Algebra is one of those topics in maths that can cause no end of problems later on if it’s not properly understood at the beginning. Recently I met a 16-year-old student who’d managed to get a long way without properly understanding algebra, but then got stuck as her questions got harder. Going right back to the basics, she was able to unravel it.
I’m going to share a method that I learnt a couple of years into my tutoring, and have slowly refined over the last decade through the help of my fellow tutors and wonderful students.
Firstly, here are the basics that you should know:
Children are often taught the basics of algebra using boxes like this:
Easier questions like this can often be solved by inspection. That’s simply the posh way of saying ‘I looked at it (or inspected it) and knew the answer.’ Students who know that adding 3 and 7 makes 10 can see that the missing number must be 7.
Drawing boxes all the time can be a bit fiddly, especially if there is more than one missing number - how do you know which box is which? So in algebra we just replace these boxes with letters. Let’s pick “a”.
In this case a = 7, because 7 + 3 = 10.
So, inspection works for easier questions like this. What happens when things get more complicated? The answer: we use the arrow method.
The ‘arrow method’ is a way of solving equations that use algebra. It takes a little time to understand but when you follow it properly, it is very hard to get questions wrong.
Solving algebraic equations is like a game. The aim is to get the letter on its own on one side of the equation. The first thing we do is to draw an arrow below the equal sign and place another equal sign there:
You don’t have to draw an arrow, it could just be a line. The main purpose of this is to separate the two sides of the equation from each other. On one side we have a + 3 and the other we have 10.
Now, let’s talk opposites:
So how do we get the ‘a’ on its own? We can see that 3 is being added to ‘a’ to make 10, so the opposite of adding 3 is to subtract 3:
When solving these equations, remember that what you do to one side you must do to the other. Since 10 – 3 = 7, we have the answer.
This method is vital for more complicated questions that can’t be solved ‘by inspection’.
Just a note:
In algebra we usually leave out the multiplication and division signs, instead using the following notation:
This also helps avoid confusion when the letter x is used to represent a number.
Next week we’ll look at how to solve some more complicated equations so make sure you check that out.
If you need some help with maths, why not have a look at Tutorfair’s website which has a whole list to choose from?
Here’s a selection of three of Tutorfair’s maths tutors:
George S - Enthusiastic UCL undergraduate
Melanie A - Gives children the mindset for success
Matthew S - First rate science and maths tutor;Cambridge graduate