = 4, D = 8, E = 16, F = 32, G = 64 and so on.
The value of Gill’s name is 64 + 256 + 2048 + 2048 = 4416.
What is the value of your name?
Change the rules so that the square root of the value of your name is 248.
In this problem, which is a precursor to algebra, students work with powers of 2 as they substitute values for their own name.
Students may have encountered one of the earlier related Number problems: Points, Level 1; Names and Numbers, Level 2; Make 4.253, Level 3; Multiples of a, Level 3; and Go Negative, Level 4.
Gill is playing with her name and with numbers. If A = 1, B = 2, C = 4, D = 8, E = 16, F = 32, G = 64 and so on. The value of Gill’s name is 64 + 256 + 2048 + 2048 = 4416.
What is the value of your name?
Change the rules so that the square root of the value of your name is 248.
If you substituted x for a consonant and 2x for a vowel what value would you get for your name if (i) you added the terms together to get the value and (ii) you multiplied the terms together?
The answers for part one of the question will depend upon the names of the students in the class.
Note that 2482 or 61504 is the target. To get 61504 as the target value, students should choose arbitrary values for each of their letters. If your name was Hemi, for example, you need to use some big numbers to get 61504. H, E and M can have any values, then the value of I would have to make up the required number. There are many ways to do this.
Suppose that your name was Gill. Then in (i) you would have x + 2x + x + x = 5x. In (ii) you’d get x.2x.x.x = 2x4.
N.B. This problem gives lots of scope for exploration. You could find the biggest valued name, the smallest valued name, a name whose value is a whole number, names whose values are halves, etc. Fo the extension, you could use x for consonants and 1/x for vowels.
Printed from https://nzmaths.co.nz/resource/doubling at 10:42am on the 29th March 2024