Pacing - Rochester City School District



|Pacing |Unit/Essential Questions |Essential Knowledge- Content/Performance | | | |

| | |Indicators |Essential Skills |Vocabulary |Resources |

| | |(What students must learn) |(What students will be able to do) | | |

| |Unit of Review |Student will review: |Students will review: |quadratic function | |

|9/4-9/13 | |A.A.19 Identify and factor the difference| |quadratic equation | |

| |1. How do you solve equations |of two squares |1. Solve multi-step |linear function |JMAP |

|8 days |with fractions using inverse | |equations (including |linear equation |A.A.19, A.A.20, A.A.22, A.A.25, A.A.27 A.A.28, A.G.4 |

| |operations or using the LCD to |A.A.20 Factor algebraic expressions |Fractions) |system of equations |A.G.8 |

| |clear denominators in the |completely, including trinomials | |parabola | |

| |equation? |with a lead coefficient of one |2. Factoring all types. |algebraic expression | |

| | |(after factoring a GCF) | |monomial |Solving Fractional Equations |

| |2. How do you factor algebraic | |3. Graph quadratic functions |binomial |Linear Equations |

| |expressions? |A.A.22 Solve all types of linear |and solve quadratic |trinomial |Factoring |

| | |equations in one variable. |equations algebraically and |polynomial |Quadratic Equations |

| |3. How do you solve quadratic | |graphically. |coefficient |Graphing Parabolas |

| |equations |A.A.25 Solve equations involving | |GCF | |

| |graphically and algebraically? |fractional expressions. Note: |4. Solve systems of linear & |multiplication property of zero | |

| | |Expressions which result in |quadratic equations |factor | |

| | |linear equations in one variable |graphically & algebraically. | | |

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| | |A.A.27 Understand and apply the | | | |

| | |multiplication property of zero | | | |

| | |to solve quadratic equations | | | |

| | |with integral coefficients and | | | |

| | |integral roots | | | |

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| | |A.A.28 Understand the difference and | | | |

| | |connection between roots of a | | | |

| | |quadratic equation and factors of a | | | |

| | |quadratic expression. | | | |

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| | |A.G.4 Identify and graph quadratic | | | |

| | |functions | | | |

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| | |A.G.8 Find the roots of a parabolic | | | |

| | |function graphically. | | | |

| | |Students will learn: |Students will be able to: |undefined term |Holt Text |

|9/16-9/27 |Chapter 1 | | |point |1-1: pg 6-8 (Examples 1-4) |

| |Foundations of Geometry |G.G.17 Construct a bisector of a given |identify, name and draw points, |line |1-2: pg 13-16 (Examples 1-5, include |

|8 days |HOLT |angle, using a straightedge and |lines, segments, rays and planes |plane |constructions) |

| | |compass, and justify the | |collinear |1-3: pg 20-24 (Examples 1-4, include |

|CCSSM |What are the building blocks of |construction |use midpoints of segments to find |coplanar |constructions) |

| |geometry and what symbols do we | |lengths |segment |1-4: pg 28-30 (Examples 1-5) |

| |use to describe them? |G.G.66 Find the midpoint of a line | |endpoint |1-5: pg 36-37 (Examples 1-3) |

| | |segment, given its endpoints |construct midpoints and congruent |ray |1-6: pg 43-46 (Examples1-4) |

| |CCSSM Fluency needed for | |segments |opposite rays | |

| |congruence and similarity |G.G.67 Find the length of a line | |postulate |Geometry Labs from Holt Text |

| | |segment, given its endpoints |use definition of vertical. |coordinate |1-1 Exploration |

| | | |complementary and supplementary |distance |1-3 Exploration |

| | | |angles to find missing angles |length |1-3 Additional Geometry Lab |

| | | | |congruent segments |1-4 Exploration |

| | | |apply formulas for perimeter, area |construction |1-5 Exploration |

| | | |and circumference |between |1-5 Geometry Lab 1 |

| | | | |midpoint |1-5 Geometry Lab 2 |

| | | |use midpoint and distance formulas |bisect |1-6 Exploration |

| | | |to solve problems |segment bisector | |

| | | | |adjacent angles | |

| | | | |linear pair |GSP Labs from Holt |

| | | | |complementary |1-2 Exploration |

| | | | |angles |1-2 Tech Lab p. 12 |

| | | | |supplementary |pg. 27: Using Technology |

| | | | |angles | |

| | | | |vertical angles |Vocab Graphic Organizers |

| | | | |coordinate plane |1-1 know it notes 1-4 know it notes |

| | | | |leg |1-2 know it notes 1-5 know it notes |

| | | | |hypotenuse |1-3 know it notes 1-6 know it notes |

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| | | | | |G.G.17, G.G.66, G.G.67 |

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| | | | | |Lines and Planes |

| | | | | |Constructions |

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| | | | | |Finding Distances |

| | | | | |Reasoning with Rules |

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|Sep 30-Dec 13 |NYSED Module 1 for Geometry |Experiment with transformations in the | | |

| | |plane | | |hments/geometry-m1-full-module.pdf |

| | |G-CO.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.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.3 Given a rectangle, parallelogram, | | | |

| | |trapezoid, or regular polygon, describe | | | |

| | |the rotations and reflections that carry | | | |

| | |it onto itself. | | | |

| | |G-CO.4 Develop definitions of rotations, | | | |

| | |reflections, and translations in terms of | | | |

| | |angles, circles, perpendicular lines, | | | |

| | |parallel lines, and line segments. | | | |

| | |G-CO.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. | | | |

| | | | | | |

| | |Prove geometric theorems | | | |

| | |G-CO.9 Prove33 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. | | | |

| | |G-CO.10 Prove27 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.11 Prove27 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. | | | |

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| |Chapter 6: Quadrilaterals |G.G.27 Write a proof arguing from a | |Polygon |Holt Text |

|12/16- | |given hypothesis to a given conclusion | |Vertex of a polygon |6-1: pg 382-388 |

|1/17 |What types of quadrilaterals | |Students will classify polygons by |Diagonal |6-2: pg 390-397 |

| |exist and what properties are |G.G.36 Investigate, justify, and apply |number of sides and shape. |Regular polygon |6-3: pg 398-405 |

|15 days |unique to them? |theorems about the sum of the measures of | |Exterior angle |6-4: pg 408-415 |

| | |the interior and exterior angles of | |Concave |6-5: pg 418-425 |

|CCSSM |CCSSM Fluency needed for |polygons |Students will discover and apply |Convex |6-6: pg 429-435 (no kites) |

| |congruence and similarity | |relationships between interior and |Parallelogram | |

| | |G.G.37 Investigate, justify, and apply |exterior angles of polygons |Rectangle |GSP from Holt Text |

| | |theorems about each interior and exterior | |Rhombus |6-2: Exploration |

| | |angle measure of regular polygons |Students will classify |Square |6-2: technology lab |

| | | |quadrilaterals according to |Trapezoid |6-5: pg 416-417 |

| | |G.G.38 Investigate, justify, and apply |properties. |Base of a trapezoid |6-6: pg 426 |

| | |theorems about parallelograms involving | |Base angle of a trapezoid | |

| | |their angles, sides, and diagonals |Students will apply properties of |Isosceles trapezoid |Geometry Labs from Holt Text |

| | | |parallelograms, rectangles, rhombi,|Midsegment of a trapezoid |6-1: Exploration |

| | |G.G.39 Investigate, justify, and apply |squares and trapezoids to |Midpoint |6-2: pg 390 |

| | |theorems about special parallelograms |real-world problems |Slope |6-3: Exploration |

| | |(rectangles, rhombuses, squares) involving| |Distance |6-3: Lab with geoboard |

| | |their angles, sides, and diagonals |Students will write proofs of | |6-4: Exploration |

| | | |quadrilaterals | |6-4: Lab with tangrams |

| | |G.G.40 Investigate, justify, and apply | | |6-6: Lab with geoboard – no kites |

| | |theorems about trapezoids (including |Students will investigate, justify | | |

| | |isosceles trapezoids) involving their |and apply properties of | |Vocab Graphing Organizers |

| | |angles, sides, medians, and diagonals |quadrilaterals in the coordinate | |6-1: know it notes |

| | | |plane | |6-2: know it notes |

| | |G.G.41 Justify that some quadrilaterals | | |6-3: know it notes |

| | |are parallelograms, rhombuses, rectangles,| | |6-4: know it notes |

| | |squares, or trapezoids | | |6-5: know it notes |

| | | | | |6-6: know it notes – no kites |

| | |G.G.69 Investigate, justify, and apply | | | |

| | |the properties of triangles and | | |JMAP |

| | |quadrilaterals in the coordinate plane, | | |G.G.36, G.G.37, G.G.38, G.G.39, G.G.40, G.G.41, G.G.69 |

| | |using the distance, midpoint, and slope | | | |

| | |formulas | | | |

| | | | | |G.G.36 and G.G.37, G.G.38-G.G.41, G.G.69 |

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| | | | | |GSP worksheets – angles in polygon |

| | | | | |GSP worksheets – quadrilateral |

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|1/21- |MIDTERM REVIEW | | | | |

|1/24 | | | | | |

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|4 days | | | | | |

| |Chapter 7: Similarity |Students will learn: |Students will write and simplify |Dilation |Holt Text |

|2/3- |and Chapter 8: (section 8-1 | |ratios. |Proportion |7-1: pg 454-459 (Examples 1-5) |

|2/28 |only) |G.G.44 Establish similarity of |Students will use proportions to |Ratio |7-2: pg 462-467 (Examples 1-3) |

| | |triangles, using the following theorems: |solve problems. |Scale |7-3: pg 470-477 (Examples 1-5) |

|15 days |How do you know when your |AA, SAS, and SSS |Students will identify similar |Scale drawing |7-4: pg 481-487 (Examples 1-4) |

| |proportion is set up correctly? | |polygons and apply properties of |Scale factor |7-5: pg 488-494 (Examples 1-3, discover 4) |

|CCSSM |What are some ways to determine |G.G. 45 Investigate, justify, and apply |similar polygons to solve problems.|Similar |7-6: pg 495-500 (Examples 1-4) |

| |of any two polygons are similar?|theorems about similar triangles |Students will prove certain |Similar polygons |8-1: pg. 518-520 (Examples 1-4) |

| |Think physically and | |triangles are similar by using AA, |Similarity ratio | |

| |numerically. |G.G.46 Investigate, justify, and apply|SSS, and SAS and will use triangle |Side |Vocab Graphic Organizers |

| |How can you prove if triangles |theorems about proportional relationships |similarity to solve problems. |Angle |7-1: Know it Notes |

| |are similar? |among the segments of the sides of the |Students will use properties of |Parallel |7-2: Know it Notes |

| |When you dilate a figure, is it |triangle, given one or more lines parallel|similar triangles to find segment |mean proportional |7-3: Know it Notes |

| |the same as creating a figure |to one side of a triangle and intersecting|lengths. |theorem |7-4: Know it Notes |

| |similar to the original one? |the other two sides of the triangle |Students will apply proportionality|geometric mean |7-5: Know it Notes |

| | | |and triangle angle bisector | |7-6: Know it Notes |

| |Similarity is a CCSSM Emphasis |G.G.47 Investigate, justify and apply |theorems. | |8-1: Know it Notes |

| | |theorems about mean proportionality: the | | | |

| | |altitude to the hypotenuse of a right |Students will use ratios to make | |GSP from Holt Text |

| | |triangle is the mean proportional between |indirect measurements and use scale| |7-2 Tech Lab p.460 |

| | |the two segments along the hypotenuse; the|drawings to solve problems. | |7-3 Tech Lab p.468 |

| | |taltitude to the hypotenuse of a right | | |7-4 Exploration |

| | |triangle divides the hypotenuse so that |Students will apply similarity | |7-4 Tech Lab p. 480 |

| | |either leg of the right triangle is the |properties in the coordinate plane | | |

| | |mean proportional between the hypotenuse |and use coordinate proof to prove | |Geometry Labs from Holt Text |

| | |and segment of the hypotenuse adjacent to |figures similar. | |7-1 Exploration 7-2 Exploration |

| | |that leg | | |7-2 Geoboard Lab 7-3 Exploration |

| | | | | |7-5 Exploration 7-6 Exploration |

| | | | | |7-6 Geoboard lab 8-1 Exploration |

| | |G.G.58 Define, investigate, justify, | | |8-1 Tech Lab with Graphing Calculator |

| | |and apply similarities (dilations …) | | | |

| | | | | |JMAP |

| | | | | |G.G.44, G.G.45, G.G.46, G.G.47 |

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| | | | | |Lesson: Midsegment Theorem |

| | | | | |Practice: Midsegment Theorem |

| | | | | |Teacher Resource: Discovering Midsegment Theorem |

| | | | | |Lesson: Similar Triangles |

| | | | | |Lesson: Similar Figure Info |

| | | | | |Lesson: Proofs with Similar Triangles |

| | | | | |Lesson: Strategies for Dealing with Similar Triangles |

| | | | | |Practice: Similarity Numerical Problems |

| | | | | |Practice: Similarity Proofs |

| | | | | |Lesson: Mean Proportional In a Right Triangle |

| | | | | |Practice: Mean Proportional in a Right Triangle |

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| | |G.G.1 Know and apply that if a line is |identify perpendicular lines |Point |Holt Text |

|3/3- |Three-Dimensional Plane Geometry|perpendicular to each of two intersecting | |Perpendicular |G.G.1-4, 6:  |

|3/14 | |lines at their point of intersection, then|identify perpendicular planes |Coplanar |3-4 Extension:  Lines Perpendicular to Planes  pg. NY |

| |1. What is the difference |the line is perpendicular to the plane | |Parallel |180A-D |

|9 days |between a line, a segment and a |determined by them |define line, segment and ray |Parallel lines | |

| |ray? | | |Parallel planes |G.G.7-10:  |

| | |G.G.2 Know and apply that through a |4. define a plane and what the |Skewed lines |Extension:  Perpendicular Planes and Parallel Planes pg. |

| |2. What is the difference |given point there passes one and only one |minimum requirements are for a |Point of intersection | NY 678A-D |

| |between the intersection of 2 |plane perpendicular to a given line |plane (3 points) |Line | |

| |lines, 2 planes, and a line with| | |Ray |G.G.10:  |

| |a plane? |G.G.3 Know and apply that through a given|know the differences in what is |Line segment |Chapter 10-1 Solid Geometry pg. 654 |

| | |point there passes one and only one line |formed when lines intersect lines, | | |

| |3. What is formed when a plane |perpendicular to a given plane |planes intersect planes, and lines | |JMAP |

| |intersects 2 other parallel | |intersect planes. | |G.G.1, G.G.2, G.G.3, G.G.4, G.G.5, G.G.6, G.G.7, G.G.8, |

| |planes? |G.G.4 Know and apply that two lines | | |G.G.9 |

| | |perpendicular to the same plane are |Understand the meaning of coplanar | |Amsco Resources |

| | |coplanar | | |Ch. 11-1: G.G.1, G.G.2, G.G.3 |

| | | |7. Understand the meaning of | |Ch. 11-2: G.G.4, G.G.7, G.G.8 |

| | |G.G.5 Know and apply that two planes are |collinear | |Ch. 11-3: G.G.9 |

| | |perpendicular to each other if and only if| | |Pearson Resources |

| | |one plane contains a line perpendicular to|8. Visualize and represent each of| |Online Mini-Quiz |

| | |the second plane |the aforementioned P.I.s that they | |Vocabulary Crossword |

| | | |will learn. | |Video: Determining Colinear Points |

| | |G.G.6 Know and apply that if a line is | | |Video: Defining a Plane |

| | |perpendicular to a plane, then any line | | |Discovery Education |

| | |perpendicular to the given line at its | | |Points, Lines, and Planes |

| | |point of intersection with the given plane| | | |

| | |is in the given plane | | |Teacher Resource |

| | | | | |Lesson: Defining Key Terms |

| | |G.G.7 Know and apply that if a line is | | |Lesson: Theorems Relating Lines and Planes |

| | |perpendicular to a plane, then every plane| | |Multiple Choice: Practice with Lines and Planes |

| | |containing the line is perpendicular to | | | |

| | |the given plane | | | |

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| | |G.G.8 Know and apply that if a plane | | | |

| | |intersects two parallel planes, then the | | | |

| | |intersection is two parallel lines | | | |

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| | |G.G.9 Know and apply that if two planes | | | |

| | |are perpendicular to the same line, they | | | |

| | |are parallel | | | |

| |NYSED Module 3 Geometry: | | | | |

|3/17- |Extending to Three Dimensions |Explain volume formulas and use them to | | | |

|3/28 | |solve problems35 | | | |

| | |G-GMD.1 Give an informal argument for the | | | |

|10 days | |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.3 Use volume formulas for cylinders,| | | |

| | |pyramids, cones, and spheres to solve | | | |

| | |problems.★ | | | |

| | |Visualize relationships between | | | |

| | |two-dimensional and three-dimensional | | | |

| | |objects | | | |

| | |G-GMD.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. | | | |

| | |Apply geometric concepts in modeling | | | |

| | |situations | | | |

| | |G-MG.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).★ | | | |

| | | | |interior of a circle |Holt Text |

| |Chapter 11 |G.G.49 Investigate, justify and apply |identify tangents, secants and |exterior of a circle |11-1: pg 746-750 (Examples 1-4) |

|3/31- |Circles |theorems regarding chords of a circle: |chords that intersect circles and |chord |(GSP models or construction on pg 748 would allow |

|4/25 | |perpendicular bisectors or chords; the |use properties to solve problems |secant |students to discover theorems 11-1-1, 11-1-2 and 11-1-3) |

| |What are the properties of lines|relative lengths of chords as compared to | |tangent of a circle |11-2: pg 756-759 (Examples 1-4) |

|20 days |and angles that intersect |their distance from the center of the |use properties of arcs and chords |point of tangency |11-4 pg. 772-775 (Examples1-4) |

| |circles and how do we use them |circle |of circles to solve problems |congruent circles |11-4 pg NY780A Extension (Example 1only , Note: This is a |

| |to solve problems? | | |concentric circles |theorem they should be able to apply to solve problems – |

| | |G.G.50 Investigate, justify and apply |investigate and understand theorems|tangent circles |pg 780C #2) |

| | |theorems about tangent lines to a circle: |regarding inscribed angles and |common tangent |11-5 pg 782-785 (Examples 1-5) |

| | |a perpendicular to the tangent at the |central angles in a circle |central angle |11-6 pg 792-794 (Examples 1-4) |

| | |point of tangency; two tangents to a | |arc |11-7 pg 799-801 (Examples1-3) |

| | |circle from the same external point; |find the measures of angles or arcs|minor arc | |

| | |common tangents of two no-intersecting or |formed by secants, chords and |major arc |GSP Labs from Holt |

| | |tangent circles |tangents that intersect a circle |semicircle |11-4 Exploration |

| | | | |adjacent arcs |11-5 Exploration |

| | |G.G. 51 Investigate, justify and apply |find the lengths of segments formed|congruent arcs |11-5 Tech Lab p. 780 |

| | |theorems about the arcs determined by the |by lines that intersect circles |inscribed angle |11-6 Exploration |

| | |rays of angles formed by two lines | |intercepted arc |11-6 Tech Lab p. 790 |

| | |intersecting a circle when the vertex is: |write equations and graph circles |subtend |Geometry Labs from Holt |

| | |inside the circle (two chords); on the |in the coordinate plane |secant segment |11-1 Exploration |

| | |circle (tangent and chord); outside the | |external secant segment |11-2 Tech Lab |

| | |circle (two tangents, two secants, or | |tangent segment |11-2 Exploration |

| | |tangent and secant) | |radius |11-5 Additional Geometry Lab |

| | | | |diameter |11-6 Additional Geometry Lab |

| | |G.G.52 Investigate, justify and apply | |center-radius form of a circle |11-7 Exploration |

| | |theorems about arcs of a circle cut by two| | | |

| | |parallel lines | | |Vocab Graphic Organizers |

| | | | | |11-1 know it notes 11-5 know it notes |

| | |G.G. 53 Investigate, justify and apply | | |11-2 know it notes 11-6 know it notes |

| | |theorems regarding segments intersected by| | |11-4 know it notes 11-7 know it notes |

| | |a circle: along two tangents from the | | | |

| | |same external point; along two secants | | |JMAP |

| | |from the same external point; along a | | |G.G.49,G.G.50,G.G.51,G.G.52,G.G.53 |

| | |tangent and a secant from the same | | |G.G.71,G.G.72,G.G.73,G.G.74 |

| | |external point; along two intersecting | | | |

| | |chords of a given circle | | | |

| | | | | |Chords, Circles and Tangents |

| | |G.G.71 Write the equation of a circle, | | |Circles and Angles |

| | |given its center and radius or given the | | |Circles Practice Regents Questions |

| | |endpoints of a diameter | | | |

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| | |G.G.72 Write the equation of a circle, | | |GSP: Angles and Circles |

| | |given its center and radius or given the | | |GSP: Segments and Circles |

| | |endpoints of a diameter. Note: The | | |GSP: Tangents and Circles from scratch |

| | |center is an ordered pair of integers and | | | |

| | |the radius is an integer. | | | |

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| | |G.G.73 Find the center and radius of a | | | |

| | |circle, given the equation of the circle | | | |

| | |in center-radius form | | | |

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| | |G.G.74 Graph circles of the form (x-h)2 | | | |

| | |+ (y-k)2 = r2 | | | |

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| |Chapter 12: Transformations |G.G.54 Define, investigate, justify, and|Students will identify and draw |Transformation |Holt Text |

|4/28- | |apply isometries in the plane (rotations, |reflections, transformations, |Image |12-1: pg 824-830 (Examples 1,2,4) |

|5/9 |How does a transformation affect|reflections, translations, glide |rotations, dilations and |Preimage |12-2: pg 831-837 (Examples 1,3) |

| |the ordered pairs of the |reflections) |composition of transformations. |Reflection in line |12-3: pg 839-845 (Examples 1,3) |

|10 days |original shape? | | |Point reflection |12-4: pg 848-853 (Example 1) |

| | |G.G.55 Investigate, justify, and apply |Students will apply theorems about |Translation |12-5: pg 856-862 (Example 1,2,3) |

|CCSSM |How does a change in ordered |the properties that remain invariant under|isometries. |Rotation |12-7: pg 872-879 (Examples 1 , 4) |

| |pairs affect the position of a |translations, rotations, reflections, and | |Isometry |pg 906-907 |

| |geometric figure? |glide reflections |Students will identify and describe|Opposite isometry |pg 910-913 |

| | | |symmetry in geometric figures. |Direct isometry | |

| |How does a scale factor affect a|G.G.56 Identify specific isometries by | |Composition of transformations |GSP from Holt Text |

| |shape, its area and its position|observing orientation, numbers of |Students will investigate |Glide reflection |12-1: Exploration |

| |in the coordinate plane? |invariant points, and/or parallelism |properties that are invariant under|Symmetry |12-2: Exploration |

| | | |isometries and dilations. |Line symmetry |12-4: Exploration |

| |Transformations is a CCSSM |G.G.57 Justify geometric relationships | |Rotational symmetry | |

| |Emphasis used to prove |(perpendicularity, parallelism, |Students will use analytical |Enlargement | |

| |similarity & congruence |congruence) using transformational |representations to justify claims |Reduction |Vocabulary development – Graphing Organizers |

| | |techniques (translations, rotations, |about transformations. |Invariant |12-1:know it notes |

| | |reflections) | | |12-1:reading strategy |

| | | | | |12-2:reading strategy |

| | |G.G.58 Define, investigate, justify, and| | |12-3:know it notes |

| | |apply similarities (dilations and the | | |12-5:know it notes |

| | |composition of dilations and isometries) | | |12-5:reading strategy |

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| | |G.G.59 Investigate, justify, and apply | | |JMAP |

| | |the properties that remain invariant under| | |G.G.54, G.G.55, G.G.56, G.G. 57, G.G.58, G.G.59, G.G.60, |

| | |similarities | | |G.G.61 |

| | | | | | |

| | |G.G.60 Identify specific similarities by| | | |

| | |observing orientation, numbers of | | |Transformational Geometry |

| | |invariant points, and/or parallelism | | |(Go to geometry section and find links under |

| | | | | |transformational geometry) |

| | |G.G.61 Investigate, justify, and apply | | | |

| | |the analytical representations for | | | |

| | |translations, rotations about the origin | | |TI 84 - transformations |

| | |of 90º and 180º, reflections over the | | |TI 84 - rotations |

| | |lines [pic], [pic], and [pic], and | | |GSP - transformations |

| | |dilations centered at the origin | | |GSP – transformations from scratch |

| | | | | |Math in movies |

| |Locus | |1. Students will state and |Locus |JMAP |

|5/12- | |G.G.22 Solve problems using compound |illustrate the 5 fundamental locus |Compound |G.G.22, G.G.23 |

|5/22 |How can each of the 5 |loci |theorems |Equidistant | |

| |fundamental loci be applied to a|G.G.23 Graph and solve compound loci in | | | |

|9 days |real world context? |the coordinate plane |2. Student will solve problems| |Basic locus theorems |

| | | |using compound loci | |Compound locus |

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| | | |3. Students will graph and | |Other Resources |

| | | |solve compound loci in the | |SEE ATTACHED PACKET |

| | | |coordinate plane | | |

| |Review Coordinate Geometry |G.G.69 Investigate, justify, and apply |Students will use coordinate |Midpoint |JMAP |

|5/27- |Proofs |the properties of triangles and |geometry to justify and investigate|Distance |G.G.69 |

|6/6 | |quadrilaterals in the coordinate plane, |properties of triangles |Slope | |

| |How can mathematical formulas be|using the distance, midpoint, and slope | |Parallel | |

|9 days |used to validate properties of |formulas | |Perpendicular |Coordinate Geometry Proofs |

| |polygons? | | |Isosceles | |

|CCSSM | | | |Equilateral | |

| |Use of coordinates to prove | | |Scalene |Other Resources |

| |geometric theorems is a CCSSM | |Students will investigate, justify |Right | |

| |Emphasis | |and apply properties of |Parallelogram |SEE ATTACHED PACKET |

| | | |quadrilaterals in the coordinate |Rectangle |Coordinate Geometry Packet |

| | | |plane |Rhombus | |

| | | | |Square | |

| | | | |Trapezoid | |

| |FINAL EXAM REVIEW | | | | |

|6/9- | | | | |Geometry Review and Formula Sheet |

|6/16 | | | | |Theorems and Properties in Geometry |

| | | | | |GeoCaching Activity |

|6 days | | | | |Geometry Jeopardy |

Blueprint for NYS Regents Exam in Geometry

There will be 38 questions on the Regents Examination in Geometry. The percentage of total credits that will be aligned with each content strand.

Geometric Relationships 8—12%

Constructions 3—7%

Locus 4—8%

Formal and Informal Proofs 41—47%

Transformational Geometry 8-13%

Coordinate Geometry 23-28%

Question Types The Regents Examination in Geometry will include the following types and numbers of questions:

28 Multiple choice (2 credits each)

6 two-credit open ended

3 four-credit open ended

1 six-credit open ended

Calculators Schools must make a graphing calculator available for the exclusive use of each student while that student takes the Regents Examination in Geometry.

RCSD Post Assessment (if applicable)

20 multiple choice questions

5 open ended questions

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CURRICULUM MAP: GEOMETRY REGENTS

RCSD- Department of Mathematics 2013-2014

CCSSM Emphasis and Fluency Recommendations Boldfaced

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