Advanced Mathematics I

ADVANCED MATHEMATICS I (SECONDARY)

ESSENTIAL UNIT 7 (E07)

(Circles and Parabolas) (July 2013)

Unit Statement: In this unit the student will explore conic sections, define circles and parabolas, write equations of circles and parabolas and graph them.

Essential Outcomes: (must be assessed for mastery)

1. The Student Will demonstrate how to cut a cone in order to get a circular, elliptical, parabolic and hyperbolic cross sections. (10.1)

2. TSW define a parabola and demonstrate the definition with a labeled picture. (10.2)

3. TSW write an equation of a parabola given the vertex and focus, or vertex and directrix. (10.2)

4. TSW define a circle. (10.3)

5. TSW write an equation of a circle given the center and radius. (10.3)

6. TSW sketch the graph of a circle given the equation of a circle. (10.3)

7. TSW student will graph a circle on a graphical calculator given the center and radius (10.3)

8. TSW apply unit facts and concepts to some Real-Life application

Introduced and Practiced Outcomes:

1. The Student Will define and sketch an ellipse.

2. TSW describe a circle as a special case of an ellipse with coinciding foci.

3. TSW review formulas for perimeter and area of a circle.

Key terms and concepts:

Parabola Directrix Diameter Vertex Circle Focus Radius

Attached Rubric or teacher-generated rubric that assesses ALL Essential Outcomes (TSWs). * Examples of possible hands-on activities for this unit: 1. Students build parabolic mirrors from paper and aluminum foil. 2. Students use a string and two pins to draw an ellipse. They cut the ellipse into different parabolas. 3. A competition among student: who can draw a better approximation of a circle with one single stroke? 4. Motion of a projectile in gravitational field follows a parabolic path.

Suggested Resources:

Textbook: Prentice Hall, Algebra 2, Pearson, ISBN -13: 978-0-13-350043-1, the online version of the textbook can be accessed at https://www.pearsonsuccessnet.com Solve it! – short exercises in the textbook/also listed in teacher resources online Practice form G, Practice form K – in teacher resources online Additional Problems - in teacher resources online Enrichment activities – in teacher resources online

Technology Links:

Teacher and student resources available through the publisher at https://www.pearsonsuccessnet.com/snpapp/login.do?method=login PhET simulation on Projectile motion: http://phet.colorado.edu/en/simulation/projectile-motion

EVALUATION RUBRIC FOUND ON FOLLOWING PAGE……………………….. Suggested Unit Evaluation Rubric - ADV MATH I – E07

 To receive a ‘B’ in the unit a student must demonstrate mastery of all TSW’s  To receive an ‘A’ in the unit a student must demonstrate ‘A’ level mastery on at least 3 of the 4 identified TSW’s

Student name:______Date:______

TSW ‘A’ LEVEL ‘B’ LEVEL Notes 1 demonstrate how to cut a Student creates neat models of Student sketches a cone cone in order to get a cones from play dough and and a cutting plane that circular, elliptical, cuts them to produce the cuts it in each of the parabolic and hyperbolic appropriate cross sectional described shapes. cross sections. shapes. 2 define a parabola and N/A Student writes a demonstrate the definition. The picture definition with a labeled shows focus, directrix picture and one point on the parabola. The distance from focus to the point and from the directrix to the point approximately fits the definition.

3 write an equation of a N/A Student can find the parabola given the vertex equation for each of the and focus, two combinations. or vertex and directrix 4 define a circle Based on the definition, Student states a correct student analyzes the following definition. statement: “Circles in reality do not exist” 5 write an equation of a N/A Student will write an circle given the center equation of a circle in the and radius form (x-h)2+(y-k)2 = r2, with center (h,k). 6 sketch the graph of a N/A The circle should be set circle given the equation in a coordinate plane with of a circle marked x,y axis, it should have a labeled center and radius. 7 student will graph a circle Student creates parametric Student needs to graph Circle is not a graph of on a graphical calculator equations in order to graph the both halves of the circle a mathematical given the center and full circle with a graphical (use both functions that function. radius calculator. represent the two halves of a circle). 8 apply unit facts and Reflects on the project and Activity clearly The criteria for concepts to some Real- consistently justifies the demonstrates mastery of demonstration of Life application mathematical concepts used key concepts of the unit mastery and beyond and how they apply to the as defined in this rubric. mastery of this TSW activity. Student articulates and is developed by the explains mathematical teacher based on the concepts used. activity (see Suggested Assessment Tools for examples of possible activities)