Georgia 7.GSR.5.5
The Standard
Given the formula for the area and circumference of a circle, solve problems that exist in everyday life.
Georgia's K-12 Mathematics Standards · Solve practical problems involving angle measurement, circles, area of circles, surface area of prisms and cylinders, and volume of cylinders and prisms composed of cubes and right prisms.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students decide whether a situation calls for circumference or area. They use the given formula, find the radius from the diameter when needed, and label answers with correct units.
What Mastery Looks Like
- A student can solve problems such as finding the border around a circular patio or the space it covers. Answers use reasonable approximations and the correct linear or square units.
Common Misconceptions
- Students often use the diameter as the radius or choose the wrong formula. They may label area with linear units or circumference with square units. Some forget to square the radius before multiplying by pi.
How to Assess It
- Give this exit ticket: “A circular garden is 12 feet across. Using C = 2πr and A = πr², find the fencing needed and the planting area.” Require units and answers to the nearest tenth.
Lesson moves
Ways to Teach It
Give pairs paper plates, string, and rulers to measure diameter, then calculate and compare each plate's circumference and area.
Have students explain whether fencing a circular garden uses area or circumference and cite the context clue.
Use matching cards with circle diagrams, dimensions, formulas, and answers, then have teams justify every completed set.
Compare pizza sizes by calculating each pizza's area and cost per square inch from a local menu.
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Related Standards
- 6.GSR.5
Solve relevant problems involving area, surface area, and volume.
- 8.GSR.8.4
Apply the formulas for the volume of cones, cylinders, and spheres and use them to solve in relevant problems.
- 7.GSR.5.4
Explore and describe the relationship between pi, radius, diameter, circumference, and area of a circle to derive the formulas for the circumference and area of...
- 7.GSR.5
Solve practical problems involving angle measurement, circles, area of circles, surface area of prisms and cylinders, and volume of cylinders and prisms compose...
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