Circumference and Area of a Circle
Length and area for a shape with no straight sides. A part of a circle is measured by its share of the whole turn, so a central angle out of 360 does for a circle what a fraction does for a bar. Mixed boundaries -- some straight, some curved -- are handled piece by piece, and rolling turns circumference into distance.
grade 7–8 GeometryRatios Draw a DiagramIdentify Subproblems
Progression (8)
g7 1. One full roll moves it its own circumference Geometry
g7 2. A part's share of a circle is its central angle's share GeometryRatios
g7 3. Measure straight parts as sides, curved parts as arcs Geometry
g8 4. Angles adding past 360° cover more than one circle Geometry
g7 5. A circle's snug square has the diameter as its side Geometry
g7 6. For equal thickness the material ratio is the area ratio GeometryRatios
g7 7. Draw a line to split it into straight and curved pieces Geometry
g7 8. Match the traced circle's circumference to the cone Geometry