MCPS Geometry Pacing Guide Jennifer Mcghee

Transcription

1 Units to be covered 1 st Semester: Units to be covered 2 nd Semester: Tools of Geometry; Logic; Constructions; Parallel and Perpendicular Lines; Relationships within Triangles; Similarity of Triangles Similarity of Triangles; Right Triangles and Trigonometry; Quadrilaterals and Polygons; Circles; Surface Area and Volume; Transformations Unit: Tools of Geometry Point Right Angle Line Obtuse Angle Semester Class: 8 days Plane Acute Angle Line Segment Adjacent Angles Parts/Year Long: 15 days Ray Vertical Angles Collinear Complementary Angles Coplanar Supplementary Angles Congruent Linear Pair Midpoint Parallel Angle Perpendicular Vertex Skew Segment Bisector Angle Bisector Manipulatives Calculator Skills Resources (Geometry B.1) (Geometry B.2) (Geometry C.1) (Geometry C.2) (Geometry C.3) (Geometry C.4) (Geometry B.3) (Geometry B.6) (Geometry B.4) (Geometry B.7) (Geometry B.8) (Geometry E.2) SOL G.3 The student will use pictorial representations, including computer software, constructions, and coordinate methods, to solve problems involving symmetry and transformation. This will include a) investigating and using formulas for finding distance, midpoint, and slope. Distance and Midpoint Formulas - Developing and applying distance and midpoint formulas

2 (Geometry C.5) (Geometry D.1) (Geometry D.2) (Geometry D.3) (Geometry D.4) (Geometry D.6) (Geometry D.7) (Geometry E.1) (Geometry E.3) (Geometry E.4) (Geometry E.5) (Geometry E.6) (Geometry E.7) (Geometry E.8)

3 Unit: Logic Reasoning and Proof Conditional Statement Conjunction Biconditional Statement Disjunction Semester Class: 6 days Converse Negation Inverse Contrapositive Deductive Reasoning Inductive Reasoning Law of Detachment Law of Syllogism Counterexample Conjecture Compound Statements Parts/Year Long: 14 days Manipulatives Calculator Skills Resources (Geometry I.1) (Geometry I.2) (Geometry I.3) (Geometry I.4) (Geometry I.5) (Geometry I.6) (Geometry I.7) (Geometry I.8) MCPS Geometry Pacing Guide Jennifer Mcghee SOL G.1 The student will construct and judge the validity of a logical argument consisting of a set of premises and a conclusion. This will include a) identifying the converse, inverse, and contrapositive of a conditional statement; b) translating a short verbal argument into symbolic form; c) using Venn diagrams to represent set relationships; and d) using deductive reasoning. Logic and Conditional Statements - Investigating symbolic form while working with conditional statements Inductive and Deductive Reasoning - Practicing inductive and deductive reasoning strategies

4 Semester Class: 8 days Parts/Year Long: 10 days Unit: Constructions SOL G.4 The student will construct and justify the constructions of a) a line segment congruent to a given line segment; b) the perpendicular bisector of a line segment; c) a perpendicular to a given line from a point not on the line; d) a perpendicular to a given line at a given point on the line; e) the bisector of a given angle, f) an angle congruent to a given angle; and g) a line parallel to a given line through a point not on the given line. Manipulatives Calculator Skills Resources Constructions - Completing constructions, using a straightedge and (Geometry B.9) compass (Geometry C.6) (Geometry C.7) (Geometry D.5)

5 Transversal Corresponding Angles Alternate Interior Angles Alternate Exterior Angles Consecutive Interior Angles Slope Negative Reciprocal Unit: Parallel and Perpendicular Lines Semester Class: 8 days Parts/Year Long: 15 days SOL G.2 The student will use the relationships between angles formed by two lines cut by a transversal to a) determine whether two lines are parallel; b) verify the parallelism, using algebraic and coordinate methods as well as deductive proofs; and c) solve real-world problems involving angles formed when parallel lines are cut by a transversal. Manipulatives Calculator Skills Resources (Geometry - SOL G.3 The student will use pictorial representations, including computer software, constructions, and coordinate methods, to solve problems involving symmetry and transformation. This will include b) applying slope to verify and determine whether lines are parallel or perpendicular. Lines and Angles - Investigating parallel lines and their relationship to special angles Slope - Exploring slope, including slopes of parallel and perpendicular lines

6 Equilateral Equiangular Isosceles Scalene Acute Obtuse Unit: Relationships Within Triangles Semester Class: 6 days Parts/Year Long: 13 days SOL G.5 The student, given information concerning the lengths of sides and/or measures of angles in triangles, will a) order the sides by length, given the angle measures; b) order the angles by degree measure, given the side lengths; c) determine whether a triangle exists; and d) determine the range in which the length of the third side must lie. These concepts will be considered in the context of real-world situations. Manipulatives Calculator Skills Resources How Many Triangles? - Investigating the triangle inequality theorem (Geometry F.1) (Geometry F.2) (Geometry F.3) (Geometry F.4) (Geometry K.9) (Geometry K.10) (Geometry M.1) (Geometry M.2) (Geometry M.3) (Geometry M.5)

7 Corresponding Parts Congruency Statement CPCTC SSS SAS ASA AAS HL Semester Class: 8 days Parts/Year Long: 15 days Unit: Congruent Triangles Manipulatives Calculator Skills Resources (Geometry J.1) (Geometry J.2) (Geometry J.3) (Geometry K.1) (Geometry K.2) (Geometry K.3) (Geometry K.4) (Geometry K.5) (Geometry K.6) (Geometry K.7) (Geometry K.8) (Geometry K.11) MCPS Geometry Pacing Guide Jennifer Mcghee SOL G.6 The student, given information in the form of a figure or statement, will prove two triangles are congruent, using algebraic and coordinate methods as well as deductive proofs. Congruent Triangles - Exploring congruent triangles, using constructions, proofs, and coordinate methods

8 Ratio Extended Ratio Proportion Similar Polygons Scale Factor Similarity Statement AA~ SSS~ SAS~ Semester Class: 7 days Parts/Year Long: 11 days Unit: Similarity of Triangles Manipulatives Calculator Skills Resources (Geometry P.1) (Geometry P.2) (Geometry P.3) (Geometry P.4) (Geometry P.5) (Geometry P.6) (Geometry P.7) (Geometry P.8) (Geometry P.9) (Geometry P.10) (Geometry P.11) MCPS Geometry Pacing Guide Jennifer Mcghee SOL G.7 The student, given information in the form of a figure or statement, will prove two triangles are similar, using algebraic and coordinate methods as well as deductive proofs. Similar Triangles - Exploring congruent triangles

9 Trig Ratio Sine Cosine Tangent Angle of Depression Angle of Elevation Triangle Triangle Leg Hypotenuse Unit: Right Triangles and Trigonometry Semester Class: 6 days Parts/Year Long: 10 days Manipulatives Calculator Skills Resources (Geometry Q.1) (Geometry Q.2) (Geometry Q.3) (Geometry Q.4) MCPS Geometry Pacing Guide Jennifer Mcghee SOL G.8 The student will solve real-world problems involving right triangles by using the Pythagorean Theorem and its converse, properties of special right triangles, and right triangle trigonometry. The Pythagorean Relationship - Exploring the Pythagorean Theorem and its converse Special Right Triangles and Right Triangle Trigonometry - Investigating special right triangles and right triangle trigonometry

10 Polygon Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Nonagon Decagon n-gon Parallelogram Rhombus Rectangle Square Trapezoid Isosceles Trapezoid Regular Pentagon Semester Class: 7 days Parts/Year Long: 15 days Unit: Quadrilaterals and Polygons SOL G.9 The student will verify characteristics of quadrilaterals and use properties of quadrilaterals to solve real-world problems. SOL G.10 The student will solve real-world problems involving angles of polygons. Manipulatives Calculator Skills Resources Properties of Quadrilaterals - Exploring quadrilaterals (Geometry G.1) (Geometry G.2) Angles in Polygons - Exploring angles in polygons (Geometry G.3) (Geometry G.4) (Geometry N.1) (Geometry N.2) (Geometry N.3) (Geometry N.4) (Geometry N.5) (Geometry N.6) (Geometry N.7) (Geometry N.8)

11 (Geometry N.9) (Geometry N.10) (Geometry S.1) (Geometry S.2) (Geometry S.3) (Geometry S.4) (Geometry S.5) (Geometry S.6) (Geometry S.7) (Geometry S.8) (Geometry S.9) (Geometry S.10) (Geometry S.11) (Geometry S.12)

12 Unit: Circles Circle Arc Radius Minor Arc Semester Class: 8 days Chord Major Arc Diameter Semicircle Parts/Year Long: 15 days Secant Area Tangent Circumference Point of Tangency Arc Length Central Angle Sector Area Inscribed Angle Center Equation of a Circle Manipulatives Calculator Skills Resources (Geometry U.1) (Geometry U.2) (Geometry U.3) (Geometry U.4) (Geometry U.5) (Geometry U.6) (Geometry U.7) (Geometry U.8) (Geometry U.9) (Geometry U.10) (Geometry U.11) (Geometry U.12) (Geometry U.13) (Geometry U.14) (Geometry U.15) (Geometry U.16) (Geometry V.1) (Geometry V.2) (Geometry V.3) MCPS Geometry Pacing Guide Jennifer Mcghee SOL G.11 The student will use angles, arcs, chords, tangents, and secants to a) investigate, verify, and apply properties of circles; b) solve real-world problems involving properties of circles; and c) find arc lengths and areas of sectors in circles. SOL G.12 The student, given the coordinates of the center of a circle and a point on the circle, will write the equation of the circle. Angles, Arcs, and Segments in Circles - Investigating angles and segments of circles Arc Length and Area of a Sector - Investigating arcs and areas Circles in the Coordinate Plane - Writing equations of circles

13 (Geometry V.4) (Geometry V.5)

14 Surface Area Composite Area Volume Prism Pyramid Cylinder Cone Sphere Hemisphere Unit: Area (2-D) Surface Area and Volume (3-D) Semester Class: 7 days Parts/Year Long: 15 days SOL G.13 The student will use formulas for surface area and volume of three dimensional objects to solve real-world problems. SOL G.14 The student will use similar geometric objects in two- or three dimensions to a) compare ratios between side lengths, perimeters, areas, and volumes; b) determine how changes in one or more dimensions of an object affect area and/or volume of the object; c) determine how changes in area and/or volume of an object affect one or more dimensions of the object; and d) solve real-world problems about similar geometric objects. Manipulatives Calculator Skills Resources Surface Area and Volume - Deriving formulas for surface area and (Geometry T.1) volume (Geometry T.2) (Geometry T.3) Similar Solids and Proportional Reasoning - Investigating similar solids (Geometry T.4) and proportional reasoning (Geometry T.5) (Geometry T.6)

15 Transformation Isometry Reflection Rotation Translation Dilation Line Symmetry Point Symmetry Rotational Symmetry y = x y = -x x-axis y-axis Horizontal Line Vertical Line Semester Class: 4 days Parts/Year Long: 10 days Unit: Transformations MCPS Geometry Pacing Guide Jennifer Mcghee SOL G.3 The student will use pictorial representations, including computer software, constructions, and coordinate methods, to solve problems involving symmetry and transformation. This will include c) investigating symmetry and determining whether a figure is symmetric with respect to a line or a point; and d) determining whether a figure has been translated, reflected, rotated, or dilated, using coordinate methods. Manipulatives Calculator Skills Resources Transformations - Identifying translations, reflections, rotations, and (Geometry O.1) dilations of polygons (Geometry O.2) (Geometry O.3) Symmetry - Exploring symmetry (Geometry O.4) (Geometry L.1) (Geometry L.2) (Geometry L.3) (Geometry L.4) (Geometry L.5) (Geometry L.6) (Geometry L.7) (Geometry L.8) (Geometry L.13) (Geometry L.14) (Geometry L.15) (Geometry L.16)