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 GMDOA Draw a DiagramIdentify Subproblems
Progression (11)
3-2 1. Segment through chained centers as radius multiples 3.OA.C.73.G.A.1
3-2 2. Diameter is twice the radius 3.OA.C.73.G.A.1
3-2 3. Rectangle sides are multiples of the diameter 3.OA.C.73.G.A.1
3-2 4. Center to edge distance is the radius 3.MD.D.83.G.A.1
3-2 5. Perimeter splits into radius arcs and straight parts 3.MD.D.83.G.A.1
3-2 6. Perimeter of shape joining circle centers 3.MD.D.83.OA.C.7
3-2 7. Perimeter of shapes from tangent circles 3.MD.D.83.OA.C.7
3-2 8. Find each radius and diameter from segments 3.OA.C.73.G.A.1
3-2 9. All radii in one circle are equal 3.MD.D.83.G.A.1
3-2 10. Polygon side equals sum of two radii 3.MD.D.83.G.A.1
3-2 11. Triangle side equals sum of two radii 3.MD.D.83.G.A.1