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2009 Pequea Valley SD Curriculum Enriched Geometry Curriculum: Course: Topic: Points, Subject Area(s): PEQUEA VALLEY SD Date: November 9, 2009 ET Lines and Planes Days: 12 Grade(s): Key Learning: Geometry is based upon 3 concepts: point, line and plane. The subdivisions of a line (segment and ray) are equally important with the pairs of rays that create angles of various types and opposite rays. Students will know how to name, sketch and measure each of these fundamental components of the geometric world. Polygons may be classified in many ways. Unit Essential Question(s): How are the basic geometric figures described, named and measured? Concept: Concept: Concept: Geometric Figures Segments Distance & Midpoint Formulas 2.5.11.B M11.C.3.1.1 Lesson Essential Question(s): How are geometric figures named and sketched? (A) Lesson Essential Question(s): What are congruent segments? (A) Lesson Essential Question(s): How is the distance between two points determined?How are the coordinates of the midpoint between two points determined? (A) Vocabulary: point, line, plane, collinear, coplanar, segment, ray, opposite rays, intersection Vocabulary: coordinate, distance, length of segment, congruent segments Vocabulary: midpoint, segment bisector, Midpoint Formula, Distance Formula Concept: Concept: Concept: Angles Polygons M 1 1 . B . 2 . 1 . 1, 2 . 3 . 1 1 . B Lesson Essential Question(s): Lesson Essential Question(s): How are angles named, measured and How are polygons classified? (A) classified? (A) Lesson Essential Question(s): (A) How are special angle pairs identified and used? (A) Vocabulary: angle, sides, vertex, protractor, congruent angles, acute, right, obtuse, straight, angle bisector, complementary angles, supplementary angles, adjacent angles, linear pair, vertical angles Vocabulary: polygon, sides, vertex, concave, convex, equilateral, equiangular, regular, triangle, quadrilateral, pentagon, hexagon, heptagon, octagon, nonagon, decagon, dodecagon, n-gon Vocabulary: Additional Information: Attached Document(s): Page 1 of 1 2009 Pequea Valley SD Curriculum Enriched Geometry Curriculum: Course: Topic: Points, Subject Area(s): PEQUEA VALLEY SD Date: November 9, 2009 ET Lines and Planes Days: 12 Grade(s): Concept: Geometric Figures point, line, plane, collinear, coplanar, segment, ray, opposite rays, intersection Concept: Segments coordinate, distance, length of segment, congruent segments - coordinate, distance, length of segment, congruent segments Concept: Distance & Midpoint Formulas midpoint, segment bisector, Midpoint Formula, Distance Formula Concept: Angles angle, sides, vertex, protractor, congruent angles, acute, right, obtuse, straight, angle bisector, complementary angles, supplementary angles, adjacent angles, linear pair, vertical angles Concept: Polygons polygon, sides, vertex, concave, convex, equilateral, equiangular, regular, triangle, quadrilateral, pentagon, hexagon, heptagon, octagon, nonagon, decagon, dodecagon, n-gon - Page 1 of 1 2009 Pequea Valley SD Curriculum Enriched Geometry Curriculum: Course: PEQUEA VALLEY SD Date: November 9, 2009 ET Topic: Reasoning Subject Area(s): Key Learning: Days: 13 Grade(s): The use of reasoning skills allows conclusions to be reached. Unit Essential Question(s): How are inductive and deductive reasoning used? Concept: Concept: Concept: Inductive Reasoning Conditional Statements M 1 1 . D . 1 . 1 . 1, 2 . 8 . 1 1 . A, 2 . 8 . 1 1 . B 2.4.11.C Deductive Reasoning & Proofs 2 . 4 . 1 1 . A, 2 . 4 . 1 1 . B Lesson Essential Question(s): What is inductive reasoning? (A) How is it used to make and test conjectures? (A) Lesson Essential Question(s): What are the various kinds of conditional statements? (A) How are they used to reach conclusions? (A) Lesson Essential Question(s): What is deductive reasoning? (A) How are the properties from algebra used in geometry? (A) How is a geometric proof developed? (A) Vocabulary: inductive reasoning, conjecture, counterexample Vocabulary: If-then form, hypothesis, conclusion, conditional, converse, inverse, contrapositive, biconditional, equivalent statements Vocabulary: deductive reasoning, Addition Property, Subtraction Property, Multiplication Property, Division Property, Substitution, Reflexive, Symmtric, Transitive, two-column proof, theorem Concept: Concept: Concept: Special Angle Pairs Lesson Essential Question(s): Lesson Essential Question(s): What can be assumed about angle pair relationships from a diagram? (A) Lesson Essential Question(s): How are the properties of special angle pairs used? (A) Vocabulary: Vocabulary: Vocabulary: Additional Information: Attached Document(s): Page 1 of 1 2009 Pequea Valley SD Curriculum Enriched Geometry Curriculum: Course: Topic: Reasoning Subject Area(s): PEQUEA VALLEY SD Date: November 9, 2009 ET Days: 13 Grade(s): Concept: Inductive Reasoning inductive reasoning, conjecture, counterexample Concept: Conditional Statements If-then form, hypothesis, conclusion, conditional, converse, inverse, contrapositive, biconditional, equivalent statements Concept: Deductive Reasoning & Proofs deductive reasoning, Addition Property, Subtraction Property, Multiplication Property, Division Property, Substitution, Reflexive, Symmtric, Transitive, two-column proof, theorem - Page 1 of 1 2009 Pequea Valley SD Curriculum Enriched Geometry Curriculum: Course: PEQUEA VALLEY SD Date: November 9, 2009 ET Topic: Lines Subject Area(s): Key Learning: Days: 10 Grade(s): Special relationships apply to angles formed by parallel and intersecting lines. Unit Essential Question(s): How do the position of coplanar lines and the measurement of the angles formed impact each other? Concept: Concept: Concept: Special angle pairs Proving Angle Relationships Proving Lines Parallel Lesson Essential Question(s): What are the special pairs of angles formed by a transversal and two lines? (A) Lesson Essential Question(s): How are the measures of angles formed by 2 parallel lines and a transversal determined? (A) Lesson Essential Question(s): What conditions will result in parallel lines? (A) What is the difference between parallel and skew lines? (A) Given parallel lines, how are angle relationships proven? (A) Vocabulary: parallel lines, skew lines, transversal, corresponding angles, alternate interior angles, alternate exterior angles, consecutive interior angles, same-side interior angles Vocabulary: Vocabulary: paragraph proof Concept: Concept: Concept: Lesson Essential Question(s): What are the slopes of parallel and perpendicular lines? (A) Lesson Essential Question(s): Lesson Essential Question(s): Vocabulary: slope, slope-intercept form, standard form Vocabulary: Vocabulary: How are lines proven parallel? (A) How is a paragraph proof written? (ET) Parallel and Perpendicular Lines M 1 1 . C . 3 . 1 . 2, M 1 1 . D . 3 . 2 . 3, 2 . 8 . 1 1 . L Additional Information: Attached Document(s): Page 1 of 1 2009 Pequea Valley SD Curriculum Enriched Geometry Curriculum: Course: Topic: Lines Subject Area(s): PEQUEA VALLEY SD Date: November 9, 2009 ET Days: 10 Grade(s): Concept: Special angle pairs parallel lines, skew lines, transversal, corresponding angles, alternate interior angles, alternate exterior angles, consecutive interior angles, same-side interior angles Concept: Proving Lines Parallel paragraph proof Concept: Parallel and Perpendicular Lines slope, slope-intercept form, standard form - Page 1 of 1 2009 Pequea Valley SD Curriculum Enriched Geometry Curriculum: Course: Topic: Congruent Subject Area(s): PEQUEA VALLEY SD Date: November 9, 2009 ET Triangles Days: 10 Grade(s): Key Learning: Congruency of triangles is determined by the distinct characteristics of the triangles. Unit Essential Question(s): How are triangles proven congruent? Concept: Concept: Concept: Triangle Characteristics Congruent Figures Proving Triangles Congruent M 1 1 . C . 1 . 3 . 1, 2 . 9 . 1 1 . G 2.9.11.B Lesson Essential Question(s): How are triangles classified? (A) Lesson Essential Question(s): What are the characteristics of congruent figures? (A) Lesson Essential Question(s): How are two triangles proven congruent? (A) Vocabulary: scalene, isosceles, equilateral, acute right, obtuse, equiangular, regular, interior angle, exterior angle Vocabulary: corresponding angles, corresponding sides, congruent figures Vocabulary: SSS, SAS, ASA, AAS, HL Concept: Concept: Concept: Lesson Essential Question(s): How will corresponding parts of congruent triangles lead to other conclusions? (A) Lesson Essential Question(s): Lesson Essential Question(s): Vocabulary: Vocabulary: Vocabulary: How are the measures of the angles of a triangle determined? (A) Corresponding Parts of Congruent Triangles 2.9.11.D Additional Information: Attached Document(s): Page 1 of 1 2009 Pequea Valley SD Curriculum Enriched Geometry Curriculum: Course: Topic: Congruent Subject Area(s): PEQUEA VALLEY SD Date: November 9, 2009 ET Triangles Days: 10 Grade(s): Concept: Triangle Characteristics scalene, isosceles, equilateral, acute right, obtuse, equiangular, regular, interior angle, exterior angle Concept: Congruent Figures corresponding angles, corresponding sides, congruent figures Concept: Proving Triangles Congruent SSS, SAS, ASA, AAS, HL - Page 1 of 1 2009 Pequea Valley SD Curriculum Enriched Geometry Curriculum: Course: Topic: Triangle Subject Area(s): PEQUEA VALLEY SD Date: November 9, 2009 ET Relationships Key Learning: Days: 9 Grade(s): Triangle relationships can be used to find and compare angle measures and distances. Unit Essential Question(s): What are the special relationships that occur within a triangle? Concept: Concept: Concept: Isosceles Triangles Square Roots M 1 1 . C . 1 . 2 . 3, M 1 1 . C . 1 . 2 . 1 M 1 1 . A . 1 . 1 . 1, M 1 1 . A . 1 . 1 . 3, M 1 1 . A . 2 . 2 . 1, 2 . 1 . 1 1 . A Pythagorean Theorem & its converse M 1 1 . C . 1 . 4 . 1, 2 . 1 0 . 1 1 . B Lesson Essential Question(s): What are the parts of an isosceles triangle? (A) Lesson Essential Question(s): How are square roots of whole numbers simplified? (A) Lesson Essential Question(s): How is the Pythagorean Theorem used? (A) How are the sides and angles of a triangle related to each other? (A) How are the square roots of fractions simplified? (A) How is the converse of the Pythagorean Theorem applied? (A) How are the basic operations performed with square roots? (A) Vocabulary: base, vertex, base angle, vertex angle Vocabulary: square root, rationalize Vocabulary: hypotenuse, leg, Pythagorean Theorem Concept: Concept: Concept: Special Right Triangles Midsegments Triangle Inequalities Lesson Essential Question(s): How are the lengths of the sides of a 45-45-90 triangle determined? (A) Lesson Essential Question(s): How are the properties of a midsegment used to solve problems? (A) Lesson Essential Question(s): When given the lengths of two sides of a triangle, how are the possible lengths for the third side determined? (A) How are the lengths of the sides of a 30-60-90 triangle determined? (A) How are the inequalities involving the sides and lengths of a triangle used to make comparisons? (A) Vocabulary: 45-45-90 triangle, 30-60-90 triangle, short leg, long leg Vocabulary: midsegment Vocabulary: Page 1 of 2 2009 Pequea Valley SD Curriculum Enriched Geometry Curriculum: Course: Topic: Triangle Subject Area(s): PEQUEA VALLEY SD Date: November 9, 2009 ET Relationships Concept: Days: 9 Grade(s): Concept: Concept: Lesson Essential Question(s): (A) Lesson Essential Question(s): Lesson Essential Question(s): Vocabulary: Vocabulary: Vocabulary: Concurrent Lines Additional Information: Attached Document(s): Page 2 of 2 2009 Pequea Valley SD Curriculum Enriched Geometry Curriculum: Course: Topic: Triangle Subject Area(s): Relationships PEQUEA VALLEY SD Date: November 9, 2009 ET Days: 9 Grade(s): Concept: Pythagorean Theorem & its converse hypotenuse, leg, Pythagorean Theorem Concept: Special Right Triangles 45-45-90 triangle, 30-60-90 triangle, short leg, long leg Concept: Midsegments midsegment Concept: Isosceles Triangles base, vertex, base angle, vertex angle Concept: Square Roots square root, rationalize - Page 1 of 1 2009 Pequea Valley SD Curriculum Enriched Geometry Curriculum: Course: Topic: Similar Subject Area(s): PEQUEA VALLEY SD Date: November 9, 2009 ET Figures Key Learning: Days: 11 Grade(s): Similar figures and proportions can be used to model real-life situations. Unit Essential Question(s): How are ratio and proportion used to identify relationships in similar figures? Concept: Concept: Concept: Ratio & Proportion Similar Polygons Proving Triangles Similar M 1 1 . D . 2 . 2 . 3, M 1 1 . A . 2 . 1 . 2, M 1 1 . A . 2 . 1 . 3 M11.C.1.3.1 2.9.11.B Lesson Essential Question(s): How are ratios simplified? (A) Lesson Essential Question(s): What are similar polygons? (A) Lesson Essential Question(s): How are tirangles proven similar? (A) How are proportions solved? (A) How is the length of a missing side found? (A) How are ratios and proportions used to solve problems? (A) What is the relationship between the scale factor and the perimeter and What is geometric mean? (A) area of similar figures? (ET) What are the properties of proportions? How are they used? (A) How are proportions used with scale drawings? (A) Vocabulary: Vocabulary: Vocabulary: ratio, proportion, geometric mean, similar polygon, scale factor, similarity AA Similarity, SSS Similarity, SAS means, extremes, Cross Multiplication, ratio Similarity Reciprocal Property, Diagonal Switch, Add Denominator Concept: Concept: Concept: Lesson Essential Question(s): How are proportional relationships applied in triangles? (A) Lesson Essential Question(s): Lesson Essential Question(s): Vocabulary: Triangle Proportionality Theorem Vocabulary: Vocabulary: Proportional Relationships Within Triangles Additional Information: Attached Document(s): Page 1 of 1 2009 Pequea Valley SD Curriculum Enriched Geometry Curriculum: Course: Topic: Similar Subject Area(s): Figures PEQUEA VALLEY SD Date: November 9, 2009 ET Days: 11 Grade(s): Concept: Ratio & Proportion ratio, proportion, geometric mean, means, extremes, Cross Multiplication, Reciprocal Property, Diagonal Switch, Add Denominator Concept: Similar Polygons similar polygon, scale factor, similarity ratio Concept: Proving Triangles Similar AA Similarity, SSS Similarity, SAS Similarity Concept: Proportional Relationships Within Triangles Triangle Proportionality Theorem - Page 1 of 1 2009 Pequea Valley SD Curriculum Enriched Geometry Curriculum: Course: PEQUEA VALLEY SD Date: November 9, 2009 ET Topic: Quadrilaterals Subject Area(s): Key Learning: Days: 10 Grade(s): The properties of quadrilaterals and other polygons can be used to find side lengths and angle measures. Unit Essential Question(s): How are the properties of quadrilaterals and other polygons used to find side lengths and angle measures? Concept: Concept: Concept: Convex Polygons Parallelograms Special Parallelograms M 1 1 . C . 1 . 2 . 2, 2 . 9 . 1 1 . C Lesson Essential Question(s): How area angle measures in convex polygons found? (A) Lesson Essential Question(s): What are the characteristics of a parallelogram? (A) Lesson Essential Question(s): What is the definition of each type of parallelogram? (A) When given angle measurement, how How can a quadrilateral be proven to is the number of sides determined? (A) be a parallelogram? (ET) What are the properties of the special parallelograms? (A) Vocabulary: diagonal, regular polygon, interior angle, exterior angle Vocabulary: parallelogram Vocabulary: rectangle, square, rhombus Concept: Concept: Concept: Lesson Essential Question(s): Lesson Essential Question(s): Vocabulary: Vocabulary: Trapezoids & Kites Lesson Essential Question(s): What is the definition of a trapezoid and a kite? (A) What are the properties of trapezoids and kites? (A) Vocabulary: trapezoid, isosceles trapezoid, kite, base, leg, base angle, midsegment Additional Information: Attached Document(s): Page 1 of 1 2009 Pequea Valley SD Curriculum Enriched Geometry Curriculum: Course: PEQUEA VALLEY SD Date: November 9, 2009 ET Topic: Quadrilaterals Subject Area(s): Days: 10 Grade(s): Concept: Convex Polygons diagonal, regular polygon, interior angle, exterior angle Concept: Parallelograms parallelogram Concept: Special Parallelograms rectangle, square, rhombus Concept: Trapezoids & Kites trapezoid, isosceles trapezoid, kite, base, leg, base angle, midsegment - Page 1 of 1 2009 Pequea Valley SD Curriculum Enriched Geometry Curriculum: Course: PEQUEA VALLEY SD Date: November 9, 2009 ET Topic: Circles Subject Area(s): Key Learning: Days: 10 Grade(s): The properties of angles, arcs, chords, tangents and secants can be used to solve problems involving circles. Unit Essential Question(s): How can the relationships between a circle and its arcs, lines, segments and angles be used to solve problems? Concept: Concept: Concept: Circle Basics Tangents Arcs M11.C.1.1.2 M 1 1 . C . 1 . 1 . 1, 2 . 9 . 1 1 . F Lesson Essential Question(s): What are the basic parts of a circle? (A) Lesson Essential Question(s): What are the properties of a tangent? (A) Lesson Essential Question(s): How are arcs named and classified? (A) How is the measure of an arc determined? (A) Vocabulary: circle, center, radius, diamter, chord, secant, tangent, concentric circles Vocabulary: Vocabulary: arc, central angle, intercepted arc, minor arc, semicircle, major arc Concept: Concept: Concept: Segments in a Circle Angles in a Circle 2.9.11.E Lesson Essential Question(s): How are the properties of chords applied? (A) Lesson Essential Question(s): How is the measure of an inscribed angle determined? (A) How are the measures of segments formed by chords, secants and tangents determined? (A) How are the measures of angles formed by chords, secants and tangents determined? (A) Vocabulary: Vocabulary: inscribed angle, inscribed polygon, circumscribed polygon Lesson Essential Question(s): Vocabulary: Additional Information: Attached Document(s): Page 1 of 1 2009 Pequea Valley SD Curriculum Enriched Geometry Curriculum: Course: PEQUEA VALLEY SD Date: November 9, 2009 ET Topic: Circles Subject Area(s): Days: 10 Grade(s): Concept: Circle Basics circle, center, radius, diamter, chord, secant, tangent, concentric circles Concept: Arcs arc, central angle, intercepted arc, minor arc, semicircle, major arc Concept: Angles in a Circle inscribed angle, inscribed polygon, circumscribed polygon Concept: Tangents - Page 1 of 1 2009 Pequea Valley SD Curriculum Enriched Geometry Curriculum: Course: Topic: Area & Subject Area(s): PEQUEA VALLEY SD Date: November 9, 2009 ET Perimeter Key Learning: Days: 12 Grade(s): The formulas for perimeter, cirumference and area can be used to find and compare measures in the real world. Unit Essential Question(s): How are the dimensions and area of plane figures determined? Concept: Concept: Concept: Parallelograms & Triangles Trapezoid, Kite and Rhombus Circumference & Arc Length Lesson Essential Question(s): How do you find the area and dimensions of parallelograms and triangles? (A) Lesson Essential Question(s): How do you find the area of a trapezoid, kite and rhombus? (A) Lesson Essential Question(s): How do you find the circumference of a circle? (A) Vocabulary: Vocabulary: Vocabulary: Concept: Concept: Concept: Lesson Essential Question(s): Lesson Essential Question(s): Vocabulary: Vocabulary: M 1 1 . D . 3 . 1 . 2, M 1 1 . B . 2 . 2 . 3, M 1 1 . B . 2 . 2 . 4, M 1 1 . B . 2 . 3 . 1, 2 . 2 . 1 1 . B Area of a Circle and a Sector Lesson Essential Question(s): How do you find the area of a circle? (A) How do you find the area of a sector of a circle (ET) Vocabulary: sector of a circle Additional Information: Attached Document(s): Page 1 of 1 2009 Pequea Valley SD Curriculum Enriched Geometry Curriculum: Course: Topic: Area & Subject Area(s): Perimeter PEQUEA VALLEY SD Date: November 9, 2009 ET Days: 12 Grade(s): Concept: Parallelograms & Triangles - base, height, composite shape, area, perimeter Concept: Area of a Circle and a Sector sector of a circle - Page 1 of 1 2009 Pequea Valley SD Curriculum Enriched Geometry Curriculum: Course: Topic: Volume Subject Area(s): PEQUEA VALLEY SD Date: November 9, 2009 ET & Surface Area Key Learning: Days: 6 Grade(s): Surface area and volume formulas can help you solve problems in three dimensions. Unit Essential Question(s): How are the surface area and volume of three dimensional shapes determined? Concept: Concept: Concept: Prisms and Cylinders Pyramids and Cones Spheres Lesson Essential Question(s): How are the volumes of right prisms and cylinders determined? (A) Lesson Essential Question(s): How are the volumes of pyramids and cones determined? (A) Lesson Essential Question(s): How is the volume of a sphere determined? (A) How are the surface areas of prisms and cylinders determined? (A) How are the surface areas of pyramids How is the surface area of a sphere and cones determined? (A) determined? (A) Vocabulary: right prism, right cylinder, surface area, lateral surface area, volume Vocabulary: pryamid, regular pyramid, slant height, cone M 1 1 . B . 2 . 2 . 1, M 1 1 . B . 2 . 2 . 2, M 1 1 . B . 2 . 2 . 4, M 1 1 . B . 2.3.1 Vocabulary: sphere, hemisphere Additional Information: Attached Document(s): Page 1 of 1 2009 Pequea Valley SD Curriculum Enriched Geometry Curriculum: Course: Topic: Volume Subject Area(s): PEQUEA VALLEY SD Date: November 9, 2009 ET & Surface Area Days: 6 Grade(s): Concept: Prisms and Cylinders right prism, right cylinder, surface area, lateral surface area, volume Concept: Pyramids and Cones pryamid, regular pyramid, slant height, cone Concept: S p h e r e s sphere, hemisphere - Page 1 of 1