Here is a puzzle: n + 3 = 7.

The letter n is standing in for a number we cannot see yet. What number could n be, so that when you add 3 you land on 7?

Each balance below shows an equation. One pan holds a letter that stands for a hidden number; the other holds a known amount, and when the beam sits level the letter has found its value. Watch the interactive work through five balances — look for where the letter's value comes from each time.

Today we work these out together on the board, and the beam tells us when the letter is right. Remember the take-away trick from before: put the number we took off back beside the answer, so the letter's pan balances both together. We'll do:

• n + 5 = 12
• x − 4 = 9
• 2y = 14 (remember, 2y means two lots of y)
• Aoife had some sweets, got 5 more, and now has 12: s + 5 = 12

Slide the letter until the beam sits level, then read off its value.

Now the practice round. Find the hidden number for each equation.

• n + 3 = 7
• x − 4 = 9
• 2y = 10
• p + 6 = 15
• 3m = 12 (3m means m + m + m, three lots of m)
• 2k + 1 = 11 (the tricky one — take the 1 off first, then halve, just like we did together)

Predict the value before you slide the letter, then use Check to confirm.