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Suggested Pacing for the Common Core Geometry Course Note: Textbook pages are for reference only. You will have to use additional resources since the text does not follow the modules completely. Unit 1: Angles and Constructions Lesson 1 2/3 Title Introduction to Geometry Constructions: Copy Segment, Equilateral Content Define: Point, Line, Plane Textbook Pages Pg: 5-13 Define: Congruence, Segments, Betweenness, Midpoint, Introduce Midpoint Formula Introduce Distance as absolute value of difference of two points and using the formula Define: angle, types of angles:acute, right, obtuse, straight ,< bisector, Introduce how to label an angle Pg: 14-35 4 Constructions: Copy an <, Bisect an <, Construct a 60 angle Pg: 36-44 5 Solve for Unknown <’s Define: Vertical <’s, Adjacent <’s, Complementary <’s, Supplementary <’s, Linear Pair, Straight < Understand a full rotation is 360 Pg: 46-54 6 Constructions: lines bisector, 45 angle Symmetry: “ right <’s along bisector Define: bisector, Right <’s, Symmetry Theorems: lines form right angles Pg: 48,55,324 7/8 Point of Concurrency: Circumcenter - bisector Incenter - < bisector *Patty Paper* Define: Concurrency, Circumcenter, Incenter Pg: 324-331 9 10 Review Test Standards Addressed: G-CO.A.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. G-CO.D.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. G-CO.D.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. Unit 2: Unknown Angles and Postulates of Equalities Lesson 1 Title Properties of Parallel Lines Content Textbook Pages Define: Parallel Lines, Transversal ,Theorem Pg: 173-186 Theorems: Alternate Interior Angles are Congruent, Alternate Exterior Angles are Congruent, Corresponding Angles are Congruent, Same Side Interior angles areSupp. 2 3 Properties of Parallel Lines Angles in a Triangle Construct parallel lines Applications Sum of Angles is 180 Types of Triangles Find missing angle/s of a triangle Engage NY Mod 1 topic B Lesson 7 Pg: 246-254 4 Angles in a Triangle Exterior angle of a Triangle Theorem Pg: 246-254 5 Write Unknown < Proofs “Informally” Define: Hypothesis, Conclusion, Conditional sentences Deductive reasoning Pg: 127-134 Postulates of Equality Reflexive, symmetric, transitive, substitution, addition, subtraction, mult, div Proofs using all definitions and postulates from this unit Pg: 136-140 6-8 9 Practice Proof Day 10 11 Review for test Test Pg: 144-159 Supplement with worksheets Standards Addressed: G-CO.C.9 1 Prove1 theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. Prove and apply (in preparation for Regents Exams). Why are TRANSFORMATIONS THE SPINE OF THE CORE? Isometries& Rigid Motions in the plane preserve distances, angles, betweeness and collinearity within transformed shapes. This leads to our new definition of congruence. Two figures are CONGRUENT if and only if one can be obtained from the other by one or a sequence of rigid motions. The non-isometric transformation of dilation leads us to investigating similarity. This definition is also revised to be viewed in the light of transformations. Two plane figures are SIMILAR if and only if one can be obtained from the other by one or a sequence of similarity transformations. (Similarity transformations included reflection, rotation, translation and dilation.) Unit 3:Transformations/Rigid Motions Lesson 1 Topic Review of Transformations Content Image and Pre- image, Clockwise and Counter clockwise, Symmetry, Review def of: Rotations, Line Reflections, Translations[Distance and < measure is preserved], Dilations[not ], Center of rotation Textbook Pages Ch 9 Pg: 621 2/3 Line Reflections Graphically and Non-graphically Constructions: Using constructions locate the line of reflection. Students understand that any point on a line of reflection is equidistant from any pair of pre-image and image points in a reflection. Characterize points on a perpendicular bisector. Graphically and Non-graphically Constructions Pg: 623-629 Graphically and Non-graphically Constructions and rotational symmetry Pg: 651-657, 663-669 4 Translations 5 Rotations, Reflections, Symmetry “Compositions” Pg: 632-636 6 Rotations Graphically and Non-graphically Constructions 7 Point Reflections Show reflection in origin as well as any point. Discuss it’s a rotation of 180, point symmetry 8/9 Apply and Construct Composition of figures 10 Applications of in terms Of Rigid Motion Show and describe compositions of transformations such as two line reflections, translation and line reflection, etc. Write in words only, no symbols. Corr. Parts of ’s are Must be able to identify corresponding parts of figures after a single transformation has occurred 11 12 Review Test Pg: 639-346 Pg: 651-656 *See directions in Engage NY modulePg:147-153 Text: Pg: 255-260 Pg: 296-299 Standards Addressed: G-CO.A.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). G-CO.A.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. G-CO.A.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. G-CO.A.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. G-CO.B.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. G-CO.B.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. G-CO.D.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. Unit 4: Triangle Congruence Lesson 1-5 Topic Congruence of triangles by SSS,SAS,ASA,AAS, HL 6 7 Showing Base Angles of an Isosceles Triangle are congruent Triangle proofs 8 9 10 Triangle proofs Review Test Content Manipulating physical forms of triangles through rigid motions to determine whether or not a pair of triangles is congruent. Students must be able to write the series of compositions of transformations from the pre-image to the image to show triangles are congruent by different methods. Students should recognize method of congruence by triangle markings and determine missing part so triangles would be congruent. Formal proofs. Proof should be done by construction as well as a formal proof. Textbook Pages Pg:264-271 Pg: 275-282 Pg: 275-284 Practice day on writing proofs including supplementary angles and CPCTC Practice day on writing proofs Ch 4 pg: 264-293 Pg. 285-291 Ch 4 pg: 264-293 Standards Addressed: G-CO.B.7 G-CO.B.8 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. Unit 5: Quadrilaterals Lesson 1 2,3 4-8 9 10 Topic Properties of Parallelograms Practice proof day on parallelograms Properties of other quadrilaterals Review Test Content Students should identify the 6 properties of a parallelogram Proofs and algebraic applications Given parallelogram, write proofs Prove quad is a parallelogram Discuss properties of rectangle, rhombus, square,trapezoid,kite Textbook Pages Pg:403-411 Supplement with old texts Pg: 423-448 Standards Addressed: G-CO.C.11 Prove2 theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals. Unit 6: Segments in Triangles and Constructions 1 Special lines in triangles: mid segment 2 Special lines in triangles: centroid 3 Special lines in triangles: orthocenter Construct a square and A regular hexagon inscribed in a circle 4 5 Sum of Interior/Exterior angles of a polygon 6 7 Review Test Construct the mid segment of a triangle and discuss the mid-segment of a triangle is parallel to the third side of the triangle and half the length of the third side of the triangle. Include midsegment of a trapezoid Construct the centroid as point of concurrency of medians. Discuss the ratios of the segments of the median. Show coordinates of centroid is the average of the three vertices of the triangle. Construct orthocenter as point of concurrency of altitudes. Using construction of copying segments and perpendicular lines, construct a square. Using the length of the radius of a circle, mark off 6 equal parts of circle to find vertices of a hexagon Using formula 180(n-2) find sum of the measures of angles of polygons, each angle, ext angle Pg:491 Pg. 440 Pg: 334-335 Module pg. 156-165 Pg: 337 See handout from Math Open Reference Pg: 393-399 Standards Addressed: G-CO.C.10 Prove2 theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. G-CO.D.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. Unit 7: Inequalities Lesson 1 Topic Basic inequality postulates Inequalities involving sides and angles of triangles 2 Inequalities involving exterior angle of triangle 3 Triangle inequality involving sides Triangle inequality proofs (optional) 4 5 Content Introduce basic inequality postulates. Show smallest angle opposite shortest side, etc Show exterior angle is greater than either nonadjacent interior angle Sum of two sides is greater than third side Practice proofs Textbook Pages Pg: 344-350 Pg: 344-350 Pg: 364-368 Throughout chapter 5 in text Review Test Standards Addressed: G-CO.C.10 Prove2 theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. Unit 8a: Scale Drawings and Dilations Lesson 1 Topic Scale Drawings 2 Making scale drawings using the ratio method 3 Constructing a line parallel to a given line in a triangle. 4 Dividing segments into n equal parts *End here for midterm Content Discuss: properties of a scale drawing: corresp angles congruent, Constant of proportionality - scale factor Students should be able to construct scale drawings of a polygon using any side and copying angles. Students should recognize scale factors when r = 1, r>1 and 0<r<1 Recall definition of dilation. Construct scale drawings given specific ratios: 1:2, etc. Using the construction of a parallel line in a triangle, discuss ratio of the segments formed. (Module refers to this as "side splitter thm". Solve numericals involving proportions. Using a compass and a ruler, use parallel lines to create segments of different ratios. Textbook Pages Pg: 511-517 Pg: 518-521 Pg: 490-498 Math Open Reference handout EngageNY module 2 pg.141 Unit 8b: Scale Drawings and Dilations continued Lesson 1/2 Topic Similar Polygons 3 Dilations as Transformations of the Plane 4 How do dilations map segments? 5 Properties Under Transformations 6 Compositions of Transformations including Dilations 7 8 Review Test Content Define similarity, ratio of similitude, Ratio of perimeters, altitudes, medians, angle bisectors Given 2 points, a center and a scale factor, draw diagrams illustrating lengths inc/dec by scale factor Given an angle, a center and a scale factor, show angle measurement remains the same. Remind students def of rigid motion and discuss previous transformations. Using coordinates, students will dilate segments given values of r. Dilation of a line. Discuss properties preserved under transformations, isometry,practice multiple transformations Identify the similarity transformation that maps preimage to image. Write as composition of transformations in words/symbols. Textbook Pages Pg: 461-475 Pg: 674-683 EngageNY module 2 pg.85 Pg: 674-683 EngageNY module 2 pg.99 Pg: 674-683 Pg: 651-689 EngageNY module 2 pg.128 Standards Addressed: G-SRT.A.1 Verify experimentally the properties of dilations given by a center and a scale factor: a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor. G-SRT.B.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity. G-MG.A.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).★ Unit 9: Similar Triangles Lesson 1 Topic The angle-angle criterion for two triangles to be similar. Similarity and the Angle Bisector Theorem Content Discuss similarity transformations as the composition of basic rigid motions and dilations, SAS, SSS,AA Textbook Pages Pg: 469-477 Pg: 501-507 2 Similarity Applications of similar polygons Numerical applications of similar triangles Use proportional parts with parallel lines Pg: 478-487 3 Proving Triangles Similar Pg: 478-487 4 Using similar triangles to show corresponding sides are proportional Using similar triangles to show cross products are equal Review Test Use definitions to prove triangles similar Extension of similar triangle proofs. Extension of similar triangle proofs. 5 6 7 Pg: 478-487 Pg: 478-487 Standards Addressed: G-SRT.A.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. G-SRT.A.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. G-SRT.B.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. G-MG.A.1 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).★ Unit 10: Applying Similarity to Right Triangles Lesson 1 Topic Special relationships within right triangles dividing into two similar sub-triangles Content Proving three triangles are similar Mean proportional theorem: Altitude is mean proportional between the segments on the hyp Mean prop thm: Leg is mean prop. Textbook Pages Pg: 501-507 2 Special relationships within right triangles dividing into two similar sub-triangles 3 Multiplying and dividing expressions with radicals Simplify, multiply and divide radical expressions Rationalizing denominators Honors: Using conjugates P19-20 Supplement with other resources 4 Adding and Subtracting radicals Pythagorean Thm Use distributive property to illustrate adding and subtracting radicals Applications finding perimeters of polygons, shaded areas Supplement with other resources 30-60-90 and 45-45-90 triangles Pg: 558-564 5 Special Right Triangles P: 501-507 Pg: 546-553 6 7 Review Test Standards Addressed: G-SRT.B.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity. Unit 11: Trigonometry Lesson 1 * Topic Trig Ratios: Sine, Cosine, Tangent 2 Trig Ratios: Secant, Cosecant and Cotangent *honors Cofunctions 3 Applications using sine and cosine 4 Applications using tangent 5 Trigonometry and the Pythagorean Theorem 6 7 Review Test Content Find trig ratios using right triangles Use trig ratios to find angle measures in right triangles Introduce reciprocal trig functions Introduce relationship between complementary angles and ratios Solve problems involving angles of elevation and depression. Solve problems involving angles of elevation and depression. Given one ratio, use pythagorean theorem to be able to find remaining trig ratios. Introduce pythagorean identity sin2x + cos2x = 1 Introduce quotient ratio : tan x = sinx /cosx Textbook Pages Pg.568-577 Pg. 578 Engage NY Module 2 Pg: 407-410 Pg: 580-586 Pg: 580-586 EngageNY Module 2 Pg:437-452 Unit 11: Trigonometry continued Lesson 1 2 Topic Area of a triangle Law of Sines 3 Law of Cosines 4 Applications of law of sines and cosines 5 6 Review Test Content Show area = 1/2 absinC Find missing side of acute triangle Find missing side of acute triangle Solve triangle problems finding sides Textbook Pages See module Pg. 588-599 Pg. 588-599 Pg. 588-599 Standards Addressed: G-SRT.C.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. G-SRT.C.7 Explain and use the relationship between the sine and cosine of complementary angles. G-SRT.C.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.★ Unit 12: Area Lesson 1 Topic Areas of Triangles, Quadrilaterals 2 Applications of Areas of Similar Figures 3 Circumference and arc length 4 5 6 7 8 9 Area of Circles and Sectors Areas of Regular Polygons Involving apothem Areas of Composite Figures Cross Sections Review Test Content Find area of: triangle, parallelogram, rhombus, kites, trapezoid Comparing the ratio of areas to ratio of sides of similar polygons Circumference and arc length, radian measure Include shaded areas Textbook Pages Pg: 779-795 Pg. 818-822 Pg. 699-713 Pg: 798-805 Pg:807-813 Pg. 807-813 Pg. 840 Standards Addressed: G-GMD.A.1 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. Unit 13: Surface Area and Volume Lesson 1 Topic Three Dimensional Space 2 Surface Areas 3 Surface Areas 4 Volume of Prism and Cylinder 5 Volume of Pyramid and Cone 6 Surface Area and Volume of a Sphere 7/8 Volume of Composite Figures 9 10 Review Test Content Introduce solid figures: Prism, cylinder, pyramid and cone Show cross-sections formed from intersection of plane and solid Find lateral area and surface area of prisms and cylinders Find lateral area and surface area of pyramids and cones Find volume of prism and cylinder. Scaling principle for volumes. Cavalieri's Principal Textbook Pages Pg.839-843 Find volume of pyramid and cone Find surface area and volume of sphere Find volume of composite 3D figures Pg. 873-878 Pg. 846-852 Pg. 854-861 Pg. 863-870 Pg. 880-886 See Exam Gen and NYS Regents Standards Addressed: G-GMD.A.1 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., G-GMD.A.3 Use volume formulas for cylinders, pyramids, cones and spheres to solve problems. G-GMD.B.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. G-MG.A.1 Use geometric shapes, their measures, and their properties to describe objects (e.g. modeling a tree trunk or a human torso as a cylinder). G-MG.A.2 Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot). G-MG.A.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). Unit 14: Coordinate Geometry 1 Slope as Rate of Change Writing the equation of a line given Slope and a point, or two points 2 Perpendicular lines and distance 3-5 Coordinate Geometry Proofs Define slope in coordinate plane as rate of change. Applications using slope Discuss relationship between slopes of parallel and perpendicular lines Write equation using point slope form and slope intercept form Discuss all points on perpendicular bisector of a line are equidistant from the endpoints Write the equation of the perpendicular bisector Prove or disprove a quadrilateral is a parallelogram, rectangle, rhombus, square, trapezoid using distance and slope. Include literal coordinates Pg. 188-195 Pg. 198-204 Pg.215-221 Pg. 419,427,436,444 6 Perimeter and Area of Polygons 7 Dividing Segments Proportionately 8 9 Review Test Using Coordinate Plane, find perimeter and area of triangles and polygonal regions. Partitioning segments on coordinate plane into ratios other than 1:1 Pg. 56-63 Supplement with worksheets Module pg. 145 Standards Addressed: 2 G-GPE.B.4 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). G-GPE.B.5 Prove 2 the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). G-GPE.B.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio. G-GPE.B.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.★ 2F Prove and apply (in preparation for Regents Exams). Unit 15: Circles - Angles Lesson 1 Title Intro to Circles Measuring angles and arcs Inscribed Angles 2 Arcs and Chords 3 Inscribed and Circumscribed circles of a triangle 4 5-7 Tangents Secants, Tangents, Chords, Angles 8 Practice day on all circle applications 9 10 Review Test Content Define circle, radius, diameter, chord, arc, concentric circles Show all circles are similar Discuss major/minor arc, semi circle, central angles. Thales Thm: Opposite angles of a quad inscribed in a circle are supplementary Diameter perpendicular to chord Congruent chords have congruent arcs, etc. Construct a circle inscribed in a triangle Construct a triangle circumscribed about a circle Tangents drawn to a circle Measuring angles and arcs formed by sec, tan, chords Putting it all together into multi-step circle questions Textbook Pages Pg. 697-705 Pg. 706-714 Pg. 723-730 Pg. 715-722 Pg. 740 Pg. 732-739 Pg. 741-749 See module for examples Standards Addressed: 3 G-C.A.2 Identify and describe relationships among inscribed angles, radii, and chords. Include3 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. G-C.A.3 Construct the inscribed and circumscribed circles of a triangle, and prove4 properties of angles for a quadrilateral inscribed in a circle. G-C.B.5 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. Include angles formed by secants (in preparation for Regents Exams). Unit 16: Circles - Segments Lesson 1 Title Segments of chords in a circle 2 Tan-sec and 2 sec segments 3 Writing the Equation of a Circle 4 Recognizing the Equation of a Circle * Equations of Tangents to Circles (honors) 5/6 7 8 9 Circle Proofs Dilating circles by construction (**optional topic) Content Finding length of chords in a circle Finding the length of tan/sec segments Write equation given center, radius Completing the square Writing equation of tan line given equation of circle, slope of tan line Using circle angles and segments to prove triangles congruent and similar. Constructing circles of scale factors greater than one and less than one, with center of dilation inside or outside the circle. Writing the equation of a circle given a scale factor. Textbook Pages Pg. 750-756 Pg. 750-756 Pg. 757-762 Pg. 757-762 Module pg. 227-236 Module pg. 237 Use ExamGen for examples. Module 2 Lesson 8 pg. 120 **See link below from Manhassetschools for a sample lesson Review Test Standards Addressed: G-C.A.1 Prove4 that all circles are similar. G-GPE.A.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. G-GPE.B.4 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). End of curriculum! 151 days of instruction including review and exams Here is a nice website that links the standards to all topics in the CC Geometry curriculum: http://www.mathsisfun.com/links/core-high-school-geometry.html GEO H – Dilating Circles by Construction: http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=3&cad=rja&uact=8&ved=0CCsQFjACahUKEwiTwcCItaHHAhXL aT4KHbTiDJ4&url=http%3A%2F%2Fmanhassetschools.org%2Fsite%2Fhandlers%2Ffiledownload.ashx%3Fmoduleinstanceid%3D3700 %26dataid%3D7804%26FileName%3DAim%25208%252010H.pdf&ei=DR7KVdOGGcvTQG0xbPwCQ&usg=AFQjCNELM6tjMrOkex704D4spPjBxiIRRA&bvm=bv.99804247,d.cWw 4 Prove and apply (in preparation for Regents Exams).