Then give them some simple calculations to do. (Amazingly, they all seem to get it wrong, so maybe do these twice before you do it on the blackboard.)
Choose a number. Multiply it by 2 (or you can say “Double it”). Add 16. Divide by 2. Subtract the number you started with.
Then get their answers. (The answer should be 8.)
2x + 16   x = 8. Do it again if most of them are wrong, then show them this. 2
Another easy one.
Choose a number. Add the next highest number. Add 9. Subtract the number you started with.
This time you can tell them what number they started with:
x + (x + 1) + 9  x = x + 10. So just subtract 10 from their answer to tell them their number.
More difficult this time.
Choose a number bigger than 5. Add 11. Multiply by 6. Subtract 3. Divide by 3. Subtract your number minus 6 (this is where they fuck up). Subtract your number plus 1. Divide by 2.
Get their answers. (The answer should be 13.)
6(x + 11)  3   (x  6) ? (x + 1) = 26. 3
After this, do something different. Tell them you are going to prove that 1=2. They have to tell you what’s wrong using the new words.
Let x = y. Then x ? y = 0; also, 2x  2y = 0. So x ? y = 2x  2y = 2(x  y) …………*
1 = 2.
Of course, to do this, you divide both sides by x ? y (when you get to *). But x ? y = 0, and you can’t divide anything by 0. This should be their explanation. Usually they just say x ? y = 0 and leave it at that. Tell them you know that. In fact, you told them that. So make them tell you more and coax the full explanation out of them.
Now prove that 2=3.
4  10 = 9  16 => 4 ? 10 + 25/4 = 9 ? 16 + 25/4 => (2 ? 5/2) squared = (3 ? 5/2) squared ……….* => 2 ? 5/2 = 3 ? 5/2 => 2 = 3.
There are two ways for them to tell you why this is wrong. At * you divided the lefthand side by 1/2 and the righthand side by +1/2. Or they could tell you that you have said (at *) that the square root of x squared is equal to x but, in fact, the square root of x squared can be +x or ?x. But you would have to help them and tell them this English also.
This can all be pretty funny. I have been called strange, stupid, etc. I counter with “Yeah, but I can tell you what’s wrong, but you can’t tell me.”
Finally, give them this to think about.3 men go to a restaurant for dinner. Dinner costs $25 so each man puts in $10. The waiter takes the $30 and brings back $5 change. Each man then takes back $1 and they leave a $2 tip. So now each man has paid $9 each and the waiter has $2. But 3 x 9 +2 = 29. Where’s the extra dollar?
Don’t write anything on the board for this. Make them listen and watch their faces. Here’s the answer. There are two ways of looking at what happened to the $30.
 30 = 3 x 9 (each man paid) + 3 (in their pocket)
 30 = 25 (meal) + 2 (tip) + 3 (in their pocket)
You can look at it one way or the other, but you can’t just take whatever numbers you want from two different equations. In other words, the $27 paid for the meal AND the tip and they have $3 in their pocket. This is just a trick with words (or numbers) to fill up the lesson.
