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Lincoln County Curriculum Math- Geometry Curriculum: Course: Topic: 3 Introduction Subject(s): LINCOLN COUNTY SCHOOL DISTRICT Date: July 16, 2010 ET to Angles and Triangles Days: 16 Grade(s): Common Assessments on what students should know and do in this unit: Page 1 of 1 Lincoln County Curriculum Math- Geometry Curriculum: Course: Topic: 3 Introduction Subject(s): LINCOLN COUNTY SCHOOL DISTRICT Date: July 16, 2010 ET to Angles and Triangles Days: 16 Grade(s): Key Learning: The defined and undefined terms in Geometry. Unit Essential Question(s): What makes a geometric figure undefined? Concept: Concept: Concept: Naming, Measuring, and Classifying Angles Special Angles Angles of a Triangle In this lesson, you will: Identify and name lines, line segments, rays, and angles. measure angles Classify angles In this lesson, you will: identify pairs of adjacent angles identify complementary and supplementary angles identify angles that are complementary and supplementary to given angles identify vertical angles identify linear pairs In this lesson, you will: Name triangles Find sums and measures of angles in triangles Use the Triangle Sum theorem Use the Exterior angle theorem Discover the Exterior Angle Inequality Lesson Essential Question(s): How are rays, lines, and line segments named, and can they be named in more than one way? (A) Lesson Essential Question(s): What are adjacent, complementary, supplementary, vertical, and linear angles? (A) Lesson Essential Question(s): How can you use the Triangle Sum Theorem and the exterior angle Theorems to find the missing Angle? (A) Vocabulary: adjacent angles, Complementary Angles, Supplementary Angles, Vertical angles, opposite rays, Linear pair, Vocabulary: interior angle, theorem, Proof, Triangle Sum Theorem, Exterior Angle, Exterior Angle Theorem, Exterior Angle Inequality, How are angles formed, named, classified, and measured? (A) (A) Vocabulary: point, line, line segment, endpoints, ray, initial point, angle, vertex, sides, straight angle, right angle, acute angle, obtuse angle, measure of an angle, degrees, congruent angles Page 1 of 2 Lincoln County Curriculum Math- Geometry Curriculum: Course: Topic: 3 Introduction Subject(s): LINCOLN COUNTY SCHOOL DISTRICT Date: July 16, 2010 ET to Angles and Triangles Days: 16 Grade(s): Concept: Concept: Classifying Triangles The Triangle Inequality Concept: In this lesson, you will: Classify triangles by angles Classify triangles by side lengths In this lesson, you will: Use the Triangle Inequality Investigate the relationship between the sides and angles of triangles. Lesson Essential Question(s): What are the different ways to classify triangles? (A) Lesson Essential Question(s): What is the Triangle Inequality? (A) Lesson Essential Question(s): (A) Vocabulary: Acute triangle, Right Angle, Obtuse angle, Equiangular triangle, Equilateral Triangle, Isosceles Triangle, Scalene triangle Vocabulary: Triangle Inequality Vocabulary: Additional Information: Attached Document(s): Page 2 of 2 Lincoln County Curriculum Math- Geometry Curriculum: Course: Vocab Report for Topic: Subject(s): LINCOLN COUNTY SCHOOL DISTRICT Date: July 16, 2010 ET 3 Introduction to Angles and Triangles Days: 16 Grade(s): Concept: Naming, Measuring, and Classifying Angles point has no length, width, or thickness but has a poisition. Named with a capital letter line has length but no width or thickness. It extends without end in two directions. You can name a line by identifying two points on the line. Capital letters with a line on top of it line segment a portion of a line between two points called the endpoints. endpoints the two points on the end of a line segment ray a part of a line that consists of an initial point and all points on the line that lie on one side of the initial point. initial point The beginning point of a ray angle a figure that is formed from two rays that extend from a common point called the vertex. vertex a common point in an angle. sides the rays of an angle Page 1 of 5 Lincoln County Curriculum Math- Geometry Curriculum: Course: Vocab Report for Topic: Subject(s): LINCOLN COUNTY SCHOOL DISTRICT Date: July 16, 2010 ET 3 Introduction to Angles and Triangles Days: 16 Grade(s): straight angle An angle that has a measure of 180 degrees right angle an angle that has a measure of 90 degrees acute angle An angle that has a measure of less than 90 degrees obtuse angle An angle that has a measure that is greater than 90 degrees measure of an angle indicates the size of an angle degrees the unit of measurement of angles congruent angles Two angles that have the same measure Concept: Special Angles adjacent angles Angles that share a common vertex and side. Complementary Angles When two angles add together to equal 90 degrees. Page 2 of 5 Lincoln County Curriculum Math- Geometry Curriculum: Course: Vocab Report for Topic: Subject(s): LINCOLN COUNTY SCHOOL DISTRICT Date: July 16, 2010 ET 3 Introduction to Angles and Triangles Days: 16 Grade(s): Supplementary Angles When two angles add together and equal 180 degrees. Vertical angles Angles whose sides form two pairs of opposite rays opposite rays Two rays on the same line that have the same initial point and extend in opposite directions. Linear pair Two adjacent angles form a linear pair if the noncommon sides of the angles are opposite rays. Concept: Angles of a Triangle interior angle the angles inside a triangle theorem a statement that has been shown, or poven, to be true. Proof The process of showing that a statement is true Triangle Sum Theorem The sum of the interior angles of a triangle is 180 degrees Exterior Angle - Page 3 of 5 Lincoln County Curriculum Math- Geometry Curriculum: Course: Vocab Report for Topic: Subject(s): LINCOLN COUNTY SCHOOL DISTRICT Date: July 16, 2010 ET 3 Introduction to Angles and Triangles Days: 16 Grade(s): formed when one of the sides of a triangle is extended into a ray. An exterior angle of a triangle is adjacent to an interior angle. Exterior Angle Theorem the measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. Exterior Angle Inequality The measure of an exterior angle of a triangle is greater than the measure of either of the nonadjacent interior angles. Concept: Classifying Triangles Acute triangle this triangle can be classified by its interior angles, and all the interior angles are acute. Right Angle this triangle can be classified by its interior angles, one of the angles is a right angle. Obtuse angle this triangle can be classified by its interior angles, one of the angles is an obtuse angle. Equiangular triangle A triangle in which all three interior angles have the same measure of 60 degrees. Equilateral Triangle A triangle in which the sides all have the same length. Isosceles Triangle - Page 4 of 5 Lincoln County Curriculum Math- Geometry Curriculum: Course: Vocab Report for Topic: Subject(s): LINCOLN COUNTY SCHOOL DISTRICT Date: July 16, 2010 ET 3 Introduction to Angles and Triangles Days: 16 Grade(s): a triangle in which at least two of the sides have the same length Scalene triangle a triangle in which none of the sides have the same length Concept: The Triangle Inequality Triangle Inequality The length of one side of a triangle is less than the sum of the lengths of the other sides of the triangle. Page 5 of 5 Lincoln County Curriculum Math- Geometry Curriculum: Course: LINCOLN COUNTY SCHOOL DISTRICT Date: July 16, 2010 ET Topic: 3 Introduction to Angles and Triangles Subject(s): Concept: Naming, Measuring, and Classifying Angles Days: 16 Grade(s): 5. Acquisition Lesson Plan for the Concept, Topic, or Skill -- Not for the Day Lesson Essential Question: How are rays, lines, and line segments named, and can they be named in more than one way? What do students need to learn to be able to answer the Essential Question? Activating Strategy: Day 1: Students will complete Brainstorming to answer the following questions to prepare them for The lesson. ? what is a constellation? Name a constellation that you know. What does the Big Dipper get its name? Why is the constellation Orion called the hunter? Day 2: Computer Software Key vocabulary to preview: Day 1: Warm up from p. 113B Day 2: Computer Software Teaching Strategies: Instruction: Day 1: Students will complete Lesson 3.1 in groups. Day 2: Computer Software Assignment and/or Assessment: Day 1: Day 2: Summarizing Strategy: Day 1: Day 2: Time (in days): 2 Page 1 of 1 Lincoln County Curriculum Math- Geometry Curriculum: Course: LINCOLN COUNTY SCHOOL DISTRICT Date: July 16, 2010 ET Topic: 3 Introduction to Angles and Triangles Subject(s): Concept: Naming, Measuring, and Classifying Angles Days: 16 Grade(s): 5. Acquisition Lesson Plan for the Concept, Topic, or Skill -- Not for the Day Lesson Essential Question: How are angles formed, named, classified, and measured? What do students need to learn to be able to answer the Essential Question? Activating Strategy: Day 1: computer software Day 2: Motivator discussion from page 121 B What is the most famous bridge that you have ever crossed? have you ever seen the Golden Gate Bridge in San Francisco, CA? What type of bridge is the Golden Gate Bridge? What does a suspension bridge look like? what does a cable -stayed bridge look like? Key vocabulary to preview: Day 1: Computer Software/Notes/formulas Day 2: Warm up from p. 121 B Teaching Strategies: Instruction: Day 1: Comptuer software/notes Day 2: Lesson 3.2 Assignment and/or Assessment: Day 1: NOTES/computer software Day 2: lesson 3.2 and student assignment 3.2 Summarizing Strategy: Day 1: Computer Software Day 2: Draw a triangle formed by three intersecting lines on the board. Label the 12 angles formed. Have students volunteer to identify all the pairs of adjacent angles, supplementary angles, vertical angles, and linear pairs. Time (in days): 2 Page 1 of 1 Lincoln County Curriculum Math- Geometry Curriculum: Course: LINCOLN COUNTY SCHOOL DISTRICT Date: July 16, 2010 ET Topic: 3 Introduction to Angles and Triangles Subject(s): Concept: Naming, Measuring, and Classifying Angles Days: 16 Grade(s): 5. Acquisition Lesson Plan for the Concept, Topic, or Skill -- Not for the Day Lesson Essential Question: What do students need to learn to be able to answer the Essential Question? Teaching Strategies: Time (in days): 1 Page 1 of 1 Lincoln County Curriculum Math- Geometry LINCOLN COUNTY SCHOOL DISTRICT Date: July 16, 2010 ET Topic: 3 Introduction to Angles and Triangles Subject(s): Concept: Special Angles Days: 16 Grade(s): Curriculum: Course: 5. Acquisition Lesson Plan for the Concept, Topic, or Skill -- Not for the Day Lesson Essential Question: What are adjacent, complementary, supplementary, vertical, and linear angles? What do students need to learn to be able to answer the Essential Question? Activating Strategy: Day 1: Motivator from page 129B How many sides does a triangle have? What is a galley kitchen? What appliances are the most used in the kitchen? What does it mean to say "work triangle" when referring to a kitchen? Do you have a galley, L-chaped, or U shaped kitchen? Day 2: computer software formulas/notes Key vocabulary to preview: Day 1: Warm up from page 129 B Day 2: Computer Software/notes/formulas Teaching Strategies: Instruction: Day 1: lesson 3.3 Day 2: Computer software/notes/formulas Assignment and/or Assessment: day 1: lesson 3.3, Student Assignment 3.3 Day 2: computer Software/notes/formulas Summarizing Strategy: Day 1: Have different students to come up to the board and draw triangles with 3 acute angles, 2 acute angles and one right angle, and two acute angles and one obtuse angle. Ask a student to draw triangles on the board, extending their sides to form and identify external angles. Day 2: Computer Software/notes/formulas Time (in days): 2 Page 1 of 1 Lincoln County Curriculum Math- Geometry LINCOLN COUNTY SCHOOL DISTRICT Date: July 16, 2010 ET Topic: 3 Introduction to Angles and Triangles Subject(s): Concept: Angles of a Triangle Days: 16 Grade(s): Curriculum: Course: 5. Acquisition Lesson Plan for the Concept, Topic, or Skill -- Not for the Day Lesson Essential Question: How can you use the Triangle Sum Theorem and the exterior angle Theorems to find the missing Angle? What do students need to learn to be able to answer the Essential Question? Activating Strategy: day 1: computer software/notes/formulas day 2: Motivator from Page 137B What is origami? Have you ever made or watched someone make any origami objects/ Why do you think we are going to use origami today? How will this help us classify triangles? with what types of triangles are you familiar? Key vocabulary to preview: Day 1: computer software/notes/formulas Day 2: Warm up from page 137 B Teaching Strategies: Instruction: Day 1: Computer Software/notes/formulas Day 2: lesson 3.4 Assignment and/or Assessment: Day 1: Computer Software/notes/formulas Day 2: lesson 3.4, Student Assignment 3.4 Summarizing Strategy: Day 1: Computer Software/notes/formulas Day 2: Ask students to sketch a triangle and provide a possible set of three angle measures for the four types of triangles that can be classified acording to their angle measure Ask several students to sketch a triangle and provide a possible set of three side lengths fo the three types of triangles that can be classified according to the lengths of their sides. Time (in days): 2 Page 1 of 1 Lincoln County Curriculum Math- Geometry LINCOLN COUNTY SCHOOL DISTRICT Date: July 16, 2010 ET Topic: 3 Introduction to Angles and Triangles Subject(s): Concept: Classifying Triangles Days: 16 Grade(s): Curriculum: Course: 5. Acquisition Lesson Plan for the Concept, Topic, or Skill -- Not for the Day Lesson Essential Question: What are the different ways to classify triangles? What do students need to learn to be able to answer the Essential Question? Teaching Strategies: Time (in days): 2 Page 1 of 1 Lincoln County Curriculum Math- Geometry LINCOLN COUNTY SCHOOL DISTRICT Date: July 16, 2010 ET Topic: 3 Introduction to Angles and Triangles Subject(s): Concept: The Triangle Inequality Days: 16 Grade(s): Curriculum: Course: 5. Acquisition Lesson Plan for the Concept, Topic, or Skill -- Not for the Day Lesson Essential Question: What is the Triangle Inequality? What do students need to learn to be able to answer the Essential Question? Activating Strategy: Day 1: motivator from page 145B have you ever tried to put something together without reading the directions? have you helped to build model airplanes or cars? have you ever helped build a shed or building? did you have to plan before you started building? how did you know what materials to purchase or how everything went togehter? Day 2: Computer software/notes/formulas day 3: Study guide for chapter 3 test day 4: Chapter three test Key vocabulary to preview: Day 1: Warm up from page 145B Day 2: Computer software Day 3: Study guide for chapter three test day 4: chapter three test Teaching Strategies: Instruction: Day 1: Lesson 3.5 Day 2: Computer software/notes/formulas day 3: study guide for chapter three Day 4: Chapter three test Assignment and/or Assessment: Day 1: Lesson 3.5 and student assignment 3.5 day 2: computer software/notes/formulas day 3: study guide chapter 3 day 4: Test chapter 3 Summarizing Strategy: Day 1: Ask students to make up combinations of side lengths that do and do not make a triangle. Have the students quiz one another as to whether the given side lengths form a triangle. day 2: computer software/ notes/formulas day 3: Study guide chapter 3 Day 4: Chapter 3 test Time (in days): 5 Page 1 of 1 Lincoln County Curriculum Math- Geometry LINCOLN COUNTY SCHOOL DISTRICT Date: July 16, 2010 ET Topic: 3 Introduction to Angles and Triangles Subject(s): Concept: Days: 16 Grade(s): Curriculum: Course: 5. Acquisition Lesson Plan for the Concept, Topic, or Skill -- Not for the Day Lesson Essential Question: What do students need to learn to be able to answer the Essential Question? Teaching Strategies: Time (in days): 0 Page 1 of 1 Lincoln County Curriculum Math- Geometry Curriculum: Course: Topic: 3 Introduction Subject(s): to Angles and Triangles LINCOLN COUNTY SCHOOL DISTRICT Date: July 16, 2010 ET Days: 16 Grade(s): What is the most viable sequence for the experiences, activities, and lessons in order to help students learn to the best of their abilities? Put the Lesson Essential Questions, activities, and experiences in order. Page 1 of 1