20 7.G.B.4 Math.7.G.4 7.G.B.4 7.GSR.5.5 7.G.B.4 7.G.4 7.G.4 7.G.4 7.G.B.3 CC.2.3.7.A.1 M07.C-G.2.2.1 MA.7.GR.1.3 MA.7.GR.1.4

Circles 7th Grade

Alabama Course of Study Standards: 20
Explain the relationships among circumference, diameter, area, and radius of a circle to demonstrate understanding of formulas for the area and circumference of a circle. Informally derive the formula for area of a circle. Solve area and circumference problems in real-world and mathematical situations involving circles.
Arizona Academic Standards: 7.G.B.4
Understand and use the formulas for the area and circumference of a circle to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
Common Core State Standards: Math.7.G.4 or 7.G.B.4 Tennessee Academic Standards: 7.G.B.3
Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
Georgia Standards of Excellence (GSE): 7.GSR.5.5
Given the formula for the area and circumference of a circle, solve problems that exist in everyday life.
Massachusetts Curriculum Frameworks: 7.G.B.4
Circles and measurement: Know that a circle is a two-dimensional shape created by connecting all of the points equidistant from a fixed point called the center of the circle. Understand and describe the relationships among the radius, diameter, circumference and circumference of a circle. Understand and describe the relationship among the radius, diameter, and area of a circle. Know the formulas for the area and circumference of a circle and use them to solve problems. Give an informal derivation of the relationship between the circumference and area of a circle.
North Carolina - Standard Course of Study: 7.G.4
Understand area and circumference of a circle. Understand the relationships between the radius, diameter, circumference, and area. Apply the formulas for area and circumference of a circle to solve problems.
New York State Next Generation Learning Standards: 7.G.4
Apply the formulas for the area and circumference of a circle to solve problems. Note: Students in grade 7 are not expected to calculate the radius of a circle given its area.
Ohio's Learning Standards: 7.G.4
Work with circles. Explore and understand the relationships among the circumference, diameter, area, and radius of a circle. Know and use the formulas for the area and circumference of a circle and use them to solve real-world and mathematical problems.
Pennsylvania Core Standards: CC.2.3.7.A.1
Solve real-world and mathematical problems involving angle measure, area, surface area, circumference, and volume.
Pennsylvania Core Standards: M07.C-G.2.2.1
Find the area and circumference of a circle. Solve problems involving area and circumference of a circle(s).
Florida - Benchmarks for Excellent Student Thinking: MA.7.GR.1.3
Explore the proportional relationship between circumferences and diameters of circles. Apply a formula for the circumference of a circle to solve mathematical and real-world problems.
Florida - Benchmarks for Excellent Student Thinking: MA.7.GR.1.4
Explore and apply a formula to find the area of a circle to solve mathematical and real-world problems.

Circumference and Area of a Circle

The diameter of a circle is the distance from one point on the circle to another point on the circle, through its center.

The radius of a circle is the distance from its center to a point on the circle.
The length of a circle's radius is half the length of its diameter.

The circumference of a circle is the distance around the circle.

Pi (

π

) is a non-repeating, non-terminating decimal which is equivalent to the ratio of a circle's circumference to its diameter. 3.14 is often used as an approximation of pi.

Circumference =

π

d or 2

π

r

Area =

π

r²

\begin{array}{rcl} Area & = & π r^{2} \\ 100 π {cm}^{2} & = & π r^{2} \\ 100 π {cm}^{2} \div π & = & π r^{2} \div π \\ 100 {cm}^{2} & = & r^{2} \\ \sqrt{100 {cm}^{2}} & = & \sqrt{r^{2}} \\ 10 cm & = & r \end{array}

\begin{array}{rcl} Circumference & = & 2 π r \\ = & 2 π (10 cm) \\ = & 20 π cm \end{array}

Circles

Alabama Course of Study Standards: 20

Arizona Academic Standards: 7.G.B.4

Understand and use the formulas for the area and circumference of a circle to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

Common Core State Standards: Math.7.G.4 or 7.G.B.4

Tennessee Academic Standards: 7.G.B.3

Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

Georgia Standards of Excellence (GSE): 7.GSR.5.5

Given the formula for the area and circumference of a circle, solve problems that exist in everyday life.

Massachusetts Curriculum Frameworks: 7.G.B.4

North Carolina - Standard Course of Study: 7.G.4

Understand area and circumference of a circle.
Understand the relationships between the radius, diameter, circumference, and area.
Apply the formulas for area and circumference of a circle to solve problems.

New York State Next Generation Learning Standards: 7.G.4

Apply the formulas for the area and circumference of a circle to solve problems.
Note: Students in grade 7 are not expected to calculate the radius of a circle given its area.

Ohio's Learning Standards: 7.G.4

Work with circles.
Explore and understand the relationships among the circumference, diameter, area, and radius of a circle.
Know and use the formulas for the area and circumference of a circle and use them to solve real-world and mathematical problems.

Pennsylvania Core Standards: CC.2.3.7.A.1

Solve real-world and mathematical problems involving angle measure, area, surface area, circumference, and volume.

Pennsylvania Core Standards: M07.C-G.2.2.1

Find the area and circumference of a circle. Solve problems involving area and circumference of a circle(s).

Florida - Benchmarks for Excellent Student Thinking: MA.7.GR.1.3

Explore the proportional relationship between circumferences and diameters of circles. Apply a formula for the circumference of a circle to solve mathematical and real-world problems.

Florida - Benchmarks for Excellent Student Thinking: MA.7.GR.1.4

Explore and apply a formula to find the area of a circle to solve mathematical and real-world problems.

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