High School: Geometry
Modeling with Geometry HSG-MG.A.3
3. Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).
Now we're getting to the fun part of geometry: playing with tangrams. Using those little plastic pieces to model neat designs, like a fox, a house, or even a swan. Unfortunately, those probably aren't the kind of design problems your students will be working on. We're talking about more about solving multi-step word problems.
Really, these types of problems differ depending on what students might be learning. It could involve calculating the maximum area of a cow's grazing plot that can be contained by 600 meters of fencing (22,500 square meters). Maybe they'll have to find the volume of a pizza box when given a surface area of 320 square inches, a height of 3 inches, and a square base (300 cubic inches). Or maybe they'll just stick to tangrams.
Whatever kinds of problems students face, they will need at least a basic knowledge of the shapes and the formulas that describe them. At the very least.
Students will also need the know-how to solve systems of equations, the mental fortitude to simplify algebraic expressions, and the plucky spirit of adventure to resourcefully draw on the vast pool of their geometric enlightenment as they pick and choose exactly which formulas will serve them best, and modify them as needed.
Tangrams have got nothing on these design problems.