Question

It has been a long time since I took Trig, Algebra, Geometry, or Calculus. Always loved math, but I teach Kindergarten now so basically 2+2 is the hardest problem I've had to solve in awhile.
My 13 year old daughter is in 8th grade. Her Algebra teacher recently changed seating arrangements. My daughter wants to sit with her last math partner, and, since he is a great influence & incredibly helpful to her in math, I am supporting her with this. Problem is, her Algebra teacher will only move her back beside her old partner if she can come up with a mathematical proof or equation proving why she should be allowed to sit beside him. The teacher said the more creative the better. A search of "fun math proofs" or "math proofs about life" essentially only yields the old "Women are the root of all evil" proof, and I am having a hard time getting inspired with that.
Any ideas? I thought about adding the letters of their names & figuring out some way to put them in an equation or figuring out a way to show the two should be adjacent with a shape or an angle. I just can't get inspired...
Help would be greatly appreciated.

Answer 1

Here's a couple of ideas.

1) Use concept of rational numbers.
Start by assigning 2 variables with a square root, representing each student.
Then multiply the 2 variables together resulting in a whole number. (canceling the square root)
Then say that being by yourself is irrational. But working together is rational.
$boy = \sqrt{3} , girl = \sqrt{3} \\ \\ boy*girl = \sqrt{3}*\sqrt{3} = 3$


2) Set up a linear equation to show how the more they work together the higher their grades will be.
For 8th grade a simple one is all that is needed.
$G = 80 + t$

where t is hours working together.
Provide a graph or table demonstrating the positive slope.

Good luck