Unit 6 - Circles
- Students should be able to apply strategic thinking and complex reasoning when solving problems involving arc length and area of a sector of a circle.
- Students should be given opportunities to use interactive tools to engage with the content in order to develop a conceptual understanding of arc length and area of a sector.
- Students should be able to identify the center and radius of a circle from an equation in standard form or from the graph of a circle.
- Students should be able to write the equation of a circle in standard form given the graph of the circle.
- Students should be able to graph a circle from the standard form equation of a circle.
- As students convert equations in general form to standard form in this course, the leading coefficient of the quadratic terms should be limited to 1.
- Students may use a variety of methods to convert the equation of a circle in general form to the equation of a circle in standard form for a specific, circumstantial purpose. One strategy used by students may include (but is not limited to) completing the square.
- Students should be given opportunities to make sense of the meaning of radians conceptually through exploration with visual tools.
- Using hands on tools and technology visualizations, students should have opportunities to explore and develop an understanding of the relationship between the radius of a circle, an arc length, and the associated radian measure.
- Students should be able to convert fluently (flexibly, accurately, and efficiently) between degree and radian measures to solve real-life problems.
- Students should have opportunities to explore and discover experimentally the relationship between radian measure and degree measure using visual tools.
- Students should be able to articulate the pattern associated with angle measures in all four quadrants of the unit circle, e.g., 150° as 180°-30°, 210° as 180°+30°, 330° as 360°-30°, etc.
- Through explorations, students develop an understanding that a unit circle has a radius equal to 1.
Textbook Connections
Module 10-2 Measuring Angles and Arcs
Students find measures of angles and arcs using the properties of circles.
Module 10-3 Arcs and Chords
Students solve problems using the relationships between arcs, chords, and diameters.
Module 10-4 Inscribed Angles
Students solve problems using inscribed angles
Module 10-5 Tangents
Students solve problems using relationships between circles and tangents.
Module 10-6 Tangents, Secants, and Angle Measures
Students solve problems using relationships between circles, tangents, and secants.
Module 10-7 Equations of Circles
Students write and graph equations of circles.
Module 11-3 Areas of Circles and Sectors
Students find areas of circles and sectors by using the formulas they derive.
Module 9-4 Special Right Triangles
Students solve problems by using the properties of 45°-45°-90° and 30°-60°-90° triangles.
Module 9-5 Trigonometry
Students solve problems using the trigonometric ratios and the inverse trigonometric ratios for acute angles.
Module 10-2 Measuring Angles and Arcs
Students find measures of angles and arcs using the properties of circles.
Module 10-3 Arcs and Chords
Students solve problems using the relationships between arcs, chords, and diameters.
Module 10-4 Inscribed Angles
Students solve problems using inscribed angles
Module 10-5 Tangents
Students solve problems using relationships between circles and tangents.
Module 10-6 Tangents, Secants, and Angle Measures
Students solve problems using relationships between circles, tangents, and secants.
Module 10-7 Equations of Circles
Students write and graph equations of circles.
Module 11-3 Areas of Circles and Sectors
Students find areas of circles and sectors by using the formulas they derive.
Module 9-4 Special Right Triangles
Students solve problems by using the properties of 45°-45°-90° and 30°-60°-90° triangles.
Module 9-5 Trigonometry
Students solve problems using the trigonometric ratios and the inverse trigonometric ratios for acute angles.