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Whitman-Hanson Regional High School provides all students with a high- quality education in order to develop reflective, concerned citizens and contributing members of the global community. Course Number 425 Course Description Title Geometry Part A Grade 10 # of Days 60 Geometry is the branch of mathematics that deals with measurement and shape. This course is designed to cover plane geometry (the study of figures in two dimensions), solid geometry (the study of figures in three dimensional space), analytical geometry (the study of position in space determined by coordinates), including transformations, and algebraic reasoning. Real life applications will be included for all topics. MAJOR COURSE OBJECTIVES: 1. Identify and use properties of basic figures of geometry to solve problems. 2. Develop inductive and deductive reasoning skills. 3. Obtain solutions to problems that are related to geometric measurements. 4. Discovering and proving triangle properties. 5. Discovering and proving polygon properties. Instructional Strategies Direct instruction Group work Individual student work Projects Quizzes Tests Unannounced quick quizzes Ticket to leave Student Learning Expectations 1. 2. 3. 4. 5. 6. Read, write and communicate effectively. Utilize technologies appropriately and effectively. Apply critical thinking skills. Explore and express ideas creatively. Participate in learning both individually and collaboratively. Demonstrate personal, social, and civic responsibility. 1 Whitman-Hanson Regional High School provides all students with a high- quality education in order to develop reflective, concerned citizens and contributing members of the global community. Course Number 426 Course Description Instructional Strategies Student Learning Expectations Title Geometry Part B Grade 10 # of Days 60 Geometry is the branch of mathematics that deals with measurement and shape. This course is designed to cover plane geometry (the study of figures in two dimensions), solid geometry (the study of figures in three dimensional space), analytical geometry (the study of position in space determined by coordinates), including transformations, and algebraic reasoning. Real life applications will be included for all topics. MAJOR COURSE OBJECTIVES: 1. Discovering and proving circle properties. 2. Use two-dimensional geometric models to represent and solve area problems. 3. Model and solve problems using the Pythagorean Theorem. 4. Use three-dimensional geometric models to represent and solve volume problems. 5. Apply the properties of similarity to model and solve problems. 6. Use the definitions of the trigonometric functions to model and solve problems. 1. 2. 3. 4. 5. 6. Direct instruction Group work Individual student work Projects Quizzes Tests Unannounced quick quizzes Ticket to leave Read, write and communicate effectively. Utilize technologies appropriately and effectively. Apply critical thinking skills. Explore and express ideas creatively. Participate in learning both individually and collaboratively. Demonstrate personal, social, and civic responsibility. 2 Chapter Class preparation 0 1.1 Building Blocks of Geometry Introducing Imp. vocabulary 1.1 1.1 1.2 & 1.3 (poolroom math and angles) Review 1.11.3 Objective To review trimester expectations -To see examples of geometry in nature and art. -To practice using compass and straightedge. Students will use computer to understand, illustrate, and label key vocabulary terms. To become familiar with common vocabulary and related those terms to geometric shapes. To understand midpoint -Review use of a protractor -To understand parts of math definition -To learn angle definitions -To review concepts presented so far -To prepare for following day’s quiz Quiz 1.1-1.3 1.4 Polygons 1.5 Triangles 1.6 Special Quadrilaterals -To assess concepts presented so far -To classify polygons -Identify the characteristics of: Equilateral polygons Equiangular polygons Regular polygons -To understand the different characteristics of triangles: Acute Obtuse Right Equiangular Scalene Isosceles Equilateral -To understand the characteristics of quadrilaterals: Quadrilateral Parallelogram Rectangle Rhombus Square 3 Review 1.4-1.6 Trapezoid Isosceles trapezoid kite -To review concepts presented so far -To prepare for following day’s quiz 4 Quiz 1.9 -To assess concepts presented so far -To reinforce word problem solving strategies 1.7 Circles -To introduce/review basic vocabulary terms 1.7 Circles Review Day -Apply all previous knowledge with angles to circles -To prepare students for following day’s test on chapter. Test Chapter 2.1 Inductive Reasoning 2.2 Linear Rule 2.2 2.4 Deductive Reasoning Review Ch 2, Sections 1, 2 & 4 Quiz Ch 2, Sections 1, 2 & 4 2.5 -To test students on concepts presented so far. Objective -To understand the concept of Inductive Reasoning which is the process of observing data, recognizing patterns and making generalizations about those patterns. -To practice to write linear rules -To understand the concept of deductive reasoning and the need to provide justification for every piece of reasoning. -To review concepts presented so far -To prepare for following day’s quiz -To assess concepts presented so far -The after quiz assignment formally states that vertical angles are congruent and linear pairs of angles are supplementary. We have already informally discussed these properties. Chapter 2.6 Special Angles on Parallel Lines Objective -To identify properties of special angle pairs when 2 parallel lines are cut by a transversal Vertical angles Corresponding angles Alternate interior angles Alternate exterior angles 5 Review Chapter 2, Sections 5&6 Quiz Chapter 2, Sections 5&6 Review Day Test Chapter 2, Sections 1 – 2, 4 – 6 Chapter 3 Constructions Chapter 3 Point of Concurrency Chapter 3 Point of Concurrency Applications Chapter 4 Sections 1 & 2 Triangle Sum Conjecture and Properties of Isosceles Triangles Chapter 4 Section 3 Triangle Inequalities Review Chapter 4 Sections 1, 2, &3 Quiz Chapter 4 Sections 1, 2, &3 Chapter 4 Sections 4 & 5 Triangle Congruence Parallel lines conjecture -To review concepts presented so far -To prepare for following day’s quiz -To assess concepts presented so far -To prepare students for following day’s test on chapter. -To test students on concepts presented so far. -To Construct with tools and folding Angle Bisectors Perpendicular Bisectors Altitudes Medians To Identify points of concurrency in different types of triangles To apply knowledge of points of concurrency to word problems. To Discover and explain the sum of the measures of the angles of a triangle To discover a relationship between the base angles of an isosceles triangle To investigate among sides and angles in triangles To discover the exterior angles conjecture -To review concepts presented so far -To prepare for following day’s quiz To assess concepts presented so far To explore shortcut methods for determining whether triangles are congruent. To discover valid and invalid 6 Shortcuts Chapter 4 Section 4 Proofs Chapter 4 Section 5 Proofs Chapter 4 Section 6 Corresponding Parts of Congruent Triangles are Congruent Review Chapter 4 Sections 4, 5, &6 Quiz Chapter 4 Sections 4, 5, &6 4.8 Special Triangles Review Day Chapter 4 congruence conjectures Practice Deductive Reasoning Skills by proving congruent triangles. Develop problem solving skills Practice Deductive Reasoning Skills by proving congruent triangles. Develop problem solving skills Show that pairs of angles or sides are congruent by identifying related triangles and proving them congruent, then applying CPCTC Practice deductive reasoning. -To review concepts presented so far -To prepare for following day’s quiz To assess concepts presented so far To investigate vertex angle bisectors of isosceles triangles Use properties of isosceles triangles to find properties of equilateral triangles -To review concepts presented so far -To prepare for following day’s quiz Chapter 4 Test To assess concepts presented so far Chapter 5 Sections 1 & 2 Interior and Exterior Polygon Angle Conjectures Discover the sum of the angle measure in a polygon Chapter 5 Kite and Trapezoid Properties Chapter 5 Section 4 Properties of Midsegments Review Discover the sum of the measures of the exterior angles of a polygon Write formulas for the measure of the interior angle of an equiangular polygon Discover Kite and Trapezoid Properties Define and discover properties of midsegments in triangles and trapezoids -To review concepts presented so 7 Chapter 5 Sections 1-4 Quiz Chapter 5 Sections 1-4 Chapter 5 Sections 5 & 6 Properties of Parallelograms and Special Parallelograms Chapter Class preparation Prerequisite Skill Review 6.0 6.1 Tangent Properties 6.2 Chord Properties Review 6.1-6.2 and prerequisite skills Quiz 6.1-6.2 and prerequisite skills 6.3 Arcs and Angles 6.3 Arcs and Angles 6.5 The Circumference/ far -To prepare for following day’s Quiz To assess concepts presented so far Discover properties of parallelogram s Discover properties of rectangles, rhombuses, and squares. Objective To review trimester expectations To review simplifying radicals -To review Pythagorean Theorem -To review Square Bionomials - Review basic properties of a circle and circle vocabulary -Discover properties of tangents of circles -Explore common tangents and tangent circles -Learn applications of tangents -Discover properties of chords to a circle -Apply properties of chords to circle problems - To review material and prepare for quiz. -To quiz students on concepts presented so far. -Discover relationships between an inscribed angle of a circle and its intercepted arc. -Discover relationships between an inscribed angle of a circle and its intercepted arc. -Calculate pi, the ratio of circumference of a circle to its 8 Diameter Ratio 6.6 Around the World 6.7 Arc Length diameter -Apply the formula for the circumference of a circle - - Review Sections 6.3-6.7 - Discover a formula for finding the length of an arc of a circle Apply the formula for arc length Review material for a quiz the next day. Quiz Sections 6.3-6.7 -To quiz students on concepts presented so far. Review Chapter 6 Chapter 6 Test -Review all material presented for chapter 6 for test next day. -To test students on concepts presented so far. Translations and Reflections Rotations - Review All Transformations Quiz on Transformations 8.1Areas of Rectangles and Parallelograms 8.2 Areas of Triangles, Trapezoids, and Kites 8.3 Area Problems 8.4 Area of Regular Polygons Be able to translate or reflect an image - Be able to rotate a figure 90, 180, 270, 360 degrees clockwise and counterclockwise - Be able to rotate a polygon using the interior angle conjecture. Review transformations for a quiz the next day. -To quiz students on concepts presented so far. -Develop the concept of area -Apply formulas to solve problems -Solve area application problems using various problem solving strategies -Develop reading comprehension and cooperative behavior -Derive a way to find area of a polygon using formulas we already have. -Apply to solve area problems 9 Review Ch 8, Sections 1-4 Quiz Ch 8, Sections 1- 4 -To review concepts presented so far -To prepare for following day’s quiz -To quiz students on concepts presented so far. -Apply area of a circle formula to problems 8.5 Area of Circles 8.5Area of Circles 8.6 Any way you slice it 8.7 Surface Area Review 8.5-8.7 Quiz 8.5-8.7 Review Chapter 8 Chapter 8 Test 9.1The Theorem of Pythagoras 9.2 The Converse of the Pythagorean Theorem 9.3 Special Right Triangles 9.3 Special Right Triangles 9.4 -. Discover formulas and methods for calculating the area of annuluses, sectors, and segments of circles. -Discover method for finding the surface area of solids -Practice when you need a formula vs. when you need a picture diagram -To prepare students for following day’s quiz . -To prepare students for following day’s test on the chapter To test students on concepts presented so far. -Understand the Pythagorean theorem more deeply -Discover the converse of the Pythagorean theorem -Practice simplifying square roots -Investigate Special Right Triangles -Use MCAS formula sheet to practice problems using special right triangles -Practice simplifying square roots -Investigate Special Right Triangles -Use MCAS formula sheet to practice problems using special right triangles -Apply the Pythagorean theorem 10 Story Problems 9.5 Distance Formula Review Chapter 9 Review Chapter 9 Test Chapter 9 10.1 The Geometry of Solids 10.2 Volume of Prisms and Cylinders 10.3 Volume of Pyramids and Cones and its converse to solve story problems - Discover the Pythagorean theorem relationship on a coordinate plane (distance formula) - Use the distance formula to find distance between two points and solve word problems. -To prepare students for following day’s test on the chapter -To prepare students for following day’s test on the chapter To assess concepts presented so far -Find the Volume of Prisms, Cylinders, Pyramids, and Cones using MCAS formula sheet 10.1 The Geometry of Solids 10.2 Volume of Prisms and Cylinders 10.3 Volume of Pyramids and Cones - Find the Volume of Irregular Based Solids 10.1 The Geometry of Solids 10.2 Volume of Prisms and Cylinders 10.3 Volume of Pyramids and Cones -Review Volume of Prisms, Cylinders, Pyramids, and Cones with Regular and Irregular Bases. 11 10.6 Volume of a Sphere 10.7 Surface Area of a Sphere Review Chapter 10 Test Chapter 10 11.1 Similar Polygons 11.2 Similar Triangles 11.2 Similar Triangles 11.3 Indirect Measurement with Similar Triangles 11.5 Proportions with Area 11.6 Proportions with Volume Review Chapter 11 Test Chapter 11 Introduction to Trig Functions Trig-Finding a Side Trig-Finding an Angle -Apply volume formula to problems involving spheres and hemispheres -Apply the surface area of a sphere formula to solve problems -To prepare students for following day’s quiz . To assess concepts presented so far - Define similar polygons - Use the definition of similar polygons to solve problems - Discover shortcut methods for determining similar triangles - Practice using proportions to find measures in similar figures. - To understand how similar triangles are formed. -Use similar triangles to solve applied problems - Discover the relationship between the areas of similar figures - Discover the relationship between the surface areas of similar solids - Apply similarity conjectures to solve problems involving area - Discover the relationship between volumes of similar solids - Apply the similarity conjectures to problems involving volume -To prepare students for following day’s test. To assess concepts presented so far - Identify the trig functions - Be able to make ratios using the trig functions - Use trig ratios and functions to find the missing side of a right triangle - Use trig ratios and functions to find the missing angle of a right triangle 12 Trig-Right Triangle Review Trig Quiz Trig - Practice finding missing sides and angles of right triangles using trig -To prepare students for following day’s quiz . To assess concepts presented so far 13