Hampton High School Geometry Lesson Plan Equation of a Circle Michelle Bousquet

Transcription

1 Hampton High School Geometr Lesson Plan Equation of a Circle Michelle Bousquet Context: This lesson is designed for a 90 minute Geometr class at Hampton High School. The class contains a maximum of 19 students. This is the second of three lessons on arc length, sector area, and the equation of a circle. Objective: The students will discover the equation of a circle using an online inquir-based activit as guided b a worksheet. The students will then work individuall or in groups to accuratel appl the equation to a worksheet as checked b the teacher at the end of class. SOL: G.1 The student, given the coordinates of the center of a circle and a point on the circle, will write the equation of the circle. Materials/Resources: Warm-Up Checklist Arc Lengths, Sector Area, and the Equation of a Circle (from previous class) Equations of Circles Computer Worksheet Laptops- 1 laptop per student Circle Booklets Scissors Glue Equation of Circle Booklet Worksheet Equations of Circles Worksheet b Kuta Software Exit Slip Content Instructional Strategies: 1. Warm up: The students will complete a warm up containing questions from previous SOL tests. While the students are completing the warm-up, take attendance. After going over the warm up, briefl introduce the topic of the da: the Equation of a Circle. 15 minutes. Pass out laptops and have students log in using student ID number and password. Have the students go to 5 minutes 3. Pass out the Equations of Circles worksheets and have the students use the website to discover the equations of circles. 0 minutes. Pass out booklets and the worksheet with booklet cutouts on it. Go through the worksheet and complete the example with the class. The students will cut out this part and glue it into their booklets. 15 minutes 5. Pass out the Equations of Circles worksheet b Kuta Software. Have the students work in groups to complete #1- and #9-11. The faster students can also do #7- and #1-1. Students will raise their hands to get the teacher to check answers before class is over.

2 0 minutes. Pass out the exit slip and have the students complete it before the leave. Evaluation: The teacher will evaluate student understanding b first b observing which students correctl discover the formula for the equation of a circle in the inquir-based online activit. Then, the students will be assessed on their abilit to accuratel complete the Equations of Circles worksheet b Kuta Software. Differentiation and Adaptations: If there is not enough time in the class period, the last worksheet can be assigned as homework or can be reviewed the next class. The teacher can also work out the exercises on the board. If there is extra time, the teacher can begin the next lesson. For individual students who finish before the rest of the class, there are additional problems on the Kuta worksheet that the should be assigned.

3 Name: Date: Equations of Circles 1. Go to Scroll down to the graph of a circle. 3. Place the center of the circle on (0,0). Put the red dot on the circle on point (-1,0).. What is the radius of this circle? 5. Look at the equation above the graph. What does it sa?. Now, put the center of the circle on (,1). Put the other red dot on (0,1). 7. What is the radius of this circle?. Look at the equation above the graph. What does it sa? 9. Now, put the center of the circle on (-1,3). Put the other red dot on (-,3). 10. What is the radius of this circle? 11. Look at the equation above the graph. What does it sa? 1. Do ou see an relationships between the center point and the radius in the equations?

4 Equation of a Circle (h,k): r: Equation: Example 1: Write the equation of a circle with diameter whose endpoints are (0,-10) and (, ). Example : Write the equation of a circle with a diameter whose endpoints are (, ) and (0, -).

5 Example 3: Write the equation of a circle with the center at (-, ) and a radius of 3cm. Example : Find the center and the radius if the equation of a circle is (x " 3) + ( + 5) = 5.

6 Kuta Software - Infinite Geometr Equations of Circles Name Date Period Identif the center and radius of each. Then sketch the graph. 1) (x 1) + ( + 3) = ) (x ) + ( + 1) = 1 x x 3) (x 1) + ( + ) = 9 ) x + ( 3) = 1 x x -1- b OB0j1k hkxustxa WShoAf7tTw3afrXeW 9LhLHCV.x EAflrlk lrliuguhats jraetsee5rjvvexde.h r nmzasdev jwwiwtyhn binufinfiktjei NGAe0oVmfe5torFo.3 Worksheet b Kuta Software LLC

7 5) + x 0 = x ) 9 = x x x 7) 9 = x x ) 1 + x + x = 0 x x Use the information provided to write the equation of each circle. 9) Center: (13, 13) Radius: 10) Center: ( 13, 1) Point on Circle: ( 10, 1) 11) Ends of a diameter: (1, 13) and (, 3) 1) Center: (10, 1) Tangent to x = 13 13) Center lies in the first quadrant Tangent to x =, = 3, and x = 1 1) Center: (0, 13) Area: 5π -- Gn0G1Ls SKfu5tqaa Skoofptwwaarlev ZLFL1Cl.F u DAQl l nrdingchktosf rtesvecrv1e1du.n c BMFad1ek gwpirthr EIhnbfpilnniJt5eV pgreroemeeitqrht. Worksheet b Kuta Software LLC

8 Warm Up Ke 3. F 3. H 31. B Equations of Circles Ke. r=1 5. x + = 1 7. r=. x + ( "1) = 10. r=3 11. (x + ) + ( " 3) = 9 Equation of a Circle Center Radius (x " h) + ( " k) = r Example 1: (x "1) + ( + ) = 100 Example : (x " 3) + ( + ) = 5 Example 3: (x + ) + ( " ) = 9 Example : Center: (3, -5) Radius: 5 Equations of Circles Kuta Software Worksheet Cop of Answers on Next Page

9 Kuta Software - Infinite Geometr Equations of Circles Name Date Period Identif the center and radius of each. Then sketch the graph. 1) (x 1) + ( + 3) = Center: (1, 3) Radius: ) (x ) + ( + 1) = 1 Center: (, 1) Radius: x x 3) (x 1) + ( + ) = 9 Center: (1, ) Radius: 3 ) x + ( 3) = 1 Center: (0, 3) Radius: 1 x x -1- H 50Z1e3 LKAuYtNav XSEodfWt7wdaRrheo KLYLNCL.S W 7AIlblT irhixg3hstwsx RrleTsuewrvNevdo.E c WMqaldmem Pwqi5tshG IsnpfBiCnii1tYea CGTeeoGmjegtDrno.b Worksheet b Kuta Software LLC

10 5) + x 0 = x Center: (, 1) Radius: 5 ) 9 = x Center: (0, 0) Radius: 3 x x 7) 9 = x x Center: ( 3, 1) Radius: 1 ) 1 + x + x = 0 Center: (, 3) Radius: 3 x x Use the information provided to write the equation of each circle. 9) Center: (13, 13) Radius: 10) Center: ( 13, 1) Point on Circle: ( 10, 1) (x 13) + ( + 13) = 1 11) Ends of a diameter: (1, 13) and (, 3) (x 11) + ( + ) = 7 13) Center lies in the first quadrant Tangent to x =, = 3, and x = 1 (x 11) + ( ) = 9 (x + 13) + ( + 1) = 9 1) Center: (10, 1) Tangent to x = 13 (x 10) + ( + 1) = 9 1) Center: (0, 13) Area: 5π x + ( 13) = 5 Create our own worksheets like this one with Infinite Geometr. Free trial available at KutaSoftware.com -- B Q901D3 XKLutaN esxoefntawwaxrkea HLOLnCa.F P halflc HrZitgdhtDs NreRs7erNvdebdV.X R FM3awdwe1 ww itth1 BIMnxfZijnRiWtDek CGdepoamDe9tFr Qf.d Worksheet b Kuta Software LLC