CCSS.Math.Content.HSG-GPE.A.1
The standard
Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
Common Core State Standards for Mathematics
What this standard means
Students need to connect a circle on the coordinate plane to distance. They should see the radius as the distance from any point on the circle to the center, then use the Pythagorean Theorem to build the equation. They also need to read an equation and identify the center and radius.
Mastery means students can move both ways: graph to equation and equation to graph. They can complete the square when needed and explain why the radius is squared. Common sticking points are sign errors with the center, forgetting to square the radius, and weak factoring when completing the square.
Ways to teach it
- Hands-on activity: Give students grid paper, a center point, string length, and colored pencils to plot circle points and write the equation.
- Discussion prompt: Ask, “Why does a circle equation look like the distance formula?” and have students justify using a right triangle sketch.
- Quick assessment: Give three circle equations, one in standard form and two needing completing the square, and ask for center and radius.
- Real-world connection: Use a map with a cell tower location and signal radius, then have students write and graph the coverage equation.
Plan a lesson for CCSS.Math.Content.HSG-GPE.A.1
Generate a complete lesson plan aligned to this standard, with objectives, activities, and materials. Free, no account needed.
Related standards
- CCSS.Math.Content.HSG-GPE.A.2
Derive the equation of a parabola given a focus and directrix.
- CCSS.Math.Content.HSG-C.A
Understand and apply theorems about circles
- CCSS.Math.Content.HSA-REI.B.4a
Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)² = q that has the same solutions. Derive t...
- CCSS.Math.Content.7.G.B.4
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 circumf...