Patterns and Algebra
Try this: Pick a number. Double the number. Add 4. Cut the number in half. Subtract the original number. Is your answer 2? If not, something went wrong. If your calculations were correct you should have 2. Now how can I possibly know this without knowing your original number? When people first hear this trick it is often very impressive, as it was for me as a child. But I'm gonna ruin it now by showing why mathematically it is obvious. This trick is a good way to introduce algebra. We can use algebra to show why this works.
2x+ 4
2x+ 4
When we divide 2X by 2, the 2s cross out and we are left with X. we also divide the 4 by 2 and are left with X+2
-x =2
-x
2
2
Where X represents the original number you chose, this equation represents what you were asked to do. Double it, add four, divide all that by 2, then subtract X.
(x+2)-x=2
Very important we keep X+2 in brackets. This represents the number we got by dividing (2X+4) by 2, Since we don't know what X is, we need to represent the number using a combination of X and numbers. The number here is two more than whatever X is.
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Now we subtract X from this number. What are we left with when we take X+2 and remove the X? Of course, w are left with 2. No matter what number X was, the result is the same.