Research-based guidance and classroom activities for teachers of mathematics

Solving equations

Solving equations is a theme within functional relations between variables. Links to relevant activities and resources are on the right hand side of this page. 

Equations are a statement of quantitative equality between two expressions.

Before diving straight into manipulations, it is helpful for students to talk about the different kinds of equations. For example, although the following are all seen as equations, only some of them can be ‘solved’ in the sense that values can be found for variables that make the equality true:

  • 2x -5 = 11 (children may be familiar with ‘hidden number’ problems)
  • 3x-5=9-2x (equality of expressions for particular values of variables)
  • 5x-10 = 5(x-2) (an identity true for all x)
  • y=2x+5 (a function which defines values for y dependent on values for x)
  • A=1/2 bh (an algorithm for finding area of a triangle, or a function, or a formula)
  • v2- u2= 2as (a formula in which values can be substituted)

Linear equations can be seen as processes that need to be undone, but a more general meaning is two expressions that need to be made equal to each other. For higher polynomials it is generally meant that a function has to be made equal to zero, as in ‘solve a quadratic’.

Algebraic methods for solving equations at school level can usually be illustrated by relating expressions graphically so that the processes have meaning in terms of functions.