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

Equality in an equation

Maths

Checking understanding of algebraic notation

Securing understanding of equality

Different types of equations

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

Which equations are represented by this bar model?

If $$31 − x = 17$$, which of these equations are also true?

The triangle has the same mass as 1 square.

The triangle has the same mass as 2 squares.

These scales are not balanced. The mass of all the square objects are the same. Which statements are definitely true?

The diagram shows a balanced scale on the left. When an operation is performed to the RHS, it is not balanced. What operation must be performed to the LHS to maintain equality?

The diagram shows a balanced scale on the left. When an operation is performed to the LHS, it is not balanced. What operation must be performed to the RHS to maintain equality?

Which expression is represented by this bar model?

Select the bar model that correctly represents the equation $$3x + 15 = x + 32$$.

Given that $$2.4 + 3.7 = 6.1$$, which of these are also true?

This bar model represents the initial equation $$x + 16 = 27$$. What needs to be done to the top bar to maintain equality?

This bar model represents the initial equation $$2x + 5 = 9$$. What needs to be done to the top bar to maintain equality?

These 4 bar models represent operations performed on the equation $$x + 12 = 19$$. Match the bar models labelled A, B, C, D  with the equivalent equation they represent .

Starter Quiz

Which expression is represented by this bar model?