Virginia SOL 6.MG.1.e
The Standard
Solve problems, including those in context, involving circumference and area of a circle when given the length of the diameter or radius.
Virginia Standards of Learning for Mathematics · The student will identify the characteristics of circles and solve problems, including those in context, involving circumference and area.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students find a circle's circumference or area from a given radius or diameter. They select the right formula, use π, and report answers with correct units.
What Mastery Looks Like
- Students choose the correct formula, find the radius when needed, and calculate accurately using π or 3.14. They label circumference with linear units and area with square units, then explain what each answer means.
Common Misconceptions
- Students may use the diameter as the radius or forget to divide the diameter by 2. They may square the wrong value, confuse circumference with area, or use linear units for area.
How to Assess It
- Exit ticket: A circular garden has a diameter of 10 meters. Find its circumference and area, show each formula, and label the units.
Lesson moves
Ways to Teach It
Give pairs circular lids, rulers, and string to measure diameter and circumference, then compare each circumference-to-diameter ratio.
Ask students to explain why doubling a circle's radius does not simply double its area.
Play a sorting game where students match circle diagrams, measurements, formulas, and correct circumference or area values.
Have students calculate the edging and surface material needed for a circular garden, table, or playground space.
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Printable 6.MG.1.e Worksheet
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Related Standards
- 6.MG.1.d
Develop the formula for circumference using the relationship between diameter, radius, and pi.
- 6.MG.1
The student will identify the characteristics of circles and solve problems, including those in context, involving circumference and area.
- 6.MG.1.a
Identify and describe chord, diameter, radius, circumference, and area of a circle.
- 6.MG.1.b.iii
Investigate and describe the relationship between diameter and circumference
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