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MATH Pacing Guide GEOMETRY Math Outcomes Outcome G.1 Month Taught Quarter Assessed 1 X 2 3 4 Students will define, prove, and apply relationships among angles, lines, segments, and patterns. Students will calculate and write equations of line relationships in the coordinate plane. Students will construct and demonstrate geometric figures. Aug-Sept 5 wks G.3 Students will define, construct, compare and justify rigid transformations on the coordinate plane. Oct – Nov 3 wks X G.4 Students will prove and demonstrate triangle congruence and triangle properties. Nov – Dec 2-3 wks X G.5 Students will demonstrate polygon properties and will use properties of polygons to set up and solve systems. Dec - Jan 4-5 wks X G.6 Students will define, demonstrate, and prove properties of circles. Jan 3 - 4 wks X G.7 Students will apply Pythagorean Theorem, special right triangles, trig ratios and equations of circles to solve word problems. Students will use and apply area formulas to solve problems. Feb 3 - 4 wks X Feb – Mar 4 - 5 wks X G.9 Students will apply volume formulas of prisms, pyramids and spheres to solve real world problems. Apr 3 – 4 wks X G.10 Students will prove, demonstrate and apply similarities of geometric figures to solve real world problems. May 3-4 wks X G.2 G.8 Updated 7-29-14 Sept – Oct 3 wks X HS Standard Reference Codes Number & Quantity The Real NNumber System RN Quantities NQ NCN NVM SP Algebra A-SSE Seeing Structure in Expressions A-APR The Complex Number System A-CED Vector & Matrix Quantities A-REI Functions F-IF Interpreting Functions Arithmetic with Polynomials & Rational Expressions Creating Equations Reasoning with Equations & Inequalities Geometry Statistics & Probability Interpreting Categorical S-ID G-CO Congruence F-BF Building Functions G-SRT Similarity, Right Triangles & Trigonometry S-IC Making Inferences & Justifying Conclusions F-LE Linear, Quadratic & Exponential Models G-C Circles S-CP Conditional Probability & Rules of Probability F-TF Trigonometric Functions G-GPE Expressing Geometric Properties with Equations S-MD Using Probability to Make Decisions G-GMD Geometric Measurement & Dimension Modeling with Geometry & Quantitative Data Statistics & Probability G-MG Geometry STANDARD REFERENCE Geometry Purpose Unit Outcome MA.G.1 Components MA.G.1.1 MA.G.1.2 MA.G.1.3 MA.G.1.4 Components Unit Outcome MA.G.2 MA.G.2.1 MA.G.2.2 MA.G.2.3 MA.G.2.4 MA.G.2.5 MA.G.2.6 MA.G.2.7 Students will develop, interpret, and apply properties of geometric figures and transformations. Students will define, prove, and apply relationships among angles, lines, segments, and patterns. Students will calculate and write equations of line relationships in the coordinate plane. Define basic geometric terms including point, line, segment, ray, angle, parallel lines, perpendicular lines, and transversal Calculate midpoint of segments within and outside the coordinate plane Prove and apply angle relationships with parallel lines cut by a transversal, vertical angles, corresponding, and alternate interior/exterior and complementary/supplementary angles Use the relationship between the slopes of parallel and perpendicular lines to write equations G-CO.1 G-GPE.6 G-CO.9 G-GPE.5 Students will construct and demonstrate geometric figures. Construct a copy of a segment and bisect the segment Construct a copy of an angle, and bisect the angle Construct perpendicular lines, including perpendicular bisection of line segments Construct a line parallel to a given line Construct an equilateral triangle, square, and regular hexagon inscribed in a circle Construct the inscribed and circumscribed circles of a triangle Construct triangle altitudes, medians, and centroids G-CO.12 G-CO.12 G-CO.12 G-CO.12 G-CO.13 G-C.3 G-CO.10 Components Unit Outcome MA.G.3 MA.G.3.1 MA.G.3.2 MA.G.3.3 MA.G.3.4 MA.G.3.5 MA.G.3.6 Components Unit Outcome MA.G.4 MA.G.4.1 MA.G.4.2 MA.G.4.3 MA.G.4.4 Components Unit Outcome MA.G.5 MA.G.5.1 MA.G.5.2 MA.G.5.3 MA.G.5.4 MA.G.5.5 Components Unit Outcome MA.G.6 MA.G.6.1 MA.G.6.2 MA.G.6.3 MA.G.6.4 MA.G.6.5 MA.G.6.6 Students will define, construct, compare, and justify rigid transformations on the coordinate plane. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments Construct and describe transformations of overlaid polygons Construct and describe composition transformations Justify transformations as functions that take points in the plane as inputs and give other points as outputs Define congruence using transformations Compare rigid and non-rigid transformations Students will prove and demonstrate triangle congruence and triangle properties. Demonstrate congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and angles are congruent Prove triangle congruence through the use of ASA, SAS, and SSS Prove and demonstrate measures of interior angles of a triangle sum of 180° Prove and demonstrate base angles of isosceles triangle are congruent Students will demonstrate polygon properties, and will use properties of polygons to set up and solve systems. Demonstrate quadrilateral properties with parallelograms, squares, rectangles, rhombus, kites and trapezoids Demonstrate polygon interior and exterior sum of angles Use coordinates to demonstrate geometric theorems algebraically. (For example, given four coordinates, is it a rectangle?) Solve systems to represent geometric figures Demonstrate the segment joining two midpoints of a triangle is parallel to the third side and half the length G-CO.4 G-CO.3 G-CO.2, 5 G-CO.2 G-CO.6 G-CO.2 G-CO.7 G-CO.8 G-CO.10 G-CO.10 G-CO.11 G-GPE.4 G-CO.10 Students will define, demonstrate, and prove properties of circles. Define and demonstrate chord properties Define and demonstrate tangent properties Demonstrate relationships among inscribed and central angles, radii and chords Prove that all circles are similar Demonstrate properties of angles for a quadrilateral inscribed in a circle Define pi and demonstrate circumference and arc length G-C.2 G-C.2,4 G-C.2 G-C.1 G-C.3 G-C.5 Components Unit Outcome MA.G.7 MA.G.7.1 MA.G.7.2 MA.G.7.3 MA.G.7.4 Components Unit Outcome MA.G.8 MA.G.8.1 MA.G.8.2 MA.G.8.3 MA.G.8.4 Components Unit Outcome MA.G.9 MA.G.9.1 MA.G.9.2 MA.G.9.3 MA.G.9.4 Components Unit Outcome MA.G.10 MA.G.10.1 MA.G.10.2 MA.G.10.3 MA.G.10.4 MA.G.10.5 MA.G.10.6 Students will apply Pythagorean Theorem, special right triangles, trigonometric ratios and equations of circles to solve word problems. Apply the Pythagorean Theorem and its converse to solve word problems Solve special right triangles and apply them to right triangles in circles Apply equation of circles to find center and radius Apply trigonometric ratios of right triangles to solve angle of depression/elevation word problems G-SRT.4 G-SRT.8, N-RN.2 G-SRT.6 G-C.2 G-GPE.1 G-SRT.6 G-SRT.8 Students will use and apply area formulas to solve problems. Use formulas to find the area of geometric figures Use coordinates to compute area and perimeter with distance formula Compute area of sectors, segments and annulus Solve area word problems Students will apply volume formulas of prisms, pyramids, and spheres to solve real world problems. Use volume formulas for prisms, pyramids, and spheres to solve real world problems Calculate volume of three dimensional objects generated by rotating two-dimensional objects Apply density and displacement to solve real world problems Apply geometric methods to solve design problems Students will prove, demonstrate, and apply similarities of geometric figures to solve real world problems. Demonstrate the properties of dilation given a center and scale factor Apply similarity transformations to decide if two figures are similar Prove triangle similarities of congruent angles and proportional sides with AA, SSS, and SAS Prove a line parallel to one side of a triangle divides the other two sides proportionally and the converse Solve similarity word problems including indirect measurement Use proportions to show a relationship with area and volume G-GPE.7 G-C.5 G-MG.2 G-GMD.1,3 G-GMD.4 G-MG.2 G-MG.3 G-SRT.1 G-SRT.2 G-SRT.3 G-SRT.4 G-SRT.5 G-MG.1