Algebra, the gateway to higher mathematics, introduces a new language of symbols and equations to young learners and challenges them to think abstractly. It is both a fascinating and formidable mathematical concept, taking students further away from their mathematical dependence on real world objects.
This shift from concrete arithmetic operations to the manipulation of variables and unknowns means that some can find algebra difficult to grasp. In fact, I’ve written about the fear of Maths in my blog here and why overcoming this is to one’s advantage.
Understanding why algebra feels challenging is the first step towards mastering it, and I’ve outlined 7 things to consider so that you can improve your algebraic comprehension!
1. Master the Basics
Walk before you can run! Ensure you have a solid understanding of basic arithmetic, fractions, decimals, and percentages, which are the foundational skills for algebra. Think about number sentences (or better known as ‘mathematical expressions’) like a tipping scale: each side needs to be equal in order to stay balanced.
Let’s look at this equation for instance:
Each side must equal the same sum: in this case, 10. We know that 2 + 8 = 10, so x = 2.
To prove this algebraically, we need to isolate the variable - a symbol representing an unknown value (usually expressed as a letter of the alphabet). To balance each side of the equation, whatever we do on one side, we must do to the other:
2. Understand the Order of Operations
Remember the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) to solve expressions correctly. Looking at this problem, what might the answer be? Highlight here (x = 1) for the answer.
This is because we solved what was in the parenthesis (or brackets) first before moving onto the next steps. Understanding the order to solve an expression will help you to solve questions like this:
3. Practice, Practice, Practice!
Like anything worth the effort, algebra requires consistent practice. Working on problems daily reinforces concepts and looking at worked-out examples in textbooks or online resources will help focus your understanding of how a problem is solved step-by-step.
There are many free online tutorials, videos, and apps on the web which can provide different perspectives on solving algebraic problems. The BBC has a terrific set of pages which explains different algebraic concepts and contains quizzes to complete along with their correct answers.
4. Seek Help When Needed
Don’t hesitate to ask for help from teachers or peers if you're stuck on a concept or problem. If the problem proves too tricky, why not consider finding a tutor with Titanium Tutors? We are home to a team of experienced and dedicated tutors and teachers who would be more than happy to guide you through any mathematical problems, or even provide you with a layer of challenge, if that is what you are looking for.
5. Break Down Problems
Tackle complex problems by breaking them down into smaller, more manageable steps. Simplifying terms reduces an initially lengthy question:
According to the National Curriculum, pupils tackling algebra will be expected to use and interpret algebraic notation, including the following:
ab in place of a × b
3y in place of y + y + y and 3 × y
a² in place of a × a, a³ in place of a × a × a; a²b in place of a × a × b
in place of a ÷ b
coefficients written as fractions rather than as decimals.
6. Double and Triple Check Your Work
Always go back and verify your solutions. Not only is this good practice, but it also helps you spot any errors in calculations and review logical steps methodically. In algebra, we can check a solution to an equation by replacing the variable in the equation with the value of the solution (also known as ‘plugging in’).
Can you tell whether x = 3 is indeed the answer by applying this back to the equation?
…Yes, because both sides will equal 13!
7. Learn to Translate Words into Maths
Practice converting word problems into algebraic expressions and equations! Not only is this skill crucial for solving real-world problems, but it also forces you to apply concrete situations into abstract expressions.
Let’s look at this example, which deals with a simultaneous equation: James is 3 times Allen's age. If I multiply their ages together, I get 48. How old are James and Allen?
Let’s express this in two equations:
James = 3 x Allen (simplified to j = 3a)
James x Allen = 48 (simplified to j x a = 48)
We can plug the first equation into the second equation, so that we only have one variable to contend with (also known as the elimination method). This combined equation becomes:
If we know that Allen is 4 years old, then James is 12 years old, as j = 3a (or James = 3 x Allen).
Acing Algebra
Algebra is the foundation for many mathematical concepts, whether navigating personal finances or pursuing advanced studies in science and technology. Algebra equips us with the tools to tackle a multitude of challenges. Embracing algebra not only enhances our intellectual agility, but also opens doors to a world of opportunity!
Blog Post Crafted by Cheryl
Cheryl manages our Admin Team, and is a qualified teacher with 5 years' experience in schools across England and Canada.
Cheryl graduated from University of Toronto with a Bachelor of Education. She tutored secondary school students in English for over nine years in Canada.
Cheryl speaks Cantonese, English and French, and in her spare time, she can be found illustrating and reading children’s books for inspiration.
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