Equations
(KS3, Year 7)

The Lesson

An equation tells us that two things are equal. Equality is denoted by the equals sign (=).

Dictionary Definition

The Oxford English Dictionary defines an equation as "a formula affirming the equivalence of two quantitative expressions, which are for this purpose connected by the sign."

Understanding Equations

An equation says that two things are equal by writing them either side of an equals sign. The value on the left is equal to the value on the right. At its simplest, an equation can tell us that a number is equal to itself:

We can include operations in equations. We can rewrite 2 = 2 as:

This is true because if 1 + 1 and 5 − 3 both equal 2, they must equal each other.

Equations in Algebra

We can use equations in algebra. An equation in algebra uses letters to represent numbers. These are called algebraic equations Let's use the letter x to stand in for a number:

This equation is only true when x = 2. Another algebraic equation is shown below:

Again, this equation is only true when x = 2. x = 2 solves the equation because both sides of the = sign are only equal when x equals 2 (2 + 3 = 5).

The Parts of an Equation

An equation is shown below. It is an equation because it has an equals sign.

Each number or letter (or both written next to each other) is a term. When the terms are added or subtracted, they form an expression.

The = Sign

The first recorded use of the equals sign = in an equation (as well as the plus + and minus − signs in an English book) was by Robert Recorde (1510 - 1558).

It appears in his book 'The Whetstone of Witte':

It is equivalent to '14x + 15 = 71' in today's notation. He chose two parallel lines of equal length, "bicause noe 2 thynges can be moare equalle."

Variables, Constants and Coefficients

  • Variables can take different values. They are shown by letters: x, y and z.
  • Constants can only take one value, like 2 or 5. They are usually shown by numbers but are sometimes shown by letters: a, b and c.
  • Coefficients are constants written in front of a variable. They are multiplying the variables. For example in the term 4x, 4 is the coefficient of x. It means x is multiplied by 4.

Equations ("Tetris" Game)

Here is an interactive game to help you learn about equations.

Tip: If the game is playing slowly, you can use the controls below to remove the background text and image to speed up the game.

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See Also

What is an operation? What is a term? What is an expression? What is a variable? What is a constant? What is a coefficient?