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COMMON CORE GEOMETRY CURRICULUM MAP Units and Topics Teaching Points (Essential Questions) Time Frame 1- Coordinate Geometry -calculate midpoints, slope, distance Sept. Assessments Homework’s Weeks -calculate points on a line segment that divide the segment proportionally -understand what makes lines perpendicular -write the equations of lines that are perpendicular through a certain point Resources engageny.org Examgen Unit Test 2-4 jmap.org Daily Summaries Stop-Light Checks for Understanding Geometry Common Core (Pearson) problemattic.com khanacademy. org deltamath.com Common Core Standards HSG-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. HSG-GP.E.B.5 Prove 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). COMMON CORE GEOMETRY CURRICULUM MAP 2- Angle Re lationships -solve algebraic problems involving complementary, supplementary, and vertical angles -discover the angle relationships formed when two parallel lines are cut by a transversal Oct. Homework’s Weeks engageny.org Examgen Unit Test 1-2 jmap.org Daily Summaries Stop-Light Checks for Understanding Geometry Common Core (Pearson) problemattic.com khanacademy. org deltamath.com HSG-CO.C.9 Prove 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. COMMON CORE GEOMETRY CURRICULUM MAP 3Constructions -use a compass and a straightedge to copy a line segment; copy an angle; construct a perpendicular bisector; bisect an angle; construct an equilateral triangle; construct a parallel and perpendicular through a given point; construct an equilateral triangle, square, and a hexagon inscribed in a circle Oct. Homework’s Weeks engageny.org Examgen Unit Test 3-4 jmap.org Daily Summaries Stop-Light Checks for Understanding Geometry Common Core (Pearson) problemattic.com khanacademy. org deltamath.com HSG-CO.D.12 Make formal geometric constructions with a variety of tools and methods. 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. HSG-CO.D.13 Construct an equilateral triangle, square, and a regular hexagon inscribed in a circle COMMON CORE GEOMETRY CURRICULUM MAP 3Transformatio ns -use the rules to perform a rotation, translation, and line reflection Nov. Homework’s Weeks Examgen Unit Test 1-3 -understand how to dilate a polygon and a line segment -understand the properties of all the transformations -identify and recognize the different transformations -perform a composition of transformations -understand congruence in terms of rigid motions engageny.org jmap.org Daily Summaries Stop-Light Checks for Understanding Geometry Common Core (Pearson) problemattic.com khanacademy. org deltamath.com HSG-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. HSG-CO.A.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself HSG-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 one another. HSG-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. HSG-SRT.A.1 Verify experimentally the properties of dilations given by a center and a scale factor. COMMON CORE GEOMETRY CURRICULUM MAP 3-Triangles -understand the relationship that the interior angles of a triangle have a sum of 180◦ -use the relationship between the interior and exterior angles of a triangle to solve problems -understand what the midsegment and its properties are -use properties of isosceles and right triangles to find missing pieces of a triangle -solve problems involving the centroid of a triangle -prove theorems about triangles in the coordinate plane Nov. Homework’s Week 4 engageny.org Examgen Unit Test Dec. Weeks 1-2 jmap.org Daily Summaries Stop-Light Checks for Understanding Geometry Common Core (Pearson) problemattic.com khanacademy. org deltamath.com HSG-CO.C.10 Prove 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 the 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 HSG-SRT.C.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems COMMON CORE GEOMETRY CURRICULUM MAP 3-Congruent Triangle Proofs -understand the meaning of corresponding parts and how to identify corresponding parts of various figures -write geometric proofs using SSS, SAS, ASA, AAS, and HL -understand that if two triangles are congruent then CPCTC can be applied -understand and use the addition, subtraction, reflexive, substitution, and transitive properties in a geometric proof -understand congruence in terms of rigid motions Dec. Weeks 3-4 (Xmas break Week 4) Homework’s engageny.org Unit Test Examgen Daily Summaries jmap.org Stop-Light Checks for Understanding Geometry Common Core (Pearson) Jan. Weeks 1-2 problemattic.com khanacademy. org deltamath.com HSG-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. HSG-CO.B.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. COMMON CORE GEOMETRY CURRICULUM MAP 3Quadrilaterals -understand the properties of a parallelogram and use them to find missing angles or line segments -understand the properties of the rectangle, rhombus, and square & use them to find missing angles or line segments - use coordinate geometry to prove theorems about a parallelogram, rectangle, rhombus, or square Jan. Weeks 3-4 (Regents Week 4) Homework’s engageny.org Unit Test Examgen Daily Summaries jmap.org Stop-Light Checks for Understanding Geometry Common Core (Pearson) problemattic.com khanacademy. org deltamath.com HSG-CO.C.11 Prove 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 HSG-CO.A.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that will carry it onto itself COMMON CORE GEOMETRY CURRICULUM MAP 4-Similarity -understand the difference between congruent and similar -use the side splitter theorem to find missing pieces of a triangle -understand when an altitude is drawn in a right triangle, proportional relationships are formed -given two figures explain if they are similar using similarity transformations -use similarity criteria for triangles to solve problems and to prove geometric relationships -use AA, SSS, and SAS to prove triangles similarity Feb. Weeks 1-4 (Winter break Week 3) Homework’s engageny.org Unit Test Examgen Daily Summaries jmap.org Stop-Light Checks for Understanding Geometry Common Core (Pearson) problemattic.com khanacademy. org deltamath.com HSG-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 sides. HSG-SRT.A.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. HSG-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 HSG-SRT.B.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. COMMON CORE GEOMETRY CURRICULUM MAP COMMON CORE GEOMETRY CURRICULUM MAP 5Trigonometric Ratios -using the trigonometric ratios to find a missing side or angle of a right triangle -understand that sine and cosine are cofunctions of each other -use the Law of Sines to find a missing side or angle of a triangle March Homework’s engageny.org Weeks Unit Test Examgen Daily Summaries jmap.org Stop-Light Checks for Understanding Geometry Common Core (Pearson) 1-2 problemattic.com khanacademy. org deltamath.com HSG-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. HSG-SRT.C.7 Explain and use the relationship between the sine and cosine of complementary angles. HSG-SRT.C.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. COMMON CORE GEOMETRY CURRICULUM MAP 6- Circles -write the equation for a circle when given its center and radius using the completing the square method -describe the relationships of the central and inscribed angles with the radii, tangent, and chords March Homework’s engageny.org Weeks Unit Test Examgen 3-4 Daily Summaries jmap.org April Stop-Light Checks for Understanding Geometry Common Core (Pearson) Weeks 1-2 problemattic.com -prove that all circles are similar khanacademy. org -understand the properties of angles for a quadrilateral inscribed in a circle deltamath.com -find the length of an arc of a circle and the area of the sector it creates HSG-C.A.1 Prove that all circles are similar HSG-C.A.2 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. HSG-C.A.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. HSG-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. HSG-GPE.A.1 Derive the equation of a circle given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. COMMON CORE GEOMETRY CURRICULUM MAP 7-Measuring in the Plane and Space Regents Review -know and apply the formulas for area, circumference, and perimeter of 2-D figures -know and apply the formulas for volume of 3-D figures -use Cavalieri’s principle to explain why objects have the same volume -identify cross sections of 3D objects and identify objects that are created by rotating 2D objects -answer Regents questions involving all the previous taught units April Homework’s engageny.org Unit Test Examgen 3-4 Daily Summaries jmap.org May Stop-Light Checks for Understanding Geometry Common Core (Pearson) Weeks Week 1 problemattic.com HSG-GMD.A.2 Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures HSG-GMD.A.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems HSG-GMD.A.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 khanacademy. org deltamath.com May Weeks Homework’s Unit Test 2-4 Daily Summaries June Stop-Light Checks for Understanding Weeks engageny.org Examgen jmap.org Geometry Common Core (Pearson) problemattic.com khanacademy. -all of the above COMMON CORE GEOMETRY CURRICULUM MAP 1-3 deltamath.com