Download Breaking down the standards: http://www.shmoop.com/common

Breaking down the standards: http://www.shmoop.com/common-core-standards/math.html
Understand and apply theorems about circles.
Prove that all circles are similar.
Videos with proofs and explanations: http://learni.st/users/S33572/boards/2983-proving-all-circles-are-similar-commoncore-standard-9-12-g-c-1
Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central,
inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to
the tangent where the radius intersects the circle.
Definitions podcast: http://teachers.henrico.k12.va.us/math/igo/08Circles/8_1.html
Task: http://www.illustrativemathematics.org/illustrations/963
Broken Pottery Task: http://mathforum.org/pow/teacher/samples––/MathForumSampleGeometryPacket.pdf
Tangent line properties: http://teachers.henrico.k12.va.us/math/igo/08Circles/8_3.html
Central Angles Inscribed Angles: http://teachers.henrico.k12.va.us/math/igo/08Circles/8_5.html
Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a
circle.
Inscribed Circumscribed Triangles and Quadrilateral Constructions:
https://share.ehs.uen.org/sites/default/files/Unit11Lesson3_0.pdf
Inscribe a Circle in a triangle: http://www.mathsisfun.com/geometry/construct-triangleinscribe.html
Circumscribe a triangle: http://math.nmsu.edu/~pmorandi/CourseMaterials/InscribedTriangles.html
Quadrilateral Inscribed Properties Proof: http://www.geom.uiuc.edu/~dwiggins/conj47.html
Quadrilateral Inscribed Properties: http://teachers.henrico.k12.va.us/math/igo/08Circles/8_5.html
Construct a tangent line from a point outside a given circle to the circle.
Applet: http://www.mathopenref.com/consttangents.html
Glenco Geometry book PG 476
Find arc lengths and areas of sectors of circles.
Emphasize the similarity of all circles. Note that by similarity of sectors with the same central angle, arc lengths are proportional to the
radius. Use this as a basis for introducing radian as a unit of measure. It is not intended that it be applied to the development of circular
trigonometry in this course.
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.
Arc Properties Podcast: http://teachers.henrico.k12.va.us/math/igo/08Circles/8_4.html
Area of sectors and Understanding radians and degrees: http://learni.st/users/S33572/boards/3056-arc-length-andradians-common-core-standard-9-12-g-c-5
Podcast Area and Circumference: http://teachers.henrico.k12.va.us/math/igo/08Circles/8_2.html
Translate between the geometric description and the equation for a conic section.
Connect the equations of circles and parabolas to prior work with quadratic equations. The directrix should be parallel to a
coordinate axis.
Derive the equation of a circle of given center and radius using the Pythagorean Theorem;
VIDEO: http://learnzillion.com/lessons/280-derive-the-equation-of-a-circle-using-the-pythagorean-theorem
Complete the square to find the center and radius of a circle given by an equation.
Gingerbread Man Problem
Completing the square to shift between: http://crmc.columbusstate.edu/Gingerbread%20Man%20Problem.pdf
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General Form: 0 = Ax^2 + By^2 + Cx + Dy + E (where (–c/2, -d/2) is the center of the circle) to standard form by
completing the square twice provides the new form of circle equations: r^2 = (x-h)^2 + (y-k)^2 (where r is the radius
of the circle and the point (h, k) is the center of the circle.)
Relate standard form of circle equation to the unit circle equation x^2 + y^2 = 1 (or sin^2 + cos^2 = 1), where h and k
are both zero because the unit circle is centered at the point (0,0) and the radius is 1.
o This should also connect to the systems of equations for the intersection of circles and linear equations
Derive the equation of a parabola given a focus and directrix. – (CLUSTER BREAKDOWN EXAMPLE)
How and why learni.st: http://learni.st/users/S33572/boards/3086-deriving-the-equation-of-a-parabola-common-corestandard-9-12-g-gpe-2
How and why? http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_conics_directrix.xml
How to with examples: http://hotmath.com/hotmath_help/topics/finding-the-equation-of-a-parabola-given-focus-anddirectrix.html
How to with examples: http://www.purplemath.com/modules/parabola3.htm
Powerpoint:
http://www.google.com/url?sa=t&rct=j&q=&esrc=s&frm=1&source=web&cd=7&ved=0CE8QFjAG&url=http%3A%2F%2F
www.wsfcs.k12.nc.us%2Fcms%2Flib%2FNC01001395%2FCentricity%2FDomain%2F7426%2FSection7.3.ppt&ei=16xc
UbzsOOG1iwKJl4C4BA&usg=AFQjCNEqYPKKde_duq3KNpUFZzsQq9y6uA
Practice problems (Also contains systems) : http://highered.mcgrawhill.com/sites/dl/free/0072450282/31563/sect13_2.pdf
Practice: Parabolas and systems: https://www.cohs.com/editor/userUploads/file/Meyn/321%20Student%20Workbook.pdf
Use coordinates to prove simple geometric theorems algebraically.
Include simple proofs involving circles.
Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by
four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at
the origin and containing the point (0, 2).
USE GEORGIA UNIT (PG 34-36)
Explain volume formulas and use them to solve problems.
Informal arguments for area an volume formulas can make use of the way in which area and volume scale under similarity
transformations: when one figure in the plane results from another by applying a similarity transformation with scale factor k, its
area is k2 times the area of the first. Similarly, volumes of solid figures scale by k3 under a similarity transformation with scale
factor k.
Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid,
and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.
(Broken down with examples of learning targets):
http://sisseton.k12.sd.us/Staff%20Documents/Math/Pit%20Stop3/Math%20Tools/GEOMETRY/Geometry_MathTool_Unit%203
.pdf
Pg with links: https://www.softchalkcloud.com/lesson/files/AG9dfynWh2i01b/Informal_Arguement_Formulas_print.html
See cavalari’s principle lesson plan (saved) http://learni.st/users/S33572/boards/3155-using-cavalieri-s-principle-todetermine-volumes-common-core-standard-9-12-g-gmd-2
Lesson Plan stockpile: https://ccgps.org/G-GMD.html
Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
Solve Systems of Equations
A.REI.7 - Solve systems of equations involving the intersection of circles and lines. Ex: finding the intersections between x2 + y2 = 1
and y = (x+1)/2 leads to the point (3/5, 4/5) on the unit circle, corresponding to the Pythagorean triple 32 + 42 = 52.