NY Next Generation Math NY-7.G.4

Math7th GradeSolve real-life and mathematical problems involving angle measure, area, surface area, and volume.

The Standard

Apply the formulas for the area and circumference of a circle to solve problems.

New York State Next Generation Mathematics Learning Standards

Teacher's field guide

What Students Need to Do: Students apply circumference and area formulas to circles in mathematical and real-world problems. They use a given radius or diameter, distinguish linear from square units, and express exact or approximate results.
What Mastery Looks Like: Given radius 7 centimeters, a student finds circumference 14 pi centimeters and area 49 pi square centimeters. The student explains why the same radius leads to different units and operations.
Common Misconceptions: Students may use diameter in place of radius in the area formula or confuse the circumference and area formulas. They may report area in linear units or round too early.
How to Assess It: Give students a circle with diameter 10 meters. Ask them to find its circumference and area, show how they determined the radius, and label units.

Lesson moves

Measure circular objects, identify radius and diameter, and apply both formulas while labeling linear and square units.
Ask students why doubling the radius does not merely double a circle's area.
Play circle-formula match with diagrams, given measures, expressions in pi, approximations, and unit labels.
Calculate edging around a circular garden and material needed to cover its surface.

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