Algebra

Using Symbols and Letters for Unknown Numbers

3rd Class · 4th Class · 5th Class · 6th Class

✓By the end of this lesson students will be able to understand that a symbol or letter can represent an unknown number.
✓By the end of this lesson students will be able to solve simple addition equations with one unknown.
✓By the end of this lesson students will be able to solve simple subtraction equations with one unknown.
✓By the end of this lesson students will be able to use inverse operations to find the value of an unknown number in an equation.

Key concepts

What is an Unknown Number?

Sometimes in maths, we have a number that we don't know yet. We can use a symbol, like a box (□), or a letter, like 'x', 'a', or 'n', to stand for this missing number. These symbols or letters are placeholders for the number we need to find.

What is an Equation?

An equation is a maths sentence that shows two things are equal. It always has an equals sign (=). For example, '3 + □ = 7' is an equation because it says that '3 plus some number' is the same as '7'.

Solving an Equation

Solving an equation means finding out what number the symbol or letter stands for to make the equation true. We want to find the value of the unknown number.

Inverse Operations

To solve equations, we often use 'inverse operations'. These are operations that 'undo' each other. Addition is the inverse of subtraction, and subtraction is the inverse of addition. For example, if you add 3, you can undo it by subtracting 3.

Key facts to remember

1A symbol (like □) or a letter (like x, a, n) stands for an unknown number.
2An equation is a maths sentence with an equals sign (=) showing two things are equal.
3Solving an equation means finding the value of the unknown number.
4Addition and subtraction are inverse operations; they 'undo' each other.
5To find a missing number, you often use the inverse operation.
6Always check your answer by putting the found number back into the original equation.

Worked examples

Example 1

Find the missing number: 3 + □ = 7

IThe equation is 3 + □ = 7.

IIWe need to find the number that, when added to 3, gives 7.

IIITo find the missing number, we can use the inverse operation of addition, which is subtraction.

IVSubtract 3 from 7: 7 - 3 = 4.

VSo, the missing number is 4.

Answer

□ = 4

You can check your answer: 3 + 4 = 7. This is correct!

Example 2

What is the value of 'x' in the equation: x - 5 = 8?

IThe equation is x - 5 = 8.

IIHere, 'x' is the unknown number. Something minus 5 gives 8.

IIITo find 'x', we use the inverse operation of subtraction, which is addition.

IVAdd 5 to 8: 8 + 5 = 13.

VSo, the value of 'x' is 13.

Answer

x = 13

Remember, 'x' is just a placeholder for the number 13. We could have used a box (□) instead.

Example 3

Solve for 'n': 12 = n + 4

IThe equation is 12 = n + 4.

IIThis means that 'n' plus 4 is equal to 12.

IIITo find 'n', we need to 'undo' the addition of 4.

IVThe inverse operation of adding 4 is subtracting 4.

VSubtract 4 from 12: 12 - 4 = 8.

VISo, the value of 'n' is 8.

Answer

n = 8

It doesn't matter if the unknown is on the left or right side of the equals sign. The method is the same!

Common mistakes

✗Using the wrong inverse operation (e.g., subtracting when you should add).
✗Not understanding that the symbol/letter represents a single number.
✗Getting confused when the unknown is on the right side of the equation.
✗Making calculation errors when performing the inverse operation.

Exam tips

★Read the equation carefully to understand what operation is being used.
★Think: 'What is the opposite operation I need to do to find the missing number?'
★Always write down your steps clearly, just like in the worked examples.
★After you find your answer, substitute it back into the original equation to check if it works.

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