Here is a closed lunch bag. Nobody can see inside, but we know it holds some counters. We do not know how many yet, so let us call that hidden number n.

If we drop three more counters into the bag, how many counters would be inside now?

In the opening we called the hidden number n. We can use any letter to stand for an unknown, so for the balances we will use x. It is doing exactly the same job that n did.

Watch three balances on the board. On each one, a bag holding x counters (and sometimes some loose counters) sits on the left pan, and loose counters sit on the right. The beam is level, so the two pans weigh exactly the same.

Look at the next one. The bag on its own balances five loose counters, so what must the bag be holding?

Now two identical bags balance ten counters. Both bags hold the same amount, so what must be inside each one?

Now we work through these balances together on the board. One pupil comes up to the board while the rest of the class predicts and checks aloud. Slide the bag value until the beam sits level. Say the value of x aloud before you check it.

• x + 3 balances 9
• x + 4 balances 6
• 3x balances 9
• 2x + 1 balances 11

Now we solve these balances one after another. Each one has a bit more to think about than the last. Predict the value of x, level the beam, and check with the class.

• x + 3 = 7
• 2x = 12
• 3x + 1 = 10
• x + 5 = 5
• 2x + 3 = 15