If you are citizen of an European Union member nation, you may not use this service unless you are at least 16 years old.
You already know Dokkio is an AI-powered assistant to organize & manage your digital files & messages. Very soon, Dokkio will support Outlook as well as One Drive. Check it out today!

G-C-1-2

Page history last edited by Brenda Butz 6 years, 3 months ago

G.C.1.2 Apply the properties of circles and relationships among angles, arcs, and distances in a circle among radii, chords, secants and tangents to solve problems using algebraic and logical reasoning.

In a Nutshell

Students will be introduced to the new relationships within circles that involve different types of angles, segments/lines and arcs, as well as the properties involving these relationships. Students will learn the formulas that allow them to find the measures of arcs and the lengths of segments inside a circle, touching a circle or intersecting a circle.

Student Actions	Teacher Actions
Develop accurate and appropriate procedural fluency: Students will decide which formula to use for a given problem. Develop Mathematical Reasoning: Students will work with the different parts of a circle and explore how these parts relate to one another (i.e. intersections, proportional relationships, sectors, etc.) Develop the Ability to Communicate Mathematically: Student will use geometric notation to denote angles, arcs, segments, lines, and rays to distinguish which part of the circle they are using.	Teachers will implement a variety of tasks that promote reasoning and problem solving by presenting problems that require them to solve for missing arcs, angles, segments or other parts of a circle. Teachers will support productive struggle by presenting tasks that require a variety of methods (i.e. formulas, models, and diagrams) to solve for measurements both inside and outside of a circle. Teachers will pose purposeful questions about distinguishing between arcs, angles, segments, lines and rays.
Key Understandings	Misconceptions
Students understand the differences between chords, secants, and tangent. Students understand the difference between central angles and inscribed angles and their angle measures in relation to their arc measure. Students understand the difference between central angles and inscribed angles and their angle measures in relation to their arc measure. Students understand that when two lines intersect inside, on, or outside a circle, there is a relationship between the size of the angles and the size of the arcs that are formed from this intersection. Students understand that when secants and/ or tangents intersect with each other or the circle there are relationships formed between the lengths of the various segments. Students can correctly name minor arcs, semicircles, and major arcs and use the correct notation for each.	Students misuse the equations for angle measurement when two secants intersect inside, on, or outside a circle. Students misuse the equations for segment length when two secants intersect inside, on, or outside a circle. Students don’t use correct notation to distinguish between angles, arcs, segments, lines, and rays.