The Manager of “Trevaskis Engineering Pty Ltd” pondered the problem that his most recent customer had given him. “I need a 50% perforated rectangular sheet (900 x 600) of metal with 10mm holes”. He thought: “What spacing should I have between the circles so that there is exactly 50% metal and 50% holes? Should the centre of the holes be in a square or triangular grid?”
I produced a worksheet: 51 Sheetmetal Engineering for this task 2 years ago. It was based on a discussion with the manager of Trevaskis Engineering Pty Ltd. So this is not a contrived problem, but a real world problem that the manager had to solve before presenting the final design and quotation to the customer. Sheet Metal Engineering is rich with applications of mathematics. Stay tuned for future posts!
In line with WCYDWT tasks proposed by Dan Meyer, I now realize that this task could be made much more open ended. Firstly the story shell could be altered to allow the student to expand the problem, and show their ability to apply their mathematical and problem solving skills. The step by step directions on the worksheet could be held back, and used for students who are struggling and need help to scaffold the problem.
Of course the problem is not purely mathematical. Minimum distances from the edge of the sheet and between holes are important so as not to weaken the sheet too much. An investigation of design formulas could be made to apply some restrictions. This task also lends itself to visualizing different hole patterns and drawing these.