Thursday, 9 May 2013

Solving equations - life from both sides

Equation problem

Solving equations can be taught time and time again, but what percentage of a class can perform the complex operations involved. What percentage could repeat what they have done a day later? To us it seems obvious that 'what we do to one side we to the other', how frustrating then that this simple procedure seems to be so difficult for many students to grasp.

I have often been bewildered by students who could solve equations one day but not have a clue the next. I would ask myself what was wrong with them? Followed by what was wrong with my teaching? What else could I do? As a young teacher I asked my colleagues what they did they reassured me the same as me and not to worry most kids don't understand equations.

The root of the problem

It is not so much being able to reach an answer that causes the problem more it is the lack of appreciation that the equation has two distinct sides. They are also equal. Once this fact is conquered the next issue is the. Realisation that what you do to one side you do to the other.

The solution

This article is about tackling the both sides problem. When this was first suggested to me I was very cynical. Why should I try this I've always taught solving equations the same way, with the same amount of success as everyone else. But I decided to give it a try. Many pupils have a problem balancing an equation. Many Maths books have  pictures of weighing scales, some letters and numbers are placed in either tray and successive numbers and letters are removed until a satisfactory result is arrived at. But it doesn't mean much to pupils, how any of them have seen scales in this digital age?. This analogy doesn't seem to help much. This is what I tried and it was really successful.

First I wrote a simple equation on the board like this.

Most pupils will be able to tell you that x is 2. But that is not the object of the exercise, you want to get them to realise that what ever you do to one side you do to the other. I know you can tell them that but it doesn't not always register. I now ask them for a number any number which I then add to both sides. For xample lets say they chose 5 I would write

Putting the arrows on and in different colours has proved to me to be very important. It places the emphasis on what we are doing to both sides not on why we are doing it, that will come later. I then ask for another number. Lets ssume someone says 100.

I quite happily write +100 on both sides and continue. I might then suggest or it could come from the students subtracting. I then give an example of subtraction.
It depends upon the class how long you continue this. You could demonstrate a few more examples on the board, or put a starting point and get pupils to come up to the board and take suggestions from the class and develop the equations that way. It is not important to find x your objective is to get them to understand how to balance equations. I would follow this up with individual work, giving them starting points and letting their creative juices flow. 
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