What the equals sign means

1. This is a balance. There is a 6 in each pan. The two sides are the same, so the beam sits level.
2. Change one side and it tips. Now there is a 4 on that side instead of a 6. The sides are not the same any more, so the beam tips. The bigger side goes down.
3. 8 + 4 balances 12. 8 and 4 in one pan. 12 in the other. 8 plus 4 is 12. So the sides are the same, and the beam is level again.
4. That is what the equals sign means. We write 8 + 4 = 12. The equals sign is doing the job of this beam. It says the two sides are THE SAME. It does not mean “the answer comes next”.
5. Here is the one that catches people. Someone has written 12 in the box of 8 + 4 = ? + 5. Now that side is 12 and 5, which is 17. Look at the beam. 17 is not the same as 12.
6. Your turn. Make it balance. The box is empty. Press the buttons to change it. Find the number that makes both sides the same, and the beam will go level.
7. 7 is the one that balances. 7 and 5 is 12. 8 and 4 is 12. Both sides are the same. So the beam is level, and the equals sign is telling the truth.
8. Last check. Same puzzle, new numbers. Think about what makes the two sides the same. 5 + 3 = ? + 2. What goes in the box? 6 · 8. Yes. 6 and 2 is 8, the same as 5 and 3, so it balances.

The equals sign means the two sides are the same. It is not a sign saying “the answer comes next”. So in 8 + 4 = ? + 5 the box is 7, because 7 and 5 is 12 as well.