When you are a young teen just learning algebra, it can feel like a whole new world. Yet, there is no running away from it because it is the foundation to so many other math topics in secondary school and beyond.
So, if your child is having trouble making sense of algebra, or always making the same mistakes in his or her math exam, we’ve got just the thing for you. Below, we’ve gathered some advice from our math tutors that will help Sec 1s who are still quite new to algebra.
Read on for tips and common mistakes that you can use in your revision or to help your child in algebra!
1. Think in terms of algebra
Algebra often stumps sec 1 students because of its ‘abstract’ nature. From dealing with numbers, there are suddenly random letters like x, y, z in math! Oh, the horrors!
But once the student understand that ‘x’ or any letter is simply a letter to represent an unknown, it becomes much easier to grasp. For ultimate beginners, it will be helpful to translate daily encounters with numbers into algebra.
Let’s say, I give you 2 apples, and now you have 7. You can easily think of it as a equation:
x+2=7, where x is the original number of apples you had.
If you want to find x, it is simply a matter of performing the same operations on each side of the equal sign (so that both sides are still equal to each other!), until one side is left with x.
In this case, you can remove the 2 on the left side of the equation by subtracting 2 to both sides.
x+2-2=7-2
and viola, this will give you the answer:
x=5
Of course, algebra becomes more difficult when things like factorisation, exponentials, and multiple unknowns enter the picture. However, getting used to ‘thinking in algebra’ and solving simple equations is the first step to master before moving on to more advanced techniques.
2. Be very, very familiar with the BODMAS rule
It’s intimidating to encounter a complex-looking algebra equation that you need to solve. Where do we begin?
In comes the BODMAS rule (or some call it by PEMDAS)! This rule is the order of operations that you should work on when encountering mathematical expressions with multiple mathematical operations.
- Bracket
- Order of power
- Division
- Multiplication
- Addition
- Subtraction
It should be noted that division and multiplication should be worked on in left to right order. For example, if multiplication appears to the left of the division sign, do the multiplication first.
The same goes for addition and subtraction – they should be worked on in left to right.
Although many students are taught the BODMAS rule, they often mess it up as they try to rush through their work. Sometimes, complicated equations can also confuse students. As such, the best advice we can give is to ‘KEEP CALM’, and read the problem properly before starting to work on it.
3. Do not mix up your factors and powers!
Has there been a time you did something like this?
(a+b)2 = a2 + b2
To be clear, that above equation is wrong!
Students who do this are often confused because they think that exponentials work the same way as factors:
2(a+b) = 2a + 2b
However, a different set of rules apply for exponentials. To work out (a+b)2, you will actually need to rewrite it into (a+b)(a+b) and expand it from there.
(a+b)2
=(a+b)(a+b)
=a(a+b)+b(a+b)
=a2+ab+ba+b2
=a2+2ab+b2
As you can see, the result is very different from the original (wrong!) answer we first showed you. Because expressions like (a+b)2 and (a-b)2 are very common in algebra problems, it is also a good idea to memorise their expanded forms to save time during the exams.
(a+b)2 = a2+2ab+b2
(a-b)2 = a2−2ab+b2
4. Remember the negative signs
In secondary school math, we are introduced to the negative sign. But because it is a pretty new concept to Sec 1 students, it is frequently misused or forgotten.
One common mistake is forgetting to consider the minus sign when factoring an expression. For example, in expanding x – 2(x+3) ,
x – 2x + 6 is the wrong answer.
x – 2x – 6 is correct.
Rather than thinking of it as just a ‘minus’, perhaps it is easier to remember that the minus sign is attached to number to the right side of it. So, when you are expanding the expression, you are not doing 2×3, but rather, (-2)x3.
Another very avoidable but often-seen pitfall is forgetting the negative sign due to poor handwriting! Always make sure that any negative signs are clearly written, obvious enough for yourself and the examiner to see.
5. Practice. A lot.
We cannot emphasise this enough. You may be able to learn all the rules well, but without practice, you cannot truly internalise it. You may take longer to recall the formulas and decide on the right steps to do, wasting precious time during the exams.
When you practice a lot of algebra questions, your brain reacts faster as it recognises the common expressions and you immediately know what to do. It will almost become a reflex!
Unfortunately, there is no shortcut to this – unless you are a mathematical genius!
Conclusion
Although there is no real ‘easy way out’ to learn algebra, we can make it slightly easier for you! At Future Academy’s secondary school math tuition, we provide plenty of practice opportunities for you to hone your algebra skills. You will get access to topical worksheets that train specific skills, as well as practice papers to get yourself used to the rigour and standards of the exams. Of course, you will also enjoy close guidance by our expert math tutors – many of whom are former teachers from top schools in Singapore!
Studying in the Integrated Programme? Not to worry, we also offer IP math tuition for students in schools like RGS, HCI, NYGH, RI, and more. Join us to get a grip on algebra for your child!