This is an algebraic and computational investigation which guides pupils to systematically discover and prove all unique integer-sided cuboids that share a fixed surface area of 250 square units.

It moves beyond simple trial and error by prompting pupils to establish logical upper and lower bounds for their variables, rearrange formulas, and utilise a spreadsheet to model and exhaustively count the solution set.

• Calculating the surface area of cuboids
• Changing the subject with factorisation
• Basic familiarity with writing formulae in MS Excel or Google Sheets

• Check the attached teacher sheet, and confirm with computer science that pupils have requisite knowledge of spreadsheets.

• It is suggested at the beginning of the lesson you go through how you might calculate a third variable in a spreadsheet given the values of two other variables. For example, you could generate Pythagorean triples by varying the values of $x$ and $y$ in a two-way table and writing a formula to calculate the value of $z$.