An equation is used to show two expressions that are equal to each other.

A variable is a quantity that can take on a range of values, often denoted by a letter.

A constant is a term that does not change; it contains no variables.

Like terms are terms that have the same set of variables and corresponding exponents.

Securing understanding of equality

Maths

Checking understanding of algebraic notation

Different types of equations

Equality in an equation

Solution to an equation

Many equations, one solution

Solving simple linear equations with an additive step

Solving simple linear equations with a multiplicative step

Preparing to solve two step linear equations

Solving two step linear equations

Rearranging to solve linear equations

Solving complex linear equations

Brackets in equations

Solving linear equations where brackets are used

Solving complex linear equations involving brackets

Solving linear equations graphically using technology

Problem solving with linear equations

In this unit, pupils learn how to rearrange an equation to find a specific value that satisfies the equation. In expressions and formulae, pupils use their understanding of rearrangement to change the subject of a formula.

In the prior unit, pupils saw that an arithmetic sequence can be represented graphically and that this is a linear relationship. Any point on the line satisfies this relationship. In this unit, pupils learn how to find a value that satisfies the relationship when the second value is known, without the aid of the graph.

In this unit pupils will learn how to find a value that satisfies a linear relationship when one value is known both with a single step operation, and multiple step operations. A variety of cases are explored including using brackets and rearranging.

Solving linear equations

Terms with the same coefficient for each variable.

Terms with the same set of variables and corresponding exponents.

Identical terms which have the same coefficient and same variables.

Terms with the same variable and different exponents. 

Which of these is the best definition for like terms?

These 5 bar models represent operations performed on the equation $$x + 9 = 22$$. Match the bar models labelled A, B, C, D and E with the equivalent equation they represent. 

This bar model represents the initial equation $$2a + 6 = 14.$$ What needs to be done to the bottom bar to maintain equality?

If $$x + 5 =2$$, which of these equations have maintained equality?

If $$a = b$$, which of the following are true?

Which expression could fill the blank on the right hand side of this equation to maintain equality?

Aisha is $$a$$ years old. Which of these is an expression for her age 2 years ago?

Andeep is thinking of a number, when he adds 2 then multiplies by 5 he gets 27. Which of these equations represents his number?

Which equations are represented by this bar model?

Select the calculation that is equivalent to $$8+4\over 4$$.

Which expression is represented by this bar model?

Match each expressions containing brackets with its expanded form. 

Securing understanding of equality

Lesson outcome