For many parents, the word “algebra” conjures up stressful memories of complex equations from their own school days. So, when you see it listed as a topic for the 11+ exam, it’s easy to feel a sense of dread.
But here’s the good news: algebra at the 11+ level is not about complicated quadratic equations. It’s simply about logic and finding the missing number in a puzzle.
At elevenplus.com, we believe any child can master the basics of algebra with a clear method and a little practice. This guide will demystify the topic and provide a simple, step-by-step framework to solve any 11+ algebra problem with confidence.
In this definitive guide, you will learn:
- What 11+ algebra really is (and what it isn’t).
- The golden rule of “balancing the equation.”
- A simple, step-by-step method for finding the value of the unknown.
- A clear worked example showing the method in action.
- Expert tips, including the importance of BODMAS/BIDMAS.
Algebra is Just a Puzzle
Before we even look at letters, let’s start with a simple puzzle. Many 11+ questions look like this:
[Image: A simple symbol puzzle, e.g., “If △ + 5 = 9, and O – △ = 3, what is O?”]
To solve this, your child instinctively knows they need to find the value of the triangle first. They can see that △ must be 4. Once they know that, they can solve the second puzzle: O – 4 = 3. Therefore, O must be 7.
That’s it. That’s algebra. Instead of using a triangle (△) or a blank box (▢), we just use a letter (a, x, n) to represent the unknown number.
The Golden Rule of Algebra: Keep it Balanced!
The most important concept in algebra is the equals sign (=). Think of it as the centre of a balanced scale. Whatever you do to one side of the equation, you must do the exact same thing to the other side to keep it balanced.
If you have a + 5 = 12, and you want to get a on its own, you need to take 5 away from the left side. To keep the scale balanced, you must also take 5 away from the right side. This is the core principle that unlocks every algebra problem.
The 3-Step Method to Find the Unknown
To solve for the unknown letter, your child needs to get it on its own on one side of the equals sign. The way to do this is by “getting rid of” the other numbers around it by using inverse operations (the opposite action).
- The inverse of add (+) is subtract (-).
- The inverse of subtract (-) is add (+).
- The inverse of multiply (x) is divide (÷).
- The inverse of divide (÷) is multiply (x).
Here is the simple, repeatable 3-step method:
- Identify the Goal: Your goal is to get the letter on its own.
- Isolate the Letter: Look at what has been done to the letter and do the inverse operation to both sides of the equation to keep it balanced.
- Calculate and Check: Perform the final calculation to find the value of the letter, then plug it back into the original equation to check your answer.
A Worked Example
Let’s apply the 3-step method to a typical 11+ question.
Question: If 4a + 7 = 35, what is the value of a?
1. Identify the Goal: We need to find the value of a. To do this, we need to get a by itself on the left side of the equation.
2. Isolate the Letter (in two steps):
- First, we need to get rid of the “+ 7”. The inverse of adding 7 is subtracting 7. We must do this to both sides to keep the equation balanced.
- 4a + 7 – 7 = 35 – 7
- This simplifies to: 4a = 28
- Now, we need to get rid of the “4”. “4a” means “4 multiplied by a”. The inverse of multiplying by 4 is dividing by 4. We do this to both sides.
- 4a ÷ 4 = 28 ÷ 4
- This simplifies to: a = 7
3. Calculate and Check:
- Calculate: We have our answer: a = 7.
- Check: Let’s plug it back into the original equation to be sure.
- (4 x 7) + 7 = ?
- 28 + 7 = 35.
- It’s correct!
[Image: A simple graphic showing a balanced scale. On one side is “4a + 7” and on the other is “35”. An arrow shows “-7” being applied to both sides.]
Expert Tips for Success
- Remember BODMAS/BIDMAS: The order of operations (Brackets, Orders, Division, Multiplication, Addition, Subtraction) is crucial. When isolating the letter, you are essentially working backwards through BODMAS.
- Translate Words into Algebra: Some questions will be presented as word problems. For example, “I think of a number, multiply it by 3, and add 4. The answer is 19. What was my number?” Teach your child to translate this into an algebraic equation: 3n + 4 = 19. This turns a wordy problem into a simple calculation.
- Practice Makes Perfect: The more your child practises these simple steps, the more automatic they will become. Confidence comes from familiarity.
Algebra at the 11+ level is a test of logic, not complex maths. By understanding the principle of the balanced scale and mastering the use of inverse operations, your child can turn this potentially intimidating topic into a source of easy marks.
Ready to put these algebraic skills to the test?
➡️ Our 11+ Maths Practice Packs are filled with algebra-style questions that will help your child master this key topic and build their confidence for the exam.
