CCSS.Math.Content.HSG-GPE.A

CCSS.Math.Content.HSG-GPE.A is a cluster heading. These are the individual standards under it.

• CCSS.Math.Content.HSG-GPE.A.1

  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...

• CCSS.Math.Content.HSG-GPE.A.2

  Derive the equation of a parabola given a focus and directrix.

• CCSS.Math.Content.HSG-GPE.A.3

  (+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

01

What Students Need to Do

Students connect equations of conic sections to their graphs and geometric features. They write equations from features and recover features from equations, often by completing the square.

02

What Mastery Looks Like

Students can identify the conic from its equation and find features such as center, radius, vertex, focus, and directrix. They can use given features to write an equation and check it against a sketch.

03

Common Misconceptions

Students often confuse radius with radius squared or reverse the signs of a center’s coordinates. They may also misread a parabola’s orientation or mix up the focus, vertex, and directrix.

04

How to Assess It

Give students the equation (x - 2)² + (y + 3)² = 16. Ask them to name the conic, state its key features, sketch it, and write a matching geometric description.

1. 01

   Plot points equidistant from a marked focus and directrix on graph paper, then connect them to build a parabola.

2. 02

   Ask students to explain how changing one value in a circle equation affects its center, radius, and graph.

3. 03

   Give pairs cards showing equations, graphs, and feature descriptions, then have them race to make correct sets.

4. 04

   Measure a satellite dish cross-section from a photo, fit a parabola, and explain what its focus represents.

• CCSS.Math.Content.HSG-CO.D

  Make geometric constructions

• CCSS.Math.Content.HSG-CO.B.6

  Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the...

• CCSS.Math.Content.HSG-GPE.B

  Use coordinates to prove simple geometric theorems algebraically

• CCSS.Math.Content.HSG-MG.A

  Apply geometric concepts in modeling situations