Curriculum & Pacing Guide

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1 Curriculum & Pacing Guide Geometry Martinsville City Public Schools By: Barry Lingerfelt

2 Martinsville City Public Schools Plan of Action The Curriculum Guides represent Martinsville City Public Schools Curriculum, which is based on the Stards of Learning for Virginia Public School the State Curriculum work. In order for curriculum to be effective, it must be composed of three important components: written curriculum, taught curriculum, assessed curriculum. Each of these components must be aligned to ensure learning at its highest level. The Curriculum Guides are a starting point in this process. The Written Curriculum:The written curriculum consists of the Curriculum Guide used in conjunction with the State Curriculum works. The Curriculum Guide provides information on which stards are taught during a given grading period, the essential vocabulary for direct instruction in that stard, theunderstings students should gain from instruction in the stard, the expected student outcomes for this stard. The next step in this process is to study the Curriculum work for the identified stard. The Curriculum work provides instructional details for how instruction on this stard should look in the classroom. The Taught Curriculum: The Curriculumwork helps the teacher unpack the written curriculum for aligned taught curriculum. It does this by providing the definitions to use in direct vocabulary instruction, content details, details on instructional strategies to use. The instructional strategy details include explanations of specific instructional methodologies names instructional tools such as manipulatives graphic organizers. Using the definitions, methodologies, content details, instructional tools provided by the Curriculum work will ensure alignment in between the written, taught curriculum, assessed curriculum. The Assessed Curriculum: Formative assessment is an integral ongoing part of the instruction process occurs on a formal informal basis at many levels. Teachers use informal assessment throughout the learning to check for student understingformal common assessments to assess student mastery plan interventions. Another level of formal assessment is the division benchmark assessment, which hasas its primary purpose to help the adults know how to adjust instruction for student success. The final level of assessment is the Virginia Stards of Learning Tests, which are based on the Stards of Learning for Virginia Public Schools the Curriculum works.martinsville City Public Schools provides many tools to assist our teachers administrators in assessment disaggregation of assessment data. Teachers have access to tools such as Tests for Higher Stards, ExamView at grades two through twelve, PALS phonological awareness literacy screening for prek through third grade, STAR reading assessment at grades two through twelve, Algebra Readiness Diagnostic Tests for grades five through twelve. Also, teachers have access to Reports Online Systems for analyzing data from classroom assessments benchmark assessments. All of this is an integral part of Martinsville s commitment to Learning for all; Whatever it takes.

3 Pacing /Time 1 st Grading period :Review Algebra Solving equations. Coefficient, variable, constant, equation Graphing calculators Refresh on Algebra using graphing calculators. 1week Scope

4 Pacing/ Time 1 st Six G Logical Arguments The student will construct judge the validity of a logical argument consisting of a set of premises a conclusion. This will include a) identifying the converse, inverse, contrapositive of a conditional statement; b) translating a short verbal argument into symbolic form; c) using Venn diagrams to represent set relationships; d) using deductive reasoning. Identify the converse, inverse, contrapositive of a conditional statement. Translate short verbal arguments into symbolic form, such as (p q) (~p ~q). Determine the validity of a logical argument Use valid forms of deductive reasoning, including the law of syllogism, the law of the contrapositive, the law of detachment, counterexamples. Select use various types of reasoning methods of proof, as appropriate. Use Venn diagrams to represent set relationships, such as intersection union. Interpret Venn diagrams. Recognize use the symbols of formal logic, which include,, ~,,,. converse, inverse, contrapositive, conditional biconditional, Venn diagram, Inductive reasoning, deductive reasoning Scope

5 Pacing/ Time Lines Angles 1 st Six G 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 coordinate methods as well as deductive proofs; c) solve real-world problems involving angles formed when parallel lines are cut by a transversal. Use algebraic coordinate methods as well as deductive proofs to verify whether two lines are parallel. Solve problems by using the relationships between pairs of angles formed by the intersection of two parallel lines a transversal including corresponding angles, alternate interior angles, alternate exterior angles, same-side (consecutive) interior angles. Solve real-world problems involving intersecting parallel lines in a plane. Parallel, transversal, interior angles, corresponding angles, alternate interior angles, alternate exterior angles, interior angles Scope

6 Pacing/ Time Triangles Logic 2nd Six G.5 Week 1 The student, given information concerning the lengths of sides /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; 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. Angle, opposite Scope Order the sides of a triangle by their lengths when given the measures of the angles. Order the angles of a triangle by their measures when given the lengths of the sides. Given the lengths of three segments, determine whether a triangle could be formed. Given the lengths of two sides of a triangle, determine the range in which the length of the third side must lie. Solve real-world problems given information about the lengths of sides /or measures of angles in triangles.

7 Pacing/ Time 2 nd Six G Triangles Logic The student will solve real-world problems involving right triangles by using the Pythagorean Theorem its converse, properties of special right triangles, right triangle trigonometry. Determine whether a triangle formed with three given lengths is a right triangle. Solve for missing lengths in geometric figures, using properties of triangles. Solve for missing lengths in geometric figures, using properties of triangles. Solve problems involving right triangles, using sine, cosine, tangent ratios. Solve real-world problems, using right triangle trigonometry properties of right triangles. Explain use the relationship between the sine cosine of complementary angles. Use another formula for the area of a triangle: 1 A = absin C. 2 Revised March 2011 Pythagorean Theorem, triangles, triangles, hypotenuse, adjacent, sine, cosine, tangent Scope

8 Pacing/ Time Triangles Logic 2 nd Six G.6 Week 4 The student, given information in the form of a figure or statement, will prove two triangles are congruent, using algebraic coordinate methods as well as deductive proofs. Congruence Scope Use definitions, postulates, theorems to prove triangles congruent. Use coordinate methods, such as the distance formula the slope formula, to prove two triangles are congruent. Use algebraic methods to prove two triangles are congruent.

9 Pacing/ Time Triangles Logic 2nd Six G.7 Week 5 The student, given information in the form of a figure or statement, will prove two triangles are similar, using algebraic coordinate methods as well as deductive proofs. Similarity, proportion, ratio Scope Use definitions, postulates, theorems to prove triangles similar. Use algebraic methods to prove that triangles are similar. Use coordinate methods, such as the distance formula, to prove two triangles are similar.

10 Pacing/ Time 2 nd Six G.3 Week 6 3 rd Six Week 1 Lines Angles The student will use pictorial representations, including computer software, constructions, coordinate methods, to solve problems involving symmetry transformation. This will include a) investigating using formulas for finding distance, midpoint, slope; b) applying slope to verify determine whether lines are parallel or perpendicular; c) investigating symmetry determining whether a figure is symmetric with respect to a line or a point; d) determining whether a figure has been translated, reflected, rotated, or dilated, using coordinate methods. Transformation, reflection, rotation, dilation, or translation, perpendicular, point symmetry, line symmetry Scope Find the coordinates of the midpoint of a segment, using the midpoint formula. Use a formula to find the slope of a line. Compare the slopes to determine whether two lines are parallel, perpendicular, or neither. Determine whether a figure has point symmetry, line symmetry, both, or neither. Given an image preimage, identify the transformation that has taken place as a reflection, rotation, dilation, or translation. Apply the distance formula to find the length of a line segment when given the coordinates of the endpoints.

11 Pacing/ Time Lines Angles 3 rd Six G.4 Week 2 The student will construct 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; g) a line parallel to a given line through a point not on the given line. perpendicular bisector, bisector, angle, angle bisector Scope Construct an equilateral triangle, a square, a regular hexagon inscribed in a circle. Construct the inscribed circumscribed circles of a triangle. Construct a tangent line from a point outside a given circle to the circle. Revised March 2011

12 Pacing /Time Circles Polygons 3 rd Six G The student will verify characteristics of quadrilaterals use properties of quadrilaterals to solve real-world problems. Solve problems, including real-world problems,using the properties specific to parallelograms, rectangles, rhombi, squares, isosceles trapezoids, trapezoids. Prove that quadrilaterals have specific properties, using coordinate algebraic methods, such as the distance formula, slope, midpoint formula. Quadrilateral, parallelograms, rectangles, rhombi, squares, isosceles trapezoids, trapezoids Scope Prove the characteristics of quadrilaterals, using deductive reasoning, algebraic, coordinate Prove properties of angles for a quadrilateral inscribed in a circle. Revised March 2011

13 Pacing /Time Circles Polygons 3 rd Six G The student will solve real-world problems involving angles of polygons. Solve real-world problems involving the measures of interior exterior angles of polygons. regular polygon, tessellate, interior exterior angles, polygon, convex Scope 4 th Six Week 1 Identify tessellations in art, construction, nature. Find the sum of the measures of the interior exterior angles of a convex polygon. Find the measure of each interior exterior angle of a regular polygon. Find the number of sides of a regular polygon, given the measures of interior or exterior angles of the polygon.

14 Pacing / Time Circles Polygons 4 th Six G The student, given the coordinates of the center of a circle a point on the circle, will write the equation of the circle. Identify the center, radius, diameter of a circle from a given stard equation. Use the distance formula to find the radius of a circle. Stard form, locus, radius, diameter Scope Given the coordinates of the center radius of the circle, identify a point on the circle. Given the equation of a circle in stard form, identify the coordinates of the center find the radius of the circle. Given the coordinates of the endpoints of a diameter, find the equation of the circle. Given the coordinates of the center a point on the circle, find the equation of the circle. Recognize that the equation of a circle of given center radius is derived using the Pythagorean Theorem. Revised March 2011

15 Pacing / Time Circles Polygons 4 th Six G The student will use angles, arcs, chords, tangents, secants to a) investigate, verify, apply properties of circles; b) solve real-world problems involving properties of circles; c) find arc lengths areas of sectors in circles. Find lengths, angle measures, arc measures associated with two intersecting chords; two intersecting secants; an intersecting secant tangent; two intersecting tangents; central inscribed angles. Calculate the area of a sector the length of an arc of a circle, using proportions. Solve real-world problems associated with circles, using properties of angles, lines, arcs. Verify properties of circles, using deductive reasoning, algebraic, coordinate methods. Chord, secants, tangent, central inscribed angles, sector, arc measure, arc length Scope

16 Pacing / Time Three Dimensional Figures 4 th Six G.13 Week 6 5 th Six The student will use formulas for surface area volume of three-dimensional objects to solve real-world problems. Find the total surface area of cylinders, prisms, pyramids, cones, spheres, using the appropriate formulas. Calculate the volume of cylinders, prisms, pyramids, cones, spheres, using the appropriate formulas. surface area, volume, cylinders, prisms, pyramids, cones, spheres Scope 1 2 Solve problems, including real-world problems, involving total surface area volume of cylinders, prisms, pyramids, cones, spheres as well as combinations of three-dimensional figures. Calculators may be used to find decimal approximations for results.

17 Pacing / Time 5 th Six G Three Dimensional Figures The student will use similar geometric objects in two- or three-dimensions to a) compare ratios between side lengths, perimeters, areas, volumes; b) determine how changes in one or more dimensions of an object affect area /or volume of the object; c) determine how changes in area /or volume of an object affect one or more dimensions of the object; d) solve real-world problems about similar geometric objects. Corresponding, ratio, scale factor Scope Compare ratios between side lengths, perimeters, areas, volumes, given two similar figures. Describe how changes in one or more dimensions affect other derived measures (perimeter, area, total surface area, volume) of an object. Describe how changes in one or more measures (perimeter, area, total surface area, volume) affect other measures of an object. Solve real-world problems involving measured attributes of similar objects.

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