2405.12 – Pickanumba 1
Translate this trick sentence. Take a number--any number you like--and add two, double the result, add ten, divide by two, and subtract the original number. The result is 7!
If n is the number you picked, what you have done, algebraically, is this: ((n + 2)x2 + 10)/2 - n. Work this out and you'll come out with 7 every time.
Students can invent their own versions of this problem. Some can get mighty complicated! You could put one up on the board for the class to do--its author is on the spot for accuracy in its construction.