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Progressive Mathematics Initiative www.njctl.org Mathematics Curriculum Unit Plan # 7 Title: Circles Subject: Geometry Length of Time: 3.5 weeks Unit Summary: The unit explores parts of a circle and the relationships between intersecting lines and circles. Learning Targets PARCC Major Clusters; Supporting Clusters; Additional Clusters + Additional Standard Conceptual Category: Geometry Domain: Circles Cluster: Understand and apply theorems about circles. Standard#: Standard: Prove that all circles are similar. G-C.1 G-C.2 Identify and describe relationships among inscribed angles, radii, and chords. G-C.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. Construct a tangent line from a point outside a given circle to the circle. +G-C.4 Cluster: Find arc lengths and areas of sectors Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. Domain: Standards for Math Practice G-C.5 Standard#: Standard: MP1 Making sense of problems and persevere in solving them. MP2 Reason abstractly and quantitatively. MP3 Construct viable arguments and critique the reasoning of others. MP4 Model with mathematics. MP5 Use appropriate tools strategically. MP6 Attend to precision. MP7 Look for and make use of structure. MP8 Look for and express regularity in repeated reasoning. Unit Essential Question: Unit Enduring Understandings: Do “how” and “where” a line(s) Tangent lines intersect a circle at a single point. intersect a circle make a difference? The angle measure of an angle that intersects a circle is related to the measure of the arc intersected. The power of a point depends on where the lines intersect in relationship to the circle. There is a relationship between central angles and arcs of a circle There is relationship between a chord, its distance from the center of a circle, and the radius of the circle. Unit Objectives: Students will be able to identify the parts of a circle. Students will be able to find the measure of angles given angles with vertices at the center, inside the circle, on the circle, or outside the circle. Students will be able to calculate the length of an arc in a circle. Students will be able to calculate the measurement of angles and arcs in radians. Geometry – Circles ~1~ NJCTL.org Students will be able to calculate the lengths of tangents, secant segments, and chords depending on the location of the intersection. Evidence of Learning Formative Assessments: SMART Response questions used throughout the unit. 4 Quizzes Summative Assessment: Unit Test Lesson Plan Topics Topic #1: Parts of a Circle Topic #2: Central Angles & Arcs Topic #3: Arc Length & Radians Quiz 1:Parts of a Circle Topic #4: Chords, Inscribed Angles, and Triangles Lab #1: Properties of Chords Lab #2: Inscribed Angles Quiz #2: Chords, Inscribed Angles & Triangles Topic #5: Tangents & Secants Lab #3: Tangent Lines Quiz 3: Tangents & Secants Topic #6: Segments and Circles Quiz 4: Segments and Circles Topic #7: Review and Unit Test Curriculum Resources: www.njctl.org/courses/math/geometry/ Lesson Components 21st Century Skills Financial, Economic, Business, and Entrepreneurial Literacy 21st Century Themes Critical Thinking and Problem Solving Communication and Collaboration Life and Career Skills Geometry – Circles ~2~ 1 1.5 2 0.5 4 0.5 4 0.5 1 0.5 2 NJCTL.org