Lesson Title:Conic Sections: Converting Circle Equations to Standard Form

Grade and Subject:9th/10th Grade Analytic Geometry (Math)Date: February 16, 2015

1. LESSON PLAN LEARNING OUTCOMES AND PROCEDURE
Essential Question(s) / Central Focus / How can we convert an equation of a circle into standard form?
Why do we need to convert an equation of a circle into standard form?
How do we identify the center and radius of a circle?
Learning Objective(s) /

Students will be able to convert equations of circles into standard form using the completing the square method. Students will also be able to identify the center and radius of a circle and graph circles on a coordinate plane.
Students will be able to write circle equations in standard form, identify the radius and center of a circle, and graph circles on a coordinate grid with 80% accuracy.
Students will be using their knowledge from the previous lesson in order to extend their knowledge of conic section circles. Previously students learned how to identify the center and radius of a circle and graph a circle on a coordinate plane. In this lesson, students will be able to use their knowledge and learn how to convert an equation of a circle in standard form.

CCGPS or GPS Standard(s) / MCC9-12.G.GPE.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.
Instructional Strategies & Learning Tasks that Support Diverse Student Needs / Introduct-ion to Lesson / To begin the lesson, students will be asked to complete a warm-up. This warm-up will contain 3 problems over identifying the center and radius of a circle and writing equations of a circle. Students will be using their previous knowledge learned from the pervious lesson in order to complete these questions. Three students will be asked to come to the board and complete one problem. Each student will also be asked to explain their reasoning to support their response. Before beginning the lesson, students will be given a short introduction of the day’s lesson and how it involves students to use their previous knowledge from the previous semester. The introduction will take approximately 5-8 minutes to complete.
Body of Lesson /

Students will take notes over using the completing the square method to write equations of circles in standard form. The notes will be given on a PowerPoint (slides 21-24). With this information, students will also be asked to identify the center and radius of the circle, which ties in information students learned in the previous lesson. During the notes, the instructor will demonstrate how to complete a set of problems. Students will also be asked to work on a problem individually to practice the mathematical procedure being taught that day. The PowerPoint will take approximately 15 minutes to complete.
Students will then be given a handout that allows students to practice the mathematical procedure and interpret their responses. On this handout, students will need to use the information learned in the previous lesson and today’s lesson. During this time, the instructor will assist students individually and provide students with immediate feedback. Students will be given approximately 10 minutes to practice.
Students will then be asked to put their handout away and complete the handout as homework. Then students will be asked to use their technological devices to complete an online game. This game will engage students in the lesson by allowing them to interact and practice using their knowledge in a different way. This game will also allow students to receive immediate feedback. The interactive game will take approximately 10 minutes to complete.

Closure / The instructor will then answer any questions still have over circles. Once questions are answered, the instructor will ask students to summarize what they learned with a partner or discuss any questions they may have over the lesson. The instructor will then ask one or two students to summarize what they learned to the class. Students will be using their knowledge and mathematical vocabulary to demonstrate that they understood the lesson. Then the instructor will explain how for the following lesson, students will have the opportunity to answer questions and practice some more problems before taking a quiz over circles. This will take approximately 5 minutes to complete.
Learning Supports: Differentiation, Modification(s)and Accommoda-tion(s) /

Students will be given written, verbal, and visual opportunities to learn the mathematical steps being taught during the lesson. This allows students to receive a variety means of instruction throughout the lesson, and a variety of learners are able to learn this mathematical procedure.
For this lesson, students will also be able to play an interactive game that will allow students to demonstrate what they know. The game assesses student comprehension over all learning objectives listed above and engages student learning in the classroom.
Students will also be able to verbally explain what they learned at the end of the lesson. Therefore allowing students to demonstrate what they learned/know using a variety of methods.
Students who have accommodations will receive constant reminders to stay on task and immediate feedback throughout the lesson. Students who struggle with this concept will be given extra support and assistance from their peers and the instructor. Students who are fast learners will be asked to assist their peers and offer support.

Formal and Informal Assessment / Students will be able to demonstrate what they know throughout the lesson.
Formal Assessment: Students will be assessed over their comprehension based on their performance on their homework (handout). Students will also be given a formal assessment in the form of a quiz. This quiz will take place two days after this lesson takes place in order to provide students with time to practice and ask any questions they may have.
Informal Assessment: Students will be assessed informally based on their discussions with their peers and explanations provided to the instructor. Students will be given many opportunities (warm-up, lecture, individual practice) to demonstrate their comprehension throughout the lesson. Students will also be informally assessed over their comprehension over conic sections: circles in the interactive game. The results of the game will determine what students as a whole understand and what misconceptions students may have.
2. RESOURCES
Academic Language / Language Functions / Thekey learning task for this lesson is: Identify.
Students will learn how to identify the center and radius of a circle given the equation of a circle. Students will need to learn how to preform the mathematical procedure (completing the square) in order to identify the radius and center of a circle.
Vocabulary / In order for students to identify the center and radius of a circle, students will need to know/learn these mathematical terms: radius, center, circle, standard form, coefficient, trinomial, perfect square trinomial, and factor.
Syntax or Discourse / Students will need to understand the mathematical procedure being used in this lesson (completing the square method). Students will need to be able to identify the standard form of a circle and interpret this equation/formula.
Materials /

A projector and computer will be needed in order to review the notes (PowerPoint) and play the interactive game over circles (Kahoot)- Game code for the game:

About 30 copies of the Conic Sections-Circles Handout

Students will need their technological devices to play the interactive game
Students will be allowed to use calculator (if needed)
Students will need paper and pencil to write notes and complete their handout

Technology / Students will be given the opportunity to demonstrate what they know during an interactive game (Kahoot). This game will assess student comprehension over the lesson and provide students with immediate feedback. The instructor will be able to use the results of the game to address any misconceptions and provide students with feedback and support. To play the game, the instructor to project the game for the class to see and students will answer questions on their own technological devices.