math · Grade 5
Geometry: Circle Radius, Diameter, and Circumference Relationships
Calculate radius from diameter and diameter from radius using d = 2r. Authentic geometric circle diagrams with complete answer key.
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Learning goals
- Define radius as a line segment from the center of a circle to any point on its boundary
- Define diameter as a line segment passing through the center connecting two points on opposite sides
- Apply the formulas diameter = 2 × radius and radius = diameter ÷ 2
Before you begin
Identify a circle's center and distinguish a radius from a line across the whole circle.
Age and grade do not measure readiness. Adjust reading or adult support to preserve the intended learning goal.
Follow the sequence
1. Practice
Practice previewGeometry: Circle Radius, Diameter, and Circumference Relationships
Practice · Independent · 15 min
Calculate radius from diameter and diameter from radius using d = 2r. Authentic geometric circle diagrams with complete answer key.
Teaching and response guide
- Model the target skill: define radius as a line segment from the center of a circle to any point on its boundary. Use the first task as a guided example before asking for an independent response.
- Check readiness first: Identify a circle's center and distinguish a radius from a line across the whole circle.
- Discuss an incorrect response using this distinction: Diameter is twice the radius; a circumference formula requires the quantity named in the question.
Watch for: Diameter is twice the radius; a circumference formula requires the quantity named in the question.
Check the answer criteria for each task. A supported explanation may have more than one acceptable response. These activities offer evidence to discuss; completing a sheet alone does not establish mastery.