Problems with two unknowns

Spine 1: Number, Addition and Subtraction – Topic 1.31

Primary KS2 Year 6
Mastery PD Materials


Equip children with strategies for solving problems with two unknowns, including using the bar model to represent relationships between known numbers, and working systematically.

Teaching points

  • Teaching point 1: Problems with two unknowns can have one solution or more than one solution (or no solution). A relationship between the two unknowns can be described in different ways, including additively and multiplicatively.
  • Teaching point 2: Model drawing can be used to expose the structure of problems with two unknowns.
  • Teaching point 3: A problem with two unknowns has only one solution if the sum of the two unknowns and the difference between them is given (‘sum-and-difference problems’) or if the sum of the two unknowns and a multiplicative relationship between them is given (‘sum-and-multiple problems’).
  • Teaching point 4: Other problems with two unknowns have only one solution.
  • Teaching point 5: Some problems with two unknowns can’t easily be solved using model drawing but can be solved by a ‘trial-and-improvement’ approach; these problems may have one solution, several solutions or an infinite number of solutions.