Week 28 CMT Style Problem - 8th Grade

Algebra Magic

Behind every magic trick is a secret, an explanation of how it’s done and why it works. In this trick, the secret is ALGEBRA. Emmy Noether (1882-1935), the great German mathematician, specialized in the study of algebra. With algebra, some of the trickiest tricks can be easily explained.

1. Try this: Record your results as you explore.
   • Choose any number
   • Add five
   • Double the result
   • Subtract four
   • Divide by two
   • Subtract the first number
   • The result?
   
   
   
2. How can you prove that this number trick will always work?
   
   
3. Let X be the number chosen at the beginning of the trick and show the algebraic explanation for the trick.
   • Choose any number
   • Add five
   • Double the result
   • Subtract four Subtract the first number
   • The result?