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Calculating Arcs and Areas of Sectors of Circles Resource:
Calculating Arcs and Areas of Sectors of Circles

This lesson unit is intended to help you assess how well students are able to solve problems involving area and arc length of a sector of a circle using radians. It assumes familiarity with radians and should not be treated as an introduction to the topic. This lesson is intended to help you identify and assist students who have difficulties in:
Computing perimeters, areas, and arc lengths of sectors using formulas.
Finding the relationships between arc lengths, and areas of sectors after scaling.

Circles and Squares Resource:
Circles and Squares

In this task, you must solve a problem about circles inscribed in squares.

All Resources From:
• Unit 7

#### Circles

Defining Circles Resource:
Defining Circles

This incomplete Core Resource supports students in making connections between the Pythagorean theorem and the equation of circles.

All Resources From:
• Unit 7

#### Circles

Formulas Involving Arc Length Resource:
Formulas Involving Arc Length

Connect visuals to arc length formulas involving the size of an angle.

All Resources From:
• Unit 7

#### Circles

GeoGebra Slider that shows the angle sum property for quadrilaterals Resource:
GeoGebra Slider that shows the angle sum property for quadrilaterals

The slider allows the interior angles of the quadrilateral to change.  the 4 interior angles of the quadrilateral are also organized with the same vertex (like a circle).  As they interior angles of the quadrilateral change, the same 4 angles change in the circular format.

All Resources From:
• Unit 2

Inscribing and Circumscribing Right Triangles Resource:
Inscribing and Circumscribing Right Triangles

A Classroom Challenge (aka formative assessment lesson) is a classroom-ready lesson that supports formative assessment. The lesson’s approach first allows students to demonstrate their prior understandings and abilities in employing the mathematical practices, and then involves students in resolving their own difficulties and misconceptions through structured discussion.

All Resources From:
• Unit 7

#### Circles

Inscribing a Triangle in a Circle Resource:
Inscribing a Triangle in a Circle

This problem introduces the circumcenter of a triangle and shows how it can be used to inscribe the triangle in a circle. It also shows that there cannot be more than one circumcenter.

All Resources From:
• Unit 7

#### Circles

Intro to Geometry: Compass Art Resource:
Intro to Geometry: Compass Art

This is a fun and inspiring description of someone's first conversation about the use of compasses - I think it could be a nice conversation at other early points in students exposure to compasses as well.
A note on math circles: Math Circles are a particular talk protocol for facilitating a discovery based conversation with a group of learners. Typically, there's a starting question and the facilitator responds to each student's contribution to the conversation with another question. It is common in math circles that the end result of the conversation is both more sophisticated and powerful than what happens inÂ a typical math classroom, however it is hard to facilitate and requires that you be willing to go with what your students are thinking about. It also helps to have a great deal of mathematical knowledge, not to mention a very engaged group of learners.

All Resources From:
• Unit 1

#### Tools of Geometry

Lucky Cow Resource:
Lucky Cow

3 Acts activity about the area of a sector.

All Resources From:
• Unit 7

#### Circles

Orbiting Satellite Resource:
Orbiting Satellite

This task provides a context for connecting an angle in radians to the arc length intercepted by the angle.

All Resources From:
• Unit 7

#### Circles

Right Triangles Inscribed in Circles 1 Resource:
Right Triangles Inscribed in Circles 1

This task provides a good opportunity to use isosceles triangles and their properties to show an interesting and important result about triangles inscribed in a circle with one side of the triangle a diameter: the fact that these triangles are always right triangles is often referred to as Thales' theorem. It does not have a lot of formal prerequisites, just the knowledge that the sum of the three angles in a triangle is 180 degrees.

All Resources From:
• Unit 7

#### Circles

Right Triangles Inscribed in Circles 2 Resource:
Right Triangles Inscribed in Circles 2

The result here complements the fact, presented in the task ''Right triangles inscribed in circles I,'' that any triangle inscribed in a circle with one side being a diameter of the circle is a right triangle. A second common proof of this result rotates the triangle by 180 degrees about M and then shows that the quadrilateral, obtained by taking the union of these two triangles, is a rectangle.

All Resources From:
• Unit 7