# The mystery-box idea Imagine a closed box. Inside is a number. You may not open it — but you can still **do things to the box**. - Box plus 3 → `x + 3` - Two boxes → `2x` - Box minus 5 → `x − 5` - Box shared into 4 equal parts → `x/4` or `x ÷ 4` ## Same box, same number If you use `x` twice in one problem, it is the **same** mystery number both times. `x + x = 2x` Not “two different surprises”. ## Different letters `x` and `y` can be different numbers — two different boxes. > Picture two gift boxes: red = x, blue = y. Do not mix their stickers. ## Picture the box, then write Close your fist. That fist is x. You still do not know the number inside. - Put 3 pebbles next to the fist → `x + 3` - Make a second identical fist → `2x` - Take 5 pebbles away (if the story says so) → `x − 5` - Split whatever is in the fist into 4 equal shares → `x/4` You did not open the fist. That is the whole point. ### Why this picture saves you later When equations get longer, students who only memorise “move to the other side” get lost. Students who see a box can ask: *what was done to my box?* Then they undo it. ### Same box, same number — a classroom trap If a question uses x three times, it is not three different secrets. It is three views of one number. `x + x + x = 3x` always, in that problem.