Radius and Diameter Relationships
Every radius of a circle is equal and the diameter is twice the radius; chaining these through touching or nested circles turns center-to-center segments and polygon sides into sums of radii. Learners fit circles in rectangles, build polygons joining centers, and compute perimeters mixing arcs and straight radius parts. It is geometric reasoning by equal-length substitution.
grade 3 GeometryMeasurement & dataOperations Draw a DiagramIdentify Subproblems
Progression (11)
g3 1. Segment through chained centers as radius multiples OperationsGeometry
g3 2. Diameter is twice the radius OperationsGeometry
g3 3. Rectangle sides are multiples of the diameter OperationsGeometry
g3 4. Center to edge distance is the radius Measurement & dataGeometry
g3 5. Perimeter splits into radius arcs and straight parts Measurement & dataGeometry
g3 6. Perimeter of shape joining circle centers Measurement & dataOperations
g3 7. Perimeter of shapes from tangent circles Measurement & dataOperations
g3 8. Find each radius and diameter from segments OperationsGeometry
g3 9. All radii in one circle are equal Measurement & dataGeometry
g3 10. Polygon side equals sum of two radii Measurement & dataGeometry
g3 11. Triangle side equals sum of two radii Measurement & dataGeometry
Bridges to competition (3)
Reasoning problems that extend this idea toward competition:
Arcs centered at polygon vertices Other
Perimeter of a figure enclosing circles Other
Diameter and radius in nested circles Pattern & rule