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.

In Pursuit of Perfection of Form

Our students often never understand how they misplaced a negative symbol or added instead of subtracting. They often think of this is a part of the math process, and it is, to an extent. Many times, to my own embarrassment, I've stood in front of a classroom and butchered a problem on the white board. My only self-medication for these "duh" moments was knowing that we deal in an unforgiving science.

But still, I often wonder why our students are so sloppy in their work. I once pulled a young man, who was an incredible basketball player, off to the side to ask how he perfected is form so well in the sport. His response was of course practice. If I would have thought about it at that time I would have paralleled his form in basketball with his form in my lecture hall, but I didn't.  I'm writing this now so that you may draw this parallel with your students.


Analyzing this

May be the key to helping your students perform this