HSG-GPE.A.1

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- HSG-GPE.A.1Derive 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.
- HSG-GPE.A.2Derive the equation of a parabola given a focus and directrix.
- HSG-GPE.A.3Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

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## 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 an equation.

20 Lesson(s)

Big Idea:

#### What is the definition of a circle, really?

Standards:

Favorites
(6)

Resources
(23)

Reflections
(2)

Big Idea:

#### Through a poster students place wax paper designs made in previous lessons on a graph then determine the equation for the conic represented by the design.

Standards:

Favorites
(1)

Resources
(25)

Reflections
(4)

Big Idea:

#### How can I put a conic on a coordinate plane so that an equation can be found?

Standards:

Favorites
(1)

Resources
(22)

Reflections
(4)

### Circles and Completing the Square (Day 1 of 2)

12th Grade Math »
Unit: Conic Sections

12th Grade Math »
Unit: Conic Sections

Big Idea:

#### Use TRIANGLES and SQUARES to find the equation of a CIRCLE?! Students use prior knowledge of perfect squares and the Pythagorean Theorem to find equations for circles.

Standards:

Favorites
(5)

Resources
(17)

### Circles and Completing the Square (Day 2 of 2)

12th Grade Math »
Unit: Conic Sections

12th Grade Math »
Unit: Conic Sections

Big Idea:

#### Use TRIANGLES and SQUARES to find the equation of a CIRCLE?! Students use prior knowledge of perfect squares and the Pythagorean Theorem to find equations for circles.

Standards:

Favorites
(1)

Resources
(14)

### Circle Review Session and Portfolio Workshop

12th Grade Math »
Unit: Circles

12th Grade Math »
Unit: Circles

Big Idea:

#### When students design their own review session and their own portfolios, you have time to work with each individual student to ensure that they get the most out of this learning opportunity.

Standards:

Favorites
(1)

Resources
(6)

### Conic Sections Unit Test

12th Grade Math »
Unit: Conic Sections

12th Grade Math »
Unit: Conic Sections

Big Idea:

#### Students show their personal knowledge of graphing and writing equations for conic sections.

Standards:

Favorites
(2)

Resources
(4)

### Conic Sections Test Review

12th Grade Math »
Unit: Conic Sections

12th Grade Math »
Unit: Conic Sections

Big Idea:

#### Students work together and ask questions as they prepare for tomorrow's unit test.

Standards:

Favorites
(2)

Resources
(4)

Big Idea:

#### Students will think deeply and apply concepts relating to Pythagorean theorem to discover the formula for a circle.

Standards:

Favorites
(3)

Resources
(22)

Reflections
(3)

### Circles on the Coordinate Plane

12th Grade Math »
Unit: Trigonometry: Circles

12th Grade Math »
Unit: Trigonometry: Circles

Big Idea:

#### All students can tell you that “y=mx+b” or “a squared plus b squared equals c squared.” Build on that and teach them to graph a circle.

Standards:

Favorites
(34)

Resources
(18)

### Old and New Knowledge of Circles

12th Grade Math »
Unit: Trigonometry: Circles

12th Grade Math »
Unit: Trigonometry: Circles

Big Idea:

#### Students explore the idea that pi and the trig ratios are really just the same shoes on different feet.

Standards:

Resources
(13)

### Problem Solving with Isosceles Triangles and Circles

12th Grade Math »
Unit: Trigonometry: Circles

12th Grade Math »
Unit: Trigonometry: Circles

Big Idea:

#### We’ve seen some of the connections between triangles and circles – here, we lay the groundwork for more!

Standards:

Resources
(14)

Big Idea:

#### Which came first, the algebra or the geometry? After this lesson, students will interplay between these two branches of mathematics.

Standards:

Resources
(14)

Reflections
(2)

### Manipulating Circles on Geogebra

12th Grade Math »
Unit: Trigonometry: Circles

12th Grade Math »
Unit: Trigonometry: Circles

### Review of Circles Learning Targets

12th Grade Math »
Unit: Trigonometry: Circles

12th Grade Math »
Unit: Trigonometry: Circles

Big Idea:

#### Students work together to review and synthesize their knowledge of circles.

Standards:

Resources
(10)

Common Core Math

### Kindergarten

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