Equations and unknown numbers
Recognise the model, justify the rule and solve independently.
IKMC Grades 7-8 - Selected Topics
State exactly what the unknown represents, including its unit, before writing an equation.
Write the same total in two ways, from a shortage and from a surplus, then set the two expressions equal.
Use $x^2-y^2=(x-y)(x+y)$ with a known nonzero sum to find a difference without finding each number.
Use integer, sign and divisibility conditions to narrow down the possible solutions, then check every remaining candidate.