“Equations are easy, Sir,” says the Year 9 pupil. “You just grab a number, chuck it on the other side of the equals and it changes sign.” So, for one example of this pupil’s theory, divide by negative 5 becomes multiply by positive 5; for another example, 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 dares to ask. “Dunno, Sir, leave me alone.”
I have had many heated discussions with colleagues over this. The problem is, of course, that the “change side, change sign” method works absolutely perfectly for a great number of equations. Indeed, pupils can sail merrily along through the world of algebra right up to GCSE and this method will not let them down. Of course, as soon as they hit quadratic equations or algebraic fractions, the boat starts to sink.
I have a two-pronged attack for teaching pupils how to solve equations. First, I make sure that pupils are happy with the order of operations. Pupils must be able to distinguish the second example above from + 3 = 5.
With Christmas still relatively fresh in the memory, I have found that talking about wrapping presents helps here. 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 the m to find out what it is, we need to deal with the divided by 4 first, before the plus 3.
Once pupils are happy with this and the idea of inverse operations, then I go down the route of the “balance 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, pupils would divide both sides by negative 2 in order to cancel out the multiply by negative 2.
It is likely to take pupils longer to be able to solve equations using this method, and some moments of frustration will lie ahead for all involved. However, it is undoubtedly more mathematically sound than whizzing things back and forth across an equals sign and watching them magically change.
Craig Barton is an advanced skills teacher from the Bolton area. He is the creator of www.mrbartonmaths.com and can be found on Twitter @mrbartonmaths
What else?
A number of resources and collections on TES Resources may help to tackle the problem. Check out mrbartonmaths’ 10-unit algebra collection or “Study Units and Equations (MEP-GCSE-Unit 10)” from CIMT.
Or why not try a fun Tarsia game to untangle algebra?
In the forums
Share your thoughts on Conrad Wolfram’s ideas about maths education.
A teacher asks how they can make algebra more appealing to their Year 11 bottom set. Can you help?
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