Lesson 1: The Geometry of Rotation—Circumference & Area
Duration of Days: 2
Lesson Objective
SWBAT: Calculate the circumference and area of a circle using the standard formulas C = pD and A = p r^2.
Solve for the area of circular segments and compound shapes found in industrial gaskets and flanges.
How do we quantify a curved object using linear numbers?
Why is p (Pi) the most critical constant in the machine shop?
Circumference, diameter, radius, p (Pi), area, sector, circular segment, chord, compound shape, flange.
CTE.MFG.B.07 (Solve problems involving area)
CCSS.Math.7.G.B.4 (Area and circumference of a circle).
Students explore the quantitative properties of circles. The purpose is to move beyond basic shapes to understand how "roundness" is calculated for material estimation and part surface area.
DOK Level: 2 (Skill/Concept)
Support: Provide a "Circle Cheat Sheet" that visually defines the difference between radius and diameter with color-coded formulas.
Extension: Have students calculate the weight of a circular steel plate given the surface area and material thickness.
"The Gasket Challenge" – Students calculate the total square inches of material needed to manufacture a specific set of circular industrial gaskets.