After students borrowed 28 books on astronomy, there were 12 books on astronomy remaining. How many books on astronomy did the library have at first? Use the Balancing Method to solve!

With the balance method you can solve equations by doing the same operation on both sides of the =-sign. The name comes from the thought behind it: A balance is an (old) weighing instrument with a scale/dish/weighing pan on both sides. On both sides of the balance you put a part of the equation.

To succeed with this method, a student simply has to apply BIDMAS and know which inverse functions are which.
So, the balance method it is. But before you can get onto teaching it, many students lack these key prerequisite understandings:

1. The equals sign means ‘the same as’ – as opposed to just ‘put the answer after this sign’.
2. Inverse operations cancel each other out and thus don’t need to be calculated.
3. Equations can be manipulated on either side.

Teaching strategies

Before you ever introduce the balance method, do the following:

Equals sign: asking students for their own definition; you’ll get some classic ‘it means here is the answer’. Push the definition of ‘the same as’.

Show examples of simple number facts using the equals sign in interesting ways: e.g. 6 = 6; or 6 = 7-1; or 2 x 6 = 9 + 3.

Ask whether these statements are true. Students should start to say ‘because 6 is the same as 7-1’. Stress such good responses. ‘Equals’ = ‘the same as’. Slowly you’ll see lightbulbs click.

Inverse operations

Start by showing lots of examples of questions like ’36 + 2 – 2 =’ that get trickier and trickier, until calculating them is too difficult. Students will then see the pattern that they cancel out. Test them, and interleave understandings of the equals sign, with quick questions