What’s it all about?

“Equations are easy, Sir,” says the Year 9 (S2) pupil. “You just grab a number, chuck it on the other side of the equals and it changes sign.” So divide by negative 5 becomes multiply by positive 5, and plus 3 is magically transformed into minus 3.

“Why does the minus 5 become a positive 5, and why do you move the plus 3 first?” the teacher asks. “Dunno, Sir.”

The “change side, change sign” method works perfectly for a great number of equations right up to GCSE, but as soon as they hit quadratic equations or algebraic fractions, it doesn’t, writes Craig Barton.

In search of solutions

I have a two-pronged attack for teaching pupils how to solve equations. First, I make sure they are happy with the order of operations. They must be able to distinguish the second example above from + 3 = 5.

Talking about wrapping presents helps. In this example, the m has first been wrapped up with a plus 3, then with a divided by 4. So, when we are unwrapping them to find out what it is, we need to deal with the divided by 4 first, before the plus 3.

Then I go down the route of the “balanced method”, where pupils record and carry out the same operation to both sides of the equation to keep things equal. So, in the first example above, they would divide both sides by negative 2 to cancel out the multiply by negative 2.

It is likely to take pupils longer to solve equations this way, but it is more mathematically sound.

Find out more

Check out mrbartonmaths’ 10-unit algebra collection or “Study Units and Equations (MEPT-GCSE-Unit 10)” from CIMT.