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Revised 7/5/10 Estimated Geometry Pacing Timeline 2010-2011 School Year Revised 7/5/10 The timeframes listed on this calendar are estimates. You may need to adjust some of them from time to time based on data to meet the needs of your students as some concepts may take less time and some may take more time. Unit Name Unit 0: B.O.Y Assessments, establishing procedures and Algebra Review (5 days) Estimated Timeframe for Instruction and Assessment Unit 1: Tools of Geometry – Chapter 1 (16 days) August 23 – September 14 Unit 2: Reasoning and Proof – Chapter 2 (9 days) September 15 – September 27 Unit 3: Parallel and Perpendicular Lines – Chapter 3 (14 days) September 28 – October 15 Unit 4: Congruent Triangles – Chapter 4 (14 days) October 19 – November 5 Unit 5: Relationships Within Triangles - Chapter 5 (14 days) November 8 – December 1 Unit 6: Polygons, Quadrilaterals – Chapter 6 and Exams (21 days) December 2 – January 19 Unit 7: Similarity – Chapter 6 (10 days) January 20– February 2 Unit 8:Right Triangles and Trigonometry – Chapter 8 (8 days) February 3 – February 16 Unit 9: Transformations – Chapter 9 (10 days) February 17 – March 3 Unit 10: Area – Chapter 10 (16 days) March 4 – April 4 Unit 11: Surface Area and Volume – Chapter 11 (18 days) April 5 – April 28 Unit 12: Circles – Chapter 12 (10 days) May 2 – May 13 Unit 13: EOC Review and Test (12 days) May 17 – May 31 August 16 – August 20 Page 1 of 40 Revised 7/5/10 Course Name: Geometry, 2010-11 Unit Title: (00)- Algebra Review Number of Days: 5 Know: Understand: Do: There are differences between equations and expressions. Many algebraic concepts are foundational for the study of geometry. Evaluate equations and simplify expressions. Linear equations can be expressed algebraically and graphically. Unit conversions require the use of ratios and proportions. Taking the square root of a number is the reverse process of squaring a number. There are procedures to evaluate an absolute value. Solve and graph linear equations. Set up and solve proportions to convert units. Use correct procedures for squaring numbers and finding square roots. Use correct procedures for finding absolute value, Page 2 of 40 Revised 7/5/10 Course Name: Geometry, 2010-11 Unit Title: (00) Algebra Review Number of Days: 5 Key Learning: Many algebraic concepts are foundational for the study of geometry. Unit Essential Question: What algebraic concepts are foundational for the study of geometry? Concept: Evaluating and Simplifying Expressions Benchmark(s): MA.912.A.1.1 MA.912.A.1.4 MA.912.G.8.3 MA.912.G.8.2 Concept: Benchmark(s): Solving and Writing MA.912.A.3.10 Linear Equations MA.912.A.3.9 MA.912.A.3.8 MA.912.G.8.2 Concept: Benchmark(s): Conversions and pg MA.912.A.1.5 826, Ratios MA.912.A.5.1 Concept: Benchmark(s): Squares and MA.912.A.1.4 Absolute Value MA.912.A.1.1 MA.912.A.1.4.3 Lesson Essential Questions: 1. How are algebraic expressions evaluated and simplified? Textbook: Vocabulary: 1. Pg 858 algebraic expression Lesson Essential Questions: 2. How are the properties of equality used to find values of variables to satisfy equations? Textbook: Vocabulary: 2. Pg 862 variable, linear equation Lesson Essential Questions: 3. How are unit conversions related to ratios? Textbook: 3. Pg 859, 864 Textbook: 4. Pg 857, 860 Lesson Essential Questions: 4. What procedures are used when squaring numbers and finding absolute value? Vocabulary: Ratio, unit conversion Vocabulary: radical, exponent, absolute value Additional Information: *During this week, you will be administrating the Differentiated Accountability (Core, K-12) assessment. *Use flexibility with teaching algebraic concepts as needed. Resources are flexible. Also included are the Language Arts Benchmarks: LA.1112.1.6.1, LA.1112.1.6.2, LA.1112.1.6.5, LA.910.1.6.1, LA.910.1.6.2, LA.910.1.6.5 Prentice Hall, Geometry, Pearson 2011, is the Pasco adopted textbook. Page 3 of 40 Revised 7/5/10 Course Name: Geometry, 2010-11 Unit Title: (01) Tools of Geometry - Chapter 1 Number of Days: 16 Know: Understand: Do: Geometric solids have nets. Geometry is a subject consisting of many symbols, rules, formulas and properties. Identify, draw and describe regular, nonregular polyhedra and their nets. Points, lines, planes, segments, angles, and rays are foundations of geometry. Segments and angles can be measured and compared. There are relationships between angle pairs. There are differences between sketches, drawings, and constructions. Distance and midpoint formulas apply to points and line segments in the coordinate plane. There are formulas for circumference, perimeter, and area for circles and rectangles. Define and compare points, lines, planes, segments, angles, and rays. Draw, measure, and classify angles and segments. Identify angle pairs and determine their measures. Use constructions to copy and bisect angles and segments. Apply formulas when finding the distance and midpoint of lines or segments in the coordinate plane. Find the area, perimeter and circumference of circles, rectangles and irregular shapes. Page 4 of 40 Revised 7/5/10 Course Name: Geometry, 2010-11 Unit Title: (01) Tools of Geometry - Chapter 1 Number of Days: 16 Key Learning: Geometry is a subject consisting of many building blocks including symbols, rules and properties. Unit Essential Question: What are the building blocks of geometry? Concept: Nets and Drawings for Visualizing Geometry Benchmark(s): MA.912.G.7.1 Concept: Points, lines and Planes Benchmark(s): MA.912.G.8.1 Lesson Essential Questions: Textbook: Vocabulary: 1. How can I represent three-dimensional figures with 1. PH 1-1 net, isometric a two-dimensional drawing? drawing, orthographic drawing Lesson Essential Questions: Textbook: Vocabulary: 2. What are the relationships between points, lines, 2. PH 1-2 point, space, line, rays, segments and planes? collinear points, plane, coplanar, ray, opposite ray, postulate, axiom Page 5 of 40 Revised 7/5/10 Concept: Benchmark(s): Measuring segments MA.912.G.1.1 and angles MA.912.G.1.3 Concept: Benchmark(s): Exploring angle Pairs MA.912.G.4.2 Lesson Essential Questions: 2. How are segments and angles measured ? Textbook: Vocabulary: 3. PH 1-3, coordinate, distance, PH 1-4 congruent segments, segment bisector, midpoint, acute angle, right angle, obtuse angle, straight angle, congruent angles, angle (vertex, sides) Lesson Essential Questions: Textbook: Vocabulary: 4. What are the different ways to describe different 4. PH 1-5 vertical angles, kinds of angle pairs? adjacent angles, complementary angles, supplementary angles, linear pair, angle bisector Concept: Basic Constructions Benchmark(s): MA.912.G.1.2 MA.912.G.4.1 MA.912.G.4.2 MA.912.G.8.6 Lesson Essential Questions: 5. How are angles and segments copied and bisected using construction techniques? Concept: Midpoint and Distance in the Coordinate Plane Benchmark(s): MA.912.G.1.1 Lesson Essential Questions: 6. How do I use the distance and midpoint formulas? Textbook: Vocabulary: 5. PH 1-6 construction, straightedge, compass, perpendicular lines, perpendicular bisector Textbook: Vocabulary: 6. PH 1-7 Distance Formula, Midpoint Formula Page 6 of 40 Revised 7/5/10 Concept: Perimeter, Circumference and Area Benchmark(s): MA.912.G.2.5 MA.912.G.6.5 Lesson Essential Questions: 7. How do I calculate the perimeter, circumference, and area of basic shapes? Course Name: Geometry, 2010-11 Unit Title: (02) Reasoning and Proof - Chapter 2 Number of Days: 13 Know: Understand: Textbook: Vocabulary: 7. PH 1-8 perimeter, circumference, area, irregular shapes Do: Additional Information: Also included are the Language Arts Benchmarks: LA.1112.1.6.1, LA.1112.1.6.2, LA.1112.1.6.5, LA.910.1.6.1, LA.910.1.6.2, LA.910.1.6.5 Prentice Hall, Geometry, Pearson 2011, is the Pasco adopted textbook Page 7 of 40 Revised 7/5/10 Logic and truth tables involve conditional statements, converses, biconditionals, definitions, negations, inverses and contrapositives. Logical statements have symbolic forms. Mathematical reasoning concepts are used Find the converse, inverse, and to make conclusions in algebra, geometry, contrapositive of a conditional statement. and real world situations. Identify and use symbolic forms of logical statements. Truth tables are used to determine truth values of propositional statements. The properties of equality and congruence apply to algebra and geometry. Conclusions about angles can be made from the way they are drawn. Some angle pairs may be classified as complementary or supplementary. Angles that are equal in measure are congruent. Complete truth tables. Use truth tables to determine truth values of propositional statements. Justify simple proofs using algebraic and geometric properties of equality and congruence. Distinguish between types of angle pairs from given diagrams. Prove angles congruent using theorems. Course Name: Geometry, 2010-11 Unit Title: (02) Reasoning and Proof - Chapter 2 - Chapter 2 Number of Days: 9 Mathematical reasoning concepts are used to make conclusions in algebra, geometry, and real-world situations. Key Learning: Page 8 of 40 Revised 7/5/10 Unit Essential Question: What are the key elements of reasoning? Concept: Patterns and Inductive Reasoning Concept: Logic and Truth Tables Benchmark(s): Lesson Essential Questions: Textbook: Vocabulary: MA.912.G.8.4 1. How is inductive reasoning used to find patterns? 2. PH 2-1 inductive reasoning, conjecture, counterexample Benchmark(s): Lesson Essential Questions: Textbook: Vocabulary: MA.912.D.6.1 2. How is logical reasoning used in geometry? conditional, hypothesis, MA.912.D.6.2 2. PH 2-2, conclusion, truth value, MA.912.D.6.3 2-3, 2-4 converse, biconditional, MA.912.D.6.4 negation, inverse, MA.912.G.8.1 contrapositive, equivalent statements, indirect reasoning, indirect proof, Law of Detachment, Law of Syllogism, deductive reasoning Concept: Benchmark(s): Lesson Essential Questions: Textbook: Vocabulary: Reasoning in Algebra MA.912.D.6.4 3. How is reasoning used to construct a formal 3.PH 2-5 reflexive property, MA.912.G.8.5 algebraic proof? symmetric property, transitive property, proof, two-column proof Concept: Benchmark(s): Lesson Essential Questions: Textbook: Vocabulary: Proving Angles MA.912.D.6.4 4. How can angle relationships be identified, solved 4. PH 2-6 theorem, paragraph proof Congruent MA.912.G.8.1 and proved? MA.912.G.8.5 Concept: Benchmark(s): Lesson Essential Questions: Textbook: Vocabulary: Concept: Benchmark(s): Lesson Essential Questions: Textbook: Vocabulary: Page 9 of 40 Revised 7/5/10 Additional Information: Also included are the Language Arts Benchmarks: LA.1112.1.6.1, LA.1112.1.6.2, LA.1112.1.6.5, LA.910.1.6.1, LA.910.1.6.2, LA.910.1.6.5 Prentice Hall, Geometry, Pearson 2011, is the Pasco adopted textbook. Course Name: Geometry, 2010-11 Unit Title: (03) Lines and Angles - Chapter 3 Number of Days: 14 Know: Understand: Do: Page 10 of 40 Revised 7/5/10 Angles are formed from intersecting lines. Angle relationships can be used to prove whether or not lines are parallel. Parallel and perpendicular line properties lead to several angle relationships. Lines in the coordinate plane can be expressed algebraically. The Triangle-Angle-Sum theorem is used to determine missing angle measures in a triangle. Classify angles formed from various types of intersecting lines. Prove lines parallel given angle relationships. Analyze linear equations to determine whether they are parallel, perpendicular or neither. Apply the Triangle-Angle-Sum Theorem to find missing angles of triangles. Relationships exist between the slopes of parallel and perpendicular lines. Use slopes of lines to prove line relationships. Knowledge of line properties can be used to construct parallel and perpendicular lines. Construct parallel and perpendicular lines given specific constraints. Course Name: Geometry, 2010-11 Unit Title: (03) Lines Angles - Chapter 3 Number of Days: 14 Key Learning: Parallel and perpendicular line properties lead to several angle relationships. Unit Essential Question: How are parallel and perpendicular line properties used to define angle relationships? Page 11 of 40 Revised 7/5/10 Concept: Lines and Angles Benchmark(s): MA.912.G.7.2 Concept: Benchmark(s): Properties of Parallel MA.912.G.1.3 lines MA.912.G.8.5 Concept: Benchmark(s): Proving Lines are MA.912.G.1.3 Parallel and MA.912.G.8.5 Perpendicular Concept: Benchmark(s): Parallel lines and MA.912.G.2.2 triangles MA.912.G.4.1 MA.912. G.8.5 Concept: Constructing Parallel and Perpendicular lines Concept: Equations of lines in the coordinate plane Benchmark(s): MA.912.G.1.2 MA.912.G.4.1 Benchmark(s): MA.912.G.3.3 Lesson Essential Questions: 1. What relationships exist between lines, planes and angles in space? Textbook: Vocabulary: 1. PH 3-1 parallel lines, skew lines, parallel planes, transversal, alternate interior angles, same-side interior angles, corresponding angles, alternate exterior angles Lesson Essential Questions: Textbook: Vocabulary: 2. What are the relationships between pairs of angles 2. PH 3-2 formed by parallel lines and transversals? Lesson Essential Questions: Textbook: Vocabulary: 3. What are the different ways to prove lines parallel 3. PH 3-3, flow proof or perpendicular? 3-4 Lesson Essential Questions: 4. What is unique about the measures of angles in triangles? Textbook: Vocabulary: 4. PH 3-5 auxiliary line, exterior angle of a polygon, remote interior angle Lesson Essential Questions: Textbook: Vocabulary: 5. How is a parallel or perpendicular lines constructed 5. PH 3-6 using only a compass and a straightedge? Lesson Essential Questions: 6. How are lines on the coordinate plane expressed algebraically? Textbook: Vocabulary: 6. PH 3-7 slope, slopeintercept form, point-slope form Page 12 of 40 Revised 7/5/10 Concept: Benchmark(s): Slopes of parallel and MA. 912.G.3.3 perpendicular lines Lesson Essential Questions: 7. What are the relationships between slopes of parallel and perpendicular lines? Textbook: Vocabulary: 7. PH 3-8 Additional Information: Also included are the Language Arts Benchmarks: LA.1112.1.6.1, LA.1112.1.6.2, LA.1112.1.6.5, LA.910.1.6.1, LA.910.1.6.2, LA.910.1.6.5 Prentice Hall, Geometry, Pearson 2011, is the Pasco adopted textbook. Course Name: Geometry, 2010-11 Unit Title: (04) Congruent Triangles - Chapter 4 Number of Days: 14 Page 13 of 40 Revised 7/5/10 Know: Understand: Do: Congruent figures have congruent corresponding parts. Properties, postulates and theorems are used to prove triangle congruence. Determine if figures are congruent by analyzing their corresponding parts. Triangles can be classified by their sides or angles. Classify triangles according to their sides or angles. Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), AngleAngle-Side (AAS), Hypotenuse-Leg (HL), and Corresponding Parts of Congruent Triangles are Congruent (CPCTC) are methods used to prove congruent triangles or congruent parts of triangles. Prove that triangles are congruent and use the concept of Corresponding Parts of Congruent Triangles are Congruent (CPCTC). Apply isosceles, equilateral and right triangle theorems to prove congruence. Isosceles, equilateral and right triangles have specific theorems to prove triangles congruent. Course Name: Geometry, 2010-11 Unit Title: (04) Congruent Triangles - Chapter 4 Number of Days: 14 Page 14 of 40 Revised 7/5/10 Key Learning: Properties, postulates and theorems are used to prove triangle congruence. Unit Essential Question: What are the important elements needed to prove that two triangles are congruent? Concept: Congruent Figures Benchmark(s): MA.912.G.2.4 Ma.912.G.4.6 Concept: Benchmark(s): Methods of Proving MA.912.G.4.3 Triangles Congruent MA.912G.4.6 Concept: Using Congruent Triangles: CPCTC Benchmark(s): MA.912.G.2.3 MA.912.G.4.4 MA.912.G.4.6 Concept: Benchmark(s): Isosceles and MA.912.G.4.1 Equilateral Triangles Lesson Essential Questions: Textbook: Vocabulary: 1. What are the characteristics of congruent figures? 1. PH 4-1 congruent polygons, corresponding parts Lesson Essential Questions: Textbook: Vocabulary: 2. What are the methods used to prove triangles are 2. PH 4-2, SSS (Side-Sidecongruent? 4-3 Side), SAS (SideAngle-Side), ASA (Angle-Side-Angle), AAS (Angle-AngleSide) Lesson Essential Questions: Textbook: Vocabulary: 3. What conclusions can I draw about triangles based 3. CPCTC on congruency statements? PH 4-4 (Corresponding Parts of Congruent Triangles are Congruent) Lesson Essential Questions: Textbook: Vocabulary: 4. How are the congruence properties used with 4. legs of an isosceles isosceles and equilateral triangles? PH 4-5 triangle, base of an isosceles triangle, vertex angle of an isosceles triangle, base angles of an isosceles triangle, corollary Page 15 of 40 Revised 7/5/10 Concept: Benchmark(s): Congruence in Right MA.912.G.4.6 Triangles MA.912.G.5.4 Lesson Essential Questions: Textbook: Vocabulary: 5. What relationships of right triangles help me prove 5. hypotenuse, legs of triangles congruent? PH 4-6 a right triangle, HL (Hypotenuse-Leg) theorem Concept: Benchmark(s): Congruence in MA.912.G.4.6 Overlapping Triangles Lesson Essential Questions: 6. How do you identify congruency in overlapping triangles? Textbook: Vocabulary: 6. overlapping PH 4-7 Additional Information: Students are expected to know their triangle classifications, if remediation is needed use PH- page 853, MA.912.G.4.1 Students will need to solve systems of equations for 4-6, review using PH- page 273 Also included are the Language Arts Benchmarks: LA.1112.1.6.1, LA.1112.1.6.2, LA.1112.1.6.5, LA.910.1.6.1, LA.910.1.6.2, LA.910.1.6.5 Prentice Hall, Geometry, Pearson 2011, is the Pasco adopted textbook Page 16 of 40 Revised 7/5/10 Course Name: Geometry, 2010-11 Unit Title: (05) Relationships Within Triangles - Chapter 5 Number of Days: 14 Know: Understand: Do: Midsegments, angle bisectors, perpendicular Important segment and angle relationships Identify various segments and their points bisectors, altitudes, and medians exist in exist within triangles. of concurrency within triangles. triangles. Prove the Triangle Midsegment Theorem Coordinate geometry can be used to prove using coordinate geometry. various geometric properties. Find the center of a circle using coordinate The are four points of concurrency that are geometry. formed by segments within triangles ( circumcenter, incenter, centroid, and Apply properties related to the segments orthocenter). within triangles. Triangle inequalities involve angles and sides of triangles. Use the triangle inequality theorems to compare sides and angles related to triangles. Construct tangents to circles. Circumscribe and inscribe circles about and within triangles and regular polygons. Page 17 of 40 Revised 7/5/10 Course Name: Geometry, 2010-11 Unit Title: (05) Relationships Within Triangles - Chapter 5 Number of Days: 14 Key Learning: Important segment and angle relationships exist within triangles. Unit Essential Question: How are segments and angles formed within triangles related? Concept: Midsegments of Triangles Concept: Perpendicular and Angle Bisectors Benchmark(s): MA.912.G.1.1 MA.912.G.4.5 Benchmark(s): MA. 912.G.4.2 Lesson Essential Questions: 1. How do I locate a triangle's midsegment? Concept: Points of Concurrency in Triangles Benchmark(s): MA.912.G.1.1 MA.912.G.4.2 MA.912.G.4.5 Lesson Essential Questions: 3. What are the properties of the four points of concurrency in a triangle? Concept: Indirect Proof Benchmark(s): MA.912.G.8.5 Lesson Essential Questions: 4. How is indirect reasoning used in proofs? Concept: Inequalities in Triangles Benchmark(s): MA.912.G.4.7 Lesson Essential Questions: 5. How are angles and sides of triangles related? Lesson Essential Questions: 2. What observations can be made about angle bisectors and perpendicular bisectors? Textbook: Vocabulary: 1. PH 5-1 midsegment, coordinate proof Textbook: Vocabulary: 2. PH 5-2 Equidistant, distance from a point to a line Textbook: Vocabulary: 3. PH 5-3, concurrent, point of 5-4 concurrency, circumcenter of a triangle, circumscribed about, incenter of a triangle, inscribed in, median of a triangle, centroid, altitude, orthocenter Textbook: Vocabulary: 4. PH 5-5 indirect reasoning, indirect proofs Textbook: Vocabulary: 5. PH 5-6 PH 5-7 Page 18 of 40 Revised 7/5/10 Additional Information: Also included are the Language Arts Benchmarks: LA.1112.1.6.1, LA.1112.1.6.2, LA.1112.1.6.5, LA.910.1.6.1, LA.910.1.6.2, LA.910.1.6.5 Prentice Hall, Geometry, Pearson 2011, is the Pasco adopted textbook. Page 19 of 40 Revised 7/5/10 Course Name: Geometry, 2010-11 Unit Title: (06) Polygons and Quadrilaterals - Chapter 6 Number of Days: 22 Know: Understand: Polygons have interior and exterior angle sums. Classification techniques and proofs can be Identify and describe convex, concave, used to identify quadrilaterals. regular, equilateral and equiangular polygons. Polygons are classified by their sides. Polygons may be convex or concave, equilateral, equiangular and regular. There are seven types of special quadrilaterals, each with distinct properties. The properties of special quadrilaterals can be proven using coordinate geometry. Do: Find the measures of interior and exterior angles of polygons. Distinguish between the different types of special quadrilaterals. Prove properties of special quadrilaterals using coordinate geometry. Page 20 of 40 Revised 7/5/10 Course Name: Geometry, 2010-11 Unit Title: (06) Polygons and quadrilaterals - Chapter 6 Number of Days: 22 Key Learning: Classification techniques and proofs can be used to identify quadrilaterals. Unit Essential Question: What types of quadrilaterals exist and what properties are unique to them? Concept: Polygon Angle-Sum Theorem Benchmark(s): MA.912.G.2.2 Concept: Properties of Parallelogram Benchmark(s): MA.912.G.3.1 MA.912.G.3.4 MA.912.G.4.5 MA.912.G.8.5 Concept: Properties of Rhombuses, Rectangles and Squares Concept: Trapezoids and Kites Benchmark(s): MA.912.G.3.1 MA.912.G.3.2 MA.912.G.3.4 Benchmark(s): MA.912.G.3.1 MA.912.G.3.2 MA.912.G.3.4 Lesson Essential Questions: 1. How do you find the sum of the measures of the interior and exterior angles of a polygon? * see Additional Information Lesson Essential Questions: 2. How are properties of parallelograms used in proofs? Textbook: Vocabulary: 1. PH 6-1 equilateral polygon, equiangular polygon, regular polygon Textbook: Vocabulary: 2. PH 6-2, parallelogram, 6-3 opposite sides, opposite angles, consecutive angles, diagonal Lesson Essential Questions: Textbook: Vocabulary: 3. What are the similarities and differences between 3. PH 6-4, rhombus, square, squares, rectangles, and rhombuses? 6-5 rectangles Lesson Essential Questions: 4. What are the unique properties of trapezoids and kites? Textbook: Vocabulary: 4. PH 6-6 trapezoid, base, leg, base angle, isosceles trapezoid, midsegment of a trapezoid, kite Page 21 of 40 Revised 7/5/10 Concept: Benchmark(s): Quadrilaterals in the MA.912.G.1.1 Coordinate Plane MA.912.G.3.1 MA.912.G.3.3 MA.912.G.4.1 MA.912.G.4.8 MA.912.G.8.5 Lesson Essential Questions: 5. How can you use coordinates to identify special figures? See Additional Information Textbook: Vocabulary: 5. PH 6-7 coordinate proof 6-8, 6-9 Additional Information: *Note* This unit will probably have to be split over quarter 2 & 3. Extra days have been added to this unit to include the days needed for Differentiated Accountability Assessment (Core, K-12) and semester testing. Algebra review on simplifying radicals PH page 424. This needs to be reviewed before you cover the coordinate plane sections (6-7, 6-8, 6-9) *Classifying polygons review is on PH page 65, 66, the book assumes that the students know these names and does not review them in chapter 6. Also included are the Language Arts Benchmarks: LA.1112.1.6.1, LA.1112.1.6.2, LA.1112.1.6.5, LA.910.1.6.1, LA.910.1.6.2, LA.910.1.6.5 Prentice Hall, Geometry, Pearson 2011, is the Pasco adopted textbook. Page 22 of 40 Revised 7/5/10 Course Name: Geometry, 2010-11 Unit Title: (07) Similarity - Chapter 7 Number of Days: 10 Know: Understand: Do: Proportions are formed by ratios and are used in unit conversions. The concepts of ratios, proportions and Set up ratios and proportions and solve similarity are strongly interrelated and using the cross-product property. necessary for solving problems with similar Similar triangles and other similar polygons figures. Use similarity properties to identify similar have congruent angles and proportional triangles and other polygons. sides. Find missing sides and segments of There are specific theorems that describe triangles using triangle proportion the proportions in triangle measurements. theorems. Page 23 of 40 Revised 7/5/10 Course Name: Geometry, 2010-11 Unit Title: (07) Similarity - Chapter 7 Number of Days: 10 The concepts of ratios, proportions and similarity are strongly interrelated and necessary for solving Key Learning: problems with similar figures. Unit Essential Question: How do ratios and proportions enable the solving of problems involving similar polygons? Concept: Ratios and Proportions Benchmark(s): MA.912.G.2.3 MA.912.G.4.4 Concept: Similar Polygons Benchmark(s): MA.912.G.2.3 Concept: Proving Triangles Similar Concept: Similarity in Right Triangles Benchmark(s): MA.912.G.4.5 MA.912.G.4.6 Benchmark(s): MA.912.G.8.3 MA.912.G.5.2 Lesson Essential Questions: 1. How do I write and evaluate proportions using ratios? Textbook: Vocabulary: 1. PH 7-1 proportion, ratio, means, extremes, extended ratio, cross products property Lesson Essential Questions: Textbook: Vocabulary: 2. What are similar polygons? 2. PH 7-2 similar figures, similar polygons, extended proportion, similarity ratio, scale factor, golden rectangle, golden ratio Lesson Essential Questions: Textbook: Vocabulary: 3. How can I prove triangles similar? 3. PH 7-3 indirect measurement Lesson Essential Questions: Textbook: Vocabulary: 4. How does the altitude drawn to the hypotenuse of a 4. PH 7-4 geometric means right triangle demonstrate the use of a geometric mean? Page 24 of 40 Revised 7/5/10 Concept: Golden Ratio Benchmark(s): MA.912.D.11.5 Lesson Essential Questions: 5. What is the Golden Ratio and how can I relate the Golden Ratio to the Fibonacci Sequence Concept: Proportions in Triangles Benchmark(s): MA.912.G.4.5 Lesson Essential Questions: 5. How do I apply the side-splitter theorem and the triangle-angle bisector theorem in order to find missing sides of a triangle? Textbook: 5. Concept Byte: Golden Ration Textbook: 5. PH 7-5 Vocabulary: Golden Ratio, Fibonacci sequence Vocabulary: Side-splitter Theorem, Triangleangle Bisector Theorem Additional Information: Also included are the Language Arts Benchmarks: LA.1112.1.6.1, LA.1112.1.6.2, LA.1112.1.6.5, LA.910.1.6.1, LA.910.1.6.2, LA.910.1.6.5 Prentice Hall, Geometry, Pearson 2011, is the Pasco adopted textbook Page 25 of 40 Revised 7/5/10 Course Name: Geometry, 2010-11 Unit Title: (08) Right Triangles and Trigonometry - Chapter 8 Number of Days: 10 Know: Understand: Do: Special right triangles are defined as 30-60- Trigonometric ratios are developed as 90 degree or 45-45-90 degree triangles. applications of right triangle geometry. Prove and apply the Pythagorean Theorem and its converse. In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse (Pythagorean Theorem). Use special right triangles to solve problems. The converse of the Pythagorean Theorem uses angles to classify triangles. The trigonometric ratios of tangent, sine, cosine, cotangent, secant, and cosecant are used to find missing angles and sides in right triangles. Set up and solve equations using tangent, sine, cosine, cotangent, secant, and cosecant functions to find missing angles and sides in right triangles. Solve real world problems involving trigonometric functions and angles of elevation and depression. Angles of elevation and depression have many real-world applications. Page 26 of 40 Revised 7/5/10 Course Name: Geometry, 2010-11 Unit Title: (08) Right Triangles and Trigonometry - Chapter 10 Number of Days: 10 Key Learning: Trigonometric ratios are developed as applications of right triangle geometry. How are the trigonometric ratios used to find unknown lengths and angle measures in diagrams and real Unit Essential Question: world scenarios? Concept: The Pythagorean Theorem and its Converse Concept: Special Right Triangles Concept: Trigonometry Benchmark(s): MA.912.G.5.1 MA.912.G.5.4 MA.912.G.8.3 Benchmark(s): MA.912.G.5.3 MA.912.G.5.4 Benchmark(s): MA.912.G.5.3 MA.912.G.5.4 Concept: Angles of Elevation and Depression Concept: Vectors Benchmark(s): MA.912.G.5.4 MA.912.T.2.1 Benchmark(s): MA.912.D.9.3 Lesson Essential Questions: Textbook: Vocabulary: 1.What problems can I use the Pythagorean Theorem 1. PH 8-1 Pythagorean triple to solve for missing sides of a triangle? Lesson Essential Questions: 2. How are the properties of special right triangles (30-60-90, 45-45-90) used to find missing sides? Lesson Essential Questions: 3. How are the sine, cosine, and tangent ratios applied to determine missing sides and angles in right triangles? * see Additional Information Lesson Essential Questions: 4. How do you use angles of elevation and depression to solve problems? Lesson Essential Questions: 4. How are vectors used to model motion and directions? Textbook: Vocabulary: 2. PH 8-2 Textbook: Vocabulary: 3. PH 8-3 trigonometric rations, sine, cosine, tangent, cotangent, cosecant, cosine Textbook: Vocabulary: 4. PH 8-4 Angle of elevations, Angles of depression Textbook: Vocabulary: 4. PH 8-5 vector, magnitude, initial point, terminal point, resultant Page 27 of 40 Revised 7/5/10 Additional Information: *Exposure to cosine, cosecant and cotangent is covered on page 539 #16-21. MA.912.T.2.1. This maybe needed for the state End of Course Exam. Also included are the Language Arts Benchmarks: LA.1112.1.6.1, LA.1112.1.6.2, LA.1112.1.6.5, LA.910.1.6.1, LA.910.1.6.2, LA.910.1.6.5 Prentice Hall, Geometry, Pearson 2011, is the Pasco adopted textbook Page 28 of 40 Revised 7/5/10 Course Name: Geometry, 2010-11 Unit Title: (09) Transformations - Chapter 9 Number of Days: 10 Know: Understand: Two dimensional objects can be reflected, translated, rotated or dilated on a plane. Transformations can be performed on two- Perform transformations (translations, dimensional shapes. reflections, dilations and scale size change) on polygons. Transformations that result in congruent images and pre-images are isometries. Some polygons can tessellate on a plane. Do: Determine the congruence, similarity, and symmetry between images and pre-images. Create and verify tessellations of polygons on a plane. Page 29 of 40 Revised 7/5/10 Course Name: Geometry, 2010-11 Unit Title: (09) Transformations - Chapter 9 Number of Days: 10 Key Learning: Transformations can be performed on two-dimensional shapes. Unit Essential Question: What are the transformations in geometry? Concept: Reflections, Translations, Rotations Benchmark(s): MA.912.G.2.4 Lesson Essential Questions: 1. How are objects reflected, translated, rotated? Concept: Symmetry Benchmark(s): MA.912.G.2.4 Lesson Essential Questions: 2. How can I identify the types of symmetry in a figure? Concept: Dilations Benchmark(s): MA.912.G.2.4 Lesson Essential Questions: 3. How can I apply dilations and scale factors to polygons to determine similarity? Concept: Compositions and Reflections Benchmark(s): MA.912.G.2.4 Lesson Essential Questions: 4. How are compositions and reflections in figures used in graphing? Textbook: Vocabulary: 1. PH 9-1, 9- transformation, 2, 9-3 preimage, image, isometry, reflection, line of reflection, translation, composition, rotation (center, angle), center of a regular polygon Textbook: Vocabulary: 2. PH 9-4 symmetry, reflectional symmetry, line symmetry, rotational symmetry, point symmetry Textbook: Vocabulary: 3. PH 9-5 dilation, center of dilation, scale factor of dilation, enlargement, reductions Textbook: Vocabulary: 4. PH 9-6 glide reflection Page 30 of 40 Revised 7/5/10 Concept: Tessellations Benchmark(s): MA.912.G.2.4 Lesson Essential Questions: 5. How can I identify symmetry and transformations in polygons that have been tessellated? Textbook: Vocabulary: 5. PH 9-7 tessellation, translational symmetry, glide reflection symmetry Additional Information: Also included are the Language Arts Benchmarks: LA.1112.1.6.1, LA.1112.1.6.2, LA.1112.1.6.5, LA.910.1.6.1, LA.910.1.6.2, LA.910.1.6.5 Prentice Hall, Geometry, Pearson 2011, is the Pasco adopted textbook. Page 31 of 40 Revised 7/5/10 Course Name: Geometry, 2010-11 Unit Title: (10) Area - Chapter 10 Number of Days: 16 Know: Understand: Do: There are formulas for circumference, perimeter, and area for circles, triangles, quadrilaterals, and regular polygons. The characteristics of two-dimensional figures can be used to calculate circumference, perimeter and area. Find the area, perimeter and circumference of circles, triangles, quadrilaterals and regular polygons. There is a relationship between area, sectors, segments, central angles, intercepted arcs, circumference and arc length in circles. Geometric models can be used to find the probability of events. Define and identify: circumference, radius, diameter, arc, arc length, chord, secant, and segment in circles. Find the probability of events using geometric models. Page 32 of 40 Revised 7/5/10 Course Name: Geometry, 2010-11 Unit Title: (10) Area - Chapter 10 Number of Days: 16 The characteristics of two-dimensional figures can be used to calculate circumference, perimeter and Key Learning: area. Unit Essential Question: What properties of perimeter, area, and trigonometry can be applied in geometric situations? Concept: Area of Triangles, Parallelograms Trapezoids, Rhombuses and Kites Concept: Area of Regular Polygons Concept: Perimeter and Areas of Similar Figures Concept: Trigonometry and Area Concept: Circles and Arcs Concept: Areas of Circle and Sectors Benchmark(s): Lesson Essential Questions: MA.912.G.2.5 1. How do I find the area of a parallelograms, triangles, trapezoids, rhombuses and kites? Benchmark(s): MA.912.G.2.5 MA.912.G.2.7 Benchmark(s): MA.912.G.2.7 Textbook: Vocabulary: 1. PH 10-1 base, altitude and height of a 10-2 parallelogram and triangle, height of trapezoid Lesson Essential Questions: 2. How can I find the area of a regular polygon? Textbook: Vocabulary: 2. PH 10-3 radius of a regular polygon, apothem Lesson Essential Questions: Textbook: Vocabulary: 3. How can I find perimeters and areas of similar 3. PH 10-4 scale factor, ratio of polygons? perimeters, ratio of areas Benchmark(s): Lesson Essential Questions: Textbook: Vocabulary: MA.912.G.2.5 4. How can I use trigonometry to find the area of 4. PH 10-5 MA.912.G.2.1 regular polygons and triangles? Benchmark(s): Lesson Essential Questions: Textbook: Vocabulary: MA.912.G.6.2 5. What is the relationship between central angles, 5. PH 10-6 circle, center, radius, congruent MA.912.G.6.4 arc length, and circumference? circles, diameter, central angle, MA.912.G.6.5 * see Additional Information semicircle, minor arc, major arc, adjacent arcs, circumference, pi, concentric circles, arc length, congruent arcs Benchmark(s): Lesson Essential Questions: Textbook: Vocabulary: MA.912.G.2.7 6. How do I find the area of circle, sector and 6. PH 10-7 sector of a circle, segment of a MA.912.G.6.5 segment? circle Page 33 of 40 Revised 7/5/10 Concept: Geometric Probability Benchmark(s): Lesson Essential Questions: Textbook: Vocabulary: MA.912.G.2.5 7. What geometric models can be used to find the 7. PH 10-8 geometric probability MA.912.G.6.5 probability of events? Additional Information: *use Concept Byte: Circle Graphs on page 687 with lesson 10-6. *You may want to do 12-5 Circles in the Coordinate Plane after 10-6 as it may be on the State EOC Exam and needs to be covered early. Also included are the Language Arts Benchmarks: LA.1112.1.6.1, LA.1112.1.6.2, LA.1112.1.6.5, LA.910.1.6.1, LA.910.1.6.2, LA.910.1.6.5 Prentice Hall, Geometry, Pearson 2011, is the Pasco adopted textbook. Page 34 of 40 Revised 7/5/10 Course Name: Geometry, 2010-11 Unit Title: (11) Surface Area and Volume - Chapter 10 Number of Days: 18 Know: Understand: Euler's formula relates the numbers of faces and vertices a polyhedron has to its edges. Surface area and volume may be calculated Find the faces, edges and vertices of for geometric solids. polyhedra using Euler's Formula. There are formulas for finding the lateral area, surface area and volume of prisms, cylinders, cones, and pyramids. There are formulas for finding the surface area and volume of spheres. Do: Use formulas to find lateral area, surface area and volume of solids. Determine how changes in the dimensions affect the surface area and volume of common geometric solids. Changing the dimensions of a geometric solid affects the surface area and volume. Page 35 of 40 Revised 7/5/10 Course Name: Geometry, 2010-11 Unit Title: (11) Surface Area and Volume - Chapter 11 Number of Days: 18 Key Learning: Surface area and volume are some of the measurements used to describe geometric solids. Unit Essential Question: How do I calculate the surface area and volume of geometric solids? Concept: Space Figures and Cross-Sections Benchmark(s): MA.912.G.7.2 Lesson Essential Questions: 1. How can I identify and analyze 3-D figures (geometric solids) and their cross sections? Concept: Surface Area of Geometric Solids Benchmark(s): MA.912.G.7.1 MA.912.G.7.5 MA.912.G.7.7 Lesson Essential Questions: 2. How do I calculate surface area of geometric solids? Concept: Benchmark(s): Volume of Geometric MA.912.G.7.5 Solids MA.912.G.7.7 Lesson Essential Questions: 3. How do I calculate volume of geometric solids? Textbook: Vocabulary: 1. PH 11-1 cross section, polyhedron, face, edge, vertex, net, Euler’s Formula Textbook: Vocabulary: 2. PH 11-2, prism, bases, lateral 11-3 faces, altitude, height, lateral area, surface area, right prism, oblique prism, cylinder, right cylinder, oblique cylinder, pyramid, cone, slant height, right cone, regular pyramid Textbook: Vocabulary: 3. PH 11-4, volume, composite 11-5 space figure, pyramids, cones Page 36 of 40 Revised 7/5/10 Concept: Surface Area and Volume of Spheres Benchmark(s): MA.912.G.7.4 MA.912.G.7.5 MA.912.G.7.7 Concept: Areas and Volumes of similar solids Benchmark(s): MA.912.G.7.6 Lesson Essential Questions: Textbook: Vocabulary: 4. How do I calculate the surface area and volume of a 4. PH 11-6 sphere, center, sphere? radius, diameter, circumference of a sphere, great circle, hemisphere Lesson Essential Questions: Textbook: Vocabulary: 5. How are the areas and volumes of similar solids 5. PH 11-7 similar solids related? Additional Information: Also included are the Language Arts Benchmarks: LA.1112.1.6.1, LA.1112.1.6.2, LA.1112.1.6.5, LA.910.1.6.1, LA.910.1.6.2, LA.910.1.6.5 Prentice Hall, Geometry, Pearson 2011, is the Pasco adopted textbook. Page 37 of 40 Revised 7/5/10 Course Name: Geometry, 2010-11 Unit Title: (12) Circles - Chapter 12 Number of Days: 22 Know: Understand: Do: There is a relationship between segments and angles formed by chords, secants and tangents of circles. The study of circles involves many aspects Define and identify diameters, arc and of geometry including lines, segments, arcs chords in circles. and angles. Determine and use measures of arcs and There is an equation for any circle graphed related angles on the coordinate plane, which is based upon the distance formula. Given the center and radius of a circle, find its equation and sketch the circle on the coordinate plane. Given the equation of a circle, name its radius and center. Page 38 of 40 Revised 7/5/10 Course Name: Geometry, 2010-11 Unit Title: (12) Circles - Chapter 12 Number of Days: 22 Key Learning: The study of circles involves many aspects of geometry including lines, segments, arcs, and angles. Unit Essential Question: What are the properties of circles and the lines, segments, arcs and angles involved with them? Concept: Tangent Lines Benchmark(s): MA.912.G.6.2 Concept: Chords and Arcs Benchmark(s): MA.912.G.6.2 Concept: Inscribed Angles Benchmark(s): MA.912.G.6.4 Concept: Benchmark(s): Angle Measures and MA.912.G.6.2 Segment Lengths MA.912.G.6.4 Concept: Circles in the Coordinate Plane Benchmark(s): MA.912.G.1.1 MA.912.G.6.6 MA.912.G.6.7 Lesson Essential Questions: 1. What causes a line to be tangent to a circle? Textbook: Vocabulary: 1. PH 12-1 tangent to a circle, point of tangency, inscribed in, circumscribed about Lesson Essential Questions: Textbook: Vocabulary: 2. How are a circle's chords and arcs related to each 2. PH 12-2 Chord, arc other? Lesson Essential Questions: Textbook: Vocabulary: 3. What is the relationship between an inscribed angle 3. PH 12-3 inscribed angle, and its intercepted arc? intercepted arc Lesson Essential Questions: Textbook: Vocabulary: 4. What is the relationship between segments and 4. PH 12-4 secant angles formed by chords, secants, and tangents of circles? Lesson Essential Questions: Textbook: Vocabulary: 5. How is the distance formula applied in the formula 5. PH 12-5 standard form of an for the equation of a circle in the coordinate plane? equation of a circle Page 39 of 40 Revised 7/5/10 Additional Information: Also included are the Language Arts Benchmarks: LA.1112.1.6.1, LA.1112.1.6.2, LA.1112.1.6.5, LA.910.1.6.1, LA.910.1.6.2, LA.910.1.6.5 *You may want to do 12-5 Circles in the Coordinate Plane earlier as it may be on the state EOC Exam. Prentice Hall, Geometry, Pearson 2011, is the Pasco adopted textbook. Page 40 of 40