A Fancy Way of Adding Zero & The Additive Identity

I have a love/hate relationship with riddles. I love them when I can solve them quickly, hate them when they keep me up at night for something that is normally too obvious for me to notice.

Here is an older riddle, if I can call it that, which your students may love.

“Take any number. Now add 5 to it. Multiply that by 2. Subtract 6. Divide by 2 and finally subtract 2 and you back to your original number. Why does this work?”

1) Let your students try it first on a couple of different numbers

2) Now let them try to figure out why it works on their own.

3) Have them write down the whole operation, paying special attention to order of operations. (((((x + 5) * 2) – 6) / 2) – 2)

4) Again, let them try to figure out why it works on their own.

5) Ask them to go through the following operation ((((5 * 2) – 6) / 2) – 2) and see what number they get (zero is the answer)

6) Ask them to restate the Additive Identity

7) Thus, this whole problem is simply a fancy way of adding zero to your initial number.